Mobile Platforms for Underwater Sensor Networks

Mobile Platforms for Underwater Sensor Networks

A thesis submitted to the University of Manchester for the degree ofDoctor of Philosophy (PhD)

in the Faculty of Engineering and Physical Sciences

2012

Mr Simon Andrew Watson

School of Electrical and Electronic Engineering,Microwave and Communication Systems Group

Simon A. Watson Mobile Platforms for USNs

2

Contents

List of Figures 8

List of Tables 13

Abstract 15

Declaration 16

Copyright Statement 16

Dedication 17

Acknowledgment 17

The Author 17

List of Publications 18

1 Introduction 191.1 Monitoring Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.1.1 Industrial Process Tomography (IPT) . . . . . . . . . . . . . . . 211.1.2 Mobile Underwater Sensor Networks (MUSNs) . . . . . . . . . . 211.1.3 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221.1.4 Hybrid Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

1.2 Industrial Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 231.2.1 Process Industry . . . . . . . . . . . . . . . . . . . . . . . . . . 231.2.2 Nuclear Storage Ponds . . . . . . . . . . . . . . . . . . . . . . . 261.2.3 Application of Mobile Underwater Sensor Networks . . . . . . . 281.2.4 Wastewater Treatment Plants . . . . . . . . . . . . . . . . . . . 29

1.3 Research Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301.3.1 Actuated Acoustic Sensor Networks for Industrial Processes . . 31

1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2 System Requirements and Current Technology 332.1 Demonstrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.1.1 Generic Requirements . . . . . . . . . . . . . . . . . . . . . . . 342.1.2 Application-Speci�c Requirements . . . . . . . . . . . . . . . . . 352.1.3 Mechatronic Requirements Summary . . . . . . . . . . . . . . . 36

2.2 Underwater Exploration Vehicles . . . . . . . . . . . . . . . . . . . . . 36

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2.3 A History of AUVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.4 AUV Classi�cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.5 Mini AUVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.5.1 Ictineu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.5.2 ODIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.6 Micro-AUVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.6.1 Sera�na . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.6.2 University of Kagawa . . . . . . . . . . . . . . . . . . . . . . . . 432.6.3 Eyeball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.7 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3 Parametric Modelling 473.1 Key Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.2.1 Added Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.2.2 Power Supply and Lifespan . . . . . . . . . . . . . . . . . . . . 53

3.3 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.3.1 Hull Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.3.2 Lifespan and Battery Charging . . . . . . . . . . . . . . . . . . 583.3.3 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.5 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4 Propulsion Systems 624.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.1.1 Vertical Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.1.2 Horizontal Plane . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.2 Types of Propulsion Systems . . . . . . . . . . . . . . . . . . . . . . . . 664.2.1 Diaphragm-Based VDS . . . . . . . . . . . . . . . . . . . . . . . 674.2.2 Micro-Pump-Based VDS . . . . . . . . . . . . . . . . . . . . . . 674.2.3 Motor/Syringe-Based VDS . . . . . . . . . . . . . . . . . . . . . 684.2.4 Mechanical Oscillators . . . . . . . . . . . . . . . . . . . . . . . 684.2.5 Piezo-Electric Oscillators . . . . . . . . . . . . . . . . . . . . . . 694.2.6 Propellers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.2.7 Vortex Ring Thrusters . . . . . . . . . . . . . . . . . . . . . . . 704.2.8 Water Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.2.9 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.3 Vortex Ring Thruster Analysis . . . . . . . . . . . . . . . . . . . . . . . 744.3.1 Prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.3.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.4 Propeller Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.4.1 Horizontal Prototype . . . . . . . . . . . . . . . . . . . . . . . . 764.4.2 Vertical Prototypes . . . . . . . . . . . . . . . . . . . . . . . . . 774.4.3 Prototype Investigation Conclusions . . . . . . . . . . . . . . . . 78

4.5 Motor and Propeller Component Selection Method . . . . . . . . . . . 804.5.1 Alternative Analysis . . . . . . . . . . . . . . . . . . . . . . . . 814.5.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

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Mobile Platforms for USNs Simon A. Watson

4.6 Force Measurement Rig . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.7 Propulsion System Summary . . . . . . . . . . . . . . . . . . . . . . . . 854.8 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5 Prototype Vehicle Design 865.1 Prototype Progression . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.2 Hull Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.3 Propeller Con�guration . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.3.1 Vertical Thrusters . . . . . . . . . . . . . . . . . . . . . . . . . . 925.3.2 Horizontal Thrusters . . . . . . . . . . . . . . . . . . . . . . . . 93

5.4 Thruster Component Selection . . . . . . . . . . . . . . . . . . . . . . . 955.4.1 System Operation . . . . . . . . . . . . . . . . . . . . . . . . . . 965.4.2 MK V Thruster Selection . . . . . . . . . . . . . . . . . . . . . 965.4.3 Lack of Component Homogeneity . . . . . . . . . . . . . . . . . 995.4.4 MK VI Thruster Selection . . . . . . . . . . . . . . . . . . . . . 103

5.5 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045.5.1 Acoustic Positioning System . . . . . . . . . . . . . . . . . . . . 1065.5.2 Pressure Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . 1095.5.3 Digital Compass . . . . . . . . . . . . . . . . . . . . . . . . . . 1095.5.4 Rate Gyroscope . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

5.6 Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1145.6.1 Velocity Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 1155.6.2 Data Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

5.7 MK V Embedded System Hardware . . . . . . . . . . . . . . . . . . . . 1175.7.1 Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1185.7.2 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1205.7.3 Actuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.8 MK VI Embedded System Hardware . . . . . . . . . . . . . . . . . . . 1215.8.1 Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1225.8.2 Analogue Board and Digital Signal Processing . . . . . . . . . . 1235.8.3 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

5.9 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1255.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

6 Motion Control for Unmanned Underwater Vehicles 1276.1 Overview of Control Systems . . . . . . . . . . . . . . . . . . . . . . . . 1276.2 Speci�cation of Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . 130

6.2.1 Quantitative Speci�cations . . . . . . . . . . . . . . . . . . . . . 1306.2.2 Qualitative Speci�cations . . . . . . . . . . . . . . . . . . . . . 131

6.3 Analysis of the Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1316.3.1 Linearisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1346.3.2 Modelling Approach . . . . . . . . . . . . . . . . . . . . . . . . 135

6.4 Unmanned Underwater Vehicle Control Systems Review . . . . . . . . 1366.5 PID Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

6.5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1386.5.2 Analysis of Controller Components . . . . . . . . . . . . . . . . 1396.5.3 Review of UUV PID Implementations . . . . . . . . . . . . . . . 143

6.6 Robust Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

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6.6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1446.6.2 Analysis of Sliding Mode Control . . . . . . . . . . . . . . . . . 1446.6.3 Review of UUV Sliding Mode Implementations . . . . . . . . . 147

6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

7 Control of Heave 1497.1 Motion Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1497.2 Simulation Environment . . . . . . . . . . . . . . . . . . . . . . . . . . 1507.3 Experimental Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 1517.4 Heave Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1517.5 MK V Implementation and Evaluation . . . . . . . . . . . . . . . . . . 152

7.5.1 Steady-State Error Elimination . . . . . . . . . . . . . . . . . . 1577.5.2 Heave Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 1587.5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

7.6 MK VI Implementation and Evaluation . . . . . . . . . . . . . . . . . . 1637.6.1 Improving the Simulation Model . . . . . . . . . . . . . . . . . . 1637.6.2 PID Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . 1687.6.3 Sliding Mode Controller . . . . . . . . . . . . . . . . . . . . . . 1697.6.4 Bounded PD Control . . . . . . . . . . . . . . . . . . . . . . . . 175

7.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

8 Control of Surge, Sway and Yaw 1808.1 Yaw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

8.1.1 Motion Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . 1818.1.2 Horizontal System Modelling . . . . . . . . . . . . . . . . . . . . 1818.1.3 MK V Implementation and Evaluation . . . . . . . . . . . . . . 1858.1.4 MK VI Implementation and Evaluation . . . . . . . . . . . . . . 188

8.2 Yaw and Heave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1918.3 Surge and Sway Simulations . . . . . . . . . . . . . . . . . . . . . . . . 192

8.3.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1938.3.2 Way-Point Guidance . . . . . . . . . . . . . . . . . . . . . . . . 196

8.4 Full 3D Control Simulations . . . . . . . . . . . . . . . . . . . . . . . . 1978.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

9 Conclusions and Future Work 2019.1 Thesis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2019.2 Review of Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . 203

9.2.1 Mechatronic Requirements . . . . . . . . . . . . . . . . . . . . . 2039.2.2 Quantitative Speci�cations for the Control Systems . . . . . . . 2059.2.3 Qualitative Speci�cations for the Control Systems . . . . . . . . 2079.2.4 Requirements Summary . . . . . . . . . . . . . . . . . . . . . . 208

9.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2089.3.1 Simulation Con�dence . . . . . . . . . . . . . . . . . . . . . . . 209

9.4 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

References 214

A Wastewater Treatment Facilities 229

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B Drag Coe�cient Graphs 231

C Propulsion System Analysis 232C.1 Micro-Pump-Based VDS . . . . . . . . . . . . . . . . . . . . . . . . . . 232C.2 Motor/Syringe-Based VDS . . . . . . . . . . . . . . . . . . . . . . . . . 232C.3 Vortex Ring Thrusters . . . . . . . . . . . . . . . . . . . . . . . . . . . 234C.4 Motor/Propeller Selection . . . . . . . . . . . . . . . . . . . . . . . . . 237

D MK VI Compass Calibration Curve 238

E Kalman Filter 239E.1 General Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239E.2 Implementation for Position and Velocity Estimates . . . . . . . . . . . 239

E.2.1 Step 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240E.2.2 Step 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240E.2.3 Step 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241E.2.4 Step 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242E.2.5 Step 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242E.2.6 Step 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

E.3 Implementation for Data Fusion . . . . . . . . . . . . . . . . . . . . . . 243

F MK VI Software Flowchart 245

G SIMULINK Model 246

H Discrete PIDγ Controller Derivation 248H.1 Addition of Low Pass Filter . . . . . . . . . . . . . . . . . . . . . . . . 250

I Linearisation 254I.1 Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

J Controller Outputs for Simulations and Experiments 258

K Surge and Sway Controller Simulation `Ideal-World' Results 266

L Additional Vertical Motion Experiment Results 268

Total Word Count: 47343

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List of Figures

1.1 Industrial Processes Spectrum . . . . . . . . . . . . . . . . . . . . . . . 201.2 Electical Tomography System [1] . . . . . . . . . . . . . . . . . . . . . 211.3 Demonstrator System for a Nuclear Storage Pond . . . . . . . . . . . . 221.4 Homogeneous Mixing of Reagents [2] . . . . . . . . . . . . . . . . . . . 241.5 Partially Segregated Fields of Gas-Liquid Reagents in a Stirred Vessel [2] 251.6 3D Image of a Stirred Vessel [2] . . . . . . . . . . . . . . . . . . . . . . 251.7 Radioactive Sludge at the Bottom of a Long-Term Storage Pond [3] . . 281.8 Modern Nuclear Storage Pond [4] . . . . . . . . . . . . . . . . . . . . . 281.9 Typical Waste Water Treatment Plant Flow Diagram . . . . . . . . . . 301.10 Research Topics Within the AASN4IP Project . . . . . . . . . . . . . . 31

2.1 Four Degrees of Freedom . . . . . . . . . . . . . . . . . . . . . . . . . . 342.2 SPURV - Self Propelled Underwater Research Vehicle [5] . . . . . . . . 372.3 Autosub from the Southampton Oceanography Centre [6] . . . . . . . . 382.4 Torpedo Shaped mini-AUVs. Left: REMUS-100 AUV [7], Right: SPARUS

AUV [8] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.5 The Ictinea AUV [9] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.6 University of Hawaii's ODIN [10] . . . . . . . . . . . . . . . . . . . . . 412.7 The Australian National Universities Sera�na . . . . . . . . . . . . . . 432.8 The University of Kagawa Spherical AUV [11] . . . . . . . . . . . . . . 442.9 Eyeball ROV [12] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.1 Reynolds Number for Varying Sphere Diameters (m) and Velocities (ms−1) 493.2 Drag Coe�cient for Varying Sphere Diameters (m) and Velocities (ms−1) 513.3 Drag Force (N) for Varying Sphere Diameters (m) and Velocities (ms−1) 523.4 Power (W ) Required for Propulsion for Varying Sphere Diameters (m)

and Velocities (ms−1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.5 Contour Plots of Lifespan (hours) for Thrust Only for Varying Sphere

Diameters (m) and Velocities (ms−1) Based on Di�ering Battery Capa-bilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.6 Contour Plots of Lifespan (hours) for Thrust and Other Components forVarying Sphere Diameters (m) and Velocities (ms−1) Based on Di�eringBattery Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.7 Myring Hull Contour [13] . . . . . . . . . . . . . . . . . . . . . . . . . . 563.8 Alternative Streamlined Hull Shapes . . . . . . . . . . . . . . . . . . . 573.9 Energy, E,(kJ), Required for 25% Utilization for Varying Sphere Diam-

eters, d (m) and Velocities, v (ms−1), 0 < Re < 2.5x106 . . . . . . . . . 593.10 Drag Force for Design Work Envelope . . . . . . . . . . . . . . . . . . . 61

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3.11 Energy Requirements for a 30 Minute Mission for Design Work Envelope 61

4.1 Forces Acting on a Sphere in Water . . . . . . . . . . . . . . . . . . . . 634.2 Forces Acting on a Sphere in Water . . . . . . . . . . . . . . . . . . . . 654.3 Diaphragm Static Vertical Displacement System. (a) Increase vehicle

Mass (b) Decrease vehicle Mass . . . . . . . . . . . . . . . . . . . . . . 674.4 WASPNet Motor/Syringe Unit [14] . . . . . . . . . . . . . . . . . . . . 684.5 Harbin Institute of Technology Micro Fish [15] . . . . . . . . . . . . . . 694.6 The Stages of Synthetic Jet Operation (Left): (A) Initial in�ow, (B) Ini-

tial Out�ow, (C) Subsequent In�ow, (D) Subsequent Out�ow. SyntheticJet Formation (Right) [16] . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.7 Vortex Ring Formation From the Side (Left) and From Below (Right) . 744.8 VRT Prototype (Left) and Corresponding CAD Image (Right) . . . . . 754.9 Propeller Propulsion Prototypes for Horizontal Motion (Left) and Ver-

tical Motion (Right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.10 Left: Prototype of a Propeller Based VDS. Right: vehicle Depth against

Time Whilst Tracking a Set-Point . . . . . . . . . . . . . . . . . . . . . 784.11 Working Envelope for Drag Force (White Area) Caused by Propeller

Based Thrusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.12 Working Envelope for Energy Consumption (White Area) Caused by

Propeller Based Thrusters . . . . . . . . . . . . . . . . . . . . . . . . . 794.13 Motor Performance Data [17] (Left), Traditional Propeller Curves [18]

(Right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804.14 Advance Velocity, Va for Varying Shaft Speeds, N , Propeller Pitches, Z

and Slip Values, S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.15 Force Measurement Rig . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.1 Breakdown of µAUV Technical Areas . . . . . . . . . . . . . . . . . . . 875.2 Top Left: MK I Prototype, Top Right: MK II Prototype, Bottom Left:

MK III Prototype, Bottom Right: MK IV Prototype . . . . . . . . . . 885.3 The MK V Hull . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.4 The MK VI Hull. Top Left: Compression Joint in Support Stand, Top

Right: External Compression Ring and Thruster Mount, Bottom Left:Tightening Jig, Bottom Right: Fully Sealed Hull . . . . . . . . . . . . . 91

5.5 Four Degrees of Freedom . . . . . . . . . . . . . . . . . . . . . . . . . . 925.6 Possible Thruster Con�gurations . . . . . . . . . . . . . . . . . . . . . 935.7 3D CAD Drawing of the Prototype Vehicle . . . . . . . . . . . . . . . . 955.8 Advance Velocity, Va vs. Shaft Speed, N for Varying Slip Values . . . . 975.9 Required Torque, Q, for Varying E�ciencies, ε and Slips, S . . . . . . . 985.10 Fully Constructed MK V Thruster Unit . . . . . . . . . . . . . . . . . . 995.11 Output Thrust Comparison for Six Thruster Units . . . . . . . . . . . . 1005.12 Movement of the Vehicle with Balanced Thrust Forces . . . . . . . . . 1005.13 Movement of the Vehicle with Imbalanced Balanced Thrust Forces . . . 1015.14 Thrust Output for Extended Force Measurement Test . . . . . . . . . . 1025.15 Angular Position of Prototype During Imbalanced Thrust Experiment . 1025.16 Output Force and Input Current for Varying Propeller Diameters . . . 1055.17 Acoustic Positioning System Set-Up . . . . . . . . . . . . . . . . . . . . 1075.18 40KT08 Acoustic Transducers Mounted in a Static Test Node . . . . . 108

9


5.19 MK VI Acoustic Positioning System Set-Up . . . . . . . . . . . . . . . 1085.20 Bench Test for PX40-015G5V and PX40-030G5V Pressure Sensors, With

and Without Averaging Filter . . . . . . . . . . . . . . . . . . . . . . . 1105.21 Experimental Set-Up for Digital Compass and Gyroscope Error Statistic

Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105.22 Error Statistic Plot for Digital Compass . . . . . . . . . . . . . . . . . 1115.23 E�ects of Electromagnetic Interference on the Compass With and With-

out Calibration Routine . . . . . . . . . . . . . . . . . . . . . . . . . . 1125.24 Non-Linear Distortion Curve for Digital Compass for MK V Prototype 1135.25 Container Used to Store Nuclear Waste . . . . . . . . . . . . . . . . . . 1135.26 Error Statistic Plot for Rate Gyroscope . . . . . . . . . . . . . . . . . . 1155.27 Comparison of Backwards Di�erentiation and Kalman Filter for Esti-

mates of Velocity using Noisy Position Data . . . . . . . . . . . . . . . 1165.28 Position Data for Kalman Tuning Experiment . . . . . . . . . . . . . . 1185.29 Velocity Data for Kalman Tuning Experiment . . . . . . . . . . . . . . 1185.30 Design for Control Circuitry . . . . . . . . . . . . . . . . . . . . . . . . 1205.31 Control Circuit PCBs - Left: Processor Board with Gyro, Top Right:

Battery Board, Bottom Right: Processor, Gyro and Battery BoardsStacked Together . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.32 MK VI PCB Stack Overview . . . . . . . . . . . . . . . . . . . . . . . . 1225.33 Design for the MK VI COntrol Circuitry . . . . . . . . . . . . . . . . . 1235.34 The MK VI PCB Stack Mounted in the Hull . . . . . . . . . . . . . . . 1245.35 The MK V Prototype (Left) and the MK VI Prototype (Right) . . . . 126

6.1 Classic Feedback Control Loop . . . . . . . . . . . . . . . . . . . . . . . 1286.2 Decomposition of the 3D control System . . . . . . . . . . . . . . . . . 1296.3 Coordinate Reference Frames . . . . . . . . . . . . . . . . . . . . . . . 1336.4 Visualisation of Thruster Allocation Matrix . . . . . . . . . . . . . . . 1346.5 High-Level Abstraction of the SIMULINK Model . . . . . . . . . . . . 1366.6 Output Response for PID Simulation . . . . . . . . . . . . . . . . . . . 1406.7 Output Response for 'P' Simulation . . . . . . . . . . . . . . . . . . . . 1416.8 Output Response for 'I' Simulation . . . . . . . . . . . . . . . . . . . . 1426.9 Output Response for 'D' Simulation . . . . . . . . . . . . . . . . . . . . 1426.10 Output Response for SMC Simulation with Sign Function and Second

Derivative Trajectory Tracking . . . . . . . . . . . . . . . . . . . . . . . 1466.11 Output Response for SMC Simulation with Saturation Function and

Second Derivative Trajectory Tracking . . . . . . . . . . . . . . . . . . 1466.12 Output Response for SMC Simulation with Saturation Function and No

Second Derivative Trajectory Tracking . . . . . . . . . . . . . . . . . . 147

7.1 Closed-Loop Response for A Step Input, Positive Buoyancy of 1g . . . 1537.2 Closed-Loop Response for A Step Input, Positive Buoyancy of 1g with

Added Gaussian Input Noise . . . . . . . . . . . . . . . . . . . . . . . . 1547.3 Closed-Loop Response for A Step Input, Positive Buoyancy of 1g with

Added Gaussian Input Noise and Low-Pass Filter . . . . . . . . . . . . 1547.4 Step Response Comparison Between Continuous and Discrete Time Sim-

ulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

10


7.5 Extended Simulation to Observe E�ects of Integral Action for Imbal-anced Mass of 1g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

7.6 Simulation of Increased Integral Action for Imbalanced Mass of 1g . . . 1587.7 Extended Simulation to Observe E�ects of Integral Action For Imbal-

anced Mass of 2g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1597.8 MK V Prototype Being Tested On-Site at NNL (Right) and in the 2m

Tank at the University (Left) . . . . . . . . . . . . . . . . . . . . . . . 1597.9 Comparison of Experimental Results for Step Input of 1m in the NNL

Pond and `Real-World' Simulation . . . . . . . . . . . . . . . . . . . . . 1607.10 3.5g of Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1607.11 Experimental Results for Step Input of 0.5m in The University Tank . 1627.12 Experimental Results for a Staircase Input . . . . . . . . . . . . . . . . 1627.13 Translational and Rotational Motion During Vertical Controller Exper-

iments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1647.14 Graphical Representation of the E�ects of the Direction of Thrust on

the Direction of Rotation Caused By Thruster Misalignment . . . . . . 1667.15 3D Simulation of Vertical Descent With Imbalanced, Time-Varying Thrust

and Vertical Thruster Misalignment . . . . . . . . . . . . . . . . . . . . 1677.16 2D Simulation of Vertical Descent With Imbalanced, Time-Varying Thrust

and Vertical Thruster Misalignment . . . . . . . . . . . . . . . . . . . . 1677.17 Comparison of Simulation and Experimental Results for a PID Con-

troller Implemented on the MK VI Prototype . . . . . . . . . . . . . . 1687.18 Simulated Response of the Sliding Mode Controller with Parameter Un-

certainties of 10% and 50% . . . . . . . . . . . . . . . . . . . . . . . . . 1707.19 Plot of the Trajectory Tracking to the Sliding Surface in the `Ideal-

World' Simulation with 10% Uncertainty . . . . . . . . . . . . . . . . . 1707.20 Plot of the Trajectory Tracking to the Sliding Surface in the `Real-World'

Simulation with 10% Uncertainty . . . . . . . . . . . . . . . . . . . . . 1717.21 Simulated Response of the Sliding Mode Controller to Staircase Input . 1717.22 Sliding Mode Controller Component Comparison for φ = 0.1 . . . . . . 1727.23 Total Vertical Thrust Output for φ = 0.1 . . . . . . . . . . . . . . . . . 1737.24 Sliding Mode Controller Response for φ = 0.4 . . . . . . . . . . . . . . 1737.25 Sliding Mode Controller Component Comparison for φ = 0.4 . . . . . . 1747.26 Total Vertical Thrust Output for φ = 0.4 . . . . . . . . . . . . . . . . . 1747.27 Comparison of Sliding Mode and Bounded PD Controllers: Simulation

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1767.28 Bounded PD Controller Experimental Results . . . . . . . . . . . . . . 1767.29 E�ects of Numerical Di�erentiated Velocity Estimates on Bounded PD

Controller Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1777.30 Comparison of Bounded PD Controller and PID Controller . . . . . . . 1787.31 Bounded PD Controller Response to Staircase Input . . . . . . . . . . . 178

8.1 Comparison of Control Systems for Ideal Scenario . . . . . . . . . . . . 1838.2 Comparison of Control Systems for Real-World Scenario . . . . . . . . 1848.3 X-Y-ψ Simulated Position for Yaw Rotation Control . . . . . . . . . . . 1858.4 Simulation of Angular Position for Vehicle Rotation Test Using the Dig-

ital Compass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

11


8.5 Measurements of Angular Position for Vehicle Rotation Test Using theDigital Compass (MK V) . . . . . . . . . . . . . . . . . . . . . . . . . . 187

8.6 Simulation Results of Translational Movement for Vehicle Rotation TestUsing the Digital Compass . . . . . . . . . . . . . . . . . . . . . . . . . 187

8.7 Measurements of Angular Position for Straight Line Test Using the Dig-ital Compass (MK V) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

8.8 Comparison of Simulation and Experimental Results for Digital Com-pass Input (MK VI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

8.9 Experimental Results for Rate Gyroscope Input . . . . . . . . . . . . . 1908.10 Experimental Results for Sensor Fusion Input Using a Kalman Filter . 1908.11 E�ects of Vertical Controller on Vehicle Rotation using MK V Prototype 1928.12 Closed-Loop Control Experiment for Heave and Yaw using MK VI pro-

totype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1928.13 Responses for Individual DOF for Horizontal Position Control . . . . . 1948.14 2D Position and Orientation . . . . . . . . . . . . . . . . . . . . . . . . 1948.15 2D Position and Orientation with the Vehicle Rotating to Face the Di-

rection of Forward Movement . . . . . . . . . . . . . . . . . . . . . . . 1958.16 2D Position and Orientation with the Vehicle at a Fixed Orientation . . 1958.17 The Di�erence Between Fixed-Time Set-Points (Left) and Line-of-Sight

Way-Points (Right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1968.18 Way Point Guidance by Line of Sight with 10cm Circle of Acceptance . 1978.19 Way Point Guidance by Line of Sight with 5cm Circle of Acceptance . 1988.20 2D Position and Orientation of the Vehicle Descending in a Spiral . . . 1988.21 3D Position and Orientation of the Vehicle Descending in a Spiral . . . 1998.22 2D Position and Orientation of the Vehicle Spelling out the Word 'Hello'

Using Way-Point Guidance . . . . . . . . . . . . . . . . . . . . . . . . . 1998.23 3D Position and Orientation of the Vehicle Spelling out the Word 'Hello'

Using Way-Point Guidance . . . . . . . . . . . . . . . . . . . . . . . . . 200

A.1 Waste Water Treatment Flow [19] . . . . . . . . . . . . . . . . . . . . . 230

B.1 Drag Coe�cient vs. Reynolds Number for All Sphere Diameters . . . . 231B.2 Drag Coe�cient vs. Reynolds Number [20] . . . . . . . . . . . . . . . . 231

C.1 PD Gamma Controller Output . . . . . . . . . . . . . . . . . . . . . . . 233C.2 Slug Length and Diameter Over a Range of Frequencies . . . . . . . . . 234C.3 Helmholtz Cavity Based VRT . . . . . . . . . . . . . . . . . . . . . . . 235C.4 Input Force for a Range of Cavity:Disk Diameter Ratios for the VCM . 236

D.1 Non-Linear Distortion Curve for Digital Compass for MK VI Prototype 238

F.1 Flowchart for the MK VI Software . . . . . . . . . . . . . . . . . . . . 245

G.1 Top Level of SIMULINK Model . . . . . . . . . . . . . . . . . . . . . . 247

I.1 Step Responses for Varying Linearization Equilibrium Points . . . . . . 257I.2 Bode Plot of Closed Loop System . . . . . . . . . . . . . . . . . . . . . 257

J.1 Control Output for Figure 7.5 . . . . . . . . . . . . . . . . . . . . . . . 258J.2 Control Output for Figure 7.6 . . . . . . . . . . . . . . . . . . . . . . . 259

12


J.3 Control Output for Figure 7.7 . . . . . . . . . . . . . . . . . . . . . . . 259J.4 Control Output for Figure 7.17 . . . . . . . . . . . . . . . . . . . . . . 260J.5 Control Output for Figure 7.18, 10% Uncertainty . . . . . . . . . . . . 260J.6 Control Output for Figure 7.18, 50% Uncertainty . . . . . . . . . . . . 261J.7 Control Output for Figure 7.21 . . . . . . . . . . . . . . . . . . . . . . 261J.8 Control Output for Figure 7.28 . . . . . . . . . . . . . . . . . . . . . . 262J.9 Control Output for Figure 7.29 . . . . . . . . . . . . . . . . . . . . . . 262J.10 Control Output for Figure 7.31 . . . . . . . . . . . . . . . . . . . . . . 263J.11 Control Output for Figure 8.1, Bounded PD Controller . . . . . . . . . 263J.12 Control Output for Figure 8.1, PIDγ Controller . . . . . . . . . . . . . 264J.13 Control Output for Figure 8.2, Bounded PD Controller . . . . . . . . . 264J.14 Control Output for Figure 8.2, PIDγ Controller . . . . . . . . . . . . . 265J.15 Control Outputs for Figure 8.13 . . . . . . . . . . . . . . . . . . . . . . 265

K.1 Responses for Individual DOF for Horizontal Position Control in `Ideal-World' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

K.2 2D Position and Orientation in `Ideal-World' . . . . . . . . . . . . . . . 267

L.1 Vertical Motion Experiment Using Bounded PD Controller on the MKVI Prototype with a Disturbance . . . . . . . . . . . . . . . . . . . . . 268

13

List of Tables

1.1 Water Quality Parameters [21] . . . . . . . . . . . . . . . . . . . . . . . 27

2.1 Di�erences Between AUV Types . . . . . . . . . . . . . . . . . . . . . . 392.2 Ictineu Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.3 ODIN Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.4 Sera�na Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.5 Kagawa Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.6 Eyeball Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.7 Comparison of Potentially Suitable Vehicles . . . . . . . . . . . . . . . 46

3.1 Internal Components and Power Consumption . . . . . . . . . . . . . . 543.2 Hull Comparison for Limited Dimensions . . . . . . . . . . . . . . . . . 573.3 Notation for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.1 Comparison of Propulsion Units . . . . . . . . . . . . . . . . . . . . . . 734.2 Notation for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.1 Overview of Prototype Vehicles . . . . . . . . . . . . . . . . . . . . . . 885.2 Comparison of Hemisphere Sealing Methods . . . . . . . . . . . . . . . 905.3 Horizontal Thruster Con�guration Comparison . . . . . . . . . . . . . . 945.4 Motion Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6.1 Control System Classi�cations . . . . . . . . . . . . . . . . . . . . . . . 1286.2 Quantitative Speci�cations . . . . . . . . . . . . . . . . . . . . . . . . . 1316.3 Equations of Motion Notation . . . . . . . . . . . . . . . . . . . . . . . 1326.4 Main Types of Controller Used on AUVs . . . . . . . . . . . . . . . . . 1376.5 Other Types of Controller Used on AUVs . . . . . . . . . . . . . . . . . 138

7.1 µAUV Heave Simulation Plant Parameters . . . . . . . . . . . . . . . . 1527.2 Continuous Time PIDγ Controller Parameters . . . . . . . . . . . . . . 1527.3 µAUV Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . 1567.4 Quantitative Speci�cation Comparison . . . . . . . . . . . . . . . . . . 157

8.1 µAUV Yaw Simulation Plant Parameters . . . . . . . . . . . . . . . . . 1828.2 µAUV Yaw Simulation Plant Parameters . . . . . . . . . . . . . . . . . 1838.3 µAUV Yaw Imperfection Simulation Parameters . . . . . . . . . . . . . 183

A.1 Water Treatment Levels [22] . . . . . . . . . . . . . . . . . . . . . . . . 229

C.1 Notation for Appendix C.3 . . . . . . . . . . . . . . . . . . . . . . . . . 237

14


Abstract

This thesis, entitled Mobile Platforms for Underwater Sensor Networks was submittedto the The University of Manchester by Mr Simon Andrew Watson on 19th October2012 for the degree Doctor of Philosophy (PhD)

The production of clean water, the generation of nuclear power and the developmentof chemicals, petro-chemicals and pharmaceuticals all rely on liquid-based processes.They are fundamental to modern society, however the real-time monitoring of suchprocesses is an inherently di�cult challenge which has not yet been satisfactorily solved.

Current methods of monitoring include on- and o�-line spot checks and industrial pro-cess tomography. Neither of these methods provides the spatial or temporal resolutionrequired to properly characterise the processes. This research project proposes a newmonitoring method for processes which can tolerate foreign objects; a mobile under-water sensor network (MUSN).

An MUSN has the potential to increase both the spatial and temporal resolution ofmeasurements and could be used in real-time. The network would be formed by anumber of mobile sensor platforms, in the form of micro-autonomous underwater ve-hicles (µAUVs) which would communicate using acoustics. The demonstrator for thetechnology is for use in the monitoring of nuclear storage ponds.

Current AUV technology is not suitable for use in enclosed environments such as storageponds due to the size and maneuverability. This thesis presents the research conductedin the development of a new vehicle µAUV. The work presented covers the mechatronicaspects of the vehicle; the design of the hull, propulsion systems, corresponding controlcircuitry and basic motion control systems.

One of the main factors in�uencing the design of the vehicle has been cost. If alarge number of vehicles are used to form a network, the cost of an individual µAUVshould be kept as low as possible. This has raised a number of technical challengesas low-cost components are often of low-tolerance. Imbalanced time-varying thrust,low manufacturing tolerances and noisy indirect sensor measurements for the controlsystems have all been overcome in the design of the vehicle.

The outcome of the research is a fully functional prototype µAUV. The vehicle isspherical in shape with a diameter of approximately 15cm, with six thruster unitsmounted around the equator (increasing the horizontal clearance to 20cm) to providethrust in four degrees of freedom (surge, sway, heave and yaw).

The vehicle has a sensor suite which includes a pressure sensor, digital compass and agyroscope which provide inputs to the motion control systems. The controllers havebeen developed and implemented on the vehicle's custom built embedded system. Ex-periments have been conducted showing that the µAUV is able to move in 3D withclosed-loop control in heave and yaw. Motion in surge and sway is open-loop, via adead-reckoning system.

15


Declaration

No portion of the work refered to in this thesis has been submitted in support of anapplication for another degree or quali�cation of this or any other university or otherinstitute of learning.

Copyright Statement

1. The author of this thesis (including any appendices and/or schedules to thisthesis) owns certain copyright or related rights in it (the �Copyright� and s/hehas given The University of Manchester certain rights to use such Copyright,including for administrative purposes.

2. Copies of this thesis, either in full or in extracts and whether in hard or electroniccopy, may be made only in accordance with the Copyright, Designs and PatentsAct 1988 (as amended) and regulations issued under it or, where appropriate,in accordance with licensing agreements which the University has from time totime. This page must form part of any such copies made.

3. The ownership of certain Copyright, patents, designs, trade marks and otherintellectual property (the �Intellectual Property�) and any reproductions of copy-right works in the thesis, for example graphs and tables (�Reproductions�), whichmay be described in this thesis, may not be owned by the author and may beowned by third parties. Such Intellectual Property and Reproductions cannotand must not be made available for use without the prior written permission ofthe owner(s) of the relevant Intellectual Property and/or Reproductions.

4. Further information on the conditions under which disclosure, publication andcommercialisation of this thesis, the Copyright and any Intellectual Propertyand/or Reproductions described in it may take place is available in the UniversityIP Policy (see http : //documents.manchester.ac.uk/DocuInfo.aspx?DocID =487), in any relevant Thesis restriction declarations deposited in the University Li-brary, The University Library's regulations (see http : //www.manchester.ac.uk/library/aboutus/regulations) and in The University's policy on Presentation ofTheses.

16


Dedication

This thesis is dedicated to my parents and my sisters, without whose sacri�ces andunwavering support, none of this would have been possible.

Thank You.

Acknowledgment

The research in this thesis would not have been as successful as it was without the helpof a number of people. I would �rst like to thank my supervisor, Dr. Peter N. Green forhis support and guidance throughout the project and for tolerating my eccentricitiesin the way I work. I would also like to thank Mr. Dominic J. P. Crutchley for hisinvaluable assistance in all aspects of my research.

This research was part of a much larger project entitled Actuated Acoustic SensorNetworks for Industrial Processes (AASN4IP) and I would like to thank the all thosewho worked on the project for their support; Prof. Trevor York, Mr. Peter R. Green,Dr. Zhigang Qu, Dr. Antonis Phasouliotis, Dr. Chithambaram Veerappan and Dr.Christos Masouros from the University of Manchester and Dr. Nikki Trigoni, Dr.Sarfraz Nawaz and Mr. Muzammil Hussain from the University of Oxford. I wouldalso like to thank the University technicians who have helped design and construct thehardware, in particular Mr. John Bramwell, Mr. Paul Shaw and Mr. Danny Vale.

Finally I would like to thank the project sponsors, the Engineering and Physical Sci-ence Research Council (EPSRC, grant F/064578/1), the National Nuclear Laboratory(NNL, in particular Dr. Steven Stanley), Yorkshire Water and Phoenix InspectionSystems. I would also like to thank the Worshipful Company of Scienti�c InstrumentMakers (WCSIM) and the Institute of Engineering and Technology (IET) for the sup-port and opportunities provided by their award schemes.

The Author

I graduated from the University of Manchester (formerly UMIST) in 2008 with a 1st

Class M.Eng (Hons.) in Mechatronic Engineering with Industrial Experience. Duringmy degree I completed a year long industrial placement as Robotic Systems Engineerat Labman Automation Ltd. in Stokelsey.

My research interests lie in the �eld of autonomous systems, more speci�cally, theirapplication in wireless sensor networks. This research project has allowed my to de-velop both my theoretical knowledge and practical implementation skills, as well ascommunication and leadership skills.

My research has been recognised by both the Worshipful Company of Scienti�c In-strument Makers (WCSIM) and the Institute of Engineering and Technology (IET). Iwas awarded a Postgraduate Scholarship by the WCSIM in 2009 and the IET's Leslie

17


H. Paddle Scholarship in 2011. This latter award has also led to an article about myresearch being published in the Manchester Evening News (M.E.N.).

List of Publications

S. A. Watson, D. J. P. Crutchley and P. N. Green, �The Mechatronic Design of aMicro-Autonomous Underwater Vehicle�, provisionally accepted for publication in In-ternational Journal of Mechatronics and Automation, May 2012.

S. A. Watson and P. N. Green, �Robust Control of a Micro-Autonomous UnderwaterVehicle (µAUV) Using Low-Tolerance Components�, presented at IFAC Workshop onNavigation, Guidance and Control of Underwater Vehicles, April 2012.

T. A. York, P. N. Green, P. R. Green, A. Phasouliotis, Z. Qu, S. Watson, M. Hussain,S. Nawaz, N. Trigoni and S. Stanley, �Acoustic Sensor Networks for Decommissioning�,Measurement and Control, Vol. 45/2, pp 48-54, March 2012.

P. N. Green, P. R. Green, M. Hussain, S. Nawaz, A. Phasouliotis, Z. Qu, N. Trigoni,S. Watson and T. York, �Mapping Legacy Storage Ponds�, Nuclear Future, 2011, vol.7, pp. 54-59.

T. A. York, P. N. Green, P. R. Green, M. Hussain, S. Nawaz, A. Phasouliotis, Z. Qu, S.Stanley, N. Trigoni, and S. Watson, �Acoustic Sensor Networks for Decommissioning�,Control & Instrumentation in Nuclear Installations, Lancaster, UK, Sept. 2011.

S. A. Watson, D. J. P. Crutchley and P. N. Green, �The Design and Technical Chal-lenges of a Micro-Autonomous Underwater Vehicle (µAUV)�, in Proc. Mechatronicsand Automation (ICMA), 2011 IEEE International Conference on, Beijing, China,2011, pp. 567-572.

S. A. Watson and P. N. Green, �A De-Coupled Vertical Controller for Micro-AutonomousUnderwater Vehicles (µAUVs)�, in Proc. Mechatronics and Automation (ICMA), 2011IEEE International Conference on, Beijing, China, 2011, pp. 561-566.

S. A. Watson and P. N. Green, �Design Considerations for Micro-Autonomous Under-water Vehicles (µAUVs)�, in Proc. Robotics, Automation and Mechatronics (RAM),2010 IEEE Conference on, Singapore, 2010, pp. 429-434.

S. A. Watson and P. N. Green, �Propulsion Systems for Micro-Autonomous UnderwaterVehicles (µAUVs)�, in Proc. Robotics, Automation and Mechatronics (RAM), 2010IEEE Conference on, Singapore, 2010, pp. 435-440.

S. Nawaz, M. Hussain, S. Watson, N. Trigoni and P. N. Green, �An Underwater RoboticNetwork for Monitoring Nuclear Waste Storage Pools�, Sensor Systems and Software,Springer Berlin Heidelberg, 2010, vol. 24, pp. 236-255.

18

Chapter 1

Introduction

Liquid-based processes are some of the most important processes undertaken by mankind

in the industrialised world. The production of clean water, the generation of nuclear

power and the development of chemicals, petro-chemicals and pharmaceuticals all de-

pend of the use of liquids in a medium to large scale. Unfortunately these liquid

processes are inherently di�cult to monitor, both in-line1 and in real-time [23].

There are two main reasons why such processes need to be monitored; money and

safety [24]. The chemical and pharmaceutical industry is worth billions of pounds and

problems with the processes could cost companies large sums of money. The utilities

(water and power generation) are also concerned with cost, however their primary

motivation is safety. A contaminated water supply or a failure of a waste storage

facility (such as happened in Fukushima in Japan in 2011[25]) could have disastrous

consequence for public health.

There are very few systems available which can measure the detailed behaviour and dy-

namics of a liquid processes. The current technology is limited to o�-line measurements,

spot measurements or industrial process tomography which can be unsatisfactory in

terms of both temporal and spatial resolution2 as will be detailed in Section 1.1.

This thesis proposes a new method of monitoring liquid-based processes, a mobile

underwater sensor network (MUSN), which has the potential to increase both the

temporal and spatial resolutions of measurements, and allow them to be taken in real

time. The network would consist of a number of mobile instrumentation platforms in

the form of autonomous underwater vehicles (AUVs) which will communicate using

acoustics.1In-line measurements are taken using sensors which are in the liquid �ow.2The temporal scale is the rate at which the process changes with time. The spatial scale is the

rate of change of position and indicates the resolution of measurements that are required to fully mapthe process.

19


Figure 1.1 shows the spectrum of processes which would bene�t from a MUSN. The

current mobile platforms available on the market are mainly aimed towards oceano-

graphic applications. These systems could be modi�ed for use in some water reservoirs

[26], however they could not be used in the smaller scale process industry or nuclear

storage ponds.

Figure 1.1: Industrial Processes Spectrum

The research discussed in this thesis aims to investigate the design of a system that can

be used in processes that are too small for current size AUVs. Since the processes range

in characteristic temporal and spatial scales, a universal system will not be possible.

The demonstrator of the system will be for use in nuclear storage ponds, however the

aim is for the design to be applicable, with only minor modi�cations, to other processes.

1.1 Monitoring Systems

Before highlighting the processes that would bene�t from MUSNs, it would be prudent

to investigate the current sensing methodologies and identify the reasons why MUSNs

may o�er a better solution. Currently there are three main strategies that are employed

to monitor liquid-based processes.

The �rst approach is to avoid in-process measurement altogether, relying on laboratory

data gleaned from pilot-plants [27]. The second is to take limited spot measurements at

speci�c times and locations3 [23]. The �nal approach is to use some form of Industrial

Process Tomography (IPT). The �rst two approaches are only able to provide limited

data, whilst IPT can provide more extensive information.3A sensor is placed at a �xed location in the process and readings are taken. The sensor may not

be kept in the process, instead placed there manually at certain times before being removed

20


1.1.1 Industrial Process Tomography (IPT)

Tomography is a method of imaging an object by sections or sectioning. It is derived

from the Greek words `tomos', meaning `to slice' and `graph', meaning `image' [28].

There are two types of IPT which are used; nonintrusive, where the sensors penetrate

the wall of the process vessel but do not protrude into the medium and noninvasive,

where the sensors are attached to the outside of the wall [1]. A typical system con�g-

uration is shown in Figure 1.2.

Figure 1.2: Electical Tomography System [1]

As well as the di�erent sensor con�gurations of the tomographic system, there are also

di�erent types of sensing signal which can be used. Hard �eld signals such as x-rays

and γ-rays produce distinct images, however due to the type of radiation being used,

they can be dangerous, bulky and expensive. Soft �eld methods use electrical signals

and tend to produce lower resolution images but are safer and cheaper [24].

1.1.2 Mobile Underwater Sensor Networks (MUSNs)

Wireless Sensor Networks (WSNs) are composed of a number of autonomous sensor

nodes which are deployed in or around the phenomenon which is to be monitored [29].

Underwater sensor networks (USNs) are an invasive measurement technique which

requires the sensors to be placed inside the process. The sensors could be permanently

�xed to the process vessel, which may provide no improvement in terms of spatial

resolution compared to traditional sensing methods. Alternatively they could be free

to move around the process, thus forming a mobile underwater sensor network (MUSN).

If the sensor nodes were able to move in the process vessel, whether passively like �ow

followers or actively like AUVs, they would have to have some method of localisation

so that the sensor data could be interpreted in a meaningful manner. The traditional

method of wireless sensor communications is via radio frequency (RF) signals, however

this method is unsuitable in liquids [30, 31]. Instead, acoustic signals are used for

communications and positioning.

21


To localize and communicate with the sensor nodes inside the process vessel, a minimum

of 3 (2D position) or 4 (3D position) base stations or anchors, mounted around the

sides, would be required [32]. A visualisation of the set-up for a nuclear storage facility

is shown in Figure 1.3. The individual sensor nodes, as well as forming an ad-hoc

network, could be controlled as a swarm, working together to monitor the process.

Figure 1.3: Demonstrator System for a Nuclear Storage Pond

1.1.3 Evaluation

There are several issues with IPT which mean that, while it may be viewed as currently

the best option for certain processes, it is by no means ideal. Traditional hard �eld

tomography equipment comes usually in the form of a �xed installation which the

object to be analysed is brought to (for example X-ray machine or MRI scanner) [33].

This set-up would be unsuitable for use with medium to large scale process vessels.

There are also inherent safety issues relating to the use of radiation.

Soft �eld devices have been tested on process vessels up to 36m3 (4m in diameter)

[34, 35], however scaling it up to the scale of a nuclear storage pond (approximately the

size of an Olympic swimming pool) may prove infeasible due to the low signal strength

in large volumes of water and the cost and logistics of mounting all the required sensors.

One other drawback of IPT, for use in liquids, is that it is limited to measuring only

physical parameters. Chemical parameters such as pH, dissolved oxygen content or

chemical composition4 cannot be measured.

4Near-infra-red absorption tomography has been used to identify hydrocarbons in gasoline vapour[36]

22


MUSNs could provide a viable alternative measurement solution. It is an untested

technology, however it has the potential to increase the temporal and spatial resolution

of measurements as well as the types of parameters measured. The technology is

invasive however and could therefore only be used in processes which can tolerate

foreign objects.

1.1.4 Hybrid Systems

Neither MUSNs or IPT are the ideal solution for industrial process measurements.

They should not be viewed as competing technologies, rather parallel streams in the

quest to obtain better measurement data. In the future the best solution may be a

hybrid system which uses MUSNs to gather data that is then fed into a tomographic

system to produce detailed 3D images [37].

1.2 Industrial Applications

Figure 1.1 in section 1 shows a range of industrial processes that could bene�t from

mobile underwater WSNs. This section investigates the possible uses in the Process

Industry, Nuclear Storage Ponds and Wastewater Treatment Plants.

1.2.1 Process Industry

The process industry is one �eld in which the use of swarms of sensor nodes could be

useful. A large proportion of the processes involve stirring vats of chemicals that are

being mixed or separated. Mixing processes can involve elements that are in any one

of the three states of matter. The most common type of mixture is a liquid and a gas.

A batch of a mixture can be worth millions of pounds. In many large-scale processes,

engineers do not have a detailed understanding of the process's dynamics. The process

vessels are often scaled-up versions of laboratory vessels meaning they have not been

optimised for large scale production. By knowing how the process occurs, the engineers

could modify the vessels to make them more e�cient, saving energy and reducing the

amount of wasted materials [38].

Process engineers usually want to measure temperature, pH, dissolved chemical con-

centration, pressure and the number and size of bubbles or particles [39, 40]. Currently,

the only way to measure many of these parameters is by non-invasive IPT. This is often

not practical and there are limits on the types of parameters which can be measured

23


(see Section 1.1.3). The use of sensor nodes that could be placed inside the process

vessel would allow a larger range of parameters to be measured.

There are three example scenarios from the process industry where AUVs would be

useful. The �rst is the homogeneous mixing of reagents in a vessel as shown in Figure

1.4. Two of the reagents are added from reservoirs whilst the third is already in the

vessel. All three reagents mix together to produce a complex spectrum of products.

The AUVs could be used as �ow followers (neutrally buoyant5 systems which follow

the streamlines of the �ow) to monitor the plumes of reagents from the entry points

and to track the chemistry of the liquid.

Figure 1.4: Homogeneous Mixing of Reagents [2]

The second scenario is in the combining of liquids and gases in a semi-batch gas-liquid

stirred reactor. The concentration of chemicals can vary in space as shown in Figure

1.5. A sensor node could act as a �ow follower carried around the tank by the impeller

and track the concentration �elds. It could then move to speci�c areas to obtain

detailed measurements of the spatial variation of the �elds. The variation in the sizes

of bubbles could also be monitored.

The third scenario is when solids are mixed with liquids. As the vessel is stirred, the

particulates become more agitated and become suspended in the liquid. The faster the

stirring, the greater the volume of solid which becomes suspended. Figure 1.6 shows

how concentration �elds of suspended solids can form. The light blue area represents

the liquid and the brown and red regions are the suspended solid concentrations (brown

to red is low to high concentration). The image was produced using 3D tomography

and the use of a sensor node could produce more accurate results.5An object is classed as neutrally buoyant if it has the same density as the surrounding �uid.

24


Figure 1.5: Partially Segregated Fields of Gas-Liquid Reagents in a Stirred Vessel [2]

Figure 1.6: 3D Image of a Stirred Vessel [2]

The three potential MUSN applications described above are all related to real-time

monitoring of live processes. Most process managers are very conservative and are

unwilling to take risks that could cost their company millions of pounds [2]. There

are a number of problems with placing sensor nodes in a live process. If the process

involves mixing then there will be agitators inside the vessel [41]. If the node is not

small enough, it could cause the agitators to become jammed and damage them or

more likely, the vehicle will be destroyed and introduce contaminates into the product.

The node also needs to have enough thruster power to hold station against any currents

caused by the agitators and also to overcome them if it starts to get sucked in.

A more realistic �rst step in the application of mobile sensor nodes in the process

industry would be as vessel inspection vehicles during shut-down maintenance. Many

of the large vessels are lined with glass on the inside to act as insulation [42]. Over time

cracks can form in the glass which eventually could cause breaches in the outer skin

of the vessel. During scheduled maintenance shut downs, the vessels are emptied and

decontaminated and maintenance personnel have to enter the vessel, often in full hazard

suit and perform a visual inspection. An alternative method used is to undertake non-

25


destructive testing where random areas are tested. Neither method is safe and both

can be time consuming and expensive.

One of the �rst stages of most extensive maintenance is the decontamination of the

process vessel. This is often done by �lling the vessel with solvents. Sensor nodes could

be used during this stage to map the insides of the vessel. To do this the vessel would

have to be full of liquid but this could be in the form of water or solvent and need

not disrupt the normal schedule. The AUVs could identify areas that need particular

attention and they could even have a camera to send back live images. Since the

process would not be running in the vessel, there would be no moving parts to collide

with and if a AUV failed it would not contaminate the product.

Another initial application could be for use in pilot vessels. These vessels are used to

test new processes before they are scaled up for full commercial use. The MUSN could

be used to gather data in the testing phase so that the performance of the process

can be monitored. Once there is con�dence in the process, the vessel can be scaled up

without the need for a MUSN to monitor it.

MUSNs could be highly bene�cial to the process industry, however there are a number

of application-speci�c challenges which could limit the adoption speed of the technol-

ogy. Initially, the system could be used as part of the maintenance routine, however

eventually it could be used to provide real-time measurements of the mixing processes

themselves.

1.2.2 Nuclear Storage Ponds

As of 30th March 2012, there were 436 civilian nuclear power plants worldwide with

another 63 under construction [43]. There are also over 270 test/research reactors

[44]. By 2006, 276,000 metric tons of heavy metal (tHM) waste had been produced,

increasing by approximately 11,500tMH (4%) a year [45]. Around two thirds of this

(190,000tHM) is stored, rather than being reprocessed, approximately 93% of it in

wet storage facilities [21]. By 2020, it is estimated that the amount of fuel in storage

facilities, both wet and dry, will have increased to 324,000tHM.

There are two types of storage ponds in nuclear facilities; at-reactor (AR) and away

from reactor (AFR) [46]. The standard procedure is for the spent fuel to be placed in

an AR pond for between 3 to 5 years to allow it to cool down [47]. The waste can then

be removed to AFR facilities (dry or wet) or be reprocessed. Often however, the waste

has been kept in the AR facilities for periods of over 20 years. Across the world, there

are over 700 AR and AFR storage ponds [46, 43] and this number will only increase

26


further as new reactors come on-line.

Water is used in storage ponds for a number of reasons [21]:

• To facilitate heat removal from the spent fuel

• To act as a biological shield

• To maintain fuel cladding integrity

• To facilitate spent fuel visual inspection

There are a number of parameters which are measured in order to to maintain the

viability of the storage ponds. Table 1.1 is taken from [21] and shows the parameters,

frequency of testing and current analysis method. Most of the measurements can only

be taken at the surface, so a detailed analysis of the ponds is not possible. The number

of these parameters which are monitored is dependent on the age of the storage facility.

Older ponds have only the basics (pH, temperature, pressure and water level) measured,

whilst newer ponds have the full range.

Table 1.1: Water Quality Parameters [21]Frequency Analysis Method

pH Daily pH ElectrodeConductivity Daily Conductivity MeterTurbidity Daily UV-Visible Spectrometer

Cl−, F−, SO2−4 Monthly (AR) Ion Chromatography

NO−3 , PO4−3 Weekly/Daily (AFR)

Inductive Coupled PlasmaMass Spec (ICPMS)

Alpha, Beta, Weekly (AR) Scintillation Countersgamma general control Daily (AFR) Ion ChamberComplete Chemical

Monthly (AR/AFR) ICPMSAnalysis

On RequestAtomic Absorption or EmissionSpectroscopy (AAS or AES)

Plasma AES

If the water quality is not kept consistent, the fuel cladding integrity can be reduced

over time. Essentially, the protective casing around the radioactive material corrodes

and forms a radioactive sludge as shown in Figure 1.7. This presents two problems;

an increased amount of radiation from the exposed fuel rods and the formation of

radioactive particulates which are di�cult to dispose of.

27


Figure 1.7: Radioactive Sludge at the Bottom of a Long-Term Storage Pond [3]

1.2.3 Application of Mobile Underwater Sensor Networks

There are two main areas where MUSNs could be of great bene�t; the monitoring of

modern facilities and the decommissioning of legacy storage ponds. Modern storage

ponds tend to be well-organised with the radioactive material stored in canisters placed

in a regular grid arrangement (see Figure 1.8) and there are detailed records of the

contents [48]. AUVs could be used to patrol such ponds in an e�ort to detect undesirable

situations, such as leaks from canisters [49]. Early warning of such problems would

enable timely action to be taken, reducing both risk and cost.

Figure 1.8: Modern Nuclear Storage Pond [4]

28


Older ponds are more problematic. The oldest date from the origins of the nuclear

power industry, in the 1950s, and there are a signi�cant number of ponds worldwide

that are between 30 and 50 years old. In the intervening years, a variety of di�erent

materials have been stored, and in some cases records of the contents of ponds are

incomplete [50, 51, 52]. In addition, long periods of immersion in water of low quality

and a lack of suitable monitoring have led to degradation of both containers and their

contents. As a consequence, the bottom of such ponds is an irregular combination of

randomly-orientated solid objects and particulate sludge, as the schematic of Figure

1.3 in Section 1.1.2 shows.

A MUSN deployed in a legacy pond could map the topology of the bottom, and identify

di�erent materials and levels of radiation. This would enable the pond's operators to

design a plan for the removal, processing and disposal of the contents of the pond.

The removal process could also be supervised by the MUSN, providing warnings of

unanticipated conditions within the pond in real-time.

The demonstrator for the system presented in this thesis will be for use in nuclear

storage ponds. The long-term aim is for use in the decommissioning of legacy ponds,

however the monitoring of modern facilities is also of interest.

1.2.4 Wastewater Treatment Plants

"Water treatment involves removal of undesirable constituents from water and then

disposal of them in the easiest and safest manner" [53]. There are two main types of

wastewater treatment plants; industrial and municiple. Municiple plants treat water

that goes back to the domestic water grid whereas the output from most industrial

plants gets used elsewhere. A basic �ow diagram of a typical waste water treatment

plant is shown in Figure 1.9 [54]. A more detailed description of the di�erent stages

can be found in Appendix A.

It is envisaged that swarms of AUVs could be used in the primary, secondary, tertiary

and advanced stages. During the primary stage, particulates are removed by means of

settling tanks. These tanks have a low �ow rate and allow the particulates to sink to

the bottom. The AUVs could be used to take samples of the particulates or undertake

maintenance inspections.

The secondary, tertiary and advanced treatment stages all involve the use of organic

or chemical additives to remove unwanted products from the water. AUVs could be

used to map the pH and temperature and show where the processes are not occurring

e�ciently. They could also be used to retrieve samples of the water or sludge that

29


Figure 1.9: Typical Waste Water Treatment Plant Flow Diagram

would be inaccessible using current measurement systems.

AUVs could also be deployed in water tanks and reservoirs. They would be used as

either tank inspection vehicles or as mapping systems. Currently, to map the bottom

of a reservoir to �nd out the levels of residue, a sonar system attached to a �oat is

used. A swarm of AUVs could reduce the time taken to map the bottom, provide

more accurate data and take a larger range of measurements such as pH levels and

temperature.

1.3 Research Overview

The purpose of this research was to investigate possible designs for AUVs for use in

MUSNs. The scope of the work was the design of the mechatronic aspects of the AUV;

vehicle hull design, provision of mobility, power systems and motion control. As will be

outlined in Chapter 2, traditional AUVs are much too large for the target applications,

meaning a new, smaller vehicle was required.

This new micro-AUV6 (µAUV) was up to an orders of magnitude smaller than typical

AUVs, much smaller and much more maneuverable. The key challenges were associ-

ated with the development of simple, cheap, robust, accurate and low-power buoyancy

6As de�ned in Section 2.4

30


(vertical displacement) and propulsion systems, suitable for very small devices, and the

development of suitable control algorithms.

1.3.1 Actuated Acoustic Sensor Networks for Industrial Pro-

cesses

The research was part of an Engineering and Physical Science Research Council (EP-

SRC) funded Wired and Wireless Intelligent Networked Systems (WINES) III project,

which aimed to design generic wireless sensing network technologies for use in liquid-

based industrial processes.

The research was entitle Actuated Acoustic Sensor Networks for Industrial Processes

(AASN4IP) and it was a collaborative venture between the Universities of Manch-

ester and Oxford and several industrial companies: The National Nuclear Laboratory,

Phoenix Inspection Systems and Yorkshire Water. The demonstrator for the project

was a `swarm' of µAUV's that could map the bottom of a nuclear storage pond.

As previously detailed, the research presented in this thesis is concerned with the

mechatronic aspects of the AUV design. Other aspects of the design (shown in Figure

1.10) have been researched by colleagues, both at the University of Manchester and the

University of Oxford. These include the communications systems, vehicle localisation,

the embedded system and sensing. The work conducted in some of these areas will be

brie�y summarised in this thesis, where they have a direct impact on the mechatronic

design.

Figure 1.10: Research Topics Within the AASN4IP Project

31


1.4 Summary

Current sensing technology for use in liquid-based industrial processes is limited in

terms of what can be measured and by cost and size. IPT is currently the best option

available to industry, however it is not scalable for use in physically large processes

such as those described in Chapters 1.2.2 and 1.2.4. For these applications there is

currently no reliable method of taking measurement. For the process industry where

IPT is mainly used, MUSNs should not be viewed as a competing technology, rather

a complementary system that could be used in conjunction with IPT to produce high

resolution measurements.

32

Chapter 2

System Requirements and Current

Technology

Section 1.2 identi�ed a number of applications which could bene�t from mobile un-

derwater sensor network (MUSN) technology, speci�cally the process industry, the

monitoring of wet nuclear storage facilities and the water industry. These applications

have several things in common.

Firstly, the work area is enclosed, unlike the ocean, where traditional autonomous

underwater vehicles (AUVs) are used. The enclosed area is also relatively small, again

compared with the ocean. This means that the the size of the vehicle will have to be

appropriately scaled down.

Secondly, the processes being investigated may contain a large amount of clutter which

needs to be avoided and maneuvered around. In the process and water industries,

this may be mixing impellers or ba�es and in the nuclear industry, this would be the

nuclear storage containers or other such objects. The µAUV developed was therefore

required to be highly maneuverable.

The scale and maneuverability of the µAUV developed during this research are what

di�erentiate it from the traditional designs. It is required to be much smaller and more

maneuverable than previous AUVs.

2.1 Demonstrator

Whilst there are a number of applications the MUSN technology is applicable to, the

demonstrator for the project will be targeted at a single one, speci�cally the monitoring

of nuclear storage ponds. As outlined in Chapter 1.2.2, nuclear storage ponds are

33


roughly the size of an Olympic swimming pool and depending on the type, modern or

legacy, the contents can be structured and documented or contain unstructured and

unknown clutter.

Even though the demonstrator is intended for a speci�c application, the ability to use it

in other processes should be kept in mind. There are several mechatronic requirements

on the design which are universal across the di�erent applications and there are several

which are speci�c to the nuclear storage problem. The requirements are therefore be

split into two categories: generic and application speci�c.

2.1.1 Generic Requirements

The generic requirements are those which apply to any of the target applications. The

�rst requirement is that the µAUV should be at least two orders of magnitude smaller

than the process vessel it is monitoring. This is so that the vehicle does not unduly

a�ect the process.

The second requirement is that the vehicle has at least three degrees of freedom (DOF),

speci�cally surge, heave and yaw [55] (illustrated in Figure 2.1). The vehicle has to

be able to maneuver to any position in the process vessel, hold station and be able to

avoid obstacles or clutter. Movement in each DOF should also be bi-directional. This

leads to the third and fourth requirements that the turning radius of the vehicle should

be zero, or as close as possible, and that movement in the vertical and horizontal planes

should be decoupled.

Figure 2.1: Four Degrees of Freedom

The decoupling of movement in the two planes and the zero turning radius are im-

portant distinctions between the design presented in this thesis and traditional AUV

technology. Sea-going AUVs tend to have coupled vertical movement, they descend by

moving forwards and using control surfaces [56, 57], although there are a number of

recent vehicles which have decoupled movement [58, 59].

The �fth requirement is that the µAUV has to run o� an independent, re-chargeable

power supply. Tethers are used in remotely operated vehicles (ROVs) and it is the main

34


reason why they are unsuitable for cluttered environments. Once the power supply has

been depleted, it needs to be recharged, otherwise the system has to be removed from

the process which may not be feasible.

The �nal requirement is that the vehicle should be constructed using low-cost, o�-

the-shelf components wherever possible. If a swarm of µAUVs is used, the cost of an

individual vehicle should be kept low to make the whole system commercially viable.

2.1.2 Application-Speci�c Requirements

The application-speci�c requirements are more detailed than their generic counterparts

and arise due to the nature of the tasks being conducted in the nuclear storage ponds.

The �rst requirement is that the µAUV is at least an order of magnitude smaller than

the clutter1 (not just the process vessel as with the generic requirements). This is to

allow the vehicle to not only move around the objects, but potentially inside them2. It

also must be large enough to house all the sensors and drive electronics.

The second requirement is that the vehicle has at least four DOF (one more than

speci�ed in the generic requirements), speci�cally surge, sway, heave and yaw. This

allows greater maneuverability and means the vehicle should be able to navigate in a

highly cluttered and unstructured environment.

The �nal three requirements are all related to the properties of the liquid the µAUV

will be operating in. The nuclear storage containers are typically kept underwater at

a depth of up to 15m, equivalent to a pressure of 250kPa. The temperature can range

from between 5◦C and 45◦C, since one of the main tasks of the water is to act as a heat

sink [21]. The pH of the water can range between 4.5 and 11.5 depending on the types

of material being stored [21]. The vehicle should therefore be designed to withstand

all of these parameters

Within the scope of this thesis, work has been conducted to meet all of the generic re-

quirements and the �rst three of the application speci�c requirements. The operational

environment parameters (temperature and pH) have not been considered as the aim

of the research is to provide a proof-of-concept system which could then be developed

further.

1The clutter in nuclear storage ponds comes in the form of storage tanks which are between 1mand 2m long.

2Some nuclear storage skips are not fully enclosed.

35


2.1.3 Mechatronic Requirements Summary

The mechatronic requirements for this research are summarised below:

• The vehicle should be 2 orders of magnitude smaller than the process vessel and

1 to 2 orders of magnitude smaller than the clutter being investigated.

• The vehicle should run on an independent, rechargeable power supply.

• 4 DOF are required: surge, sway, heave and yaw. Motion in the roll and pitch is

unnecessary and will be inhibited by careful ballasting of the vehicle.

• Movement in all DOF should be bi-directional.

• Propulsion in planes parallel to the surface of the pond (x-y plane) should be

decoupled from depth-wise propulsion (z-axis).

• The vehicle should be able to maintain station at a given position and orientation

(x,y,z,ψ) in Earth-Fixed Coordinates (See Section 6.3).

• The turning radius of the vehicle should be 0mm.

• The vehicle should be constructed using low-cost, o�-the-shelf components wher-

ever possible.

Having identi�ed the requirements for the mechatronic system, it is prudent to assess

the technology which is currently available, both commercial and academic, and to

identify if any of it is suitable for the target application. The rest of this chapter is

dedicated to this analysis.

2.2 Underwater Exploration Vehicles

There are two main classes of underwater vehicles that can be used for remote ex-

ploration: Remotely Operated Vehicles (ROVs) and Autonomous Underwater Vehicles

(AUVs). ROVs are tethered submersibles that are controlled by a human operator

who is in a safe environment [60]. They were originally used for salvage and rescue in

situations where it was too dangerous to send divers, however they are most commonly

used for deep sea exploration and as inspection systems for underwater pipelines and

other such facilities.

ROVs have been used in nuclear storage ponds, however they were deemed to be

unsuitable due to the tether. The tether was liable to get caught on the clutter,

causing damage to itself, the ROV and the object it was caught on. Tethers are also

36


unsuitable in closed environments, i.e. where the process vessel has a lid on it. The

alternative is therefore to consider AUVs.

2.3 A History of AUVs

The history of AUVs can be traced back as far as 1866 and the development of the

Whitehead torpedo, although this was used for destructive purposes rather than sci-

enti�c research/investigation. The development of a system that could obtain oceano-

graphic data started in the 1950s with the advent of neutrally buoyant �oats [61]. The

�rst modern AUV was SPURV (Self Propelled Underwater Research Vehicle), Figure

2.2, which was designed in 1957 at the Applied Physics Laboratory of the University

of Washington [62]. SPURV was 3.1m long, weighed 454kg and could travel to a depth

of just over 3km [5].

Figure 2.2: SPURV - Self Propelled Underwater Research Vehicle [5]

The Development of AUVs over the next 30 years was relatively slow, with only a few

systems successfully being built such as the University of New Hampshire's EAVE and

the Russian Shirshov Institute of Oceanology's SKAT [63]. This was due to a lack of

technological capabilities in terms of processing power and power storage.

During this time, AUVs were developed for two main purposes; scienti�c research

and military use. The US military developed the AUSS (Advanced Unmanned Search

System) in the 1980's to search for sunken ships and aircraft [64]. This system had

an autonomous mode but the missions were supervised by human operators on the

surface. The military investigated using multiple AUSSs to increase the search speed,

e�ectively forming a crude wireless sensor network [65].

It was only in the 1990's that research into the development of AUVs began in earnest.

MIT developed a range of AUVs within the Odyssey project [66] and collaborated

37


with the Woods Hole Oceanographic Institution (WHOI) to develop REMUS (Remote

Environmental Monitoring UnitS) [7], while the Southampton Oceanography Centre

developed the Autosub, shown in Figure 2.3 [6]. AUVs also started becoming com-

mercially viable in the 90's and several companies started developing and selling them

[67].

Figure 2.3: Autosub from the Southampton Oceanography Centre [6]

During the early part of the 21st century, commercial AUV development increased

dramatically and by 2009 there were over 600 AUVs being used across the world for

either surveys, research or military use [68].

2.4 AUV Classi�cation

While originally conceived to gather data about the oceans, modern AUVs are now used

for a variety of applications such as seabed mapping, pipeline surveys, mine sweeping

and environmental surveys [67, 68]. They can be categorized into six distinct groups

according to parameters such as size and weight [69]. These groups are Micro-Vehicles,

Mini-Vehicles, Sea-going Vehicles, Hovering Vehicles, Surface Vehicles and Gliders.

Table 2.1 shows the di�erences between the di�erent types. The table is based on the

categories presented in [69] but also includes analysis from other sources.

Table 2.1 shows that for the underwater exploration vehicle being developed in this

project to be classed as `micro', it must weigh less than 5kg and be less than 0.5m

long. This is in keeping with the aim of designing the system to be around an order

of magnitude smaller than the clutter in nuclear storage ponds, as detailed in section

2.1.2.

38


Table 2.1: Di�erences Between AUV TypesType Length Weight PurposeMicro < 0.5m < 5kg Cooperative sensor networks

Mini < 2m < 100kgMilitary, cooperative sensor networks,

short-range ocean missionsSea-going > 2m 1− 2tonnes Long-range, high-depth ocean missionsHovering 3− 4m < 1tonne Oceanographic data gatheringSurface < 2m < 100kg Oceanographic data gatheringGliders < 1m < 100kg Oceanographic data gathering

Most development in the �eld of AUVs is concerned with ocean-going vessels that are

of `mini' size and larger, such as REMUS [70], ORCA [71], SPARUS [58], Girona [59]

and ODIN [72] vehicles.

A brief review of the designs of `mini' AUVs will be provided. However, as this work

is principally concerned with the development of vehicles in the `micro' class, more

detailed attention will be given to vehicles such as Sera�na [73], Eyeball [74] and the

µAUV being developed at the University of Kagawa [11].

2.5 Mini AUVs

As de�ned in Table 2.1, a mini-AUV is less than 2m long and weighs less than 100kg.

According to the market survey presented in [68], the majority of AUVs being used

in 2009 were in this category. Most mini-AUVs (and most sea-going AUVs) are the

classic torpedo shape [70, 58] as shown in Figure 2.4. This shape is a function of the

applications for which they are used.

Figure 2.4: Torpedo Shaped mini-AUVs. Left: REMUS-100 AUV [7], Right: SPARUSAUV [8]

Ocean-based missions, whether for commercial surveys or academic research, are con-

ducted over long distances (10s to 100s of kilometers) and over extended periods of

time [75, 76]. Reducing the power consumption of the vehicle by decreasing the drag

(see Chapter 3) is the reason for the streamlined hull.

39


There are mini-AUVs which are not streamlined, although they are usually used for

shorter duration missions in coastal areas or other large bodies of water such as dams

[26]. Two examples are the Ictinea AUV [9] and the ODIN AUV [72].

2.5.1 Ictineu

The Ictineu AUV was designed at the the University of Girona for the Student Au-

tonomous Underwater Challenge - Europe (SAUC-E) [9]. It has since been used for a

number of projects including habitat mapping and dam inspection [26]. The vehicle

can be operated as an AUV or as a tethered ROV.

Figure 2.5: The Ictinea AUV [9]

Table 2.2 presents a review of the vehicle capabilities [77]. It can be seen that the

vehicle is relatively small, has high maneuverability and a large sensor suite. In terms

of application use, it would be suitable for use in the water reservoirs, as reported in

[26], although its size means that it could not be used in nuclear storage ponds.

Table 2.2: Ictineu ReviewSize 0.74m x 0.465m x 0.524m

Weight 52KgDOF 4: Surge, Sway, Heave and Yaw

Power Supply Lead Acid BatteriesPropulsion Systems 4 - 6 x Propeller-Based Thrusters, 250W each

Sensing CapabilitiesCameras, Imaging Sonar, Doppler Velocity Log (DVL),Compass, Attitude and Heading Reference System

and PressureControl Algorithms PID

Testing Extensive: SAUC-E, Coastal Mapping, Dam Inspection

40


2.5.2 ODIN

The Omni-Directional Intelligent Navigator (ODIN) AUV was developed in 1991 at

the University of Hawaii as a test bed for control algorithms for underwater vehicles

[72]. Over the next decade, it was used extensively in the development of advanced

control algorithms for �ne motion control. The current incarnation is ODIN III which

was built in 2003.

ODIN III, shown in Figure 2.6 is spherical in shape with a diameter of 0.63m. Eight

propeller-based thrusters are mounted around the equator to provide 6 DOF movement.

One of the advantages of the ODIN AUV is the thruster redundancy which the eight

thrusters provide. The vehicle can either be operated via a tether or be autonomous

[10]. There is also a manipulator mounted to the outside of the vehicle. Table 2.3

summarises the vehicles capabilities [78]

Figure 2.6: University of Hawaii's ODIN [10]

Table 2.3: ODIN ReviewSize 0.63m Diameter

Weight 125KgDOF 6: Surge, Sway, Heave, Roll, Pitch and Yaw

Power Supply 24 Lead Gel BatteriesPropulsion Systems 8x Propeller ThrustersSensing Capabilities Sonar, Pressure, Temperature, IMUControl Algorithms PID, Adaptive, Custom

Testing Extensive in Pools

41


2.6 Micro-AUVs

There are very few functional µAUVs in existence, either commercial or academic. The

majority of AUV development is for the Marine Sciences where vehicles are larger so

that they can withstand tidal currents and also carry a greater sensor payload.

Of the available vehicles, Sera�na from the Australian National University is the most

established [73], although the Eyeball AUV from MIT [74] and the vehicle being de-

veloped at the University of Kagawa [79] are also of interest. It should be noted that

the development of both the MIT and Kagawa vehicles started after this research had

begun.

There are a number of other µAUVs which have either been designed purely as an

academic exercise and not implemented, such as MIT's Pipsqueak and MicROV [80, 81],

or for which there is very limited reported data such as Hydron [82, 83] and Nanoseeker

[84]. Due to this, the rest of this section will concentrate on the well documented

vehicles; Sera�na, Eyeball and Kagawa.

2.6.1 Sera�na

The aim of the Sera�na project is to investigate the possibility of using a swarm of

small, autonomous underwater vehicles for exploration, mapping and monitoring of

ocean spaces. The 0.45m long AUV was developed around 2002/2003 and uses 5

thrusters to move around, as shown in Figure 2.7 making it highly maneuverable and

able to swim against moderate ocean currents. The vehicle capabilities are shown in

Table 2.4.

All data and images regarding this project have been obtained from the Sera�na project

website [73]. There are a large number of publications with regards to the use of Sera�na

for oceanographic data gathering, however there are very few with regard to the design

of the vehicle itself.

Communication between the AUV's is achieved using long-wave radio transmitters

operating at 122kHz with a range of < 6m and a data rate of 1024 − 8192bits/s,

whilst acoustic sensors allow for range, bearing, and identi�cation of the location of all

neighboring AUV's. The payload consists of a sonar sensor module, compass, pressure

sensor and linear accelerometers. The AUV's cannot recharge their power source so

once the power is low, they have to be retrieved and recharged.

42


Figure 2.7: The Australian National Universities Sera�na

The project is investigating �xed/�exible formation mapping of the ocean bed, specif-

ically bathymetric mapping and isocline identi�cation. Simulations have used up to

hundreds of AUV's in complex geometric formations, however recent work (2008/2009)

has been in the area of polygonal formation mapping, where around six AUV's have

been utilised [85].

Table 2.4: Sera�na ReviewSize 0.455m x 0.21m diameter

Weight 3Kg - 4Kg (estimated)DOF 5: Surge, Heave, Roll, Pitch and Yaw

Power Supply Batteries (unknown type)Propulsion Systems 5x Propeller ThrustersSensing Capabilities Pressure, Compass, Sonar, AccelerationControl Algorithms Unknown

Testing Extensive in Pools

2.6.2 University of Kagawa

The University of Kagawa in Japan has recently developed a spherical underwater

robot with the aim of eventually using it as part of a wireless sensor network [86].

Publications regarding this vehicle were only available in 2011. The AUV uses three

water-jets to provide propulsion and the initial prototypes were around 400mm in

diameter. Their aim is to reduce this diameter to around 200mm. The vehicle has

been tested in a swimming pool, however there appear to be no publications on �ne

motion control or communications.

43


Figure 2.8: The University of Kagawa Spherical AUV [11]

Table 2.5: Kagawa ReviewSize 0.4m

Weight 6.5KgDOF 3: Surge, Heave and Yaw

Power Supply 2 x LiPo and 4 x Rechargeable AA BatteriesPropulsion Systems 3x Water JetSensing Capabilities Rate Gyroscope, Pressure SensorControl Algorithms Unknown

Testing Limited in a Pool

2.6.3 Eyeball

The Eyeball ROV has been developed at the Massachusetts Institute of Technology

(MIT) and is designed for the inspection of hazardous environments such as those

found in nuclear facilities [74]. The vehicle is spherical with a diameter of around

200mm and is moved by a pair of water-jet thrusters and an internal eccentric mass [87].

Publications regarding this vehicle were only presented in 2011. An initial prototype

has been constructed but not extensively tested.

Table 2.6: Eyeball ReviewSize 0.2m Diameter

Weight 1.35KgDOF 4: Surge, Roll, Pitch and Yaw

Power Supply Batteries (unknown type)Propulsion Systems 2x Water-Jet Thruster + Eccentric MassSensing Capabilities Gyroscope, Accelerometer, CameraControl Algorithms PID

Testing Limited in a Pool

44


Figure 2.9: Eyeball ROV [12]

2.7 Evaluation

Section 2.4 investigated systems that are relevant to this research project. Table 2.7

shows a comparison of vehicles which are of interest with respect to the generic and

application speci�c requirements of the project. The traditional DOF are surge, sway,

heave, roll, pitch and yaw. For this analysis they will be denoted by 1, 2, 3, 4, 5 and 6

respectively.

It can be seen that none of the systems identi�ed ful�ll all of the generic and application

speci�c requirements. The system which is of most interest is Sera�na. This AUV is

highly maneuverable, with de-coupled motion in the vertical and horizontal planes.

However, the maximum length is 0.45m, which is over twice the desired length. The

systems from Kagawa University and MIT are also of interest, however they are both

in the early stage of development and limited testing has been conducted on them.

Also, neither of these vehicles existed until after this research had started.

2.8 Summary

This section has discussed the state-of-the-art in unmanned underwater vehicle (UUV)

technology. Current AUV technology is principally targeted at the oceanographic com-

munity and is not suitable for use in the applications investigated in Section 1.2, mainly

due to the size and lack of maneuverability. AUVs can be classi�ed according to length

and weight and the most relevant vehicles have been identi�ed and investigated. Ta-

ble 2.7 shows which systems may be of interest to this project. While some of them

can satisfy some of the requirements, none of them were designed for the applications

described in Section 1.2.

45

Simon A. Watson Mobile Platforms for USNsTable2.7:

Com

parisonof

Potentially

SuitableVehicles

System

DOF

0Turning

De-coupled

Independent

Longest

Working

Practical

Radius

PlaneMotion

PowerSupply

Dimension

Depth

Implementation

Ictineu

1,2,3,6

33

30.74m

100m

3

ODIN

1,2,3,4,5

33

30.63m

?3

Sera�na

1,3,4,5,6

33

30.45m

?3

Kagaw

a1,2,3,5,6

33

30.4m

?3

Eyeball

1,4,5,6

35

30.2m

?3

46

Chapter 3

Parametric Modelling

Chapter 2 investigated the designs of current AUVs, both large-scale oceanographic

systems, and smaller vehicles which may be suitable for this project. It was concluded

that there was currently no AUV available, either commercially or research-based,

which would be suitable for use in nuclear storage facilities. This meant that a new

vehicle had to be designed. It was decided that the best way to do this was to start

from scratch, instead of modifying a current design. This meant that the vehicle could

be tailored to the exact needs of the project.

The starting point for the design was to assess the requirements of the vehicle and

feed the outcomes into a simple parametric model. Essentially this process was a

design-space exploration which would be used to obtain initial estimates of some of

the broad design parameters such as size, drag force (and thrust), velocity and power

consumption (battery life). The rest of this chapter details the work undertaken in

developing this parametric model and assessing its results.

3.1 Key Assumptions

The starting point for the parametric model should be an idealised representation of

the object and the environment it is in [88]. In this scenario, the shape of the vehicle

should be spherical, as a sphere is symmetrical about all axes, and the environment

should be a vacuum, where all parameters are theoretically perfect.

The purpose of this parametric model however, was to investigate the e�ects of moving

in a resistive �uid so that the impact of the vehicles size and speed upon the operational

life could be investigated. The medium in which the sphere was modelled in was a basic

47


Newtonian incompressible �uid1, namely pure water [90]. An incompressible �uid has

constant density for constant temperature, however as the temperature changes, so

does the density. The temperature of the water was set to 10◦C and it was assumed

that there were no impurities which would cause density changes. The assumption was

also made that the depth was constant.

The other parameters which have to be modelled are the size of the sphere and the

velocity at which it moves through the water. It was decided to investigate a range

of both these parameters. Chapter 2.4 identi�ed a number of mini- and micro-AUVs

which may have been suitable for this project. It was decided to set the upper bound

for the diameter to be 0.5m, the maximum length of a µAUV. This diameter is in line

with the application speci�c requirement in Chapter 2.1.2, that the vehicle be up to

an order of magnitude smaller than the clutter which is 1m to 2m in length.

The upper bound for the velocity was set to 5ms−1, much faster than AUVs of com-

parable size, however it was deemed prudent to consider a large operating envelope.

3.2 Model

A body moving through an incompressible �uid, speci�cally water, will have a drag

force, Fd, acting upon it. If the velocity, v, is constant, the thrust force will equal the

drag force. The drag force on a sphere is a function of the sphere diameter, D, and

the velocity, density, ρ, and dynamic viscosity, µ, of the �uid as shown in Equation 3.1

[91]. The indices b, c, d and e are unknown values.

Fd = f (D, v, ρ, µ)

Fd = CdDbvcρdµe

(3.1)

The term Cd is the drag coe�cient and is a dimensionless term used to quantify the

drag of an object in a �uid. The coe�cient comprises the e�ects of two types of �uid

drag; skin friction or frictional drag (the friction of the �uid against the surface of the

object) and form drag or pressure drag (the drag caused by the shape of the object).

1A Newtonian �uid has a constant viscosity for a �xed temperature and pressure [89].

48


By using dimension analysis, it can be demonstrated that the drag coe�cient, can be

related to the Reynolds number, Re [91]. The Reynolds number for can be calculated

using Equation 3.2 [92], where ν is the kinematic viscosity. Figure 3.1 shows a plot of

Re for varying sphere diameters and velocities.

Re =vD

ν(3.2)

Figure 3.1: Reynolds Number for Varying Sphere Diameters (m) and Velocities (ms−1)

Empirical relationships exist between the drag coe�cient and the Re [20], however

they typically only apply to the range Re < 3x105. Figure 3.1 shows that the Re

was in the range Re < 2.5x106, meaning that the standard relationships would be

inapplicable. Two high Re relationships were therefore identi�ed and compared. The

�rst used asymptotic matching to split the relationship into four trends for di�erent

ranges of Re as shown in Equation 3.3 [20].

49


ϕ1 =(24Re−1

)10+(21Re−0.67

)10+(4Re−0.33

)10+ (0.4)10

ϕ2 =1

(0.148Re0.11)−10 + (0.5)−10

ϕ3 =(1.57x108Re−1.625

)10ϕ4 =

1

(6x10−17Re2.63)−10 + (0.2)−10

Cd =

[1

(ϕ1 + ϕ2)−1 + (ϕ3)

−1 + ϕ4

]−1/10(3.3)

The second method used an approximation series method to develop a relationship as

shown in Equation 3.4 [93]. Both methods allow the drag coe�cient to be calculated

for the range Re < 106.

K1 (Re, n) =1− 0.5exp (0.182) + 10.11Re−2/3exp(0.952Re−1/4

)− 0.03859Re−4/3exp

(1.30Re−1/2

)

K2 (Re, n) =0.037x10−4Re1exp(−0.125x10−4Re

)− 0.116x10−10Re2exp

(−0.444x10−5Re

)Cd = K1 (Re, n) +K2 (Re, n) (3.4)

Both proposals give similar results and for the purpose of this model, there was no

reason to favour one approximation over the other. It was therefore decided to use

the second approximation [93] as it appeared to be more extensively cited. Figure

3.2 shows the drag coe�cient for the range of sphere diameters and velocities. A 2D

representation for all diameters of Cd against Re is shown in Appendix B and it can

be seen that it is similar to the experimental and analytical data presented in [20].

The decrease in drag coe�cient at high Re is related to the change in �ow regime in

the boundary layer from laminar to turbulent. The �ow adjacent to the surface of an

object is called the boundary layer and is key in determining the drag experienced by

a body [91]. At low Re, the �ow regime is laminar meaning the �uid moves around the

object in a steady and orderly fashion. As the Re increases, the �ow regime becomes

turbulent and the �uid moves irregularly around the object [92].

50


Once the drag coe�cient has been calculated, the drag force can be found using Equa-

tion 3.5 [94]. Figure 3.3 shows the drag force for the range of sphere diameters and

velocities. The drag force ranges from 0N to >750N. It can be seen that the area of low

drag coe�cient shown in Figure 3.2 (and more easily seen in Figure B.1 in Appendix

B) does not correspond to the lowest drag force. This can be attributed to the fact that

the change in drag coe�cient due to moving from laminar to turbulent �ow, is small

compared with the e�ects of the drag coe�cient due to the change in sphere diameter

and velocity, which are both squared.

Fd =1

2CdπAρv

2 (3.5)

The assumption is made that the sphere is travelling at a constant velocity which means

that the drag force is equal to the thrust force. The power, P , required to produce

this thrust force, here called the input power, can be found using Equation 3.6. The

assumption is also made that there is 100% e�ciency. The plot of the input power is

shown in Figure 3.4. It can be seen that the required power ranges from 0W to nearly

5kW.

P = Fdv (3.6)

Figure 3.2: Drag Coe�cient for Varying Sphere Diameters (m) and Velocities (ms−1)

51


Figure 3.3: Drag Force (N) for Varying Sphere Diameters (m) and Velocities (ms−1)

Figure 3.4: Power (W ) Required for Propulsion for Varying Sphere Diameters (m) andVelocities (ms−1)

52


3.2.1 Added Mass

For the basic model, it was assumed that the velocity was constant. For more advanced

versions of the model, this is not the case and the phenomenon of added mass had to

be taken into account [95]. When an object moves in a �uid it must displace the the

surrounding �uid. In air, since the density is so low, the additional force required to

move the surrounding air is low. This is not the case in water as the density is much

higher. The additional force can be modelled as an added mass to the object so that

mt = m + ma, where mt is the total mass, m is the mass of the object and ma is the

added mass. The added mass for a sphere, moving rectilinearly, can be approximated

by Equation 3.7, where r is the radius of the sphere [96].

ma =2

3ρπr3 (3.7)

3.2.2 Power Supply and Lifespan

Chapter 2.1.1 stated that the µAUV has to run o� an independent, re-chargeable power

supply. Rechargeable batteries are the only viable option and there are several types

available; NiMH, Li-Ion and Li-Poly being the most common. Of these, Li-Ion is the

most readily available and o�ers very good energy density [97]. A number of readily

available Li-Ion battery packs were considered as power supplies, ranging in voltage

and capacity.

A new parameter called lifespan, Ls, is introduced to provide a measure of how long

the µAUV can operate before the batteries are depleted. This is an important value to

calculate as retrieval of a `dead' node in a hazardous environment could be dangerous

and costly. The navigational algorithms will require an estimate of the lifespan so

that re-charging can be integrated into the mission pro�le. It can be estimated using

Equation 3.8, if the powers supply voltage, V , and capacity, Icap in terms of Amp Hours

(Ah), are known.

Ls =IcapV

P(3.8)

Figure 3.5 shows contour plots of the lifespan in hours. The plots are for the power

consumption from the continuous thrust requirements. It can be seen that the lifespan

reduces dramatically as the velocity increases. There is therefore a trade-o� between

lifespan and operational range based on the vehicles velocity.

53


Figure 3.5: Contour Plots of Lifespan (hours) for Thrust Only for Varying SphereDiameters (m) and Velocities (ms−1) Based on Di�ering Battery Capabilities

The basic model considers the mechanical power requirements, however there are other

components inside the vehicle which are detailed in Table 3.1. Estimates of the number

of components and their potential power consumption are also given. The total power

shown is for a worst case scenario and assumes that all of the components are active

all of the time. The values shown in Table 3.1 were estimated from data sheets and

conversations with expert colleagues.

Table 3.1: Internal Components and Power ConsumptionComponent Size (mm) Number Power(W)

Processor with DSP 80x80x15 1 1.98Propulsion System and Drivers 80x80x15 1 2.35

Pressure Sensor External 1 0.05Temperature Sensor External 1 0.05Acoustic Transducers External 1 12

Sensor Drivers 80x80x15 1 N/AVoltage Reg 80x80x15 1 N/APower Supply Unknown 1 - 3 N/A

Total Power 16.43

54


Adding this constant power drain to that of the thrusters, unsurprisingly, reduces the

lifespan as shown in Figure 3.6. It can be seen that once the vehicle reaches a certain

size (around 200mm in diameter) and velocity (around 3ms−1), the thrust power drain

becomes the dominant component.

Figure 3.6: Contour Plots of Lifespan (hours) for Thrust and Other Componentsfor Varying Sphere Diameters (m) and Velocities (ms−1) Based on Di�ering BatteryCapabilities

3.3 Results and Analysis

The parametric model was developed to facilitate the analysis of the mechatronic re-

quirements identi�ed in Chapter 2.1.3. This section presents this analysis and draws

conclusions with regard to some of the design parameters of the µAUV.

For the complete design envelope (all sphere diameters and velocities), the model

showed that the Re was in the range 0 < Re < 2.5x106 (Figure 3.1). The corre-

sponding drag coe�cient ranged from 0.1 to 0.45 depending on the Re (Figure 3.2 and

Figures B.1 and B.2 in Appendix B). The drag force (and hence thrust force) was

in the range Fd < 1kN (Figure 3.3) while the required input power was in the range

P < 5kW as shown in Figure 3.4.

55


Taken in isolation, the results presented do not help reduce the design envelope to a

point where an actual prototype vehicle could be developed. To reach that point, the

results were analysed in three separate sections, in conjunction with the mechatronic

requirements from Chapter 2; hull shape, lifespan and battery charging and velocity.

3.3.1 Hull Shape

The parametric model considered only a spherical hull shape due to its symmetrical

nature. Before making further analysis with regards to thrust forces and power con-

sumptions, it seems prudent to brie�y investigate alternative hull shapes. Of all the

AUVs analysed in Chapter 2, only ODIN, Eyeball and the Kagawa AUV were spherical

[10]. Most of the AUVs are based around a streamlined hull like a torpedo.

A good example of a streamlined shape is the Myring hull contour which was designed

to provide low drag [98] (shown in Figure 3.7). This is the shape of the RAV AUV hull

[13].

Figure 3.7: Myring Hull Contour [13]

The drawback of streamlined bodies is that they have a restricted internal volume and

tend to have low drag only in one axis as shown in Table 3.2. Simulations showed

that for a Myring hull to have the same volume as a 200mm sphere, it would have to

be approximately 860mm long, which is too long to be practically useful in cluttered

environments.

Other streamlined bodies were also considered (using CAD simulations [99]) and are

shown in Figure 3.8, however the decrease in drag in one axis did not justify an increase

in drag in the other axis and a reduction in volume. This is highlighted in Table 3.2,

which provides a normalised drag and volume comparison with respect to a 200mm

diameter sphere.

The requirements for high maneuverability and low power consumption, coupled with

the need to �t a not inconsiderable number of components in a small space, lead to

the conclusion that a sphere is the best option for the hull shape. A sphere is equally

maneuverable in all directions and has the largest usable volume. This means that the

56


Figure 3.8: Alternative Streamlined Hull Shapes

Table 3.2: Hull Comparison for Limited Dimensions

Hull Shape DimensionsNorm. Norm. Norm. Norm.x-axis y-axis z-axis Volumedrag drag drag

Cylinder φ150mm x 200mm 0.603 0.965 0.961 0.664Flying Saucer φ200mm x 75mm 0.167 0.169 3.061 0.349

Myring 30/110/1.25/0.4365/10 0.012 0.263 0.263 0.012Pill 200mm x 100mm x 150mm 0.434 0.557 2.046 0.563

Sphere φ200mm 1 1 1 1

results from the parametric model can be used without the need for a new drag model

to be introduced.

As speci�ed in Chapter 2.1.3, the physical dimensions of the µAUVs should be at

least an order of magnitude smaller than the clutter that is being investigated. In the

nuclear storage ponds, most of the clutter will be in the form of storage containers that

typically have dimensions 2m x 1m x 1m. This would indicate that the hull should be

in the order of 100mm in diameter.

Section 3.2.2 identi�ed a number of components which would need to �t inside the

hull and CAD simulations indicated that to a diameter of at least 130mm would be

required. This was based on early prototype circuit designs and commercially available

components. This is consistent with the conclusions of the previous paragraph. It was

decided to build in a margin of error to the diameter in case larger components were

required. The target diameter was therefore set to 150mm. For a sphere of diameter

150mm, the drag-force was in the range 0 < Fd < 37N for velocities 0 < v < 5ms−1.

57


3.3.2 Lifespan and Battery Charging

Section 3.2.2 de�ned the important parameter, lifespan, as a measure of how long the

µAUV can operate before running out of power. As the lifespan reduces, the µAUV

spends an increasing fraction of its time recharging rather than performing its mission.

In Section 3.2.2, Li-Ion batteries were identi�ed as the power supply and to fully charge

one would take approximately 2 hours [97]. In general the charging voltage is 4.2V/cell.

If the voltage is lower than this, the cell will not charge. The length of time to charge

is dictated by the charging current and must be kept within the manufacturer's rating.

A new parameter, utilisation, is introduced which is a ratio of the time spent on

missions compared with charging. The aim would be to get this value as high as

possible, preferable over 100% (i.e. it spends longer on missions than it does charging).

For this model, the decision was made to investigate the worst-case scenario, the lowest

utilisation value that would be acceptable. Discussions with expert colleagues indicated

that the minimum acceptable mission length would be 30 minutes, giving a utilisation

of 25%.

As expected, as the velocity increases, so does the drag force and the required power

(for a 150mm sphere this was in the range 0 < P < 185W ). This in turn means that

more energy is being consumed and therefore the lifespan of a node is decreased.

Using the power values shown in Table 3.1 (worst case scenario, assuming all subsystems

are on all the time), the energy required to run for 30 minutes was calculated. Figure

3.9 shows a plot of the energy required. The shaded areas represent diameters and

velocities that cannot be considered due to size constraints of internal volume (below

130mm) and physical size of the batteries2 (100kJ curve). The remaining white area

represents the potential operating envelope.

3.3.3 Velocity

The model shows that to maximize the lifespan, the velocity should be kept as low as

possible. For a sphere with diameter 150mm (Section 5.2), the energy required for 25%

utilization is almost doubled when the velocity is increased from 1ms−1 to 3ms−1.

The aim therefore should be to keep the velocity less than 1ms−1, which is comparable

to other AUVs (Section 2.2). At this velocity and with enough energy to complete a

2The larger the energy storage capacity, the larger the physical size. It was found that size requiredto store more than 100kJ was too big to �t in the hull.

58


Figure 3.9: Energy, E,(kJ), Required for 25% Utilization for Varying Sphere Diameters,d (m) and Velocities, v (ms−1), 0 < Re < 2.5x106

30 minute mission, a 150mm diameter µAUV could travel approximately 36 lengths

(1.8km) of an Olympic sized swimming pool (50m x 25m x 10m).

A simple scanning pattern could require the vehicle to do lengths of the pool at 1m

intervals across the width, on a single horizontal plane. This could provide a topological

map of the contents of the bottom. If other sensor readings were required, the pattern

could be repeated at other depths.

A single plane scan would require the vehicle to travel just under 25 lengths (24 lengths

plus 23m traversing). An individual vehicle could achieve this, however if more detailed

measurements are required it would have to recharge �rst. If measurements were

required on planes at 1m depth intervals, a single vehicle would have to execute 7

missions. By using a swarm of µAUVs, the mapping could be distributed and conducted

in a shorter time with reduced individual energy depletion, for example, 7 µAUVs could

complete the mapping in 1 mission.

If the µAUV velocity is reduced, the thrust requirement decreases and the lifespan

increases. The number of lengths that could be achieved without recharge would de-

crease however. The model shows that if the velocity is halved to 0.5ms−1, the energy

requirements reduce by 12%, but the number of lengths decreases by 50%.

59


Essentially, the slower the vehicle moves, the less distance it can travel but the longer

it can operate before running out of power. This is because the dominating power

consumer becomes the internal components rather than the propulsion system.

3.4 Summary

On the basis of the results and discussion presented in the previous section, the µAUV

will be spherical in shape with a target diameter of between 130mm and 200mm.

The velocity will be < 1ms−1 and the power supply will be a Li-Ion battery pack

with a capacity of < 100kJ. Figure 3.10 shows the work envelope (white area) and

corresponding drag forces. It can be seen that the drag force is approximately < 3N.

Figure 3.11 shows the energy requirements for a 30 minute mission for the design work

envelope. It can be seen that the most energy that would be required would be around

40kJ.

With these design criteria a single µAUV would be able to be able to complete, at

most, 36 lengths of an Olympic sized pool, however a crude map would require 250

lengths. Multiple vehicles could be used to map the pond in a quicker time.

Also highlighted is the need for some means of recharging the vehicles. Removal from

the pond and was ruled out after discussions with the National Nuclear Laboratory so

some type of recharge stations will be required. The development of such stations falls

outside the remit of this thesis.

3.5 Notation

Table 3.3: Notation for Chapter 3Fd Drag Force D Sphere Diameterv Fluid Velocity ρ Fluid Densityµ Fluid Viscosity Cd Drag Coe�cient

b, c, d, e Arbitrary Indices Re Reynolds Numbern Drag Coe�cient Index A Area of Object Normal to FlowP Input Power K1, K2 Drag Coe�cient Variablesmt Total Mass of Object ϕ1, ϕ2, ϕ3, ϕ4 Drag Coe�cient Variablesm Mass of Object ma Added Mass of Objectr Radius of Sphere Ls LifespanV Voltage I Current

60


Figure 3.10: Drag Force for Design Work Envelope

Figure 3.11: Energy Requirements for a 30 Minute Mission for Design Work Envelope

61

Chapter 4

Propulsion Systems

The propulsion system is one of the most important parts of the µAUV. Chapter 2

highlighted the fact that the vehicle has to be highly maneuverable, however Chapter

3 showed the need for low power consumption.

There are a large number of propulsion systems that are used in modern aquatic vehi-

cles. Unfortunately, many systems that are used on larger vehicles are unsuitable for

use with the applications described in Section 1.2 due to the physical size and power

requirements. At the other end of the spectrum, there are systems that are too small

and would not provide enough propulsive thrust to move the node.

One of the requirements outlined in Chapter 2 was that the vertical and horizontal

motion should be decoupled. This means that if the vehicle moves in the vertical

plane, it could stay at a �xed horizontal location. The propulsions systems for vertical

and horizontal motion could therefore utilise di�erent technologies and the analysis in

the rest of the chapter will re�ect this.

This chapter starts with a summary of the di�erences between motion in the horizontal

and vertical planes and how this a�ects the types of propulsion system which could be

viable. This is followed by a brief summary and review of eight di�erent propulsion

systems which have been identi�ed as possible solutions.

On the basis of the analysis of the eight propulsion systems, the most suitable can-

didates are evaluated. This includes details of mathematical models, simulations and

prototypes which were developed. Once the propulsion system(s) have been selected,

the impact on the design envelope from Chapter 3 will be considered.

62


4.1 Theory

There are several forces which act upon a vehicle when submerged. These forces are the

buoyancy force Fb, the gravitational force Fg, the drag force Fd and the external thrust

force, FT , as shown in Figure 4.1. It is assumed that z is positive in the downwards

direction.

Figure 4.1: Forces Acting on a Sphere in Water

The requirement that motion in the two planes is decoupled leads to the assumption

that the equations of motion are independent and can be considered separately.

4.1.1 Vertical Plane

There are three main types of vertical displacement systems (VDSs) used in modern

underwater vehicles; dynamic VDS, static VDS or combined [100]. With a dynamic

VDS, the vehicle is positively buoyant and will therefore �oat. Diving is achieved by

using the propulsion system and control surfaces that are vectored down and which force

the vehicle underwater. Alternatively the propulsion system itself could be vectored.

Static VDSs change the density of the vehicle by allowing water in or out. The vehicle

then descends/ascends to a depth where it has the same density as the surrounding

water. The combined method is where the vehicle uses dynamic diving but also has a

static system that is adjusted as it descends.

The two primary forces acting on an underwater vehicle when it is limited to vertical

movement are the buoyancy force and the gravitational force as shown in Figure 4.1.

If these two forces are equal, i.e. the vehicle has the same density as the surround-

ing water, it is classed as neutrally buoyant, as described in Equation 4.1. g is the

gravitational constant, V is the volume of the vehicle and m is its mass.

63


Fb = Fg

ρgV = mg(4.1)

The density of water is a function depth, however it only changes over large values (>

100m). As outlined in Chapter 2, the maximum depth for the demonstrator vehicle

will only be 15m meaning that the density of water can be viewed as constant. The

density of water also change with temperature and chemical composition, however this

will not be considered at this stage.

If a neutrally buoyant vehicle has no vertical momentum, it will hover at a depth where

the water density is the same as that of the vehicle. If the vehicle is not neutrally

buoyant, an external thrust force, equal and opposite to the imbalanced buoyancy

force, is required to allow the vehicle to hover.

A dynamic VDS would only work only if the external thruster units were permanently

turned on to counteract the positive buoyancy. The control system would be relatively

simple, however there may be steady-state errors caused by the buoyancy force [55].

This type of VDS would also have high power consumption due to the thruster units

being permanently turned on.

A classical static VDS would not work as the density of the water is assumed to be

constant, so the vehicle would just rise to the surface or sink to the bottom. Instead, it

could be used to impart momentum to the vehicle by altering the buoyancy. This would

be achieved by adding or removing mass from the vehicle which could be mechanically

complex on a small scale. It would, however be more adaptable to localised variations

in water density.

If an actuation system is used to impart momentum to the vehicle, additional forces

appear as shown in Figure 4.2. The new forces are the drag force, Fd, and the external

thrust force, FT , caused by either an added force from a thruster unit or an additional

weight.

The equation relating the forces, based on Newton's Second Law, is shown in Equation

4.2. The equation for drag force is taken from Section 3.2. mT is the total mass of the

sphere, including added mass (Section 3.2.1).

Fz = Fg + FT − Fb − Fdd(mz)

dt= mg + FT − ρgV −

1

2ρACd(

dz

dt)2

mTd2z

dt2+ z

dmT

dt= mg + FT − ρgV −

1

2ρACd(

dz

dt)2 (4.2)

64


Figure 4.2: Forces Acting on a Sphere in Water

For a static system, the thrust force occurs due to the mass added or removed from

the vehicle. This imbalanced mass is denoted by mi and thus the equation of motion

can be re-written as shown in Equation 4.3.

z =mg

mT

+mig

mT

− ρgV

mT

− ρACd2mT

|z|z − m

mT

z (4.3)

For the dynamic system, the mass is not changed and so m = 0 and thus the equation

of motion is simpli�ed to Equation 4.4. The squared velocity term in the drag part

of the equation has been replaced with the empirically derived |z|z. This is because

as the vehicle changes direction, so too does the drag force and a simple squared term

does not take this into account. The equation of motion can therefore be written as

shown in Equation 4.6.

z =mg

mT

+FTmT

− ρgV

mT

− ρACd2mT

|z|z (4.4)

4.1.2 Horizontal Plane

The equation relating the forces in the horizontal plane is shown in Equation 4.5. At

this stage only movement in one dimension, X, is considered. The vehicle is assumed to

be neutrally buoyant, so the gravitational and buoyancy forces negate each other and

there is no mass �ow, meaning dmTdt

= 0. The equation of motion therefore simpli�es

to Equation 4.5 which is rearranged into Equation 4.6 for solution.

65


Fx = FT − Fdd(mx)

dt= FT −

1

2ρACd(

dz

dt)2

mTd2x

dt2= FT −

1

2ρACd(

dz

dt)2 (4.5)

x =FTmT

− ρACd2mT

|x|x (4.6)

4.2 Types of Propulsion Systems

All propulsion systems can be split into one of two categories: arti�cial or biomimetic.

Arti�cial propulsion systems are not found in nature and have been designed by man,

for example, propellers or water jets. Biomimetic systems are based on propulsive

methods found in nature such as those of �sh or squid.

In total, there are eight propulsion systems which have been identi�ed as potential

candidates, four arti�cial and four biomimetic. The selected propulsion methods

are a Diaphragm-Based VDS, Mechanical Oscillators, a Micro-Pump-Based VDS, a

Motor/Syringe-Based VDS, Piezo-Electric Oscillators, Propellers, Vortex Ring Thrusters

and Water Jets.

Of these systems, three are considered for vertical motion only; the diaphragm, the

micro-pump and the motor/syringe, whilst the other �ve are considered for motion in

either, or both planes.

This part of the chapter provides a brief overview of how each propulsion system works,

vehicles they are currently used on and an estimate of how much force they produce

and power they consume.

66


4.2.1 Diaphragm-Based VDS

This arti�cial, static VDS uses an elastic membrane stretched over a reservoir to change

the density of the vehicle. As the membrane is pulled back, water is drawn in through

an ori�ce. When it is pushed back, the water is expelled as shown in Figure 4.3.

Small scale diaphragm systems are mainly found in micro-pumps with a �xed �ow rate

[101, 102].

Figure 4.3: Diaphragm Static Vertical Displacement System. (a) Increase vehicle Mass(b) Decrease vehicle Mass

To be able to ingest/expel variable volumes of water would mean modelling the non-

linear change in volume caused when the membrane is stretched as in Figure 4.3.

Variable volume diaphragms are not widely available and developing a custom device

would be complex and time-consuming process. There do not appear to be any current

AUVs that use diaphragms for the control of vertical motion.

4.2.2 Micro-Pump-Based VDS

Micro-pumps are used in a wide variety of processes and industries such as aerospace,

pharmaceuticals and the medical sector [103]. A micro-pump-based VDS would be of

the static variety and would work by pumping water in and out of a reservoir to change

the density of the vehicle.

There are several designs of micro-pump currently available; impeller, diaphragm and

peristaltic being the main types. The primary problem with micro-pumps is achieving

bi-directional �ow. The only ones that are small enough and have this function are

peristaltic pumps which use a cam to squeeze water round a tube in the housing.

There are also issues with low �ow-rates which would mean the vehicle would be very

67


unresponsive. As with the diaphragm, there is no evidence of current AUVs using

micro-pumps as a means of vertical propulsion.

4.2.3 Motor/Syringe-Based VDS

The motor/syringe method is an arti�cial static VDS and consists of a syringe and a

plunger which is actuated by a linear stepper motor as shown in Figure 4.4. As the

plunger is moved up the syringe, water is ingested, increasing the mass of the vehicle

and allowing it to sink. As the plunger is pushed down the syringe, water is expelled

allowing the vehicle to rise.

Figure 4.4: WASPNet Motor/Syringe Unit [14]

This system was used in both the WASPNet [14] and the WASPNet II [99] projects

where the aim was to create a neutrally buoyant vehicle that could move to any given

depth to take measurements. The WASPNet project had some success with a prototype

system, although the controller was not based on an analytical model. The WASPNet

II project aimed to build on the work undertaken in [14], however the prototype had

mechanical issues due to the complexity of the design and the controller was highly

oscillatory [99].

4.2.4 Mechanical Oscillators

Biomimetic mechanically oscillating systems are designed to mimic �sh propulsion

on the basis that they are often more maneuverable, stable and quieter than stan-

dard propeller-based AUV designs [104, 105]. Movement is typically achieved through

mechanically-actuated oscillating �ns. Two good examples of this type of propulsion

system are Robotuna from MIT [106] and MT1 from the University of Essex [104].

The simplest design uses �apping plates to provide thrust [107], however more complex

systems use multiple joints and linkages to produce a multi-stage �n oscillation [104].

68


Mechanical oscillators can produce forces greater than 1N but consume up to 34W of

power [105].

Most �sh are unable to swim backwards or rotate on the spot and this is re�ected in

their mechanical counterparts. This could possibly be overcome by the use of multiple

�ns and control surfaces [107] but is impractical when compared with the other possible

propulsion systems being investigated. The low maneuverability, high complexity of the

design and high power consumption mean that, in the context of this work, mechanical

oscillators are not a suitable means of propulsion.

4.2.5 Piezo-Electric Oscillators

Biomimetic piezo-electric propulsion units use oscillating piezo-electric materials in-

stead of mechanically-actuated �ns to mimic �sh movements to provide thrust [108].

Shaped Memory Alloys (SMA) [15], Electro-Active Polymers (EAP) [109], Ionic Con-

ducting Polymer Films (ICPF) [110] or polymeric arti�cial muscles [111] can can also

be used. An example of this type of system is shown in Figure 4.5.

Figure 4.5: Harbin Institute of Technology Micro Fish [15]

This technology is still in the development stage and there is a large amount of research

being undertaken. The forces produced are very small, often less than a milli-Newton

[108, 110]. The voltages required to activate the piezo-electric materials can be as high

as 150V [112] which would be unsuitable for the current application. This propulsion

method also su�ers from the same maneuverability constraints as the mechanical os-

cillators. This type of propulsion system is very small however and may ultimately be

suitable for the smaller end of the application spectrum [113].

69


4.2.6 Propellers

Propellers are widely used in underwater and surface vehicles and are classed as an

arti�cial propulsion system. The propeller is attached to a motor and can be provide

thrust in both directions for reasonable power consumption. Good maneuverability

can be achieved by using multiple propeller/motor units.

Chapter 2.4 highlighted the fact that propellers are the most widely used method of

propulsion for AUVs. Propulsion based on propellers is a mature technology which is

well understood and documented. Problems arise however, with the analytical analysis

and characterisation when the electric motors and propellers become very small.

Force tests using a number of small DC motor/propeller combinations suggested that

a thrust of between 10mN and 100mN could be expected (more details can be found

in Section 5.4). The power consumption was between 0.15W and 0.3W.

4.2.7 Vortex Ring Thrusters

Vortex Ring Thrusters (VRTs), synthetic jet actuators or zero-mass pulsatile jet ac-

tuators are biomimetic propulsion systems which attempt to mimic squid or jelly�sh

locomotion. VRTs are an attractive method of propulsion due to the ability to perform

low speed underwater maneuvers [114].

A basic VRT consists of an actuator moving a diaphragm that moves water in and out

of a cavity through a small ori�ce. When the water is expelled, the boundary layer of

the �uid �owing through the ori�ce separates and rolls into a vortex ring at the edge

of the ori�ce [114]. As this is repeated, more vortices are formed which entrain �uid,

forming a synthetic jet [16, 115] as shown in shown in Figure 4.6. This synthetic jet

provides the propulsive force.

The prototype VRTs that have been constructed at the University of Colorado have

used a variety of actuation systems and while their aim is to design a system that

is physically small enough and provides enough thrust to work in an ellipsoidal AUV

approximately 25cm wide [16], power consumption has not been considered in any of

the literature to date.

There are three types of VRT actuation systems that have been used by the University

of Colorado: solenoid-based [116], voice coil-based [16] and a motor and cam arrange-

ment [117]. The solenoid and motor/cam systems have been successfully integrated

into AUV systems, namely RAV [13] and CALAMAR-E [117] respectively. The voice

coil system appears to have been tested as a stand alone unit only. Unfortunately,

70


Figure 4.6: The Stages of Synthetic Jet Operation (Left): (A) Initial in�ow, (B) InitialOut�ow, (C) Subsequent In�ow, (D) Subsequent Out�ow. Synthetic Jet Formation(Right) [16]

all of the systems are too big and draw too much power to be of use for this project.

There is however, scope to attempt to miniaturize the systems that have already been

designed.

4.2.8 Water Jets

Water jets are another popular form of arti�cial propulsion, but not traditionally used

for underwater vehicles. Water is sucked in via a pump, accelerated, then ejected from

a nozzle. In classical water jet systems, the water is ejected above the water line into

the air. This is because the output jet of water produces less thrust when it is ejected

underwater compared with in air.

In 2011, there were two separate publications regarding AUVs which use water jets

as the main form of propulsion; one from the University of Kagawa in Japan [86]

and the other from Harbin Engineering University in China [118]. The target size of

the �rst vehicle was similar to this project, however the initial prototype was around

400mm in diameter. Initial testing showed the potential for high maneuverability,

however �ne motion control was lacking. The second vehicle was 1m in diameter and

no experimental results have appeared to date.

The University of Kagawa water jets could provide up to 7.2N of thrust [119] with an

input voltage of 7.2V and a current drain of 3.5A. In total, the propulsion system could

draw up to 75.6W. It was found that as the vehicle descended, the propulsive force

decreased due to the increase in water pressure [11].

71


4.2.9 Review

Table 4.1 shows a comparison table for the eight propulsion systems. Of these systems,

only two, the vortex ring thrusters and the propellers, were considered as viable options

for movement in the two planes.

All three of the specialist VDSs, diaphragm, micro-pump and motor/syringe, are of the

static variety whereby the density of the vehicle is modi�ed by the addition or removal

of water. Simulations and basic prototypes of both the micro-pump and motor/syringe

were made and it was found that the complexity of the controller was very high and

that it tended towards being unstable. Without a way to measure the volume of water

inside the reservoir, it was impossible for the control system to return the vehicle to

the point of neutral buoyancy. For this reason, all three static VDSs were eliminated as

viable options. Details of the simulations and experiments can be found in Appendix

C.

The remaining �ve propulsion systems could all be used for both horizontal and vertical

movement. Both the mechanical and piezo-electric oscillations provide low maneuver-

ability and were either too large and consumed too much power, or too small and did

not provide enough force.

Publications on water jet propulsion were only identi�ed towards the end of the work

and whilst showing potential for mid-scale AUVs (larger than 200mm), they are cur-

rently too large, power consuming and su�er from reduced thrust as the depth increases.

The remaining two propulsive options are therefore vortex ring thrusters and pro-

pellers. VRTs produces low thrust but are not bi-directional. They could be used as

maneuvering jets for lateral or vertical movement.

Propellers are the most widely used propulsion method and are a mature technology.

They can provide variable, bi-directional thrust whilst consuming relatively little power.

The main challenges are related to obtaining characteristic data for the small scale

components.

Having identi�ed VRTs and propellers as the most suitable candidates, a more detailed

analysis of of the two options was undertaken and is detailed in the next two sections

of this chapter.

72


Table4.1:

Com

parisonof

PropulsionUnits

Size(m

m)

Thrust

Powerper

Bi-Direc.

Mechanical

Controller

Considerfor

Considerfor

(N)

Unit(W

)Complexity

Complexity

Horizontal

Vertical

Diaphragm

75x35

x35

N/A

1.5

3Medium

High

55

Mechanical

>200

>1

upto

345

High

Low

55

Oscillations

Micro-Pump

50x25

x25

N/A

0.12

3Medium

High

55

Motor/Syringe

90x35

x35

N/A

1.5

3High

High

55

Piezo

10-80

<0.0001

<1

3Low

Medium

55

Oscillations

Propeller

φ20

x30

0.01

-0.1

>0.5

3Medium

Low

33

VRT

φ35

x40

<0.01

>1

5Medium

Low

33

WaterJet

120

>7

>25

5Medium

Low

55

73


4.3 Vortex Ring Thruster Analysis

Having identi�ed VRTs as a potential candidate for movement in both planes, a more

in-depth examination of the method was required. As outlined in Chapter 4.2.7, a

synthetic water jet is formed by vortices which are generated around the ori�ce of the

diaphragm. Figure 4.7 shows the actual formation of these vortices. The model for a

synthetic jet is detailed in [114, 115] and an analysis of it can be found in Appendix C.

Figure 4.7: Vortex Ring Formation From the Side (Left) and From Below (Right)

4.3.1 Prototype

In Chapter 3, it was concluded that for the desired operating envelope, the required

thrust force could be up to 3N (assuming the largest diameter sphere travelling at

the highest velocity). Initial force measurements on small scale propellers, detailed in

Chapter 4.4, indicated a thrust of around 10mN could be provided1. This was therefore

the target force of the VRT prototype so that a fair evaluation of the two systems could

be undertaken.

Since none of the prototypes developed at the University of Colorado are suitable for

this work due to their size (too large) and power consumption (too big), it was decided

to attempt to design a miniaturized version which could produce the desired thrust.

The three main actuation methods used in previous designs were solenoids, voice coil

motors and motor/cams.

A number of solenoids and voice coil motors were identi�ed, however the average power

consumption was around 7W, which is about 3 times the estimate used in Chapter 3.

This would reduce the lifespan of the vehicle signi�cantly. If a motor/cam arrangement

were used at a frequency of 20Hz [117], the motor shaft speed would have to be 20rps

or 1200rpm. Small DC motors with gearboxes are available which have a shaft speed

1The e�ects of a low thrust force are discussed in Section 4.4.3

74


of up to 1400rpm and a power consumption of up to 0.21W, however the design would

be mechanically complex.

Small scale voice coil motors (VCMs) are an alternative low-power option. Miniature

VCMs are used in digital video cameras as a replacement for stepper motor lens focusing

systems. [120] describes how a small scale VCM can be designed with the battery

energy consumption being minimised. A device is manufactured that runs o� 2.97V,

30mA and has a maximum stroke of 5.21mm. The moving component weighs 1.8g and

the rise time is 44ms.

The output force of the VCM was measured for a range of input currents and for a

current of 30mA, the force was 11.76mN. The physical dimensions of length, width

and height were not given. The analysis in Appendix C shows that for a cavity:disk

diameter ratio of 1:1 (requiring the lowest input force), to generate 10mN of thrust the

required input force is 18.9mN, which is greater than the output force of the VCM. An

input force of 11.76mN would correspond to an output force of 6mN.

Another option is to use a piezo-electric linear actuator such as the PI P-653 from

Physik Instrumente (PI) Ltd [121]. The actuator is mounted on a PCB and the entire

package is 11mm x 15mm x 8mm and has a stroke length of 2mm. The input voltage

and current were 5VDC and 100mA and the stroke period was around 100ms. The

maximum output force was 150mN.

A prototype was designed and tested, with the dimensions for the cavity calculated

using the model in Appendix C. Figure 4.8 shows the prototype which was constructed,

along with a CAD image. Unfortunately it was found that the actuator did not provide

enough force to break the surface tension of the water around the ori�ce.

Figure 4.8: VRT Prototype (Left) and Corresponding CAD Image (Right)

75


4.3.2 Summary

VRTs o�er an attractive alternative method of low speed propulsion, however not for

this work. The technology is relatively new and research is still ongoing. The reasons

why VRTs are not suitable at the moment are the size and power consumption of the

actuators. Current linear actuator technology is either too big or draws too much

power to be feasible in small scale vehicles. The development of a small, low power

linear actuator would be an interesting topic of research for the future.

4.4 Propeller Analysis

Having discounted VRTs as a means of propulsion in the previous section, propellers

are the only option left to be analysed. Propellers are used in all sizes of marine vehicles

ranging from ocean liners to AUVs. Small-scale propellers can be found on bath toys

such as remote control submarines.

A number of prototypes were constructed which used propeller-based thruster units

obtained from remote control submarines. These prototypes, shown in Figure 4.9,

were used to investigated the feasibility of small scale thruster units for use in both the

horizontal and vertical planes.

Figure 4.9: Propeller Propulsion Prototypes for Horizontal Motion (Left) and VerticalMotion (Right)

4.4.1 Horizontal Prototype

The purpose of the initial horizontal thruster prototype was to investigated whether

the small scale thrusters from the submarine provided enough thrust to move a larger

hull and also to observe the e�ects of mounting the thrusters around the equator of

the sphere.

76


The submarine was placed inside the spherical hull (a mortar shell) and the motors

were removed and attached the outside. By reconnecting the motors to the submarine

prototype could be controlled using the remote control handset. The mortar shell was

slightly positively buoyant.

The prototype had good maneuverability but the propellers did not give equal thrust.

This was due to the motor/propeller units being mass produced and being made to

low tolerances. The issue of component homogeneity was not limited to the thrusters

from the submarine and is discussed further in Section 5.4.3.

4.4.2 Vertical Prototypes

The vertical thrust prototype served two main purposes; to investigate the use of small

propeller thrusters in the vertical plane and to gain experience developing a simple

embedded system running a closed-loop controller.

The vertical prototype consisted of one of the submarine propellers mounted vertically

on top of the spherical hull to provide bi-directional thrust. The submarine was located

inside the sphere so that the prototype could be controlled remotely. Initial tests in

a 1m deep tank using the remote control handset as a manual controller, showed that

the system could hover at a given depth once all momentum had been removed from

the system.

A more advanced prototype which replaced the remote control submarine with a custom

embedded system was subsequently developed. This prototype, shown in Figure 4.10,

had two contra-rotating propellers to remove unwanted rotations around the z-axis.

Using the equations of motion detailed in Chapter 4.1, a basic control system was

developed to move the prototype to a given depth and hold station. The model assumed

a spherical vehicle of diameter 100mm, a water temperature of 5◦ C, a drag coe�cient

of 0.47 [122] and a propeller thrust force of 10mN. The system was neutrally buoyant

throughout the simulation.

As with the micro-pump and motor/syringe systems (Appendix C), the control strategy

employed was a PDγ controller. Figure 4.10 shows the actual response of the prototype.

Depth was measured using a pressure sensor. It can be seen that the vehicle was able

to move to a given depth and hold station for an extended period of time.

77


Figure 4.10: Left: Prototype of a Propeller Based VDS. Right: vehicle Depth againstTime Whilst Tracking a Set-Point

4.4.3 Prototype Investigation Conclusions

The prototypes constructed and tested in the previous two sections showed that small-

scale propeller-based thruster units were a viable option to provide movement in both

the horizontal and vertical planes. Since none of the other methods investigated in

this chapter were deemed to be suitable, propellers were selected as the method of

propulsion.

A number of issues were identi�ed during the prototype testing including imbalanced

thrust and unwanted rotational torques. These issues are considered in greater detail

in Chapter 5.

The estimated thrust output of a number of propeller units tested ranged between

10mN and 100mN. This would have the e�ect of reducing the maximum operating

velocity to between 0.12ms−1 0.18ms−1 and reducing the working envelope (white area)

as shown in Figure 4.11.

The e�ect on the energy consumption is shown in Figure 4.12. It can be seen that

the required energy for a 30 minute mission decreases to a maximum of approximately

29kJ. The new working envelope means that the number of lengths able to be travelled

(assuming maximum velocity) decreases from 36 to 11. This further highlights the

need for a swarm of vehicles to be used to map the ponds.

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Figure 4.11: Working Envelope for Drag Force (White Area) Caused by PropellerBased Thrusters

Figure 4.12: Working Envelope for Energy Consumption (White Area) Caused byPropeller Based Thrusters

79


4.5 Motor and Propeller Component Selection Method

The thruster units on the prototypes used components for which no data was available

concerning the component parameters such as motor shaft speed and torque or propeller

pitch. Using thruster units scavenged from other vehicles was not a viable option so a

method of selecting suitable DC motors and propellers was required.

Small-scale DC motors are widely used in industry, for example in the robotics and

automation sector and therefore manufacturers readily provide characteristic data. Ex-

ample performance data from a typical of a DC motor, is shown in Figure 4.13.

Propellers can be characterized by using a series of non-dimensional coe�cients [123];

the advance ratio, the thrust coe�cient, the torque coe�cient and the power coe�cient.

These can be combined with the motor parameters to �nd the thrust, e�ciency and

speed of a given motor/propeller combination. A standard plot of the coe�cients is

shown in Figure 4.13.

Figure 4.13: Motor Performance Data [17] (Left), Traditional Propeller Curves [18](Right)

The traditional method of matching motors and propellers and calculating the output

thrust uses both the propeller coe�cient curves and the motor characteristic data. The

step-by-step process for selection can be found in Appendix C.4.

The propeller coe�cient curves are usually generated by the manufacturer, however for

small scale propellers, the curves are often not provided. This is because the end-users

are either hobbyists or toy manufacturers who do not need it. Generating the data

in-house is di�cult, time consuming and requires specialist equipment. There has been

some work investigating small scale propellers [124, 125], however these references only

investigate a small range of diameters. This means that the traditional method of

component selection cannot be used.

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4.5.1 Alternative Analysis

The data usually available for small scale components is as follows: for propellers; the

pitch and the diameter. For motors; the shaft speed, output torque, e�ciency and

current consumption. Using only these parameters, a method for identifying whether

a particular combination was feasible was developed. Due to the level of uncertainty in

some of the unmeasured parameters, the method was not used as an accurate model,

instead, it was used as a guide for component selection.

As indicated above, the two pieces of data which can be obtained for nearly all pro-

pellers are diameter and pitch. The pitch of a propeller, Z, (measured in meters) is the

distance that it would travel axially if it were rotated 360◦ in a solid. If the propeller

was rotated at Nrps (N revolutions per second), it would move axially at a rate of

NZms−1. This velocity is called the advance velocity [18].

Water is not a solid there will be a di�erence in the axial displacement and the propeller

pitch. The propeller will move a shorter distance than expected in a solid. The

di�erence, expressed in terms of a percentage, is called slip [126], which is established

empirically. By including the slip, the advance velocity can be written as shown in

Equation 4.7.

Va = NZ(1− S) (4.7)

Slip is estimated through experimentation by measuring the actual speed of a vehicle

and comparing it with the theoretical speed, based on the pitch of the propeller and

the shaft speed of the motor. Unfortunately, the method does not take into account the

shape of the hull (and therefore the drag), nor the e�ciency of the thruster unit. The

literature suggests that the slower the vehicle, the greater the slip, however the slow

vehicles tend to have higher drag pro�les [126]. This is one of the sources of inaccuracy

in this method so values across the full range were used.

Another factor which can a�ect the advance is the wake [126]. The water �ow around

an object generates turbulence behind it in the form of a wake. If the propeller is

situated behind the vessel, as in most boats and submarines, the wake can reduce the

advance velocity. For the purpose of this analysis, it was assumed that the propellers

were mounted around the equator of the sphere (see Section 5.3) and therefore not

in�uenced by the wake.

For a given range of propeller pitches and shaft speeds, based on available components,

the advance velocity can be found. Figure 4.14 shows the advance velocity for a range

of slip values.

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It is assumed that the advance velocity of the propeller is the same as the velocity of

the vehicle. In Section 4.4.3, the working envelope for the vehicle was reduced due to

the potential thrust output of propeller thruster units. This reduced the maximum

operating velocity to around 0.15ms−1. Figure 4.14 shows that, as long as the slip is

not prohibitively large, this operating velocity could be achieved.

Ideally the operating range of shaft speeds should be as large as possible for control-

lability as there are problems with inertial forces and non-linearities when the shaft

speed is very low. Using the graphs shown in Figure 4.14, a suitable propeller pitch

can be chosen.

Having chosen a propeller pitch and identi�ed a range of shaft speeds, the next stage

is to investigate what shaft torque is required from the motor. The required thrust

force can be calculated using the parametric model described in Chapter 3. The output

thrust is related to the shaft torque by the propeller e�ciency (translational e�ciency),

as shown in Equation 4.8 [18]. This can be re-arranged to calculate the required shaft

torque.

ε =TVa

2πNQ(4.8)

As with the slip, the propeller e�ciency can be found experimentally or estimated from

the literature. The motor torque at a speci�c shaft velocity can be found using a data

sheet (or measured experimentally), while the thrust force can be measured. For a

given propeller, the advance velocity can be estimated, using Equation 4.7 and hence

the e�ciency can be calculated using Equation 4.8.

The problem with estimating the propeller e�ciency in this manner is that it relies on

slip, which has already been identi�ed as being inaccurate. The e�ciency of a thruster

can vary between individual units due to a lack of component homogeneity (see Section

5.4.3). For this analysis, the e�ciency was estimated from the literature as 40%.

4.5.2 Example

Assume that the propeller selected has a diameter of 20mm, the target vehicle speed

is 0.1ms−1 and that the slip is 70%. A pessimistic value for slip is used to investigate

a poor quality system. Using Equation 4.7, the required shaft speed can be calculated

as 1200rpm.

82


Figure 4.14: Advance Velocity, Va for Varying Shaft Speeds, N , Propeller Pitches, Zand Slip Values, S

83


The diameter of the vehicle is assumed to be 150mm (Section 5.2) and using the

parametric model from Chapter 3, the required thrust force can be calculated as 40mN.

If the e�ciency is 40% (chosen to be low for the same reason a high slip value is used),

Equation 4.8 can be used to calculate the required shaft torque. In this example the

value is 0.16mNm.

This means that the target motor should have a shaft speed range of up to 1200rpm with

an output torque of up to 0.16mNm. These parameters correspond well to available

motors and suggest that o�-the-shelf small scale components will be suitable for use on

the vehicle however, con�rmatory measurements are required. The selection of suitable

motors and propellers for the vehicle is covered in detail in Section 5.4.

4.6 Force Measurement Rig

The ability to measure the output force of the thruster units is important, especially

with respect to the control systems. To this end, a force measurement rig was con-

structed for in-house testing and is shown in Figure 4.15.

The propulsion unit is attached to an Omega LCL-227G full bridge thin beam load cell

[127]. The output voltage from the load cell is proportional to the de�ection of the beam

which, in turn, is proportional to the weight of the load. Using these relationships, the

thrust force of the unit can be found. The load cell was connected to a data-logging

multimeter so that large numbers of readings could be taken quickly and e�ciently.

The nominal output error of the load cell was ±20%, however this could be reduced

by calibrating the system.

Figure 4.15: Force Measurement Rig

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The force measurement rig was used during the course of the research to evaluate a

variety of motor/propeller combinations (Section 5.4.4) and to investigate the force

output di�erences between thruster units (Section 5.4.3).

4.7 Propulsion System Summary

This chapter has identi�ed, analysed and compared eight di�erent propulsion systems

that could be used to provide movement in both the horizontal and vertical planes. It

has been concluded that propeller-based thruster units using small electrical motors

are the most suitable option for both planes.

Propeller-based thruster units consume relatively little power, provide the desired

thrust, are bi-directional and have relatively low complexity both mechanically and

with regard to the control systems. Prototypes propulsion systems for both the ver-

tical and horizontal planes have been successfully tested. A method to aid in the

selection of motors and propellers has been developed due to the lack of data required

to perform the traditional selection procedure.

4.8 Notation

Table 4.2: Notation for Chapter 4Fb Buoyancy Force Re Reynolds NumberFg Gravitational Force Va Advance VelocityFT Thrust Force T ThrustFd Drag Force Z Pitch of PropellerFz Resultant Force in Z S SlipFx Resultant Force in X ε Propeller E�ciencyρ Density of Water Q Motor Torqueg Gravitational Constant t TimeV Volume of Sphere J Advance Ratiom Mass of Sphere KT Thrust Coe�cientmT Total Mass of Sphere KQ Torque Coe�cientmi Imbalanced Mass KP Power Coe�cientA Normal Area of Sphere N Rotational Speed of MotorCd Drag Coe�cient D Diameter of Propeller

85

Chapter 5

Prototype Vehicle Design

In Chapters 3 and 4, it was concluded that the µAUV should be spherical in shape and

that the propulsion system, for movement in both the horizontal and vertical planes,

would use propeller-based thrusters.

One of the main focuses of the project was practical implementation in terms of both the

mechanical design and the corresponding control systems. To achieve this, a prototype

vehicle had to be constructed. Over the course of the project, six distinct prototype

vehicles were designed and tested, each a re�nement on the previous version. The Mk

V and Mk VI vehicles were the only prototypes to have the full 4 degrees of freedom

(DOF) movement capabilities outlined in Chapter 2 and will be the main focus of this

chapter. The MK V was the �rst fully operational vehicle whilst the MK VI was a

re�nement of the MK V design.

The vision for the prototype µAUV to be used in the demonstrator system, was a

vehicle which had movement capabilities in 4 DOF and was controlled by software

running on embedded system hardware (ESH). The ESH was required to perform a

number of tasks; interface with the input sensors, execute the control algorithms and

log input and output data. A modular approach was taken to the design, as detailed

in Section 5.7. This allowed additional circuitry to be added, such as a digital signal

processor for interfacing with the acoustic positioning system (APS).

The sensor suite envisaged include a pressure sensor for depth measurements, a digi-

tal compass and rate gyroscope for angular position and velocity measurements, and

acoustic transducers for communications, horizontal positioning (the APS) and obsta-

cle detection. The development of the acoustic transducer systems was conducted by

other members of the AASN4IP project.

86


Although not within the remit of this thesis, considerations were also given to docking

and recharging. Initial thoughts were that the docks would be attached to the edges

of the pond at the surface and the vehicle would rise up into them. The vehicle would

then be recharged by either direct contact or inductive charging.

Figure 5.1 shows how the overall design was split into speci�c technical areas. The rest

of this chapter will focus on detailing the work conducted in each of these areas.

Figure 5.1: Breakdown of µAUV Technical Areas

5.1 Prototype Progression

As stated previously, there were a total of six prototype vehicles developed during

the project. Table 5.1 shows the capabilities and purpose of each version. Whilst

this chapter concentrates on the designs of the MK V and MK VI prototypes, it is

important to give a brief summary of the �rst four which are shown in Figure 5.2.

Details of the MK I, MK II and MK III vehicles are given in Chapter 4, however this

section will provide an additional summary.

The �rst prototype (MK I), shown in the top left of Figure 5.2, was developed as part

of the propulsion systems analysis in Section 4.4.1. It was constructed to investigate

the use of small propeller-based thrusters for horizontal movement, on a vehicle whose

size was similar to that identi�ed in Chapter 3. The hull was a 100mm diameter sphere

with two horizontal propeller-based thrusters, taken from a remote control submarine,

attached diametrically opposite each other on the equator. The submarine itself was

inside the sphere so that the vehicle could be controlled remotely and so that no

additional electronics were required.

87


Figure 5.2: Top Left: MK I Prototype, Top Right: MK II Prototype, Bottom Left:MK III Prototype, Bottom Right: MK IV Prototype

Table 5.1: Overview of Prototype Vehicles

Prototype PurposeMovement

ESH SensingPlanes

MK IInvestigate suitability of

HorizontalO�-the-shelf

Nonesmall-scale propeller- remote controlbased thruster units submarine

MK IIInvestigate suitability of

VerticalO�-the-shelf

Nonesmall-scale propeller- remote controlbased thruster units submarine

MK IIIInvestigate basic control

Vertical Custom Boards Pressuresystems for verticalmotion

MK IVInvestigate e�ects of

Horizontal Custom Boards Pressurelow-tolerancecomponents

MK VFirst full mechatronic Horizontal,

Custom BoardsPressure,

prototype Vertical Compass,Gyroscope

MK VIFull vehicle prototype, Horizontal,

Custom BoardsPressure

able to integrate Vertical Compass,APS Gyroscope

88


The MK II prototype, shown in the top right of the Figure 5.2, was similar to the MK

I, however it was designed to investigate vertical movement (Section 4.4.2). The hull

was 125mm in diameter and had a single propeller mounted on the top. As with the

MK I, a remote control submarine was placed inside the sphere to allow for manual

control.

The MK III prototype, shown in the bottom left of Figure 5.2 was the �rst of the

automated vehicles developed on the project. The purpose of the vehicle was to gain

experience in developing ESH and translating control algorithms developed in MAT-

LAB into `C'. The remote control submarine was replaced with custom ESH which

allowed basic control algorithms to be used to control the depth of the vehicle. Two

contra-rotating vertical propellers were mounted on the top to reduce unwanted ro-

tational torques. Figure 4.10 in Section 4.4.2 shows experimental results from tests

conducted with the MK III prototype.

The MK IV prototype was meant to be the �rst full capability vehicle, however prob-

lems with the hull design (leaks in the main seal and the power switch) prevented this.

The hull was 150mm in diameter and two horizontal thrusters were mounted on the

equator. Custom electronics allowed independent, automated control of the thrusters

which were based on electric DC motor/propeller combinations chosen through the

process described in Section 5.4 (instead of using thrusters from o�-the-shelf vehi-

cles). This prototype was used primarily to highlight technical issues with regard to

low-tolerance components which will be discussed in more detail in Section 5.4.3.

The MK V prototype was the �rst prototype vehicle capable of movement in both

the horizontal and vertical planes. Its design subsumed the developments made on

previous vehicles. It was used as a test bed for control system development for over

a year and was tested both at the University and also at o�-site facilities provided by

the National Nuclear Laboratory. Over its lifetime, several modi�cations were made

to improve functionality. The MK VI prototype was a re�nement of the MK V which

incorporated these modi�cations. The rest of this chapter details the design of the MK

V and subsequently the MK VI prototypes.

5.2 Hull Design

As outlined in section 3.4, the target diameter for the spherical hull was between

130mm and 200mm. Access was required to the internal components of the vehicle so

a sealable entry point was necessary. The MK V and VI prototypes both had hulls

with a diameter of 150mm due to the availability of suitable materials; speci�cally,

89


acrylic hemispheres. This meant that the non-permanent seal was situated around the

equator of the vehicle.

For the MK V prototype, three di�erent methods of non-permanent sealing were tested:

a friction lock, a �ange and a screw-thread. Table 5.2 shows a comparison. It was found

that the friction lock method did not work well under pressure and that the �ange

increased the horizontal clearance of the vehicle by around 25% which was deemed un-

acceptable. The screw-thread was the most complex to fabricate, however it performed

well under pressure and did not a�ect the horizontal clearance as it was mounted on

the inside of the hull. This reduced the internal volume; however this was viewed as

an acceptable trade-o�.

Table 5.2: Comparison of Hemisphere Sealing Methods

Seal TypeFabrication Performance External InternalComplexity Under Pressure Protrusion Protrusion

Friction Lock Low Poor 0% 0%Flange Medium Good 25% 0%

Screw-Thread High Good 0% 15%

The hull constructed for the MK V prototype is shown in Figure 5.3. It consists

of two clear acrylic hemispheres which are connected via a screw-thread and o-ring

arrangement. All of the electronics are mounted in the bottom half of the vehicle,

leaving the top half free to be removed. The clear acrylic was chosen so that de-

bugging status lights could be visible without having to mount them on the outside of

the hull as with the MK IV prototype.

Figure 5.3: The MK V Hull

90


Whilst the screw-thread arrangement worked, it was not aesthetically pleasing, nor was

it reliable. Several hulls were made and all of them leaked, though the severity of the

leak varied. For the MK VI hull, a new type of seal was made. The two hemispheres

were compressed together by an external clamp by means of a screw thread as shown

in Figure 5.4. The thruster units were mounted on to this clamp section and the whole

arrangement tightened to 25Nm.

The o-ring was set into a groove which was also �lled with silicone grease. The entire

structure was constructed from aluminium which made the screw-thread more robust,

the construction easier and improved the aesthetics.

Figure 5.4: The MK VI Hull. Top Left: Compression Joint in Support Stand, TopRight: External Compression Ring and Thruster Mount, Bottom Left: Tightening Jig,Bottom Right: Fully Sealed Hull

5.3 Propeller Con�guration

Chapter 4 identi�ed the type of propulsion system to be used, however the actual con-

�guration of the thruster units had to be considered. The maneuverability requirements

of the vehicle, discussed in Chapter 2, are summarised below:

91


• The vehicle should have four DOF; surge, sway, heave and yaw (Figure 5.5)

• The vehicle should have a turning radius of zero mm

• Movement in the horizontal and vertical planes should be decoupled

Figure 5.5: Four Degrees of Freedom

5.3.1 Vertical Thrusters

The work undertaken in Section 4.4.2 showed that to reduce the rotational torque

imparted to the node in the form of yaw by the propeller, two thruster units were

required which rotated in opposite directions. This was for when the propellers were

mounted on the top of the node.

A design decision was made to mount the vertical thrusters around the equator instead

of on the top. This was for two reasons; �rstly to improve the robustness and secondly,

to keep the top free for recharging circuitry.

By placing the thrusters on the equator, the node will still be subject to the yaw

rotational torques, albeit at reduced levels. Unfortunately, placing them on the equator

introduces unwanted torques in roll and pitch, however these can be reduced by the

use of two thruster units diametrically opposite each other.

Since roll and pitch are not required, the unwanted rotational torques were eliminated

by carefully ballasting the vehicle. By lowering the vehicle's centre of gravity below

the geometric centre, the required thrust force to rotate it in roll and pitch increases.

Simple calculations based on the location and quantity of ballast used suggested that a

thrust force of 11N would be required to rotate in roll and pitch. The maximum force

available was approximately 100mN meaning that movement in roll and pitch was not

possible.

The orientation of the thrusters was chosen with the propellers below the line of the

equator, facing down. This was so that they did not interfere with the acoustic trans-

ducers which were to be mounted on the top hemisphere of the vehicle (Section 5.5.1).

92


5.3.2 Horizontal Thrusters

In this section, options for the con�guration of the horizontal thrusters will be re-

viewed. According to the requirements, the horizontal thrusters need to provide at

least three degrees of freedom independently of the vertical movement. There are

several con�gurations possible with increasing numbers of thrusters. There are two

con�icting requirements in the horizontal plane; keep the number of thrusters low so

that the power consumption and space requirements are reduced whilst keeping the

maneuverability as high as possible. Figure 5.6 shows the four con�gurations which

were considered.

Figure 5.6: Possible Thruster Con�gurations

The �rst con�guration (Figure 5.6a) utilizes two thrusters placed diametrically opposite

each other around the equator. The thrusters provide bi-direction movement in the x

(or y) direction as well as a rotation around the z-axis.

The second con�guration (Figure 5.6b) has three thruster units placed around the

equator of the node at 120◦ intervals. This allows movement in any direction on the

horizontal plane by vector control of the motors (i.e. determining the vector compo-

nents of thrust required to enable the node to move in a straight line). It also provides

rotation around the z-axis.

The third con�guration (Figure 5.6c) uses four thrusters with two diametrically oppo-

site pairs orthogonally placed around the equator. This allows bi-directional movement

in both the x and y directions as well as rotation around the z-axis. There is a degree

of redundancy since both pairs can provide yaw movement.

The �nal con�guration (Figure 5.6d) also utilizes four thrusters. In this case a pair of

thrusters provides movement in the x (or y) direction and a rotation, while the other

pair are mounted such that they provide movement only in one direction. To achieve

this movement one propeller rotates forward while the other rotates backwards.

Table 5.3 shows a comparison of the four con�gurations in terms of power, component

requirements, maneuverability, control complexity and robustness. The choice of con-

93


�guration will be a trade-o� between these parameters. The `best' option will be the

one which balances robustness with simple control and low power consumption.

The power consumption is based on the motors selected in Section 5.4 and driver

circuitry designed in Section 5.7 and is 0.21W/motor and 150nW/driver. The force

output of the thruster unit is related to the angular speed of the motor which is

controlled by the input voltage. The voltage level is control by using pulse-width

modulation and varying the duty-cycle. This signal can easily be generated by a

microcontroller, however an additional driving circuit is required to provide the required

current.

The power consumption used in this analysis assumes the worst case scenario when

the voltage is set to maximum. This will not always be the case, although that will be

dependent on the type of control system which is used.

Robustness has been de�ned for this analysis as a measure of the number of thrusters

that have to fail before the number of degrees of freedom drops to 1. It is calculated

as a ratio of the total number of thrusters available to the number of failed thrusters.

A larger number implies a less robust con�guration.

Table 5.3: Horizontal Thruster Con�guration ComparisonCon�g. No. Components Power DOF Control Robustness

1 2 1 dual driver up to 0.42W 2 Simple 0.52 3 2 dual drivers up to 0.63W 3 Complex 0.333 4 2 dual drivers up to 0.84W 3 Simple 0.254 4 2 dual drivers up to 0.84W 3 Simple 0.5

By analysing the data in Table 2.7, it can be seen that Con�guration 1 is the best in

terms of power consumption and number of components. The control system is simple,

however it only has 2 degrees of freedom and is not very robust.

Con�guration 2 is more robust than Con�guration 1, however its controller is more

complex as the vector components for each motor would have to be calculated. The

controller complexity makes this con�guration unattractive when compared to conven-

tional thruster arrangements.

Con�guration 3 is the most robust, with 3 out of the 4 thrusters having to fail before

the number of DOF drops to 1. The controller is also simple, however there is a

redundant degree of freedom (yaw can be achieved using either the x- or y- thruster

pair). The �nal con�guration also has a simple control system, however it is less robust

than con�guration 3 as only 2 of the 4 propellers have to fail before maneuverability

is compromised.

94


Although power and space are limited in the vehicle, robustness and maneuverability

should take precedence. In this case, con�guration 3 can be viewed as the best option.

It is the most robust of the systems, has the largest number of DOF and also has a

simple control system. It has the potential to draw the most power due to the number

of motors, however the power usage is dependent on the control algorithms and not all

of the motors have to be operated at the same time.

Choosing con�guration 3 means the the propulsion system for the node will consist

of 6 propeller-based thruster units; 2 mounted vertically with the propellers facing

downwards and four mounted in pairs, orthogonal to each other. All the thrusters

would be mounted around the equator. This would require a total of 6 full-bridge

motor driver circuits (to allow for bi-directional movement).

Figure 5.7 shows a 3D CAD image of the prototype with the selected thruster con�g-

uration.

Figure 5.7: 3D CAD Drawing of the Prototype Vehicle

5.4 Thruster Component Selection

The next stage of the development of the prototype vehicle was to select appropriate

motors and propellers. Based on the requirements identi�ed in Chapter 2, the complete

thruster unit needs to:

• Provide su�cient force

• Be low powered

95


• Be physically small

5.4.1 System Operation

The �rst stage of the selection process was to identify the primary mode of operation for

the vehicle. For the demonstrator application, this would be low speed maneuvering (>

0.1ms−1) to enable safe navigation around the unstructured and cluttered environment.

The controllable variable in a DC motor/propeller thruster is the motor shaft speed.

This is usually controlled by changing the voltage of the motor. At low input voltages,

the shaft speed is low, and the inertia of the shaft can stall the thruster unit. The

thrust output at low speeds is also non-linear and the exact output force cannot be

guaranteed.

As detailed in Section 4.5.1, the slip reduces the e�ciency of the thruster unit by

reducing the axial displacement per revolution. The slip increases as the vehicle velocity

(and hence shaft speed, for a �xed propeller pitch) decreases [126], suggesting that the

motors should be operated at high shaft speeds.

At high speeds however, the advance velocity can become very high depending on the

pitch of the propeller. This leads to the conclusion that the overall thruster unit should

have high shaft speed and low propeller pitch to improve controllability.

5.4.2 MK V Thruster Selection

The approach taken to the selection of the MK V thruster components was to �nd

the physically smallest motors and propellers which could provide the required output

force. For a 150mm diameter sphere travelling at a maximum velocity of 0.1ms−1, the

required force (using the parametric model in Chapter 3) is 40mN.

The model used to calculate the thrust values can be viewed as inaccurate due to

the fact that it models the hull as a perfect sphere. Since the thrusters are mounted

externally on the equator, the drag force will increase. The scale of this increase is

di�cult to estimate so an additional 30% was added to the drag force, equivalent to a

hull diameter increase of approximately 20mm. The new required thrust force therefore

increases to 52mN. The con�guration of the thrusters is such that force is produced

via a pair of diametrically opposite units, so the force requirement from an individual

thruster unit is 26mN.

The required thrust force for the vertical thrusters will be higher than that of the

horizontal thrusters. The vehicle was made positively buoyant so that it �oated to the

96


surface and could be recovered easily. This meant that there was an additional force

that the vertical thrusters had to overcome. As will be discussed in Section 7.5.2, the

magnitude of the buoyancy force was di�cult to set, however it ranged between 10mN

and 30mN. The vertical thrusters therefore need to produce either 5mN to 15mN extra

force each or the vehicle would move slower in the vertical plane.

The propeller selected for use was the Graupner 25mm M2 Threaded, 3 Blade Plastic

Propeller (Right and Left Hand versions1). The propeller had a diameter of 25mm, a

pitch of 13mm and had the smallest diameter/largest pitch available in both left and

right handed forms.

Using the guide outlined in Section 4.5.1, the relationship between shaft speed and

advance velocity for varying values of slip can be found and is shown in Figure 5.8. It

can be seen that to travel at a velocity of up to 0.1ms−1, the motor shaft speed should

be in the approximate range 0 - 2300rpm. This assumes that the slip is less than 80%.

Figure 5.8: Advance Velocity, Va vs. Shaft Speed, N for Varying Slip Values

Figure 5.9 shows the torque requirements for a range of e�ciencies and slip values. It

can be seen that the largest torque required would be approximately 0.54mNm (10%

e�ciency and 0% slip, which is unrealistic), however if the e�ciency is greater than

30%, the torque, regardless of the slip value, is less than 0.2mNm.

1Left and Right Handed Propellers are rotated in opposite directions to provide force in the samedirection. This reduces any rotational torques which may be produced.

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The simulations indicate that for a propeller with a pitch of 13mm, to travel at a

velocity of up to 0.1ms−1, the electric motor has to have a shaft speed of up to 2300rpm

and a torque output of around 0.2mNm. This assumes a worst-case scenario with high

slip and low e�ciency.

There was only a limited selection of o�-the-shelf motors available and the most suitable

was a coreless Inline Gearmotor from Precision Microdrives. The motor was 6mm in

diameter and 16mm long and had a gearbox ratio of 25:1, giving a shaft speed range of

0 - 1400rpm. The torque at peak e�ciency was approximately 0.6mNm. The maximum

shaft speed slightly less than desired, however the torque output is greater. Overall,

the motor meets the requirements and the complete thruster unit is shown in Figure

5.10.

Figure 5.9: Required Torque, Q, for Varying E�ciencies, ε and Slips, S

The motor of the thruster unit was encased in a perspex housing which was glued

to the side of the hull. The shaft bearing the propeller protruded from this housing

as shown in Figure 5.10 and was a point of failure. It was found that even gentle

knocks caused the shaft to irreparably snap o�. This was a major issue with regards to

robustness when navigating con�ned and cluttered environments. The solution was to

add a protective cage, similar to a propeller shroud, which was attached to the motor

housing.

Figure 5.11 shows the output force for six thruster units, measured using the force rig

98


Figure 5.10: Fully Constructed MK V Thruster Unit

detailed in Section 4.6. The graph shows three units using a right hand propeller and

three using a left hand propeller. Force readings were taken for force generation in

both directions (forwards and backwards2).

Of the six thruster units, only three of them provide the desired thrust (26mN) in

the forward direction and only one of them in the reverse. Five of the six provide

greater than 24mN in the forward however (within 10% of the target thrust), which

was viewed as an acceptable output. The di�erence in the directional thrust output is

caused by the shape of the propeller. Propellers are designed to provide thrust in one

direction, but can be operated in reverse, with some loss of thrust output. The e�ect

of this would be that the vehicle would move backwards more slowly than forwards.

This is not a major problem because if speed is required, the vehicle can rotate and use

the thrusters in the forward direction. There are several other interesting observations

which can be made with regards to the thrust outputs which are discussed in the next

section.

5.4.3 Lack of Component Homogeneity

Figure 5.11 shows that there is a signi�cant lack of homogeneity between the thruster

units, which could have a detrimental e�ect on performance and controllability of the

vehicle. It can be seen that the output force between units varies signi�cantly. In the

forward direction (positive force), this variation is up to 174%, reletive to the smallest

output, and in the backward direction (negative force), the variation is as large as

272%. The force also appears to vary between the two types of propeller (right and

left hand).

2To move forwards using a right hand propeller, it needs to be rotated anti-clockwise. To moveforwards using a left hand propeller requires it to be rotated clockwise.

99


Figure 5.11: Output Thrust Comparison for Six Thruster Units

The con�guration of the thrusters (Section 5.3) is such that forward movement is

achieved by turning on a pair of diametrically opposite thruster units. Individually,

the thruster units each provides both forward movement and a rotational torque around

the vertical axis (yaw). In the ideal situation, the two thrusters would provide opposite

and equal rotational torques which cancel each other out and only provide forward

movement as shown in Figure 5.12.

Figure 5.12: Movement of the Vehicle with Balanced Thrust Forces

If the forces from the two thrusters are di�erent, there will be an imbalanced rotational

torque. This will have the e�ect of causing the vehicle to move in a curved trajectory

as shown in Figure 5.13. The e�ects of the imbalanced thrust force are exacerbated

by the shape of the hull. The rotational drag of a sphere is very low compared to

other potential hull shapes, due to its axial symmetry, however the requirements of the

100


application demanded high maneuverability.

Figure 5.13: Movement of the Vehicle with Imbalanced Balanced Thrust Forces

The imbalanced thrust force issue could be addressed in one of two ways: better compo-

nents or within the control system. Higher tolerance components would suggest higher

costs which is undesirable. Calculations show that a rotation of 0.01832◦s−1 (maximum

resolution of the rate gyroscope which will be discussed in Section 5.5.4) would require

an imbalanced thrust of only 118nN. Obtaining components of this tolerance would be

impractical as well as expensive. The solution is therefore to ensure that the control

system is robust enough to compensate for unwanted rotations.

The thrust forces shown in Figure 5.11 were calculated by averaging force readings

taken over tens of minutes. A closer examination of the thrust output during this

period shows that the force varies over time, as shown in Figure 5.14. The cause of

this variation was not identi�ed, however there was evidence of overheating (scorch

marks) found on several of the motors, suggesting that temperature variations may be

to blame. Thruster overheating cannot be fully removed, however it can be mitigated

by constructing any motor housings using heat conducting material.

The conclusion of the analysis of the thruster units is that they produce time-varying,

imbalanced force which must be accommodated in the control system.

The e�ects this are highlighted in Figure 5.15 which show results from an experiment

conducted using the prototype vehicle. The µAUV was placed in the water and the

surge motors were set to full power in the forward direction. The graph shows a plot

of angular rotation against time. If the thrusters produced balanced force, the angular

rotation would be zero. If the force was imbalanced but constant for all time, the

rotation would also be constant. It can be seen that the rotation is not zero (indicating

imbalanced force) and is variable (indicating time-varying force). The time variation

is large enough that the direction of rotation changes twice at approximately 130s and

150s.

101


Figure 5.14: Thrust Output for Extended Force Measurement Test

Figure 5.15: Angular Position of Prototype During Imbalanced Thrust Experiment

102


5.4.4 MK VI Thruster Selection

The lack of thruster homogeneity a�ected the movement of the MK V prototype in

the horizontal and vertical planes in di�erent ways. In the horizontal plane, the e�ect

was to cause the vehicle to move in a curved trajectory as described in the previous

section. In the vertical plane, this did not occur as the vehicle was ballasted in such a

way as to negate movement in roll and pitch.

The problem in the vertical plane was caused by buoyancy and the fact that the

thrusters provided just enough thrust to move the vehicle. As detailed in Section 5.4.2,

the required thrust force from an individual unit was 26mN. This value was higher for

the vertical thrusters as the µAUV was made positively buoyant so that if the power

failed, it �oated to the surface.

As will be detailed in Section 6, the vehicle is open-loop unstable in the vertical axis

due to the buoyancy. If the thrust is less than the buoyancy force, the vehicle will not

be able move downwards (assuming positive buoyancy). The di�culty arose in setting

the buoyancy of the node due to the �ne margin for error and the fact that the density

of water can change between tests due to temperature and impurities.

Whilst this problem was solved through careful, but time consuming ballasting of the

MK V prototype, it was decided for the MK VI prototype to try and increase the force

output of the thrusters. Larger motors were considered but there were no suitable

candidates which rotated at the desired shaft speed (Figure 5.8 in Section 5.4.2). A

new 6mm motor, the TGPP06 from TT Motors, with the same speci�cations as the

MK V motors, was identi�ed and used as it was 5 times cheaper and helped ful�l the

aim of keeping the cost of the vehicle low.

Another method for increasing the thruster force output is to increase the size of the

propeller. This strategy was investigated by comparing the thrust output (measured

using the force rig in Section 4.6) for a number of di�erent sized propellers, whilst using

the same motor.

Figure 5.16 shows a comparison of output force and input current for a range of pro-

peller diameters using the TGPP06-B motors. Initially, the peak e�ciency current

of the motors was thought to be 70mA. The graph shows that the current draw of

the motors when using the 35mm propeller is 70mA, suggesting that the motor was

running at peak e�ciency.

When using the 25mm propeller (the propellers used on the MK V prototype), it can

be seen that the current draw is only around 55mA, suggesting that the motor was

not running at maximum e�ciency. The increase of 15mA (27%) in current (0.045W

103


power increase) corresponds to an increase in force of 32mN (100%).

There is a trade-o� between the physical size of the thruster unit, the power consump-

tion and the output force. It was decided that the doubling of the thrust force for only

a 27% increase in current consuption and a 10mm increase in propeller diameter was

justi�ed within the scope of this work. During prototyping, a decreased lifespan was

acceptable.

During the writing of this thesis, it was established that the peak e�ciency of the

TGPP06-B motors was actually 150mA, not 70mA. This means that the arguments

used for propeller selection, based on the motor e�ciency, are incorrect, however the

selection of the 35mm propeller can still be justi�ed.

The propellers with diameters 55mm and 65mm can be discounted based on their size.

The diameter of the hull is 150mm and using the large propellers would increase it by

at least 50%. The thruster units would have to mounted on spars so that the propellers

did not interfer with the hull as well. The controllability of the thrust output is also

less as the control variable (motor input voltage) is �xed between 1V and 3V.

This leaves the 35mm and 40mm propeller as the viable alternatives. The 40mm

propeller provides around 16mN more thrust, however it draws around 11mA more

current. The force output of the 35mm propeller was su�cient for vertical motion (see

Chapter 7) and less current is drawn than if the 40mm propeller were used, which

means that the lifespan is greater. The choice of propeller should be re-examined as

part of any future work on the vehicle design.

It should also be noted that the pitch of the propeller increased along with the diameter.

The pitch for the 35mm propeller was 18mm, an increase of 5mm compared with the

propeller used on the MK V. This has the e�ect of increasing the velocity of the vehicle.

5.5 Sensors

As previously detailed, the vehicle has four DOF: surge, sway, heave and yaw. To

accurately control the movement in each degree, input sensors are required to provide

a combination of acceleration, velocity and/or position. One of the novel aspects of

this research is the challenge of developing suitable controllers when there is limited

and noisy input data.

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Figure 5.16: Output Force and Input Current for Varying Propeller Diameters

Due to the small scale of the vehicle, many sensors which are traditionally used in

AUVs are unsuitable. Often, control systems use velocity and positional data as inputs

to a control loop [55], however this may not be possible in this situation due to the

lack of suitable sensors. Table 5.4 shows the possible sensors available for each degree

of freedom.

Table 5.4: Motion SensorsDegree of Freedom Sensor

Surge Acoustic, Linear AccelerometerSway Acoustic, Linear AccelerometerHeave Acoustic, Linear Accelerometer, PressureYaw Acoustic, Inertial Gyroscope, Magnetic Compass

The main sensor for measuring translational movement in the horizontal plane is the

Acoustic Positioning System (APS). Position is a by-product of the acoustic commu-

nications. Velocity and acceleration can also be derived, although the errors increase

with each di�erentiation.

Linear accelerometers were also considered for horizontal motion measurements, how-

ever preliminary tests of a µAUV put the maximum acceleration in the order of 1mg3 or

0.01ms−2. This value is around the noise threshold of most linear accelerometers which

3'g' is the acceleration due to gravity

105


are usually designed for accelerations above ±1g. For this reason, linear accelerometerswere not investigated further.

There are three options available for the heave DOF, the APS, linear accelerometers and

pressure sensors. As discussed above, current linear accelerometers are not sensitive

enough and as will be detailed in Sections 5.5.1 and 5.5.2, the accuracy and simplicity

of the pressure sensor mean that it was used as the sole depth measurement sensor.

There are two input sensors currently available for the heading control; a digital com-

pass and a rate gyroscope. These provide measurements of both angular position and

velocity. The combination of a digital compass and rate gyroscope is the traditional

method of obtaining angular measurements for AUV heading controllers. These sen-

sors however, are subject to noise, interference and drift, issues which have a greater

e�ect on the µAUV designed for this project due to the physical design and the target

application as will be discussed in Sections 5.5.3 and 5.5.4.

5.5.1 Acoustic Positioning System

The APS is used to obtain estimates of the horizontal position and consists of two parts:

land-based base stations and a vehicle-based positioning sub-system. The process of

obtaining the position of the vehicle is called localization and the basic arrangement is

shown in Figure 5.17.

The APS for this work was a custom design which was developed within the AASN4IP

project (section 1.3.1). The design was independent of the work presented in this

thesis and therefore only a high level description of it will be given. The system was

not available for integration during this work, however it should be available by the

end of the AASN4IP project (see Section 9.4).

To obtain a set of three coordinates (X, Y and Z), signals from four separate base sta-

tions need to be received by the µAUV. For this project, the base stations are Neptune

Sonar Ltd T204 transducers which are specially designed for underwater communi-

cations and positioning [128]. They are mains powered, have a hemispherical beam

pattern and operate between 40kHz and 70kHz.

Once the signals from the four base stations have been received by the µAUV, four

separate Time of Flights (ToF) are calculated. From these, the range to individual

base stations can be estimated and the 3D position calculated using trilateration [129].

The acoustic sensors on the µAUV are SensComp 40KT08 piezo transducers [130].

They are primarily designed for use in air, however they can be used successfully in

water. The operating voltage for this project is ±7.5V at a frequency of 40kHz. The

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Figure 5.17: Acoustic Positioning System Set-Up

beam angle is approximately 120◦. Figure 5.18 shows the transducers mounted in a

static test node. It is envisaged that they will be mounted in the same way when when

integrated on to the MK VI prototype.

Unfortunately this method is very processor intensive and to execute it requires the use

of a high-end Digital Signal Processor (DSP). For the MK VI prototype, this device

was not available, so an alternate method was implemented.

Figure 5.19 shows this alternate method, the computationally expensive calculations

are done by a PC on land. The vehicle has four transducers which transmit the same

signal to the base stations at the same time. The received signal is captured and

processed on a PC and the position estimated. The position data is then transmitted

back to the µAUV via a �fth base station [129].

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Figure 5.18: 40KT08 Acoustic Transducers Mounted in a Static Test Node

Figure 5.19: MK VI Acoustic Positioning System Set-Up

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5.5.2 Pressure Sensor

Vertical position can be estimated accurately from pressure due to the fact that the

pressure in water increases linearly with depth. The pressure sensor selected for the

project was from the Omega PX40 family. These devices measure relative pressure

over a range of between 0psi - 15psi/30psi/100psi/150psi and output a voltage between

0.5V - 4.5V [127].

Two di�erent pressure sensors were used on the prototypes: the PX40-015G5V and the

PX40-0300G5V which allowed depth to be measured up to 10m and 20.5m respectively.

The MK V used the 20.5m device and the MK VI the 10m device due to the availability

of the devices.

To ensure a high enough depth resolution, the pressure sensor was connected to a 16-

bit analogue-to-digital converter (ADC). The ADC selected was a Linear Technology

LTC1864 with a resolution of 16-bits over a voltage range of 5V. This means that

the resolution is 76µ V/div [131]. The ADC was connected to the ESH via a serial

peripheral interface (SPI) as detailed in Section 5.7.

Figure 5.20 shows the estimated depth for both types of pressure sensor when tested

on a bench. It can be seen that the raw data (blue) for both sensors has a standard

deviation of around 0.025m - 0.028m. This was reduced by implementing a simple

averaging 32-point averaging �lter in software which reduces the standard deviation by

an order of magnitude.

5.5.3 Digital Compass

The digital compass that is used is a Honeywell HMC6343 device. This unit measures

the Earth's magnetic �eld, is tilt compensated, has a resolution of 0.1◦ and an accuracy,

when level, of 2◦RMS [132]. The compass is connected to the ESH (Section 5.7) via an

I2C communications bus. The raw data from the compass is angular position, however

for many control systems, angular velocity may also be required. This can be obtained

by di�erentiating the position data. This was achieved through a Kalman �lter as

detailed in Section 5.6.

The compass is mounted above the ESH printed circuit board (PCB) to reduce elec-

tromagnetic interference. To obtain error statistics for the compass, the vehicle was

placed on top of a non-magnetic box so as to avoid external magnetic interference from

supports in benches, walls or �oors as shown in Figure 5.21. The ESH was connected

to a desktop PC and the compass data streamed directly to it. Figure 5.22 shows a

graph of the normalized compass output when stationary.

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Figure 5.20: Bench Test for PX40-015G5V and PX40-030G5V Pressure Sensors, Withand Without Averaging Filter

Figure 5.21: Experimental Set-Up for Digital Compass and Gyroscope Error StatisticExperiments

Analysis of data gathered from the compass over multiple experiments showed that

the noise was Gaussian in nature, however the standard deviation varied between 0.1

and 0.25, with the corresponding variance between 0.01 and 0.0625. This noise in the

110


position data is ampli�ed when di�erentiated to get angular velocity. For the data

in Figure 5.22, the mean angular velocity is 0◦s−1, however the standard deviation is

3.09 and the variance is 9.54. This is the primary reason a Kalman �lter was used to

calculate the velocity. The error statistics were required for accurate simulations of the

control systems and as inputs for the Kalman �lter.

Figure 5.22: Error Statistic Plot for Digital Compass

As well as su�ering from random noise, the compass is also subject to interference from

other magnetic �elds. In this application, there are two sources of external magnetic

�elds which could a�ect it; �elds generated by the µAUV and those generated by

objects in the pond environment.

The magnetic �eld generated by the µAUV is a combination of magnetic �elds from

the DC electric motors and electromagnetic �elds generated by the embedded system.

These magnetic �elds can be viewed as being constant, or slowly varying, and can be

e�ectively eliminated via careful calibration as detailed below.

Figure 5.23 shows a plot of angle against time for an experiment where the compass

was placed inside the µAUV and the entire system was rotated in increments of 45◦.

The vehicle was placed on the experimental rig in Figure 5.21 and kept at each angle

for approximately 30s. An orientation grid was placed under the vehicle which was

rotated by hand. The estimated accuracy of the rotations was ±2◦.

The green line in Figure 5.23 shows the uncalibrated angle, and it can be seen that it

111


does not match the actual rotations (red lines). The distortion caused by the electro-

magnetic �elds is non-linear, as shown in Fig. 5.24.

Figure 5.23: E�ects of Electromagnetic Interference on the Compass With and WithoutCalibration Routine

A calibration algorithm was written based on a piecewise linear approximation of the

distortion curve and its e�ects are shown by the blue line in Figure 5.23. It can be seen

that the calibration routine means that the compass value matches the actual rotations

much better than without it.

The calibration curve shown in Figure 5.24 was generated using the MK V prototype.

Since the MK VI prototype had di�erent PCBs, the calibration routine had to be

conducted again. The calibration curve for the MK VI can be found in Appendix D.

The contents of nuclear storage ponds tend to be ferrous cannisters stored inside ferrous

containers. Both the containers and canisters modify or distort the Earth's magnetic

�eld which is likely to cause inaccurate readings from the compass. Unlike the constant

PCB-generated magnetic �elds, these can be viewed as being time varying making it

impossible to remove the e�ects by calibration.

Figure 5.25 shows an example of a container used to store nuclear waste. A simple

experiment was conducted using one of these containers to investigate the in�uence on

the digital compass readings. The vehicle, with the compass in, was placed 1m away

from the container and moved in 25cm steps towards it whilst the orientation was kept

112


Figure 5.24: Non-Linear Distortion Curve for Digital Compass for MK V Prototype

constant. It was found that the angular position readings changed by around 8◦. This

experiment should be repeated in the future to con�rm the results.

Figure 5.25: Container Used to Store Nuclear Waste

A compass and gyroscope are traditionally used together to achieve maximum stability

and accuracy for angular parameters. Compasses tend to have long-term stability but

are noisy. Gyroscopes traditionally have short-term accuracy but long-term positional

drift [133], as will be discussed in the next section. The compass is also a�ected by

113


external magnetic �elds, a problem which does not usually concern ocean-going AUVs.

The nature of the application in this project however means that there is a high chance

of interaction with such �elds. This means that the gyroscope may have to be used in

isolation in some operational scenarios.

5.5.4 Rate Gyroscope

The rate gyroscope used in the MK V and MK VI vehicles is an Analogue Devices

ADIS 16265 programmable digital gyroscope sensor. It has three range scales; ±80◦s−1,±160◦s−1 and ±320◦s−1 and a resolution of 14-bits which ranges from 0.01832◦s−1 to

0.07326◦s−1 per least signi�cant bit (LSB) [134]. The gyroscope is connected to the

ESH via a Serial Peripheral Interface (SPI). The raw data from the gyroscope is angular

velocity, however angular position can be obtained by integration, either directly, or as

part of the Kalman �lter.

In tests, the gyroscope was mounted so that the axis of rotation was aligned with that

of the compass. The experimental con�guration to obtain the error statistics was the

same as shown in Figure 5.21 in the previous section.

The value of angular velocity measured by the gyroscope is subject to Gaussian noise

as shown in Figure 5.26. The error statistics are of the same magnitude as the compass

with a standard deviation of 0.107 and a variance of 0.0115. When integrated to obtain

position however, this noise has the e�ect of causing the position estimate to drift over

time. It was found that the magnitude of this drift depended on the accuracy of the

initial calibration, however it was also found to be time-varying.

The positional drift makes the gyroscope, in its raw state, unsuitable for angular posi-

tional measurements. The magnitude of the drift can be reduced by careful calibration,

however as it is time varying, it cannot be completely eliminated. It can however be

combined with the compass data in a Kalman �lter as detailed in Section 5.6.

5.6 Kalman Filter

The traditional method for state estimation in navigation systems is the Kalman �lter,

or variations of it. It was �rst described in 1960 and is well understood. It provides an

estimate of the states of a process by minimizing the mean of the squared error [135].

The fundamental equations and derivation are well documented and a comprehensive

description for the discrete form is given in [135].

114


Figure 5.26: Error Statistic Plot for Rate Gyroscope

The Kalman �lter was used in two di�erent capacities within this work. The �rst was

to provide estimates of velocity given noisy positional data for movement in the vertical

(and eventually horizontal) plane and the second was to combine the data from the

compass and gyroscope to get better estimates of angular position and velocity.

5.6.1 Velocity Estimation

The only input sensor in the vertical plane was a pressure sensor which provided posi-

tional data (Section 5.5.2). As detailed in Chapter 7, one of the controllers implemented

required both position and velocity data as inputs.

To obtain a velocity value, the position data must be di�erentiated. A basic method

to do this is to use a backwards di�erence scheme. A problem arises however, if

the positional data is subject to noise. The backwards di�erence method ends up

di�erentiating the noise and the di�erentiated signal cannot be retrieved [136].

The Kalman �lter provides a more robust alternative. The basic equations for the dis-

crete form are given in Appendix E.1. The process model used is shown in Equation 5.1,

whilst the measurement noise covariance matrix was obtained through o�-line statisti-

cal analysis of pressure sensor data. The process noise covariance matrix was set to the

Identity matrix which essentially meant that the position values were passed through

115


the �lter. The tuning of the Kalman �lter is a topic which should be investigated in

future work. T is the sample period.

x−k =

[1 T

0 1

]xk−1 (5.1)

Figure 5.27 shows a comparison of the backwards di�erence method and a Kalman

�lter, obtained through simulation. The input is a sine wave with added Gaussian

noise which has a variance based on statistical analysis of the pressure sensor data.

It can be seen that the numerically di�erentiated values are much larger than those

obtained using the Kalman �lter. Further investigations indicated that the variance is,

on average, two orders of magnitude larger using numerical di�erentiation than with

the Kalman �lter.

Figure 5.27: Comparison of Backwards Di�erentiation and Kalman Filter for Estimatesof Velocity using Noisy Position Data

The equations for the Kalman �lter were converted into a form which could be im-

plemented in software on the ESH and can be found in Appendix E.2. The results of

experiments with and without the Kalman �lter for velocity estimation are discussed

in Chapter 7.

116


5.6.2 Data Fusion

The second use of the Kalman �lter was to fuse together the data from the compass

and the gyroscope to obtain more accurate estimates. As discussed in Sections 5.5.3

and 5.5.4, the compass provides stable but noisy data, whilst the gyroscope provides

less noisy data but which is subject to drift.

The basic equations for the �lter are the same as for velocity estimation (given in

Appendix E.2), however this time there are two inputs and the measurement noise

covariance matrix contains error statistics for both the compass and gyroscope. The

�lter was implemented in software on the ESH (the equations can be found in Appendix

E.3) and tuned using real data.

Figures 5.28 and 5.29 show the results for an experiment conducted using a turntable.

The vehicle was placed on the turntable and rotated backwards and forwards. The

values for the process noise covariance matrix are given at the top of the graphs. It can

be seen that the Kalman �ltered estimates of both position and velocity have less noise

than the compass data and the position estimate does not drift as with the gyroscope.

It was observed that the tuning of the process noise covariance matrix, especially

with regards to the angular velocity estimates, was very important. When a single

measurement device is used, the position (or velocity) estimate is directly related to

the original data by integration (or di�erentiation). When two measurement sensors

are fused using a Kalman �lter, the two estimates may not be directly related (i.e. if

you di�erentiate position, you will not get the velocity estimate). Care has to be taken

to ensure that the two estimates are suitably matched.

The results of experiments conducted using the Kalman �lter for data fusion are dis-

cussed in Chapter 7.

5.7 MK V Embedded System Hardware

The embedded system hardware comprises all the control circuitry which is required to

independently control the six thruster units detailed in Section 5.4 and interface with

the relevant input sensors. It can be broken down into four distinct areas: processing,

sensing, power and actuation. The sensing has already been discussed in Section 5.5.

The other three areas will be considered in the rest of this section.

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Figure 5.28: Position Data for Kalman Tuning Experiment

Figure 5.29: Velocity Data for Kalman Tuning Experiment

5.7.1 Processing

The MK V prototype only had the pressure sensor, digital compass and rate gyroscope

which required very little in terms of processing power. The main processors were

therefore small microcontrollers.

118


The family of microcontrollers chosen for the processing were the Microchip PIC range.

This was due to the in-house experience of using such devices. Unfortunately there

was no microcontroller available which could run 6 DC motors at the same time. The

most capable could run up to 4 motors using specialist PWM driver modules. This

meant that two microcontrollers were needed to control all 6 motors.

The microcontroller chosen was the PIC18F4431, an 8-bit system with a specialist

DC motor interface [137]. One microcontroller (designated primary) interfaced to four

of the motors (the horizontal thrusters) whilst the other microcontroller (designated

secondary) was connected to the vertical motors and to the sensors. The two processors

communicated via an SPI bus.

The PIC18F4431 microcontrollers are limited in their communication bus capabilities.

Microchip devices typically have hardware peripherals to support communications,

however each of these processors only has a single master/slave SPI or a slave I2C

peripheral. This was enough to communicate with the gyroscope and pressure sensor,

however not the compass. To communicate with the compass, a software master I2C

was written, by a colleague, to emulate a hardware peripheral. Emulated peripherals

often run slower than their hardware counterparts, however the reduction in speed did

not a�ect execution of the control system.

To communicate with the sensors, the hardware SPI on the secondary processor had to

be in master SPI mode. However, to communicate with the primary microcontroller, it

had to be in slave mode. The complexity of running the SPI in both modes was high so

a much simpler software SPI was written for the processor-processor communications.

The hardware SPI could not operate at a slow enough frequency to connect to the

software SPI, so the software version was implemented on both processors.

To aid in the analysis of the experiments, it was desirable to store the input and

output data used by the ESH. This data could be stored in non-volatile memory on

the microcontrollers or on external �ash memory devices. The PIC18F4431 had limited

program memory so only about 30s of sensor data could be stored and state estimation

algorithms could not be implemented. The lack of program memory was also caused by

the use of emulated software communication peripherals which required a large number

of instructions. The solution to this problem was to add a third microcontroller which

could perform both state estimation and store the sensor data. Figure 5.30 shows the

design of the system.

The ESH design contained both analogue and digital components which had to be kept

separate to reduce noise interference. This was achieved by having a split ground plane

and two independent power regulators.

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Figure 5.30: Design for Control Circuitry

The external diameter of the hull was 150mm (Section 5.2), however once the seal was

added, the internal diameter reduced to 130mm. A modular approach was taken to the

design of the PCBs to increase the �exibility of the design to reduce space. Additional

boards could be added to the design with relative ease and, since the hull was curved,

boards could be made di�erent sizes to ensure that they �tted.

For the MK V, two PCBs were constructed; one for the processor and one for the power

regulation as shown in Figure 5.31. The processor board was 80mm x 80mm and the

gyroscope and compasses were directly mounted on to it.

5.7.2 Power

Section 3.3 identi�ed the power supply as being a Li-Ion batter pack with a potential

capacity of up to 100kJ. The pack chosen for the prototype had a voltage of 7.5V

and a capacity of 59.4kJ. Given the diameter of the vehicle (150mm) and the target

velocity and thrust (0.1ms−1 and 40mN) from earlier in the Chapter and assuming the

power consumption used in Chapter 3, the lifespan of the vehicle can be estimated

at approximately 60 minutes. This is twice the target lifespan for a mission used in

Chapter 3.

Two voltage levels were required on the processor board; 5V for the sensors and pro-

cessors and 3V for the actuators. The power board, shown in Figure 5.31 used switch-

mode, step-down voltage regulators. Two of these provided 5V outputs whist the third

120


provided a 3V output. Two 5V supplies were required so that the pressure sensor could

have a dedicated supply to reduce noise.

Figure 5.31: Control Circuit PCBs - Left: Processor Board with Gyro, Top Right:Battery Board, Bottom Right: Processor, Gyro and Battery Boards Stacked Together

5.7.3 Actuation

To obtain bi-directional control of the DC motor, a full-bridge driving circuit was

required. The device chosen for this was the Allegro A3901 which is capable of driving

two DC motors. To vary the speed of the node, the shaft speed of the motor is

controlled. This is achieved by providing a PWM signal to the motor (as described in

Section 5.3). The standard PWM frequency for DC motors is around 20kHz, just above

the threshold of human hearing. These PWM signals were provided by the specialist

modules on the microcontroller described in Section 5.7.1.

5.8 MK VI Embedded System Hardware

The MK VI prototype was a re�nement of the MK V and had the capability to interface

with the APS. This meant that new circuitry had to be integrated which would operate

the transducers and perform the signal processing necessary to support communica-

121


tions. In terms of the mechatronic systems, there were no major changes, however the

opportunity was taken to improve the design the MK V PCB.

The driving of the acoustic transducers and the signal processing associated with com-

munications and localisation required two new PCBs, so the entire embedded system

became a stack of PCBs. The order of boards is shown in Figure 5.32. The power

board had a large connector which ran the full height of the stack on to which the

other boards connected. Three pillars provided support in between each board.

The Analogue board and DSP board (shown in Figure 5.32) were mounted above

the battery board, with the motor controller board on top. This was to allow easy

connection of the gyroscope and compass which had to be as far away from sources of

electromagnetic interference as possible (Section 5.5.3).

Figure 5.32: MK VI PCB Stack Overview

5.8.1 Processing

One of the major issues with the MK V processor design was the number of hardware

communication peripherals required to connect to all the sensors. To solve this, the

third microcontroller, originally only used for state estimation and data logging, was

upgraded to a processor which could connect to all the input sensors via hardware

peripherals (a PIC18F67K22). This reduced the amount of code required and simpli�ed

the design. Figure 5.33 shows the MK VI architecture.

122


The master processor was interfaced to all the sensors, including the APS and con-

ducted the navigation (in the form of �xed way points), state estimation and data

logging. The relevant sensor inputs were transmitted to the motor controller proces-

sors via a hardware SPI bus which was signi�cantly faster than the MK V software

implementation.

Figure 5.33: Design for the MK VI COntrol Circuitry

5.8.2 Analogue Board and Digital Signal Processing

The analogue board and corresponding digital signal processing board were designed

by another member of the AASN4IP project team. The analogue board connected to

the four transducers which were mounted on the µAUV and included all the required

�lters and ampli�ers.

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The analogue signals are sent to small digital signal processor (dsPIC) which runs the

modulation/de-modulation algorithms required for localisation (Section 5.5.1). The

coordinates are sent to the motor control board via an SPI bus.

5.8.3 Power

The power board was re-designed to incorporate the extra voltage requirements of the

analogue and DSP boards. In addition to the 5V and 3V lines from the MK V design,

±7.5V and 3.3V rails were also added. The complete PCB stack is shown in Figure

5.34.

During the writing of the software, the vehicle was powered from a bench-top power

supply which measured the current draw. Taking into account the increased current

consumption when the thrusters are used in the water, the lifespan of the vehicle

(considering only the mechatronic aspects) was estimated to be between 5.5 and 7

hours. This is signi�cantly longer than the target of 30 minutes from Chapter 3 and

represents a utilisation of between 275% and 350%.

If the power consumption of the APS is considered as well, the estimated lifespan

reduces to approximately 3.5 hours, representing a utilisation of 175%. This is based

on a worst-case scenario where the vehicle is permanently transmitting.

Figure 5.34: The MK VI PCB Stack Mounted in the Hull

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5.9 Software

The software for both the MK V and MK VI ESH was written in the `C' programming

language and developed in the Microchip MPLAB environment. This environment

supported in-circuit debugging which simpli�ed the development of the code. Each

processor ran di�erent code, although they all used some common functions. In total,

approximately 4800 lines of code were written for the MK V prototype and approxi-

mately 5000 lines for the MK VI.

A �owchart of the interactions between the three processors on the MK VI ESH is

shown in Figure F.1 in Appendix F. The Master processor controls the timings for

the control loop by using interrupts from a timer module. Communication with the

sensors and with the other processors was executed sequentially.

To decrease the execution time on the embedded system, the initial control systems

for the MK V prototype were implemented using �xed-point arithmetic to reduce the

number of �oating-point calculations [138]. This implementation method was re-visited

when the MK VI prototype was developed.

It was found that due to the small number of terms in the di�erence equation being

evaluated, the di�erence in execution time between the �xed-point and �oating-point

versions was very small. The reduction in execution time was negated by the fact that

the Microchip `C' libraries do not have a rounding function which rounds to the nearest

integer (they only have ceiling and �oor functions). A custom rounding function had

to be written which increased the overall implementation time. For this reason, the

controllers on the MK VI prototype were implemented using �oating-point arithmetic.

5.10 Summary

This chapter has discussed the development of a number of prototype µAUVs which

have been built during this research. Particular attention has been paid to the MK V

and MK VI prototypes which were used extensively as test beds for the motion control

systems. The development of the hull, propulsion system, sensing capabilities and the

embedded system have been discussed in detail and the issues that have arisen have

been identi�ed and relevant solutions implemented.

Estimates of the power consumption of the MK VI prototype suggest that the lifespan

would be between 3.5 hours and 7 hours depending on the number of thrusters being

used and the how often the APS used. The lifespan estimate represent a utilisation

125


of between 175% and 350% which is far greater than the original target of 20%, or 30

minutes, from Chapter 3.

The MK V and MK VI prototypes are shown in Figure 5.35. The MK V prototype was

used successfully for over a year as a test bed for the development of control algorithms

for movement in both the vertical and horizontal planes. The vehicle was tested both

within the university and at a facility provided by one of the industrial partners, the

National Nuclear Laboratory (NNL). The MK VI was used for approximately 4 months

as a demonstrator for the capabilities of the vehicle.

Figure 5.35: The MK V Prototype (Left) and the MK VI Prototype (Right)

126

Chapter 6

Motion Control for Unmanned

Underwater Vehicles

Chapter 5 outlined the development of two fully functional prototype µAUVs, which

were used as test beds for the development of motion control algorithms. This chapter

presents a review of control systems which have been used in other unmanned under-

water vehicles (UUVs)1 and de�nes the basic model of the µAUV which will be used

as the basis of controller development.

The motion control systems are responsible for moving the vehicle between a start

point and an end point. The generation of the end points is the task of higher level

navigation routines [139], which are beyond the scope of this work. The end points

for the control systems developed during this research were manually generated and

hard-coded in software.

6.1 Overview of Control Systems

The classical feedback control system contains two main parts; the controller, C, and

the plant, G, as shown in Figure 6.1. The plant is a model of the dynamics of the real

world system and its form directly a�ects the choice of both the control system and

the mathematical analysis approach.

The overall aim is to develop a control system which will move the µAUV to a given

set of coordinates in 3 dimensions with a speci�ed orientation in yaw (movement in

roll and pitch is not possible due to ballasting, Section 5.3.1). As detailed in Chapter

1UUVs encompass both autonomous underwater vehicles (AUVs) and remotely operated vehicles(ROVs)

127


Figure 6.1: Classic Feedback Control Loop

5, the design of the node allows for movement in 4 degrees of freedom (DOF) via the

use of six thruster units.

There are two levels of control system which will be considered in this thesis: high-level

and low-level. The high-level control is concerned with the navigation of the vehicle

and the generation of way points. This is only considered brie�y in Chapter 8. The

low-level control is concerned with the motion of the vehicle and the direct control of

the thruster units. The development of low-level motion control systems is the primary

focus of Chapters 7 and 8.

The two levels of control use di�erent types of set-points. The low-level control use

static set-points, i.e., they are �xed in time. Any changes in the set-point will occur at

pre-de�ned times. The high-level control will use dynamic set-points. Changes in the

set-points are dependent on the vehicle location rather than time (discussed further in

Section 8.3.1).

The full 3D control system (low-level) can be broken down into several simpler control

systems which can be developed separately and integrated at a later date. This reduces

the complexity of the design task and is only possible due to the de-coupling between

the DOF. However, as will be discussed in Chapter 7, unwanted coupling may lead to

the controllers having to be modi�ed to compensate.

Each control system can be classi�ed in terms of the number of inputs and outputs as

shown in Table 6.1 [140]. The more inputs or outputs there are, the more complex the

control system. It is often desirable to try and convert multiple input, multiple output

(MIMO) systems into several single input, single output (SISO) systems which can be

joined together [141].

Table 6.1: Control System Classi�cationsSISO Single Input Single OutputSIMO Single Input Multiple OutputMISO Multiple Input Single OutputMIMO Multiple Input Multiple Output

128


Figure 6.2 shows a block diagram of the decomposition of the control system for the

µAUV. The overall controller is a MIMO system, since there is positional data for each

of the 4 DOF as the inputs and control signals to 6 thrusters as the outputs. It can

be split into two separate MIMO systems, one for the vertical position and one for the

horizontal position.

Figure 6.2: Decomposition of the 3D control System

Whilst the provision of movement in the two planes has been de-coupled, there is still

an unwanted, but important coupling between the vertical and horizontal planes as

will be detailed in Section 7.6.1. This comes in the form of a rotation when the node

moves vertically caused by the vertical thrusters not being exactly perpendicular to

the horizontal plane. This means that there are components of thrust in surge, sway

and yaw.

The controller for the depth of the node (ignoring rotation for the present) is either

a SIMO system with depth as the input and the two vertical motors as outputs, or

MIMO with both depth and velocity as inputs. Since roll and pitch are negated by the

ballasting, the force produced by the two thrusters can be modelled as a point force

acting through the centre of the vehicle. This means that the controller is either a

SISO or MISO system.

The yaw controller is a MIMO system if both the rotational position and velocity are

used as inputs. This can be simpli�ed by only using position, at which point it becomes

a SIMO system. The last of the control systems relates to horizontal position and so

is a MIMO system which cannot easily be simpli�ed due to coupling terms (Section

6.3). The two thrusters cannot be modelled as a single force either as rotation in yaw

is required.

The three horizontal controllers, surge, sway and yaw, all try and control the same four

thruster units. This could be problematic since the output of an individual thruster unit

129


is saturated. If the outputs of all three controllers are added together, the combined

output may reach the saturation level. If a large thrust force from one motor is required

and a small output from another, the saturation may cause the overall outputs to be

incorrect. To overcome this, a form of adaptive resistive mixing was used [142]. The

outputs to all the motors are scaled with respect to the largest output (pre-saturation).

This ensures that one controller does not dominate the other two.

Slotine & Li [143] provide a procedure for the development of control systems which is

given below:

• Specify the desired behaviour and select actuators and sensors

• Model the physical plant by a set of di�erential equations

• Design a control law for the system

• Analyze and simulate the resulting control system

• Implement the control system in hardware

This chapter will cover the �rst three stages of this procedure and will include general-

ized discussions of the development of the plant and the suitablilty of di�erent control

systems. Chapter 7 will present the control systems which were implemented on the

prototype vehicle and the corresponding results and analysis.

6.2 Speci�cation of Behaviour

There are two main types of behavioural speci�cation for the development of control

systems: quantitative and qualitative. Quantitative speci�cations are more suited to

linear control design and include rise-time, overshoot and settling time. Qualitative

speci�cations are more suited to non-linear control design and include stability, robust-

ness and cost [143]. The speci�cations for the 3D control system for this project will

be a combination of the two.

6.2.1 Quantitative Speci�cations

The quantitative speci�cations are those which are concerned with the physically re-

alisable outputs of the control system such as overshoot and steady-state (SS) error.

The real values are dependent on the dynamics of the plant, the measurement noise of

the input sensors and the tuning of the control system.

130


The speci�cations detailed in Table 6.2 are the estimates based on the application

environment (Section 2.1) and the sensors (detailed in section 5.5). As the vehicle will

move both both linearly and rotationally, speci�cations have been given for the three

individual controllers; vertical, horizontal and rotational.

Table 6.2: Quantitative Speci�cationsOvershoot SS Error SS Osc. Amp. SS Osc. Freq.

Vertical ≤25mm ≤ ±25mm ≤ ±15mm ≤1HzHorizontal ≤50mm ≤ ±50mm ≤ ±25mm ≤1HzRotational ≤5◦ ≤5◦ ≤ ±5◦ ≤1Hz

6.2.2 Qualitative Speci�cations

The qualitative speci�cations are those which deal with the inputs to the control sys-

tem such as parameter uncertainties, measurement noise and stability. As with the

qualitative parameters, the speci�cations detailed below are the estimates based on

an analysis of the application environment (Section 2.1) and the sensors (detailed in

Section 5.5).

• The system must be globally stable

• The system must be robust to thrust force variation between thruster pairs of up

to 50%

• The system must be robust to individual thruster force variations of up to ±25%

• The system must be robust to measurement noise

• The system must be robust to parameter uncertainties of up to ±10%

• It must be possible to implement on the embedded system hardware (ESH)

6.3 Analysis of the Plant

The �rst step of developing a control system is to generate the di�erential equations

which describe the plant. The full generalized equations of motion are shown in 6.1

and the expanded 4 DOF form is shown in Equations 6.2 and 6.3. This plant model is

the standard model used for underwater vehicles [144, 12] and is taken from [55]. The

notation is given in Table 6.3.

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Mν + C(ν)ν + D(ν)ν + Γ(q) = τ

q = Bν (6.1)

m+ma 0 0 0

0 m+ma 0 0

0 0 m+ma 0

0 0 0 I

ν1

ν2

ν3

ν6

+

0 −mν6 0 maν2

mν6 0 0 −maν1

0 0 0 0

0 0 0 0

ν1

ν2

ν3

ν6

+

dt|ν1| 0 0 0

0 dt|ν2| 0 0

0 0 dt|ν3| 0

0 0 0 da|ν6|

ν1

ν2

ν3

ν6

+

0

0

mig

0

=

τ1

τ2

τ3

τ6

(6.2)

q =

cos(q6) − sin(q6) 0 0

sin(q6) cos(q6) 0 0

0 0 1 0

0 0 0 1

ν1

ν2

ν3

ν6

(6.3)

Table 6.3: Equations of Motion NotationM Inertia Matrix C Coriolis and Centripetal MatrixD Drag Matrix Γ Vector of Restoring Forcesτ Vector of Thrust Forces B BF to EF Jacobianν Body-Fixed Velocities q Earth-Fixed Velocitiesm Mass of Node ma Added Mass of Nodemi Imbalanced Mass of Node I Moment of Inertiadt Translational Drag Coe�cient da Angular Drag Coe�cientE Thruster Con�guration Matrix F Vector of Thruster Forcesg Gravitational Constant r Radius of Node

At this point, it is important to note that di�erent coordinate reference frames are

employed in the above equations. There are two coordinate reference frames as shown

in Figure 6.3. The global reference frame is known as the Earth-Fixed (EF) frame and

is assumed to be an inertial frame. Consider a rectangular vessel, such as a storage

pond. The origin (0,0,0), could be set as the bottom left hand corner. Positions within

the pond would then be calculated from this origin and would be classed as being EF.

The Body-Fixed (BF) coordinate frame has an origin which is `attached' to the centre

of the vehicle. To an external observer in the EF reference frame, the BF origin appears

132


to move. If the observer is in the BF frame, the origin is �xed. Equation 6.2 is in the

BF reference frame, however positional coordinates are given in the EF frame so a

Jacobian (Equation 6.3) is required to transform between them [55].

Figure 6.3: Coordinate Reference Frames

It can be seen that the surge, sway and yaw DOF are open-loop stable (if ν = 0 and

ν = 0, the required thrust force τ = 0), however the heave DOF is open-loop unstable

due to the buoyancy force. This means that to hold station at a given depth, the

heave control system will have to be permanently on. This will e�ect the lifespan of

the vehicle, however it cannot be avoided.

The forces acting in each degree of freedom, τx, are related to the individual thruster

units via the thruster allocation matrix shown in (6.4) [145]. Figure 6.4 shows a visu-

alisation of the thruster allocation matrix. The coloured arrows indicate the direction

of movement when the thruster is set to forwards. The coloured dot represents vertical

thrust coming out of the page (upwards thrust).

τ = EF

τ1

τ2

τ3

τ6

=

1 1 0 0 0 0

0 0 1 1 0 0

0 0 0 0 1 1

−r r −r r 0 0

F1

F2

F3

F4

F5

F6

(6.4)

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Figure 6.4: Visualisation of Thruster Allocation Matrix

As highlighted in Figure 6.2 in Section 1, the full system can be split into three simpler

systems which can be analysed separately. The next stage of analysis is to identify

whether the plant is non-linear and to decide whether it should be linearised. This can

be done for the entire plant, before it is separated.

6.3.1 Linearisation

Linear systems are more widely understood than non-linear systems and it is easier

to design control systems for them. For some non-linear systems, linearisation can

provide an acceptable approximation of the dynamics which can then be controlled. A

di�culty with linearisation is that it has to be performed around an equilibrium point.

If the system deviates by any substantial amount from the chosen equilibrium point,

the linear approximation becomes invalid.

AUVs often have highly non-linear dynamics which contain large numbers of uncertain-

ties and disturbances which cannot be easily measured. This presents several challenges

when it comes to linearisation. The scale of the problem is increased by the maneu-

verability of the vehicle.

[146] explains that for an n DOF vehicle, linearisation produces a system of order 2n

to be controlled. In the case of the vehicle used in this work which has 4 DOF, the

system to be controlled would be 8th order. This would be time consuming and the

results may not be accurate. For this reason, the decision was made not to linearise

the plant in its entirety for the purpose of control system design2.

2A linearisation of the heave DOF was conducted for the purpose of sampling frequency estimationand is detailed in Section 7.5

134


6.3.2 Modelling Approach

Once the decision not to linearise the plant had been made, the next decision was the

mathematical approach which should be taken in designing the feedback control system.

There are two options available: traditional input/output di�erential equations or a

modern state-space representation.

Classical control theory is based around a frequency domain analysis and uses transfer

functions formed from the input/output di�erential (or di�erence) equations to repre-

sent the system [147]. It is generally restricted to linear feedback SISO systems [148].

There are well established analysis and tuning techniques for the controllers such as

root locus analysis, Nyquist/Bode plots and the Ziegler-Nichols tuning rules for PID

controllers [149].

The classical approach appears to be ruled-out for the design of the controllers for the

µAUV due to the non-linear plant and the fact that it is a is MIMO system. A slightly

modi�ed version can be used however for the development of a controller for the single

DOF, uncoupled depth controller which is a SISO system.

Even though the plant is non-linear, a symbolic representation can be developed using

SIMULINK, and a transfer function of a linear controller can be derived. The drawback

is that the tuning of the controller has to be done manually (either by hand or through

a brute-force automated simulation regime). This is the approach that was taken

for the depth controller due to its relative simplicity (see Chapter 7). This symbolic

representation approach can be used with non-linear control theory and is used in [55]

for a number of di�erent scenarios and control strategies.

The modern state-space representation of a system uses a series of �rst order di�erential

equations which relate to the set of input, output and state variables. Analysis is

conducted in the time-domain as opposed to classical control which is conducted in the

frequency domain. The state-space representation is used extensively for non-linear

MIMO systems [150].

Analysis of the plant showed that deriving an accurate state-space representation was

non-trivial due to the non-linearities such as actuator saturation. For this reason, it was

decided to proceed using the symbolic representation of the Input/Output di�erential

equations.

The top-level of the SIMULINK model which was developed can be found in Appendix

G. Further details of how the model works are given in Chapter 7. A high-level

abstraction of the model is shown in Figure 6.5.

135


Figure 6.5: High-Level Abstraction of the SIMULINK Model

6.4 Unmanned Underwater Vehicle Control Systems

Review

Control tasks can be split into two categories: regulation (or stabilization) and track-

ing (servo-control) [143]. Regulation tasks require the system to stabilize around an

equilibrium point, for example temperature control in an oven or the altitude control

of an aircraft. Tracking tasks require the output of the system to track a time varying

trajectory such as a robotic car following a speci�c path.

From these de�nitions, it can be seen that the three control problems identi�ed at the

start of this chapter can be viewed as either stabilization or tracking depending on

the mission requirements. For example, if the vehicle is required to move to a speci�c

position and take a measurement reading, this is regulation problem. If the vehicle

is navigating through a cluttered environment on a given trajectory, it is a tracking

problem.

There are many di�erent types of controllers which have been used for UUVs. The most

widely used are Proportional Integral Derivative (PID), sliding mode and adaptive

controllers, or variations of them. Table 6.4 shows a list of the UUVs which use these

controllers. These three account for approximately 90% of the implemented controllers

identi�ed. A brief review of some of the successfully implemented controllers is given

in the next section.

There are however many other control strategies which have been successfully imple-

mented on AUVs and a list of them is shown in Table 6.5. In total, Tables 6.4 and 6.5

cover 56 di�erent AUV/controller combinations which represent a large section of the

research-based AUV �eld. Details of the control systems for commercial AUVs are not

widely available. Of these 56, only 19 of them have been fully implemented and tested

on a UUV. There are several reasons behind this disparity.

Firstly, many of the controllers have been designed purely in simulation and not tested

in the real world because the hardware is not available. Secondly, the di�erence be-

tween the simulated environment and the real world may be su�cient to cause the

136


controller not to work or the project may have �nished before the controller could be

fully implemented, tested and published.

Table 6.4: Main Types of Controller Used on AUVsType of Controller UUV Implementation

PID

ARCS [151] YICTINEU [9] Y

KwaZulu-Natal AUV [152] YOBERON [153] YODIN [154] YORCA [155] Y

REMUS [156, 157] YSPARUS [158] YSubjugator [159] YTHETIS [160] YARIES [161] N

Phantom S2 [162] NUTM [163] N

Fuzzy PID Phantom S2 [162] NNeural Network PID No Speci�c UUV [164] N

MPSO PID No Speci�c UUV [165] N

Sliding Mode

Benthos RPV-430 [166] YHamuburg ROV [167, 168] Y

Subjugator [159] YEAVE [146] NJASON [169] NMUST [170] NREMUS [57] N

Fuzzy Sliding Mode OEX-C [171] Y

Adaptive Sliding ModeNo Speci�c UUV [172] N

JASON [169] NAdaptive Fuzzy Sliding Mode No Speci�c UUV [173] N

Adaptive

ODIN [174, 175, 176] YTaipan 2 [177] N

No Speci�c UUV [178] NNo Speci�c UUV [179] N

Neural Network AdaptiveManta-Ceresia [180] Y

R2D4 [181] NAdaptive Fuzzy Neural Network No Speci�c UUV [182] N

Fault-Tolerant Control LawODIN [183, 145, 144, 184] YNo Speci�c UUV [185] N

State Feedback LinearizationCanterbury AUV [186] N

USM-AUV [187] NNo Speci�c UUV [188] N

137


Table 6.5: Other Types of Controller Used on AUVsType of Controller UUV Implementation

DisturbanceNPS Phoenix [189] Y

Compensation ControlNonlinear Gain-Scheduling INFANTE [190] Y

Formation Control SERAFINA [85] N

S-Surface/S-PlaneAUV-XX [191] NMAUV-II [192] NOID-I [193] N

Lyapunov-Based TrackingNo Given UUV [194] NNo Speci�c UUV [195] N

HPSO-based FuzzyNational Key Lab AUV [196] N

Neural NetworkSmith Control Scheme

ARGO [197] Nwith LQG/LTRState-Dependent

REMUS [198] NRiccati Equation (SDRE)

H2/H∞ No Speci�c UUV [199] NFuzzy ARPA UUV [200] N

Robust Cascade RRC [201] NCross-Track Controller C-SCOUT [202] NReceding Horizon

No Speci�c UUV [203] NTracking Control

Multivariable ControlNo Speci�c UUV [204] N

using LQG/LTR

6.5 PID Control

A logical starting point in the choice of control methodology for the µAUV is to consider

the most commonly implemented UUV control systems, speci�cally PID and Sliding

Mode. The next two sections will give a brief overview of these two control methods.

6.5.1 Overview

The PID controller is the most common type of control system in use, accounting for

around 90% of industrial controllers [205]. The name of the controller is an acronym

for its constituent components; Proportional (P), Integral (I) and Derivative (D).

PID controllers are mainly used for linear time invariant (LTI) SISO systems and are

138


therefore usually expressed in the form of a transfer function (TF) in the Laplace

domain. Many di�erent structures are used, however the most common are the ideal

and the parallel forms [206]. For the purpose of this work, the parallel form was used

(Equation 6.5) due to its �exibility. To provide increased tuning �exibility, the integral

and derivative gains were separated from the time constants. Kp is the proportional

gain, Ki is the integral gain, Kd is the derivative gain, Ti is the integral time constant

and Td is the derivative time constant.

C(s) = Kp +Ki

Tis+KdTds (6.5)

Technically, the TF shown in Equation 6.5 is unrealisable due to the non-causal nature

of the derivative action. To overcome this, the pure derivative term is replaced by an

approximate derivative as shown in Equation 6.6 [205]. The new parameter, γ, is called

the derivative gain and as it increases, the approximate derivative term approaches the

pure derivative term [205]. This type of controller is referred as PIDγ controller.

C(s) = Kp +Ki

Tis+

KdTds

1 + γTds(6.6)

As with the controller structure, there are many types of tuning rules which can be

applied to the system. Tuning can be achieved using a number of methods including

step responses, frequency responses and minimization. The most well known of these

is the Ziegler-Nichols method [207, 208]. The type of tuning used is dependent on the

design requirements of the system, such as performance criteria or robustness [206].

When a PID controller is used in conjunction with a non-linear plant, tuning by tradi-

tional methods may become very di�cult. In this case, manual tuning may have to be

conducted, or more computationally complex approaches based on, for example, neural

networks [164].

6.5.2 Analysis of Controller Components

It is important to understand the e�ects of each of the constituent components of the

PID controller so that tuning can be conducted e�ciently. To illustrate this, a short

example is presented, taken from [209].

139


The example uses the ideal form of the PID control law as shown in Equation 6.7. e(t)

is the error at time instant t. Figure 6.6 shows the output response when the controller

was used in conjunction with the plant described by the transfer function G(s) =4

s2+5s+4. Figure 6.6 also shows the individual control outputs. For this simulation, Kp

= 3.3, Ti = 2.9 and Td = 0.2.

u(t) = Kp

(e(t) +

1

Ti

∫ T

0

e(τ)dτ + Tdde(t)

dt

)(6.7)

Figure 6.6: Output Response for PID Simulation

To obtain a good output response, the controller parameters need to be tuned. When

tuning a PID controller, the target is to reduce the transitory time, minimise the

overshoot and ensure the steady-state error is zero. Unfortunately there is a trade-o�

between the transient response and the steady-state error. Figures 6.7, 6.8 and 6.9

show the responses when only the proportional, integral and derivative actions are

used respectively.

The proportional component, Kpe(t), only acts on the error at time instant t and

the response is shown in Figure 6.7. Proportional control can decrease the transient

response time, however it produces a steady-state error.

140


The integral component, KpTi

∫ t0e(τ)dτ , is an accumulation of the error over time and

the response is shown in Figure 6.8. During steady-state, the integral action ensures

that the output reaches the desired target, i.e. it eliminates the steady-state error.

The transient response however, is poor for the integral controller (there are large

oscillations).

The derivative component, KpTdde(t)dt

, predicts the future response of the desired output

and forces the system output to follow it. This has the e�ect of reducing the transitory

regime (overshoot and settling time). The response for the derivative action is shown

in Figure 6.9.

Figure 6.7: Output Response for 'P' Simulation

141


Figure 6.8: Output Response for 'I' Simulation

Figure 6.9: Output Response for 'D' Simulation

142


6.5.3 Review of UUV PID Implementations

Table 6.4 in the previous section identi�ed 10 UUVs which have successfully imple-

mented a PID controller. Of these 10 vehicles, performance data has not been pub-

lished for 5 of them (SPARUS [158], REMUS [156], ORCA [155], Ictineu [9] and ARCS

[151]) however the apparent success of the vehicles suggests that the performance was

acceptable.

Experimental data for the other 5 vehicles was available and all but 1 of them had, in

general, good performance. The KwaZulu Natal AUV [152] used PID control for all

DOF. The depth controller provided a response which oscillated in steady-state (SS)

with an amplitude of 0.2m and a frequency of 0.1Hz. The heading controller oscillated

in SS, however the amplitude and frequency were not constant. The horizontal control

system had an accuracy of less than 0.5m.

The OBERON AUV [153] used PID controllers for depth/altitude. The vehicle mission

presented was to stay at a �xed height above the sea �oor (1.5m). The vehicle was able

to do this with a standard deviation of 0.2m. It is interesting to note that OBERON

was positively buoyant and the thrusters were permanently turned on to overcome this.

ODIN was used as a test bed for controller development for many years and several

forms of PID controller were implemented on it [154]. A manually tuned PID controller

provided adequate performance, however an adaptive tuning algorithm was developed

to overcome PID performance degradations caused by disturbances.

The THETIS AUV used a PI controller with an antiwind-up compensator [160]. The

parameters were manually tuned and from the published results, the best results had

an overshoot of approximately 2.5cm with slight oscillations in SS.

The �nal vehicle, Subjugator [159] su�ered from poor performance when there was noise

or disturbances. A Sliding Mode Controller was used in place of the PID controller.

6.6 Robust Control

One of the biggest problems in designing control systems lies in the accuracy of the

model for the plant which is to be controlled. There are two types of inaccuracies

which can arise in the modelling of the plant; parametric uncertainties and unmodelled

dynamics. Underestimating the drag of a vehicle would be a parametric uncertainty

143


whilst treating the drag of a vehicle as linear, rather than quadratic, would be an

unmodelled dynamic [143].

6.6.1 Overview

There are two main control strategies which can be used in dealing with these issues;

robust control and adaptive control. The two approaches have di�erent strengths and

weaknesses but are not mutually exclusive and can be combined to provide higher

performance but at greater computational expense. Both types of controller are non-

linear.

Robust control is well suited to dealing with disturbances, quickly varying parameters

and unmodelled dynamics whereas adaptive control is suited to dealing with uncer-

tainties in constant or slowly varying parameters. Adaptive control also requires less

prior knowledge of the plant [143] than robust control.

A popular robust control strategy is the Sliding Mode Control (SMC) method. As

Table 6.4 illustrates, this type of controller has been successfully implemented on at

least four UUVs.

6.6.2 Analysis of Sliding Mode Control

SMC is used generally modelled in state-space and the aim is to get the state x to

track a speci�c time-varying trajectory xd =[xd xd xd

]in the presence of modelling

inaccuracies [143]. For this to be successful, the initial desired state xd(0) = x(0),

i.e. there should be no step changes at time t = 0. If there are step changes, the

tracking will only be achieved after a transient. As detailed in Section 7.6.3, the SMC

implemented on the µAUV used the simpli�cation of step changes in the input instead

of time-varying trajectories. Modifying the inputs so that they are time-varying will

form part of the future work.

To illustrate the robustness to parameter uncertainties and the e�ects of chattering and

tracking trajectory simpli�cation, a simple example is presented, taken from [143]. The

equation of a second order system is given by Equation 6.8, where there is uncertainty

in the parameter α(t) such that 1 ≤ α(t) ≤ 2.

144


x = f + u

x+ α(t)x2 cos 3x = u (6.8)

The estimation error on the plant, f , is bounded by some known function F such that

|f − f | ≤ F , where f is the estimate of the plant. Given the bounded uncertainty,

f = −1.5x2 cos 3x and F = 0.5x2| cos 3x|.

The sliding surface is de�ned in Equation 6.9. The aim of sliding mode control is to

ensure that s = 0 [143]. The control law which will ensure that this criteria is met is

given by Equation 6.10. u is the continuous control law and is described by Equation

6.11. The speci�c control law for this example is given in Equation 6.12. λ = 20 and

η = 0.1.

s = ˙x+ λx (6.9)

u = u−Ksgn(s) (6.10)

u = −f + xd − λ ˙x

k = F + η (6.11)

u = 1.5x2 cos 3x+ xd − 20 ˙x− (0.5x2| cos 3x|+ 0.1)sgn(s) (6.12)

Figure 6.10 shows the output response of the system when the input is given by

xd = sin(πt2

). α was set to | sin t| + 1. It can be seen that there is a high level of

control action in the form of chattering. To reduce this, a saturation function can be

used instead of the sign function. The saturation function takes the form shown in

Equation 6.13 and the response when this is used is shown in Figure 6.11. φ was set

to 0.1.

sat

(s

φ

)=

{sgn(s) if | s

φ| > 1

sφ

otherwise(6.13)

145


Figure 6.10: Output Response for SMC Simulation with Sign Function and SecondDerivative Trajectory Tracking

Figure 6.11: Output Response for SMC Simulation with Saturation Function and Sec-ond Derivative Trajectory Tracking

146


Figure 6.11 shows that the control action has reduced and there is less chattering. This

reduction in chattering comes at the price of increased tracking error. The tracking

error increases further if the second order trajectory derivative, xd, is removed as shown

in Figure 6.12.

Figure 6.12: Output Response for SMC Simulation with Saturation Function and NoSecond Derivative Trajectory Tracking

6.6.3 Review of UUV Sliding Mode Implementations

Three vehicles implemented a Sliding Mode Controller; Benthos RPV-430, the Ham-

burg ROV and Subjugator. The Benthos RPV-430 was the �rst AUV to use Sliding

Mode and the performance of the controller was concluded to be good [166]. The

parameter uncertainties for the model were 50%.

The Hamburg ROV's implementation was successful, however there was approximately

5cm overshoot on the initial set-point and minor oscillations at SS [167]. When im-

plemented on the Subjugator AUV, the control strategy performed acceptably in the

presence of parameter uncertainties.

147


6.7 Summary

This chapter has reviewed the di�erent types of control system which have been devel-

oped for UUVs. 56 UUV/controller combinations have been identi�ed, however only

19 of them have been implemented. The main two control strategies which have been

used are PID and Sliding Mode and these have been reviewed in more detail.

The ideal 4 DOF equations of motion for the µAUV have also been presented. These

equations are non-linear and coupled and a justi�cation for not linearising them has

been given. The method of modelling (symbolic Input/Output di�erential equations)

has also identi�ed and justi�ed.

148

Chapter 7

Control of Heave

Chapter 6 introduced the ideal model for the prototypes developed in Chapter 5. A

review of control systems used on other AUVs was also conducted and two controllers,

PID and Sliding Mode, were identi�ed as being of interest to this work.

It was concluded in Chapter 6 that the control system for 3D movement could be

separated into a number of simpler controllers for heave, yaw and surge and sway. The

individual controllers could be developed and tested in isolation before being merged.

The decision was made to start the control system design using the heave DOF. This

was done for two reasons. Firstly, the input sensor (pressure, Section 5.5.2) was reliable

and stable. The input sensors for yaw su�ered from high levels of noise and drift

(Sections 5.5.3 and 5.5.4) and the acoustic positioning system (APS) for horizontal

position estimates was not available (Section 5.5.1).

The second reason was that the model for heave was relatively simple, as it had no

cross-coupling terms with other DOF. Controllers developed for heave could also, in

principle, be used as a basis for surge and sway control.

This chapter presents the work conducted on the development of a heave controller

using both the MK V and MK VI prototype vehicles. Development of controllers for

yaw and surge and sway are detailed in Chapter 8. The control outputs of selected

simulations and experiments can be found in Appendix I.1.

7.1 Motion Scenarios

Before developing a control system, the type of motion required needs to be considered.

As detailed in Section 2.1, the demonstrator for the AASN4IP project is for use in a

149


nuclear storage facility. Two modes of operation were initially envisaged for the vehicle:

continuous mapping and spot measurements.

A simple mapping scheme, as described in Section 3.3.3, would require the vehicle to

travel lengths of the storage pond at a speci�c depth. Once measurements have been

taken at one depth, the vehicle would descend to the next depth and repeat the process.

Taking spot measurements would require the vehicle to move to a speci�c location and

hold station whilst samples are collected.

From the operational modes described, the set-point inputs for the vehicle could be

either a step or a staircase (a series of steps). These are the two types of inputs which

were used during simulation and in experimental testing.

7.2 Simulation Environment

As outlined in Section 6.3.2, the chosen method of computationally modelling the plant

and controllers was a symbolic representation of the input/output di�erential equations

based in MATLAB/SIMULINK.

Each DOF was modelled as a separate sub-system which allowed simulations to be

conducted on each one independently or all together. An individual DOF could be run

in either open-loop or closed-loop mode. The parameters for the model were edited in

an accompanying MATLAB m-�le which allowed changes to be made with ease.

To solve the di�erential equations, a �xed-step discrete time solver was used. The

time step was nominally 0.1s, however this could be varied for each DOF to allow for

accurate modelling of di�erent controller operating frequencies.

The model could operate in either `ideal-world' or `real-world' mode. The `ideal-world'

mode simulates the vehicle without measurement errors, noise or thruster variations.

These can be added by switching to `real-world' mode which was controlled by a single

variable in the m-�le.

The inputs to the model were set using a signal builder which could generate mul-

tiple signals at the same time with a range of complexities such as steps, staircases

or sine waves (for advanced horizontal motion simulations). Any inputs, outputs or

intermediary parameters could be saved to the workspace and plotted on graphs for

analysis.

Non-standard functions such as the Kalman �lters and the thruster matrices were

implemented using embedded MATLAB functions. These functions were written at the

level of abstraction of `C' code to facilitate porting to the embedded systems hardware.

150


7.3 Experimental Facilities

During the course of the work, three testing facilities, suitable for heave control experi-

ments, were available. The �rst was a 1m deep oil drum which was used to test the MK

V prototype. The second was 6m x 6m x 6m concrete pond operated by the National

Nuclear Laboratory (NNL) at their Workington facility. This was only available once

and was used for both depth tests and initial yaw control experiments using the MK

V vehicle.

The �nal test facility was a 2m x 1m x 1m tank which only became available after the

visit to the NNL facility. Both the MK V and MK VI prototypes were tested in this

tank. Results will be presented from tests conducted at the NNL facility and the 2m

tank.

7.4 Heave Model

The equation of motion for heave, isolated from Equation 6.2 in Section 6.3 is shown

in Equation 7.1. mt is the total mass of the vehicle (including added mass), mi is the

imbalanced mass1, g is the gravitational constant, dt is the drag force and τ is the

thrust force.

mtν3 + dt|ν3|ν3 +mig = τ3 (7.1)

As discussed in Section 6.3, the heave DOF is open-loop unstable due to the buoy-

ancy force. This means that the thrusters will have to be permanently turned on to

overcome it. This buoyancy force will also cause a steady-state (SS) error which can

be compensated for in the control system by adding an additional term to the thrust

output [55]. This requires an estimate of the magnitude of the imbalanced force which

is di�cult to achieve in a practical environment. For this reason the term was not

added to the controller. Alternatively, integral action can be used to reduce the SS

error as will be discussed in Section 7.5.1.

One of the sources of non-linearities in the heave model is actuator saturation (maxi-

mum and minimum thrust force), and was modelled using Equation 7.2. The values of

Fmax and mi were di�cult to estimate and were therefore classed as free parameters.

When analysing the experimental data and comparing it with the simulations, these

1This is the mass causing the negative or positive buoyancy and not the ingested mass, as detailedin Chapter 4, for a static VDS.

151


two parameters were used to tune the simulation so that it matched the experimental

results.

−Fmax ≤ τ3 ≤ Fmax (7.2)

7.5 MK V Implementation and Evaluation

The initial attempt at heave control was based on a PIDγ scheme as described in

Section 6.4. The controller was developed using the SIMULINK model described in

Section 7.2 before being translated into `C' and implemented on the prototype vehicle.

The heave DOF was modelled in isolation with respect to the other 3 DOF. Table 7.1

shows the parameter values which were used in the plant. These values are similar to

those used in the parametric model in Chapter 3.

Table 7.1: µAUV Heave Simulation Plant ParametersParameter Value Parameter Value

mt 2.65kg mi 0.001kgdt 4.1527N |Fmax| 0.08mN

The initial version of the simulation model was implemented in continuous time. This

did not represent the actual implementation, however it made development of the

controller easier. Figure 7.1 shows the closed-loop response for a step input of 1m. The

simulation was executed in the `ideal-world' mode so there was no measurement noise.

The parameters for the controller (Equation 6.6 in Section 6.4) are given in Table 7.2.

These parameters were obtained through a manual tuning process.

Table 7.2: Continuous Time PIDγ Controller ParametersParameter Value Parameter Value

kp 1 Ti 200ki 0.01 Td 0.25kd 20 γ 0.05

It can be seen in Figure 7.1, that the response has a rise time of approximately 12s and

a SS error of -10mm. This error is caused by both the buoyancy force and too little

integral action as discussed in Section 7.5.1.

In the prototype implementation, the input to the heave controller is obtained from

a pressure sensor (Section 5.5.2). The measurements from the sensor are subject to

152


Figure 7.1: Closed-Loop Response for A Step Input, Positive Buoyancy of 1g

Gaussian noise and so the next step of the controller design was to investigate what

e�ect this noise had on the response.

Gaussian noise was added to the simulation with a variance of 6.97x10−6m2. The

error statistics were obtained from experiments conducted on the pressure sensor as

described in Section 5.5.2. Figure 7.2 shows the step response and it can be seen that

the addition of the noise has caused both high and low frequency components to appear

in the response.

The derivative term in the controller can amplify high-frequency components of the

noise (Section 5.6) and therefore a low-pass �lter was added to the design [210]. The

transfer function of the �lter is shown in Equation 7.3. Y is the output of the �lter, kfis the �lter gain and Tf is the �lter time constant. Figure 7.3 shows the step response

(green) when the low-pass �lter coe�cients are both set to 1 (obtained through a

process of trial and error). It can be seen that the response is almost identical to the

original simulation results in Figure 7.1.

Y (s) =kf

Tfs+ 1E(s) (7.3)

153


Figure 7.2: Closed-Loop Response for A Step Input, Positive Buoyancy of 1g withAdded Gaussian Input Noise

Figure 7.3: Closed-Loop Response for A Step Input, Positive Buoyancy of 1g withAdded Gaussian Input Noise and Low-Pass Filter

154


To implement the controller on the embedded system, it is necessary to discretise

the transfer function. This can be achieved by applying the Bilinear Z Transform,

or Tustin approximation [211]. The full transformation from the continuous time to

discrete time forms can be found in Appendix H. The resulting di�erence equation is

shown in Equation 7.4, with u the output of the controller, e the input of the controller

and hn the discretised controller coe�cients (given in Appendix H).

u[n] =h1u[n− 1] + h2u[n− 2] + h3u[n− 3]+

h4e[n] + h5e[n− 1] + h6e[n− 2] + h7e[n− 3]

(7.4)

An initial estimate for the required sampling frequency was obtained by a simple lin-

earization of the plant. The linearised form was not used for any other control design

due to the problems highlighted in Section 6.3.1.

The sampling frequency can be estimated by calculating the bandwidth of the closed

loop transfer function. The general rule is that the sampling frequency should be 2

to 30 times the closed loop bandwidth [212, 213]. The linearisation was done using a

Taylor series expansion and can be found in Appendix I.

The bandwidth of the resulting closed loop system was found to be 0.1567Hz, meaning

that the sampling rate should be between 0.31Hz and 4.65Hz. Higher sampling fre-

quencies could be used and may improve the response of the controller. Initially, the

sampling frequency was set to 1Hz, although this was later changed increased to 10Hz

so as to match the sampling frequency of the yaw control (discussed in Chapter 8).

The coe�cients estimated for the continuous time simulation required re-tuning after

discretisation and are shown in Table 7.3, which leads to the di�erence equation in

Equation 7.5. As discussed in Section 5.9, �xed-point arithmetic was used for the

MK V implementation. Figure 7.4 shows a step response comparison between the

continuous time simulation and the di�erence equation implementation.

It can be seen that the discretised implementation tracks its continuous time counter-

part well, however there is a slightly larger steady state error of approximately 30mm.

This suggests that the discrete time form of the controller is less robust to the e�ects

of the buoyancy force. The cause of this could be due to the rounding functions used

in the �xed-point implementation.

155


Table 7.3: µAUV Simulation ParametersParameter Value Parameter Value

kp 0.5 Ti 100ki 0.01 Td 2kd 1 γ 0.05

u[n] =3u[n− 1] + 3u[n− 2]− u[n− 3]+

6e[n]− 5e[n− 1]− 6e[n− 2] + 5e[n− 3]

(7.5)

Figure 7.4: Step Response Comparison Between Continuous and Discrete Time Simu-lations

Table 7.4 shows a comparison of the simulated response parameters and the quantita-

tive speci�cations given in Section 6.2.1. It can be seen that the controller meets all

but one of the speci�cations. It has already been established that the SS error is a

function of the ballasting and could increase if the vehicle is ballasted incorrectly. As

will be discussed later in the chapter, the rise time also dependent on the ballasting of

the vehicle.

156


Table 7.4: Quantitative Speci�cation ComparisonSpeci�cation Simulation

Overshoot ≤25mm 0mmSS Error ≤ ±25mm -30mm

SS Osc. Amp. ≤ ±15mm ±10mmSS Osc. Freq. ≤1Hz 0.1Hz

7.5.1 Steady-State Error Elimination

In the simulations shown in Figures 7.1, 7.2, 7.3 and 7.4, there has been a steady-state

error caused by the imbalanced buoyancy force. The use of integral action in the PID

controller should have eliminated this however, as discussed in Section 6.4.

Figure 7.5 shows an `ideal-world' simulation based on Figure 7.4, run for an extended

period of time. It can be seen that the integral action does eventually eliminate the SS

error, however it takes over an hour to do so. To reduce this time, the integral action

could be increased, however this would increases the transient e�ects such as overshoot

as shown in Figure 7.6.

Figure 7.5: Extended Simulation to Observe E�ects of Integral Action for ImbalancedMass of 1g

157


Figure 7.6: Simulation of Increased Integral Action for Imbalanced Mass of 1g

Simulations also show that the magnitude of the buoyancy force also a�ects the re-

sponse. Figure 7.7 shows the response when the imbalanced mass is increased to 2g.

It can be seen that the integral action takes even longer to eliminate the SS error. The

control outputs for each of these simulations can be found in Appendix I.1.

These simulations show that there is a trade-o� between transient response and SS

error. The integral action can eliminate the SS error, however the length of time it

takes to do so depends on the magnitude of it and the magnitude of the buoyancy force.

Tuning the integral action for a speci�c buoyancy force may provide a poor response

if that force changes, suggesting that some form of adaptive integral action may be

required. This is a topic for future work.

7.5.2 Heave Experiments

The controller was implemented on the MK V embedded system hardware and exper-

iments conducted at a number of test facilities (detailed in Section 7.3). The experi-

mental results presented here are taken from tests conducted in the NNL facility and

in the 2m tank in the university. Figure 7.8 shows the MK V being tested in the NNL

pond (right) and the 2m tank (left).

The �rst set of experiments to be conducted had the vehicle descending to a single depth

158


Figure 7.7: Extended Simulation to Observe E�ects of Integral Action For ImbalancedMass of 2g

Figure 7.8: MK V Prototype Being Tested On-Site at NNL (Right) and in the 2mTank at the University (Left)

and holding station there. Pressure readings (depth) were stored in the embedded

system's �ash memory and were accessed after the experiment. Figure 7.9 shows a

comparison of a `real-world' simulation (green) against actual depth (red) for a step

input of 1m. It can be seen that the actual experimental data di�ers signi�cantly from

the simulated response during the rise time, shown in Figure 7.4, however the two agree

closely once the target depth is reached.

The two free parameters, mi and Fmax, were varied in an attempt to match up the

simulation with the experimental results as shown in Figure 7.9. The values that

159


Figure 7.9: Comparison of Experimental Results for Step Input of 1m in the NNL Pondand `Real-World' Simulation

provided the best �t were mi = 3.5g and Fmax = 35.3mN. Although there is no easy

way of directly and accurately measuring the imbalanced mass of the node, 3.5g appears

to be a highly plausible value.

Ballasting of the µAUV was done by trial and error and consisted of adding or removing

lead shot from the vehicle. A mass of 3.5g is equivalent to approximately 50 pieces of

lead shot. The total lead shot in the vehicle is estimated at over 8000 pieces which

highlights the challenge in achieving accurate ballasting. Figure 7.10 shows 3.5g of

water.

Figure 7.10: 3.5g of Water

Direct thrust measurements for the MK V, taken prior to the thrusters being mounted

on the hull, suggested a total thrust output of 37mN downwards and 69mN upwards.

160


The di�erence between the values is due to the shape of the propeller. It can be seen

that the estimated thrust force (for downwards) is only 1.7mN (5%) less than the

directly measured value.

The upward drift of the µAUV observed in the experimental results in Figure 7.9,

is most likely caused by the thrusters not producing enough thrust to overcome the

positive buoyancy force. When the µAUV is near the set-point, the controller reduces

the output thrust so as to reduce the velocity. If this thrust is too low, a drift will occur.

If the system is negatively buoyant, this drift is downwards and has been observed in

other tests.

The solution to the above problem is to increase the thrust force around the set-point,

however this has the e�ect of increasing the amplitude of oscillation, which means that

there is a trade-o� between drift and oscillations.

The single depth test was repeated with the same µAUV in the 2m tank within at the

university. Due to the depth restrictions, the set-point was changed to 0.5m. Figure

7.11 shows the step response. For this test, the free parameters in the simulation were

changed to 28mN and +1.5g, to optimise agreement between the simulation and the

experiment. These estimates of thrust and buoyancy are in broad agreement with

the values obtained by comparing the NNL tests results with the simulation. One of

the thruster units developed a minor fault2 prior to the test which could explain the

reduction in estimated thrust.

The second set of experiments required the µAUV to descend to and ascend from mul-

tiple depths and the results are shown in Figure 7.12. This experiment was conducted

in the NNL pond with the µAUV positively buoyant. The vehicle was required to move

between depths of 0.33m, 0.66m and 1m, staying stationary for approximately 40s at

each one.

The green line in Figure 7.12 shows the simulated response with the free parameters

being set to 35.4mN and +1g. The response undershoots the set-point on the descent

and overshoots on the ascent. The actual response (shown in light blue) does not,

however, do this. Approximately 150s into the experiment, the µAUV overshoots the

set-point and for the ascent, behaves as if it were negatively buoyant.

An analysis of the bottom step of Figure 7.12 indicates that for the simulation to match

the actual response, mi should be -1g. This would suggest that the µAUV had leaked

and taken on water. Assuming this scenario to be true, the simulation was modi�ed

to take into account a change of mass.

2It was visually observed that the thruster unit was rotating signi�cantly slower than expected.

161


Figure 7.11: Experimental Results for Step Input of 0.5m in The University Tank

Figure 7.12: Experimental Results for a Staircase Input

The modi�ed simulation is indicated by the red line. It was estimated that the µAUV

had taken on approximately 2g of water during the time period 130s to 170s, changing

162


the buoyancy from +1g to -1g. It then took on a further 1g of water at around 200s

and 0.5g around 250s. In total, the simulation suggests that 3.5g of water leaked into

the µAUV over the course of the experiment.

Leakages of small amounts of water are di�cult to identify when the µAUV is inspected

after the experiment as the water runs into the lead shot ballast. Separate tests of the

MK V hull indicated that it leaked small amounts of water at depths below 1m.

7.5.3 Summary

A PIDγ controller was developed for heave for the MK V prototype and was successfully

implemented and tested at two di�erent test facilities. It was found that mechanical

problems with the hull seal meant that the magnitude and sign of the SS error was not

constant due to changes in the buoyancy force. Ballasting was also found to impact

the SS error.

7.6 MK VI Implementation and Evaluation

The development of the MK VI prototype provided an opportunity to improve the

vertical controller by modifying the existing controller, improving the simulation model

and by investigating other control strategies.

Two major changes were initially made to the MK VI: the control frequency was in-

creased to 10Hz and the controller was implemented in �oating-point form.

The control operating frequency was initially chosen based on an estimate of the band-

width of the closed loop transfer function (Appendix I). As will be discussed in Chapter

8, the sampling frequency for the yaw control was 10Hz. To simplify the software im-

plementation, all the vertical controller was modi�ed to operate at the same frequency.

As discussed in Section 5.9, it was found that the �xed-point implementation of the

controller was slower than the �oating-point implementation due to a custom rounding

function which was required. Floating-point implementations can be more accurate so

this method was on the MK VI.

7.6.1 Improving the Simulation Model

During experimental testing of the vertical control system, it was observed that there

was both undesired rotational and translational movement in the horizontal plane.

163


Unfortunately, the assumptions made with regard to the decoupling of the individual

DOF in the model (Section 6.3) are overly simplistic.

Figure 7.13 shows plan-view stills from a video of one of the experiments. Time in-

creases through images 1 to 4. It can be seen that at the start, the vehicle is pointing

upwards in the frame. As it descends, it rotates anticlockwise through 90◦(image 2).

Once it reaches its set depth, it starts rotating clockwise and translating towards the

right and slightly upwards (image 3). It continues this clockwise motion but moves

downwards in a spiral movement (image 4). The total translational distance moved

towards the right is around 0.5m.

Figure 7.13: Translational and Rotational Motion During Vertical Controller Experi-ments

Having observed that the real vehicle did not behave as expected, the sources of model

inaccuracies had to be identi�ed. One of the aims of the project is to use o�-the-

shelf components wherever possible so that the cost of an individual µAUV is kept

as low as possible. This raises a number of challenges due to the fact that low-cost

components are often low-tolerance. There are two main issues which impact on the

model described in Section 6.3: lack of component homogeneity and µAUV fabrication

tolerances.

The lack of component homogeneity (time-varying and imbalanced thrust) was iden-

ti�ed and discussed in Section 5.4.3, however the e�ects were not modelled in the

simulation. The two e�ects of time-varying and imbalanced thrust can be modelled

in di�erent ways. The imbalanced thrust was modelled by modifying Equation 7.2 so

that there were di�erent values for Fmin and Fmax for each of the thrusters. O�-line

experiments with the motors suggest that the time variability could be modelled by

164


adding sinusoidal noise to the thrust value so that Equation 7.2 can be written as

Equation 7.6.

Fmin ≤ FB ≤ Fmax

F = FB + AF sin(ωF t+ ϕF )(7.6)

In the model, the output thrust is bounded before the noise is added. For the purposes

of the simulation, the noise frequencies were set between 0.05Hz and 0.1Hz, with an

amplitude of up to ±10% of Fmax and a phase change between thrusters of up to

60◦. These values were based on experimental results from the force measurement rig

(Section 4.6).

The second major challenge was related to the fabrication of the hull and the mounting

of the thruster units. As highlighted in Figure 7.13, motion in the vertical plane ap-

peared to cause horizontal rotation and translation. The direction of rotation changed

once the vehicle had reached the set-point and observations suggested that this was

related to the direction of thrust.

It was hypothesised that the heave thrusters were not mounted exactly vertically. This

meant that there were components of force acting in the other three DOF, e�ectively

coupling all four DOF. The coupling between motion in the vertical plane and the

horizontal plane was modelled by accounting for the geometry of mis-alignment in

the thruster allocation matrix as shown in Equation 7.7. Figure 7.14 is a graphical

representation of how the direction of thrust would a�ect the direction of rotation.

The thrust components were calculated based on a angle of rotation from the Z-axis to

the X- and Y-axis (α and β respectively). Using the direction cosine rule, the overall

angle of rotation from the Z-axis (γ) can be calculated.

τ1

τ2

τ3

τ6

=

1 1 0 0 cos(α5) cos(α6)

0 0 1 1 cos(β5) cos(β6)

0 0 0 0 − cos(γ5) − cos(γ6)

−r r −r r − cos(α5)r cos(α6)r

F1

F2

F3

F4

F5

F6

(7.7)

If the vertical thrusters are misaligned, it seems logical that this may also be the case for

the horizontal thrusters. However, the vehicle is ballasted in such a way that movement

in roll and pitch is not possible. The distribution of the mass in the vehicle means that

the components of force caused by horizontal misalignment do not have any a�ect on

165


Figure 7.14: Graphical Representation of the E�ects of the Direction of Thrust on theDirection of Rotation Caused By Thruster Misalignment

the other DOF.

The hypothesis was tested by simulating the µAUV descending to a depth of 1m. The

thruster mis-alignments were initially set as follows: α5 = 89◦, α6 = 89.5◦and β5 and

β6 = 90◦(i.e. no mis-alignment with respect to the y-axis). Figures 7.15 and 7.16 show

the results.

Figure 7.15 shows a 3D plot of the trajectory of the vehicle (red line) and the orienta-

tion (black arrow). It can be seen that the µAUV rotates and moves laterally in the

horizontal plane.

Figure 7.16 shows the 2D plot (a plan view of the X-Y plane) of the same simulation.

The vehicle starts at the position (0,0) facing right. As it descends, it rotates anti-

clockwise and moves horizontally in a spiral. Once it has reached the x position of

around 0.2m, it starts to rotate clockwise. This is when the µAUV has reached the

target depth and the motors have changed direction. Since the vehicle has been made

slightly positively buoyant to aid recovery if power fails, the thrusters have to be

constantly active even when the set-depth has been reached. At the target depth,

the motors alternate direction to overcome the buoyancy force. The horizontal spiral

continues, but the radius decreases as the motors are continually changing direction to

keep at the set depth.

166


Figure 7.15: 3D Simulation of Vertical Descent With Imbalanced, Time-Varying Thrustand Vertical Thruster Misalignment

Figure 7.16: 2D Simulation of Vertical Descent With Imbalanced, Time-Varying Thrustand Vertical Thruster Misalignment

167


The results of the simulation match very well with the observations made during the

actual experiments. The most important observation to come out of the simulations

was the order of magnitude of the misalignment angle necessary to cause spiralling. For

the simulations shown in Figures 7.15 and 7.16, the angles were 0.5◦ and 1◦ respectively

from the vertical, relative to the X-axis. These angles were obtained through a processes

of systematic simulation study.

The current standard of fabrication within the university is not su�cient to eliminate

misalignments of this order. More expensive fabrication methods could be employed,

but this would negate the aim of developing a low-cost vehicle. The coupling issues

must therefore be addressed by the control system.

7.6.2 PID Controller

The same PID controller as used with the MK V prototype was implemented on the

MK VI with the two modi�cations detailed earlier; an increased sampling rate and a

�oating-point implementation. Figure 7.17 shows the results of an experiment con-

ducted in the 2m tank.

Figure 7.17: Comparison of Simulation and Experimental Results for a PID ControllerImplemented on the MK VI Prototype

168


Figure 7.17 also shows the simulated response. The buoyancy mass was tuned to -1g

and the total thrust force to Fmin = -67mN and Fmax = 39mN. It appears as if there

is more measurement noise compared to the MK V data, however this is attributed to

the increased sampling frequency.

It was found that another of the plant parameters had to be modi�ed to ensure that the

simulations matched the experimental data. The drag force for the vehicle was based on

the model used in Chapter 3 and assumed that the hull was a perfect sphere. With the

addition of the hull seal and the thruster collar, this assumption did not hold true. To

match the simulation, the vertical drag had to be increased by a factor of 16. This value

was selected after a systematic tuning process. A number of other experiments were

conducted using the PIDγ controller and this increased drag appeared to be consistent.

7.6.3 Sliding Mode Controller

The second control system identi�ed as being of interest in Chapter 6 was Sliding

Mode. This control scheme is classed as robust and suited to dealing with disturbances

and unmodelled dynamics. The general form is given in Equation 7.8, however a form

speci�c to this work is shown in Equation 7.9 [143].

u = u−Ksat(s/φ) (7.8)

u = (m(xd − λ ˙x) + d|x|x)−Ksat(s/φ) (7.9)

With K = |(m(xd − λ ˙x) + d|x|x)|+ η and η > 0.

u is the control output, m is the estimated mass, λ the gradient of the sliding surface, d

the drag estimate, K the switching gain, s the sliding surface, φ the boundary thickness

and η the switching gain constant.

The simulated response of the sliding mode controller (SMC) to a step input is shown

in Figure 7.18. The simulator was operating in the `real-world' mode. The controller

parameters were manually tuned as follows: λ = 0.2, φ = 0.1, η = 1 and the parameter

uncertainty was set to +10%. The thrust values were the same as used in the simulation

for Figure 7.17. It should be noted that the second order derivative of the trajectory

tracking has been removed (set to zero) for simpli�cation.

Figure 7.18 shows that the steady-state response of the SMC is much better than that

of the PIDγ controller shown in Figure 7.17 (it is less oscillatory). Increasing the size

of the parameter uncertainty to 50% [166] had no noticable e�ect on the performance.

169


Figures 7.19 and 7.20 show the trajectories tracking to the sliding surface for both the

`ideal' and `real' world simulations with 10% uncertainty.

Figure 7.18: Simulated Response of the Sliding Mode Controller with Parameter Un-certainties of 10% and 50%

Figure 7.19: Plot of the Trajectory Tracking to the Sliding Surface in the `Ideal-World'Simulation with 10% Uncertainty

Figure 7.21 shows the response to a staircase input (with a parameter uncertainty

170


Figure 7.20: Plot of the Trajectory Tracking to the Sliding Surface in the `Real-World'Simulation with 10% Uncertainty

of 10%). As with the step input, the steady-state response is better than the PIDγ

controller.

Figure 7.21: Simulated Response of the Sliding Mode Controller to Staircase Input

171


The SMC is made up of two parts; the continuous control law, u, and the sliding

surface, Ksat(s/φ) [143]. The e�ect of each of these components, relative to the �nal

control output are shown in Figure 7.22. It can be seen that the e�ect of the continuous

control law is small in comparison to the sliding surface (approximately an order of

magnitude).

Figure 7.22: Sliding Mode Controller Component Comparison for φ = 0.1

To achieve the performance shown in Figure 7.18, a very small boundary thickness

was used. This has the e�ect of switching the thrust output between the minimum

and maximum values as shown in Figure 7.23. This is similar to the chattering e�ect

observed when a sign function is used instead of a saturation function [143]. Based

on the power consumption of the motors (V = 3V, Imax = 65mA), the total energy

consumed was 10.5J.

If the boundary layer thickness is increased, the relative size of the di�erent compo-

nents decreases as shown in Figure 7.25. In this simulation, the boundary thickness is

0.4. The e�ect of this is to reduce the amount of thrust required as shown in Figure

7.26, however the performance is worse as shown in Figure 7.24 (there is a very small

overshoot and steady-state error of around 20mm). The energy consumption calculated

in this simulation was 5J.

172


Figure 7.23: Total Vertical Thrust Output for φ = 0.1

Figure 7.24: Sliding Mode Controller Response for φ = 0.4

173


Figure 7.25: Sliding Mode Controller Component Comparison for φ = 0.4

Figure 7.26: Total Vertical Thrust Output for φ = 0.4

174


The conclusion that can be drawn is that, for the magnitude of the model parameters

used in this simulation, there is a trade-o� between performance and energy consump-

tion. One factor that needs to be considered is the quality of the thruster units.

As detailed in Section 5.4.3, the individual thruster units have low tolerances. In

addition to the time-varying imbalanced thrust, the thrust output at low voltages

cannot be guaranteed. The output thrust is non-linear with voltage and observations

have indicated that the thrust output at low voltages may not be what is expected.

This means that the thrusters may not be able to provide the thrust shown in Figure

7.26.

In terms of the controller performance, it is desirable to minimise the overshoot so that

the vehicle does not collide with objects in the pond. When the thrust output issues

are taken into account, this suggests that a thin boundary layer should be used.

The drawback with using a thin boundary layer is the energy consumption. The

controller with a boundary thickness of 0.4 consumed approximately 48% less energy

than when a boundary thickness of 0.1 was used. Whilst energy consumption is an

important consideration, the performance and thrust output outweighs it. This decision

may be revisited in future designs.

7.6.4 Bounded PD Control

In the previous section, it was observed that SMC had a better steady-state response

compared with the PIDγ controller. It was also observed that the continuous control

law component of the controller, was much smaller than the sliding surface component.

If the continuous law component is removed, it can be seen that the SMC simpli�es to

a bounded PD controller as shown in Equation 7.10.

u = Ksat

( ˙x+ λx

φ

)(7.10)

Figure 7.27 shows a comparison of the bounded PD controller and the full SMC. It can

be seen that there is very little di�erence between the two controllers. The parameters

of the bounded PD controller were the same as the SMC but with the gain, K = 1.

The bounded PD controller was implemented on the MK VI prototype and Figure 7.28

shows the results of an experiment conducted in the 2m tank. It can be seen that the

response is stable with a SS error of approximately 20mm. The oscillations observed

with the PIDγ controller in Figure 7.17 are not present, apart from towards the end

when the vehicle collided with the side of the tank due to the unwanted horizontal

175


movement discussed in Section 7.6.1. This experiment (without the collision) was

repeated a number of times with the similar results.

Figure 7.27: Comparison of Sliding Mode and Bounded PD Controllers: SimulationResults

Figure 7.28: Bounded PD Controller Experimental Results

176


At this point it should be noted that the bounded PD controller requires both positional

data and velocity data as inputs3, unlike the PIDγ controller which only requires

position. As discussed in Section 5.6, a Kalman �lter was required to obtain accurate

velocity estimates and the response when used is shown in Figure 7.28. Figure 7.29

shows the results of an experiment where the Kalman �lter was not used and the

velocity was obtained through numerical di�erentiation.

Figure 7.29: E�ects of Numerical Di�erentiated Velocity Estimates on Bounded PDController Response

A direct comparison of the bounded PD controller and the PIDγ controller was con-

ducted by changing the controller in software once the vehicle had reached the set-point.

Figure 7.30 shows the bounded PD controller operating for the �rst 80s then the PIDγ

controller operating thereafter. It can be seen that the performance of the bounded

PD controller is better than that of the PIDγ based approach.

Figure 7.31 shows the results of an experiment conducted using a staircase input. It

can be seen that the controller performs as expected. As with the MK V experiment

in Figure 7.12, the MK VI leaked and the buoyancy changed from positive to negative,

however it was more robust to the change compared with the PIDγ controller shown

in Figure 7.12 in Section 7.5.2.

3The SMC also requires both position and velocity data.

177


Figure 7.30: Comparison of Bounded PD Controller and PID Controller

Figure 7.31: Bounded PD Controller Response to Staircase Input

178


7.7 Summary

This chapter has presented the development of control systems for vertical motion of

the µAUV. A comprehensive model was developed in SIMULINK/MATLAB which

allowed the controllers to be simulated before being implemented on the prototype

vehicles.

Initially, a PIDγ controller was implemented on the MK V prototype and experiments

conducted at facilities both within the university and operated by the NNL showed

good performance. Free parameters in the simulation were tuned to better match the

experimental data. Additions were made to the model to account for experimental

observations such as coupling between motion in the horizontal plane and the vertical

axis and thruster variations.

A more robust control strategy was also investigated in the form of a sliding mode

controller. It was observed that the performance was better than the PID controller,

however the speci�c tuning meant that the continuous control law did not have a

signi�cant a�ect. A simpli�cation of the SMC, in the form of a bounded PD controller

was simulated and tested which had the continuous control law removed.

The bounded PD control was implemented on the MK VI prototype and experiments

showed that the performance of the controller was better than that of the PID con-

troller. The need for a Kalman �lter to obtain accurate velocity estimates was also

con�rmed.

179

Chapter 8

Control of Surge, Sway and Yaw

Chapter 7 presented the simulation and implementation of control systems for the heave

degree of freedom (DOF). The next stage of controller development was to design a

controller for the yaw DOF. This controller would mitigate the e�ects of the unwanted

rotations observed when moving in the vertical plane (Section 7.6.1).

Once the yaw controller was completed, investigations into closed-loop control for surge

and sway could be conducted. Due to the lack of sensors for horizontal positioning,

the surge and sway controllers could only be simulated.

This chapter presents the simulations and experimental results with regards to the

development of the low-level yaw control system. It also presents the investigation,

using simulations only, into surge and sway control and subsequently, full 3D control.

It also discusses basic high-level navigation routines and presents simulations of them.

The control outputs of selected simulations and experiments can be found in Appendix

I.1.

8.1 Yaw

As detailed in Chapter 5.5, the input sensors available for yaw were a digital compass

and a rate gyroscope. The compass provided stable but noisy measurements, whereas

the gyroscope provided less noisy measurements which were subject to drift. A Kalman

�lter was developed in Section 5.6 which fused the two data measurements together to

try and obtain a better estimate of rotational position and velocity. The yaw controllers

implemented were tested using all three measurement methods.

It was established in the previous section, that a Bounded PD controller was both

robust and computationally inexpensive and therefore the best option available for the

180


heave DOF. For completeness, all three controllers (PID, Sliding Mode and Bounded

PD) were simulated for the yaw DOF.

8.1.1 Motion Scenarios

Within the scope of the practical implementations of this work, there are two mo-

tion scenarios which were applied to the yaw DOF: station-keeping and step input.

The station-keeping scenario requires the vehicle to stay at a �xed orientation. This

is needed to overcome the e�ects of the unwanted rotations caused by the vertical

thrusters.

The second scenario requires the vehicle to rotate to a given orientation and stay there.

This could be used when the µAUV is scanning a particular area or when it is combined

with the surge and sway controllers as part of a horizontal controller or open-loop dead-

reckoning system. A modi�ed version of this scenario is rotating to the points of the

compass and holding station at each one.

For the basic dead-reckoning system, the vehicle was tasked to stay on a heading of 0◦

for a �xed period of time before rotating to a heading of 180◦. This movement scenario

was also used for the surge and sway controller simulations.

Two other movement scenarios were used for the surge and sway control simulations:

moving in a 1m square both facing the direction of forward travel and staying at

a �xed heading, and moving in a downward spiral of a diameter of 1m. This last

scenario incorporated the heave control system.

8.1.2 Horizontal System Modelling

To investigate the design of the yaw controller, the model of the plant requires three

DOF in body-�xed coordinates; surge, sway and yaw. The equations of motion are

shown in Equations 8.1 and 8.2. Table 8.1 shows the parameter values used in the

simulations. The moment of inertia, I, is for a solid sphere.

For the purpose of these simulations and experiments, it was assumed that only the

surge thrusters were being used, to make the design of the control system easier.

181


mt 0 0

0 mt 0

0 0 I

ν1ν2ν6

+

0 −mν6 maν2

mν6 0 −maν1

0 0 0

ν1ν2ν6

+

dt|ν1| 0 0

0 dt|ν2| 0

0 0 da|ν6|

ν1ν2ν6

= τ (8.1)

q =

cos(q6) − sin(q6) 0

sin(q6) cos(q6) 0

0 0 1

ν1ν2ν6

(8.2)

τ = EF

τ =

1 1

0 0

r −r

[T1T2

]

−Fmax ≤ τ ≤ Fmax

(8.3)

Table 8.1: µAUV Yaw Simulation Plant ParametersParameter Value Parameter Value

mt 2.65kg I 0.00398kgm2

dt 4.1527N da 0.0232Nmr 0.075m |Fmax| 0.04N

The yaw DOF was linearised to obtain an initial estimate of the required sampling

frequency as conducted for the heave DOF in Section 7.4. The sampling frequency

range was estimated to be between 44Hz and 660Hz. Unfortunately the maximum

sampling frequency of the compass was 10Hz (Section 5.5.3), which is much lower than

the required frequency. The slower sampling frequency may reduce the performance of

the yaw controller.

Figure 8.1 shows a simulated comparison of the three di�erent controllers when the

vehicle is subject to a step input. The step is applied after 30s which means that it

subsumes both the motion scenarios described previously; station keeping for the �rst

30s then a step input followed by another period of station keeping.

The parameters for the controllers are given in Table 8.2. The parameters were tuned

manually. The simulation was conducted in the `ideal-world' simulation mode.

It can be seen that both the bounded PD and SMC controllers have better responses

182


Table 8.2: µAUV Yaw Simulation Plant ParametersParameter Value Parameter Value

kp 0.05 γ 0.05ki 0.001 Ti 1000kd 1.5 Td 0.05λ 1 φ 0.35K 0.01 Mass Estimate +10%

Drag Estimate +10%

Figure 8.1: Comparison of Control Systems for Ideal Scenario

than the PIDγ controller and that the SMC has the quickest rise-time. Figure 8.2

shows the comparison when the simulation was conducted in `real-world' mode. The

parameters for the `real-world' noise are shown in Table 8.3 and were based on error

statistics from the compass, observations made during thruster force experiments and

the qualitative speci�cations.

Table 8.3: µAUV Yaw Imperfection Simulation ParametersParameter Value Parameter ValueFx1max 0.04N Fx1min 0.02NFx2max 0.02N Fx2min 0.01NAx1 ±50%Fx1max Ax2 ±25%Fx2maxfx1 0.2Hz fx2 0.1HzPx1 0 Px2 0

183


Figure 8.2: Comparison of Control Systems for Real-World Scenario

It can be seen in Figure 8.2, that the PIDγ controller is not robust to the imperfections

added to the simulation. Further analysis indicated that it was the measurement noise

which caused the decreases in performance. The SMC and bounded PD controller

are more robust to the noise, however an oscillation has been introduced, primarily

caused by the measurement noise, although further simulations, with a higher sam-

pling frequency, suggested that the low sampling frequency of the compass may be a

contributing factor.

Whilst the SMC performed marginally better in simulations, the bounded PD con-

troller was easier to implement and had previously been implemented on the heave

DOF (Section 7.6.4). For this reason, the bounded PD controller was chosen for im-

plementation.

At this point, it is worth considering what the e�ects of the coupling is between the

yaw DOF and the surge and sway DOF. Figure 8.3 shows a plot of X-Y position (red

line) and orientation (black arrows) for the bounded PD controller in the scenario from

Figure 8.2. It can be seen that the vehicle moves forwards in the x-direction before

rotating in an arc and moving back. The cause of this movement was identi�ed as a

combination of the imbalanced thrust and the di�erence in thrust between forwards

and reverse. The only way to ensure that the vehicle stays at a given location is to

have closed-loop surge and sway control.

184


Figure 8.3: X-Y-ψ Simulated Position for Yaw Rotation Control

8.1.3 MK V Implementation and Evaluation

Only experiments using the digital compass were conducted on the MK V yaw controller

due to technical problems with the rate gyroscope. The experiments were conducted

in the 2m tank in the University.

Two di�erent scenarios were considered during the experiments. The �rst scenario was

to rotate the vehicle through 90◦ intervals and to hold station at each position for a

period of approximately 6s to 8s1. A simulation of the scenario is shown in Figure

8.4 with the experimental results shown in Figure 8.5. It can be seen that the µAUV

rotates to all the desired set points and that the amplitude of the oscillation observed

in the experiments is less than that recorded from the simulations in Figure 8.4 (around

5◦).

The spike in the response at around 67s is caused by the vehicle colliding with one

of the walls of the tank. During these experiments, translational movement is open-

1The set-points were �xed in time (changing every 10s) so the length of time held at each pointwas dependent on the time taken to rotate.

185


loop meaning that when tested in con�ned areas, there is a chance of such collisions.

This translational movement is con�rmed by the simulation results shown in Figure

8.6 which shows the X-Y position of the node for the simulation of Figure 8.4.

The second experiment was to move the vehicle in a straight line on heading of 0◦ for

20s, then rotate 180◦ and head back. The results obtained when using the compass are

shown in Figure 8.7. As with the �rst experiment, the µAUV tracked the set point with

oscillations less than the simulations predicted. The experiment was recorded using

a video camera, and the video sequence con�rms the small amplitude. In total, the

vehicle travelled approximately 1m in the 20s and rotated at a rate of approximately

45◦s−1.

The experiments conducted using the MK V prototype showed that a bounded PD

controller was a viable method and showed good results when given a step input or

a staircase input. Translational movement in the horizontal plane was caused by the

imbalanced thrust and di�erence between forward and reverse thrust output and can

only be eliminated by implementing closed-loop surge and sway control.

Figure 8.4: Simulation of Angular Position for Vehicle Rotation Test Using the DigitalCompass

186


Figure 8.5: Measurements of Angular Position for Vehicle Rotation Test Using theDigital Compass (MK V)

Figure 8.6: Simulation Results of Translational Movement for Vehicle Rotation TestUsing the Digital Compass

187


Figure 8.7: Measurements of Angular Position for Straight Line Test Using the DigitalCompass (MK V)

8.1.4 MK VI Implementation and Evaluation

The MK VI prototype allowed the controller developed for the MK V to be tested with

the digital compass, the rate gyroscope and the Kalman �lter sensor fusion as inputs.

Whilst the MK VI was being constructed, simulations were conducted with regard to

complete horizontal control, i.e. closed-loop surge, sway and yaw. The details of the

simulations are discussed in Section 8.3, however it was found that the yaw controller

parameters had to be re-tuned to take into account the interactions with the surge

and sway controllers. The modi�ed parameters were λ = 0.3, φ = 1 and K = 1. The

experiments conducted took the form of a step input of 180◦ applied after a period of

30s, similar to the MK V experiments.

Figure 8.8 shows a comparison of simulation and experimental results when using the

digital compass. It can be seen that they match fairly closely. The simulation thrust

parameters were tuned so that Fx1max = 50mN, Fx1min = 25mN, Fx2max = 40mN and

Fx2min = 20mN. These values are similar to those obtained from force measurement

tests conducted on the thruster units.

188


Figure 8.8: Comparison of Simulation and Experimental Results for Digital CompassInput (MK VI)

The experiment was repeated using the rate gyroscope as the input sensor and the

results are shown in Figure 8.9. The performance of the gyroscope is not as good

as the digital compass and the vehicle appears to drift. The likely cause of this is

the inherent drift observed in gyroscopes (Section 5.5.4). The oscillations around the

set-point are lower in frequency than with the compass, however there is less noise.

Finally, the experiment was conducted using the sensor fusion Kalman �lter described

in Section 5.6. The results are shown in Figure 8.10 and it can be seen that the

performance is the worst of the three input methods. The amplitude of the oscillations

is the largest, as is the overshoot.

The overshoot and increase in amplitude of the oscillations may have been caused by

magnetic interference on the compass due to a large steel frame around the edge of

the tank. This was not observed in the compass only tests as the vehicle stayed in

the middle of the tank, however in the Kalman �lter test, the vehicle had moved to

the edge by the time it had started to rotate. This highlights an issue which will have

to be investigated in the future (Section 9.4), which is when to switch from using the

compass due to magnetic interference.

189


Figure 8.9: Experimental Results for Rate Gyroscope Input

Figure 8.10: Experimental Results for Sensor Fusion Input Using a Kalman Filter

190


The experiments conducted using the MK VI prototype have shown that of the three

input methods, using the digital compass provides the best performance. However,

this only holds true if the µAUV is not near any magnetic objects. If this happens,

the compass data becomes unreliable.

Both the gyroscope and the sensor fusion Kalman �lter performed worse than ex-

pected. The gyroscope was subject to drift which should have been reduced signif-

icantly through calibration routines. One potential issue with the Kalman �lter is

tuning its response to fuse data from two di�erent sources which do not directly relate

to each other (i.e. integrating the gyroscope angular velocity does not yield compass

position). The use and implementation of the Kalman �lter, or an alternative form

of state estimation, is something that requires additional investigation in the future

(Section 9.4).

8.2 Yaw and Heave

Section 7.6.1 highlighted the problem of unwanted coupling between movement in the

vertical axis and the horizontal plane. Running the yaw controller in conjunction

with the heave controller should eliminate the unwanted translational and rotational

movement. Figure 8.11 shows the results of an experiment conducted using the MK V

prototype when only the vertical controller was used without a yaw controller. It can

be seen that the vehicle rotates and that the direction changes once the set-point is

reached.

Figure 8.12 shows the results of experiments conducted using the MK VI prototype

when both heave and yaw have closed-loop control. In this scenario, the vehicle is

executing a horizontal plane dead-reckoning routine, as described in the previous sec-

tion, whilst descending. The digital compass was used as the input sensor for the yaw

controller and it can be seen that the unwanted rotations have been eliminated.

The experiment presented in this section highlights the current capabilities of the

µAUV: depth control, rotational control and dead-reckoning. These capabilities are

the same as most AUVs. Videos of the individual aspects can be found on [214].

The routine has been used to demonstrate the vehicle to a number of industrialists

and researchers from Sella�eld Ltd, The Idaho National Laboratory (INL), the Korean

Atomic Energy Research Institute (KAERI) and Rolls Royce.

191


Figure 8.11: E�ects of Vertical Controller on Vehicle Rotation using MK V Prototype

Figure 8.12: Closed-Loop Control Experiment for Heave and Yaw using MK VI proto-type

8.3 Surge and Sway Simulations

As discussed in Section 5.5.1, the input sensors for horizontal position estimates were

not available. This meant that control for horizontal position could only be simulated.

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Based on the successful results obtained in Sections 7 and 8.1, bounded PD controllers

were used. All four horizontal thrusters were utilised instead of just two as used for

yaw control.

8.3.1 Simulations

Figure 8.13 shows the responses for each individual DOF to the scenario described in

the previous section. For these simulations, both the surge and sway thrusters were

used. Figure 8.14 shows the 2D position (red line) and orientation (black arrow) of

the vehicle. The simulation was run in the `real-world' mode and used the compass for

angular position/velocity measurements and included horizontal measurement noise

with a variance of 2.77e-4m2 (based on initial estimates of the acoustic positioning

system accuracy of ±5cm). Imbalanced thrust forces, the same as used for the yaw

simulations (Table 8.3 in Section 8.1.2), we're also simulated.

Figures 8.13 and 8.14 show that individual bounded PD controller for surge and sway

can be combined with the bounded PD controller for yaw to provide closed-loop hor-

izontal control. The parameters of the surge and sway controllers were both identical

and set as follows λ = 0.25, φ = 0.1 and K = 1. It was found that the original param-

eters for yaw (Section 8.1.3) had to be changed as they provided poor performance.

This was due to the interactions between the three controllers. In essence, each of the

horizontal thrusters is being controlled by two di�erent controllers. To ensure that

one controller does not always dominate, the control outputs were combined using an

adaptive form of resistive mixing (Section 6.1).

It can be observed in Figure 8.14, that the motion in surge and sway appears to be

worse (on the initial heading) than in the open-loop dead-reckoning simulations shown

in Figure 8.3. The surge and sway controllers have reduced the turning radius of the

vehicle, however the measurement noise from the APS has meant that the vehicle

appears to be oscillating in surge and sway. The actual e�ect of this on the MK VI

prototype can only be investigated once the APS has been integrated.

Figures 8.15 and 8.16 show simulations of the vehicle moving in a square path of length

1m. The vehicle starts at position (0,0) and moves towards the left in each simulation.

Figure 8.15 shows the vehicle rotating to face the direction of travel, whilst Figure 8.16

shows the vehicle with a �xed orientation for the entire mission. This shows that both

the surge and sway thrusters can be used in independently.

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Figure 8.13: Responses for Individual DOF for Horizontal Position Control

Figure 8.14: 2D Position and Orientation

194


Figure 8.15: 2D Position and Orientation with the Vehicle Rotating to Face the Direc-tion of Forward Movement

Figure 8.16: 2D Position and Orientation with the Vehicle at a Fixed Orientation

195


8.3.2 Way-Point Guidance

The issue of higher level navigation and guidance is beyond the scope of this work;

nevertheless it was considered prudent to undertake some initial investigations and

simulations with regard to basic navigation. As discussed in Section 6.1, the set-points

for the simulations and experiments presented so far in this chapter and in Chapter 7

have been static, i.e. they have changed at pre-de�ned times.

An alternative method to the �xed-time set-points is way-point guidance. In this

method of movement, the mission is described by a series of way-points and circle of

acceptance. Once the vehicle reaches the circle of acceptance, the way point auto-

matically changes to the next one in the list [55]. The di�erence is shown in Figure

8.17.

Figure 8.17: The Di�erence Between Fixed-Time Set-Points (Left) and Line-of-SightWay-Points (Right)

The equations governing the way point guidance are given in Equations 8.4 and 8.5.

This method is called as way point guidance by line-of-sight. The heading of the

vehicle is calculated from Equation 8.4, whilst Equation 8.5 establishes whether or not

the way-point should change. xd(k) and yd(k) are the way point coordinates in x- and

y-, x(t) and y(t) are the x- and y-coordinates and ψd(t) is the desired heading. ρo is

the radius of the circle of acceptance.

ψd(t) = tan−1(yd(k)− y(t)

xd(k)− x(t)

)(8.4)

[xd(k)− x(t)]2 + [yd(k)− y(t)]2 ≤ ρ2o (8.5)

196


Figures 8.18 8.19 show simulations of the square movement scenario applied using the

way point guidance method. Figure 8.18 has a circle of acceptance of 10cm, whilst

Figure 8.19 has a circle of acceptance of 5cm. The slight deviations observed at the

top of the �gures is caused by the discontinuity in the tan function at 180◦.

Figure 8.18: Way Point Guidance by Line of Sight with 10cm Circle of Acceptance

8.4 Full 3D Control Simulations

Having successfully simulated closed-loop horizontal control in the previous section,

the next logical step was to include the heave DOF and simulate full 3D control. The

potential capabilities of the vehicle are shown in Figures 8.20 and 8.21. The �gures

show a simulation of the vehicle descending in a spiral with the vehicle facing in the

direction of forward motion. This was achieved using �xed-time set-points.

The capabilities of the way-point guidance are shown in Figures 8.22 and 8.23. This

simulation was conducted in the `ideal-world' mode with very small circles of accep-

tance, however it shows that the vehicle is able to travel to a large number of way-points

at di�erent depths, always facing the direction of travel.

197


Figure 8.19: Way Point Guidance by Line of Sight with 5cm Circle of Acceptance

Figure 8.20: 2D Position and Orientation of the Vehicle Descending in a Spiral

198


Figure 8.21: 3D Position and Orientation of the Vehicle Descending in a Spiral

Figure 8.22: 2D Position and Orientation of the Vehicle Spelling out the Word 'Hello'Using Way-Point Guidance

199


Figure 8.23: 3D Position and Orientation of the Vehicle Spelling out the Word 'Hello'Using Way-Point Guidance

8.5 Summary

This chapter has presented the simulation and implementation of a yaw controller using

both the MK V and MK VI prototypes. A bounded PD controller was found to be the

best option and was implemented successfully on both prototypes. Three input sensor

options were available for the yaw controller; digital compass, gyroscope and a fusion

of the two using a Kalman �lter.

It was found that using the digital compass provided the best performance, however

this will not be the case when magnetic interference is present. Both the gyroscope and

Kalman �lter su�ered from some degree of drift and the data fusion problem should

be the focus of future work.

Simulations were also conducted on closed-loop control for horizontal position. Bounded

PD controllers were again used for surge and sway. The simulations indicated that,

once the yaw controller had been re-tuned, the combination of three independent con-

trollers for horizontal position control was a viable solution. An initial investigation

into way point guidance by line of sight was also conducted and simulation results

appear to be promising.

Simulations were also conducted for full 3D closed-loop control which were also suc-

cessful. Implementation of these control system will be conducted once the acoustic

positioning system is completed.

200

Chapter 9

Conclusions and Future Work

The work in this thesis set out to investigate the viability of small autonomous un-

derwater vehicles which could be used to form a mobile underwater sensor network to

monitor liquid-based processes. The scope of the work was the mechatronic aspects

of the vehicle which included the hull, propulsion systems, the corresponding control

circuitry and basic motion control systems.

The work conducted can be viewed as a success. To the best of the author's knowledge,

the world's smallest functional AUV, with the capacity to have have a communications

link and a comprehensive sensor suite, has been developed. This new µAUV has the

capabilities of a traditional AUV; depth control, heading control and a dead-reckoning

system, however there are plans to integrate an acoustic positioning system which will

allow closed-loop control for translational movement. Simulations of full 3D control

have been conducted and it is envisaged that the APS will be integrated and the

relevant control systems tested by the end of September 2012.

9.1 Thesis Summary

It was established that there were no suitable AUVs for use in the monitoring of small-

to medium-scale liquid processes (Chapter 1) and that a new vehicle would have to be

designed. During the course of the work, several other Universities started work on

developing µAUVs; however this work was started �rst.

A basic parametric model was developed and it was used to investigate the physical

parameters of the vehicle including size, velocity, thrust requirements and lifespan. To

increase the lifespan, the vehicle was made slow-moving. This meant that to complete

a monitoring mission in a reasonable time-scale, a swarm of vehicles would be required.

201


The hull shape was chosen to be spherical to maximise both maneuverability and

internal volume. Other more streamlined hulls could have been used, however the

reduction in drag (and therefore power) in a single DOF could not be justi�ed when

compared to the increase in drag in the other DOF and the reduction in internal

volume.

A review of propulsion systems for small-scale vehicles indicated that propellers coupled

to DC electric motors would be the most suitable option. Other promising alternatives

were vortex ring thrusters (VRTs) or piezo-electric actuation. Unfortunately there are

no suitable small-scale, low-power linear actuators available for use in the VRTs and

the piezo-electric actuators are too small for the size of vehicle identi�ed in the para-

metric model. Development of VRT actuators would be an interesting topic for further

research as would the development of highly miniaturised vehicles (discussed further

in Section 9.4) and sensors that could be propelled by the piezo-electric actuators.

One of the aims of the work was to use o�-the-shelf components wherever possible.

Unfortunately this often meant that the tolerances of the components were low, which

was a problem particularly evident with the propulsion system. The low-tolerances

caused problems in terms of imbalanced, time-varying thrust force which adversely

a�ected the movement of the vehicle and required robust control strategies to mitigate.

Several prototype vehicles were developed with the �nal version being designated the

MK VI. The vehicle was developed within the university with the control circuitry and

corresponding software being custom designed and constructed by the author.

Both the MK VI and its predecessor (the MK V) were used to test control systems for

closed-loop control of the heave and yaw DOF. PID, Sliding Mode and Bounded PD

controllers were all investigated and the bounded PD controller was found to be the

most suitable option.

It was found that the PID controller was found to be less robust to noise than the other

two controllers. A more robust strategy, Sliding Mode Control (SMC), provided better

performance, however it was found that there was a trade-o� between performance (in

terms of overshoot and steady-state error and oscillations) and required thrust output

(and therefore power consumption). The better performance was chosen over power

consumption due to problems with low thrust output. This allowed the SMC to be

simpli�ed to become a bounded PD controller.

The bounded PD controller required both position and velocity estimates and it was

found that direct di�erentiation of the position data provided noisy velocity estimates

which were unusable. To overcome this, a Kalman �lter was implemented.

A Kalman �lter was also used to fuse data from the digital compass and gyroscope

202


for yaw control. It was found that the performance using the fused data was worse

than using the digital compass on its own. It is thought that the poor performance of

the Kalman �lter for yaw when compared to the Kalman �lter used for heave, may be

related to the sampling frequency of the yaw controller, which was lower than required

due to hardware limitations.

Experiments were successfully conducted with the heave and yaw controllers running

in parallel and a basic dead-reckoning system implemented for translational motion.

The experiment shows that the µAUV has the same capabilities as a traditional AUV

in terms of motion. Simulations of full 3D control were also conducted and provided

promising results. Basic way-point guidance using line-of-sight was also simulated.

9.2 Review of Requirements

A number of requirements for the research were outlined in terms of the overall vehicle

(Section 2.1.3) and the control systems (Sections 6.2.1 and 6.2.2). Some of these

requirements were set towards the start of the work [215], however some of them were

identi�ed during the course of the research. To evaluate the success of the project,

the capabilities of the �nal prototype (the MK VI) should be compared against these

requirements. Aspects of the design and certain issues that have arisen will be discussed

in further detail in Section 9.3.

9.2.1 Mechatronic Requirements

The mechatronic requirements related to the overall vehicle design. They were a com-

bination of generic requirements for a µAUV for use in industrial process, and the

application speci�c requirements for the nuclear storage ponds.

The vehicle should be 2 orders of magnitude smaller than the process vessel and 1 to 2

orders of magnitude smaller than the clutter being investigated.

The vehicle has a horizontal clearance of 200mm and a vertical clearance of 150mm.

The demonstrator is for use in a nuclear storage pond (50m x 25m x 10m) with clutter

varying in length between 1m and 2m. It can be seen that the MK VI prototype

therefore meets this requirement.

The vehicle should run on an independent, rechargeable power supply.

The MK VI prototype is powered by two 7.5V Li-Ion rechargeable battery packs. There

is currently no way to recharge these batteries without removing them from the vehicle;

203


however shore-based recharge stations are a topic for future research.

The original target for the vehicle lifespan was 30 minutes which represented a utilisa-

tion of 25% (Section 3.2.2). Estimates of the MK VI power consumption indicated that

the lifespan was between 5.5 and 7 hours, depending on the number of thrusters being

used. If the circuitry for the communications and localisation is taken into acount, the

lifespan is estimated to be around 3.5 hours. This represents a utilisation of 175%, 7

times longer than the original requirement.

4 DOF are required: surge, sway, heave and yaw. Motion in the roll and pitch is

unnecessary and will be inhibited by careful ballasting of the vehicle.

The MK VI has the capability to move in all 4 DOF however, closed-loop control

has only been demonstrated in heave and yaw. Full 3D closed-loop control will be

demonstrated once the acoustic positioning system has been integrated.

Movement in all DOF should be bi-directional.

The thruster units are propeller-based and allow movement in both directions. The

force output in reverse is lower than in the forward direction due to the design of the

propellers. This reduction in force a�ected the closed-loop yaw control and meant that

the vehicle was unable to rotate on the spot without closed-loop surge and sway control

(Section 8.1.2). In the vertical plane, the reduced force limited the magnitude of the

imbalanced mass which could be tolerated.

Propulsion in planes parallel to the surface of the pond (x-y plane) should be decoupled

from depth-wise propulsion (z-axis).

Movement in the vertical axis is independent of movement in the horizontal plane;

however there is some unwanted coupling between them. When the vehicle moves in

the vertical direction, there are unwanted rotational torques and forces which cause

the vehicle rotations and translational movement. The rotations can be eliminated by

operating both the heave and yaw closed-loop controllers, however total elimination

of the translational movement can only be achieved with closed-loop surge and sway

control.

The vehicle should be able to maintain station at a given position and orientation

(x,y,z,ψ) in Earth-Fixed Coordinates (See Section 6.3).

This requirement has not yet been met due to the acoustic positioning system being

unavailable. The heave and yaw closed-loop controllers have been tested and the MK

VI prototype is able to stay at a given depth and on a given heading.

204


The turning radius of the vehicle should be 0mm.

The turning radius of the vehicle is not 0mm and simulations and experimental ob-

servations suggest that it is in the region of 0.1m to 0.2m. The cause of this is the

imbalanced thrust force and the di�erence in the force output of the thrusters in the

forward and reverse directions. Simulations indicate that the turning radius can be

reduced to 0mm when surge and sway closed-loop control are used in conjunction with

the yaw closed-loop control.

The vehicle should be constructed using low-cost, o�-the-shelf components wherever

possible.

The vehicle has primarily been constructed using low-cost o�-the-shelf components.

The hull, propellers, motors, sensors and the discrete components for the PCBs are all

standard components. The hull seal, motor mounting ring and PCBs are all custom-

built. The estimated cost of the mechatronic components (not including labour for

construction) is less than ¿500.

Of the eight requirements, six have been met. The two that have not be achieved are

due to the acoustic positioning system being unavailable.

9.2.2 Quantitative Speci�cations for the Control Systems

The quantitative speci�cations for the control system were concerned with the physi-

cally realisable outputs. Speci�cations were given separately for the vertical, horizontal

and rotational controllers. The review of the controllers is based on the MK VI proto-

type.

Vertical Controller: Overshoot ≤25mm, Steady-State Error ≤ ±25mm, Steady-StateOscillation Amplitude ≤ ±15mm, Steady-State Oscillation Frequency ≤1Hz

The bounded PD controller for the heave DOF, implemented on the MK VI prototype,

had no overshoot.

In the ideal scenario (neutral buoyancy), the controller had no steady-state error. When

the vehicle was not neutrally buoyant however, it was found the the steady-state error

was dependent on the magnitude and sign of the imbalanced mass. The larger the

imbalanced mass, the greater the steady-state error. This error could be reduced by

adding a compensation term to the control output [55], however this would require

knowledge of the size of the imbalanced mass. It was found that this was not an easy

value to estimate during experiments, however an adaptive estimate could be added in

the future.

205


There were no stead-state oscillations observed in the output that were not a function

of the measurement noise.

Horizontal Controller: Overshoot ≤50mm, Steady-State Error ≤ ±50mm, Steady-StateOscillation Amplitude ≤ ±25mm, Steady-State Oscillation Frequency ≤1Hz

The horizontal control systems were not implemented on the MK VI due to the acoustic

positioning system being unavailable. The speci�cation review is therefore based on

the simulations that were conducted. A discussion on the validity of this approach can

be found in Section 9.3.

The overshoot in the simulations was 0mm, however the steady-state error was approx-

imately 25mm. As with the vertical controller, there are no steady-state oscillations

that are not a function of the measurement noise.

Rotational Controller: Overshoot ≤5◦, Steady-State Error ≤ ±5◦, Steady-State Oscil-lation Amplitude ≤ ±5◦, Steady-State Oscillation Frequency ≤1Hz

The yaw controller had the worst performance of the two controllers developed for the

MK VI prototype. The performance of the controller depended on which of the input

sensors (compass, gyroscope or a Kalman data fusion) was used.

The best performance was obtained using the compass. The overshoot was approxi-

mately 6◦ and the steady-state error was around 2◦. The steady-state oscillations had

an amplitude of approximately ±4◦ with a frequency of 0.66Hz.

When the gyroscope or the Kalman data fusion were used, the performance was worse.

The control output su�ered from drift of up to 15◦ over a 30s experiment, however

the amplitude and frequency of the oscillations was similar to those observed when the

compass was used.

It was concluded that several factors may have contributed to the relatively poor per-

formance of the yaw controller: the uncertainties in the modelling of the rotational

dynamics of the vehicle, the low sampling frequency of the input sensors and the in-

herent problems with the sensors (magnetic interference for the compass and drift for

the gyroscope). These are discussed further in Section 9.3. The fusion of the gyroscope

and compass data did not improve the performance.

It can be seen that the controllers for translational movement not only meet the spec-

i�cations, but provide responses which are better than desired. The yaw controller

however had a worse response than expected and the fusion of the compass and gyro-

scope data to provide a robust estimate of rotational parameters should be a topic for

further research as will be discussed in Section 9.4.

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9.2.3 Qualitative Speci�cations for the Control Systems

The qualitative speci�cations are related to the dynamics of the system and the inputs

and outputs.

The system must be globally stable

No formal mathematical proof of stability was derived for any of the control systems

developed for this research. It was observed that all three control systems were stable

in that they converged to the set-point. An experiment with regards to disturbance

rejection was conducted on the heave controller by manually pushing the vehicle down-

wards once it had reached the set-point. As can be seen in Figure L.1 in Appendix L,

the controller moves the vehicle back to the set-point.

The system must be robust to thrust force variation between thruster pairs of up to 50%

For the heave controller, the di�erence between the thrust outputs is not as important

as the combined thrust. If the total thrust output is less than the force generated by

the imbalanced mass, the vehicle will either rise to the surface or sink to the bottom.

Simulations have been conducted with thruster variations of up to 50% for the hori-

zontal control and the performance varied only slightly in terms of steady-state error

(an increase of up to 25mm) and the rise-time (increased by approximately 5s).

The system must be robust to individual thruster force variations of up to ±25%

Simulations have been successfully conducted with thruster variations of up to ±50%.

The system must be robust to measurement noise

It was found that the PIDγ controller was not robust to measurement noise (oscil-

lations appeared in steady-state), however the bounded PD controller was, for the

translational controllers. The bounded PD rotational controller was less robust, how-

ever the problems with the input sensors are not limited to traditional measurement

noise.

The system must be robust to parameter uncertainties of up to ±10%

The controllers were originally tuned on a simulator which did not have an accurate

representation of vehicle drag, however when they were implemented, the steady-state

response was within the speci�cations. The drag in the simulation was increased by up

to a factor of 20 and the performance of the controller stayed within the speci�cations

indicating that the bounded PD controller was robust to parameter uncertainties.

207


It must be possible to implement on the embedded system hardware (ESH)

Both the PIDγ and bounded PD controllers have been successfully implemented on

the ESH.

It can be seen that most of the qualitative speci�cations for the control systems have

been met. A formal proof of global stability has not been derived, however this could

be a topic for further research. The controllers appear to be robust to both thruster

variations and parameter uncertainties. All of the controllers have been successfully

implemented on the ESH.

9.2.4 Requirements Summary

In total there were 17 sets of requirements for the mechatronic system and the con-

trollers. 14 of these requirements have been successfully met. Two mechatronic require-

ments (full 3D control and turning radius of 0mm) were not met. The yaw controller

qualitative speci�cations have also not been met. The potential causes of the poor

performance are discussed in Section 9.3. The global stability of the controllers has

not been formally proven, however observations and experiments have indicated that

they are stable.

9.3 Discussion

Having reviewed the speci�c requirements for the µAUV, it is of interest to consider

its capabilities with respect to the target application. Chapter 3 outlined a scenario

whereby a vehicle executed a simple search pattern by travelling lengths of a pool,

spaced 1m apart, at a single depth. Approximately 25 lengths would be required to

complete one depth.

As discussed earlier in this chapter, the lifespan of the vehicle, assuming the acoustic

positioning system is used, is approximately 3.5 hours. An initial estimate of the

surge velocity of the vehicle, based on video footage of the dead-reckoning experiments

described in Chapter 8, was 0.04ms−1. At this velocity, the vehicle would be able to

travel 504m, or just over 20 lengths of a storage pond.

The ability to only travel 20 lengths means that the vehicle would have to re-charge

before completing the proposed mission. This highlights the need to distribute the task

between several vehicles. Both the lifespan and the surge velocity may be able to be

increased, thereby increasing the operational range. The lifespan could be increased

208


by reducing the number of transmissions made by the communications system and the

velocity may be increased when the surge and sway controllers are integrated.

9.3.1 Simulation Con�dence

One of the questions raised during the review of the requirements was the validity of

using simulations to assess the performance of closed-loop surge and sway control, and

full 3D control. This relates to the level of con�dence in the simulation results.

The simulation was developed using an iterative approach. It started with the para-

metric model (Chapter 3), which was built in MATLAB in the continuous-time `ideal-

world'. When it was transferred to the SIMULINK environment, the complexity was

increased by separating the individual DOF (Chapter 6) and converting to discrete time

to simulate the implementation environment (Chapter 7). During the development of

the control systems, measurement noise and thruster imperfections were added.

The control systems developed using the `real-world' form of the model were imple-

mented on the MK V and MK VI prototypes. The results of the controller experiments

were compared with the initial simulations. Several free-parameters (thrust force and

imbalanced mass, Section 7.5.2) were tuned in the simulation along with parameters

such as the drag of the vehicle. The tuned simulations were then compared to other

experiments to see if the new parameter values were correct.

The process of comparing the experimental results with the simulations is shown for

the heave and yaw DOF in Sections 7.6 and 8.1.4 respectively. The level of con�dence

in the heave DOF simulations is high, a number of experiments have been conducted

which match the simulations. The main parameter (which was not classed as a free-

parameter) which required tuning, was the vertical drag. This was increased by a factor

of 16.

Since the dynamics of the heave DOF are similar to the dynamics of the surge and sway

DOF, the assumption has been made that the simulations provide an fairly accurate

representation of the vehicle response. It is acknowledged however, that more tuning

of the simulation may be required.

There are more uncertainties in the parameters of the yaw DOF simulation, and there-

fore less con�dence, than with the translational DOF. In the simulation, the inertia of

the vehicle is based on a solid sphere, which is not an accurate representation. The in-

ertia is di�cult to calculate for the actual vehicle, unlike the mass which is required for

the translational DOF. The rotational drag is also uncertain, however this was tuned,

as with the heave DOF. The current drag estimate is 20 times larger than the initial

209


estimate.

Another potential problem with the yaw control system is the sampling frequency of the

sensors. Initial estimates suggested that a sampling frequency of at least 44Hz would

be required, however the maximum sampling frequency of the compass was 10Hz. This

may account for some of the oscillations observed.

The comparison of experimental results with simulations suggests a high level of con-

�dence can be assumed when the digital compass is used, however this is not the case

when the gyroscope or Kalman �lter are used. To date, the gyroscope drift has not

been modelled satisfactorily and when the Kalman �lter is used, modelling two data

inputs, which have been observed to be not directly related (integrating gyroscope

angular velocity does not yield compass angular position), has proven to be di�cult.

9.4 Future Work

The work presented in this thesis concerns a proof-of-concept vehicle which is not

ready to be used, in its current form, in any of the live processes identi�ed in Chapter

1. There are still aspects of the design which need to be completed. Primary among

them is the integration of the acoustic positioning system which would allow full 3D

closed-loop control to be tested and also allow communications with base-stations and

other vehicles so that sensor data can be sent back to the operator. If this is suc-

cessful, the next stage will be to re-design the vehicle so that it is more suitable for

commercialisation.

In terms of future research, the most obvious avenue would be navigation and guidance

of the vehicle in cluttered environments. To be able to form a geometrical layout map

of the nuclear storage pond, an obstacle detection system would have to be developed

and integrated. The sensors could be either acoustic transducers or lasers. Initial work

conducted during the ASSN4IP project by colleagues, suggested that acoustic sensors

had a minimum working range of 0.5m. Any object closer than this distance could

not be detected due to `ringing' in the transducer1. Lasers could be an alternative or

in conjunction for close-range detection. The e�ectiveness of the lasers depends will

depend on the turbidity of the water.

The integration of an obstacle detection system would allow exploration algorithms

and routines to be developed and tested. Initially a single vehicle could be used,

however cooperative exploration is a topic of great interest. The level of autonomy

1The transducer vibrates when transmitting and these vibrations take a �nite time to die down.If the return signal is received before the vibrations have stopped, the signal may not be seen.

210


verses automation is of interest, for example, if the vehicles are controlled by a central

shore-based computer which generates the way-points, with only low-level control being

executed on the µAUV, the vehicles would be classed as automated. In this method, if

a vehicle descends into a canyon and requires other vehicles to act as virtual anchors2

so that communication to the base-stations is not lost, the central controller would task

the other vehicles as required. The µAUVs would be more automated than autonomous

in this scenario.

To be classed as autonomous, the vehicles would have to execute the exploration algo-

rithms and generate the way-points themselves. Assistance from other vehicles would

have to be requested directly and would require node-to-node communications. The

central controller would task a vehicle to explore an area of the environment and the

µAUV would go and do it without any further assistance or commands. This is a more

complex approach, however it would be cooperative exploration.

State estimation is another topic which requires further research. Simple Kalman �lters

were used with varying degrees of success. Alternatives to Kalman �lters such as non-

linear observers could be investigated. A more accurate model of the yaw DOF could

also be developed and the combined use of the digital compass and rate gyroscope

requires investigation.

Experimental results indicated that better performance was obtained when the compass

was used as the input sensor. Unfortunately, the compass is susceptible to magnetic

interference and the clutter in the nuclear storage ponds is ferrous. This means that

the compass can only be used in clear water. How and when to switch to using the

rate gyroscope is an interesting challenge and may require input from the obstacle

detection sensors. Re-calibrating the gyroscope mid-mission to reduce drift could also

be investigated.

Other areas of research could include the development of docking and recharge stations

so that the vehicles operate for extended periods of time. The current lifespan of the

vehicles is estimated to be around 3.5 hours. It is envisaged that the vehicles would be

left for weeks or months without being removed form the environment so battery charg-

ing is required. There are three possible charging methods; direct contacts, inductive

charging or battery swapping.

Initial investigations into inductive charging suggest that it may not be feasible due

to the ine�ciencies in the system which generate a large amount of heat, and the

complexities of the circuits that may be required [216]. Automatic battery swapping

2Virtual anchors would allow the descending vehicle to estimate its position. They essentially actas relays between the vehicle and the base-stations.

211


is mechanically complex, although it would mean that the vehicles would not have to

stay docked for long periods of time. Direct contact charging may be the most suitable

option initially, although ensuring that the charging pads connect properly, are the

correct polarisation and do not short-circuit in the water, are all interesting challenges.

The integration of a comprehensive sensor package also requires consideration. Cur-

rently the vehicle has no sensors that are not required for the control system. Along

with the obstacle detection sensors discussed earlier, temperature and radiation level

sensors should also be integrated. A video camera would be desirable, however trans-

mitting video over an acoustic channel is very challenging [217]. In the interim, a store

and dump approach may be the only option.

The addition of a radiation level sensor raises the issue of the radiation hardening of

the electronics. The level of shielding required will depend on the type and levels of the

radiation in the storage pond. Plans are in place to investigate the e�ects of radiation

on the electronics in collaboration with the University of Manchester's Dalton Institute.

This would be done by placing the vehicle next to a controlled radioactive source and

using shielded test circuitry to monitor the e�ects on the vehicle electronics.

Miniaturisation of the vehicle so that it could operate in even more con�ned areas

is also an potential topic for further investigation. The vehicle which has been been

presented in this thesis could be made smaller, potentially halved in size. Reducing the

size of the vehicle raises a number of challenges with respect to power, communications

and sensing.

One of the limiting factors in size identi�ed in Chapter 3 was the size of the battery.

Finding batteries which are small but have high energy density is di�cult. This means

that the lifespan of the vehicle may be dramatically reduced to the point where it

becomes not viable. Energy harvesting may be a solution to this problem. If the

vehicle is too small, the sensors and antennas which can be mounted become limited.

A number of very small vehicles were identi�ed in Chapter 4, such as the piezo-electric

actuated �sh. The main issue with such vehicles was the lack of suitable communication

systems or sensors which can be mounted on them.

The �nal topic of future work which is considered in this thesis, is utilising the technol-

ogy, developed for the monitoring of nuclear storage facilities, for di�erent applications.

The demonstrator for the µAUVs was for use in a legacy storage pond, however the

vehicles could be used in modern facilities. Chapter 1,identi�ed a number of potential

applications including the chemical process industry and the water industry. During

the course of this work, using the vehicles in the water and waste water industries has

been suggested by a number of industrialists. The vehicles could be used in reservoirs

212


or water holding tanks, or modi�ed to be used in pipelines.

213

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Appendix A

Wastewater Treatment Facilities

Table A.1: Water Treatment Levels [22]Treatment Level DescriptionPreliminary Removal of wastewater constituents such as rags,

sticks, �oatables, grit and grease that may causemaintenance or operational problems with the treat-ment operations, processes and ancillary systems.

Primary Removal of a portion of the suspended solids and or-ganic matter from the wastewater

Advanced Primary Enhanced removal of suspended solids and organicmatter from the wastewater. Typically accomplishedby chemical addition or �ltration

Secondary Removal of biodegradable organic matter (in solutionor suspension) and suspended solids. Disinfection isalso typically included in the de�nition of conven-tional secondary treatment

Secondary with nutrientremoval

Removal of biodegradable organics, suspended solidsand nutrients (nitrogen, phosphorus or both nitrogenand phosphorus)

Tertiary Removal of residual suspended solids (after secondarytreatment), usually by granular medium �ltration ormicroscreens. Disinfection is also typically a partof tertiary treatment. Nutrient removal is often in-cluded in this de�nition

Advanced Removal of dissolved and suspended materials re-maining after normal biological treatment when re-quired for various water reuse applications

229


FigureA.1:Waste

Water

TreatmentFlow[19]

230

Appendix B

Drag Coe�cient Graphs

Figure B.1: Drag Coe�cient vs. Reynolds Number for All Sphere Diameters

Figure B.2: Drag Coe�cient vs. Reynolds Number [20]

231

Appendix C

Propulsion System Analysis

C.1 Micro-Pump-Based VDS

The analytical model used was based on Equation 4.3 and simulated using MATLAB

and SIMULINK. The model assumed a spherical node diameter of 100mm, a water

temperature of 5◦C, a drag coe�cient of 0.47 and that the system was initially neutrally

buoyant. These parameters were based on the parametric modelling in Chapter 3 and

the available prototype hardware and facilities.

A simple PDγ controller was used, however it was found that the system was closed

loop unstable, shown in Figure C.1. This was because there was no measure of the

volume of water inside the vehicle. The plant forces the controller to be a bang-bang

system as the micro-pump can only be forward, backward or o�. Alternative control

strategies could be investigated, however due to resource constraints, this was not

taken any further. The system could however be used in the future as a method of

maintaining neutral buoyancy if the nodes are used in water that has a temperature

gradient due to the fact that the water density is a function of temperature.

C.2 Motor/Syringe-Based VDS

An analytical model for the plant and a controller were both completed in [218]. The

controller was a PD system that was designed around a linearised form of the non-

linear plant. The simulations indicated that the node would oscillate around the set

depth much like the micro-pump system, however it was closed-loop stable. A fuzzy

logic controller was also simulated but had the same oscillatory output problems.

In [99], a three-stage lead-lag compensator with a pre-�lter was simulated which was

232


Figure C.1: PD Gamma Controller Output

again based around the linearised plant. The output depth tracked the set depth

with no oscillations or steady-state error. This suggests that a more complex control

strategy could allow the micro-pump system to be closed loop stable as the two models

are similar.

It was found that the system was very dependent on the mechanical construction of

the syringe/plunger and the motor/syringe mounting. If the motor/syringe were not

aligned accurately, the plunger did not travel straight and became jammed in the

syringe. If the plunger was too tight a �t in the syringe, the motor had insu�cient

force to move it but if it was too loose, a seal was not created and water leaked through.

The system was also very bulky compared with other options that were considered.

The unit was 90mm x 35mm x 35mm and weighed 69g in contrast to the micro-pump

system that was 50mm x 25mm x 25mm and weighed around 35g. The mechanical

issues along with the oscillatory nature of the PD controlled plant meant that the

motor/syringe was not considered as a viable means of vertical displacement for this

project.

233


Figure C.2: Slug Length and Diameter Over a Range of Frequencies

C.3 Vortex Ring Thrusters

The model used in the following analysis is taken from [114, 115]. The synthetic jet

can be modelled as a �nite length 'slug' of water. The dimensions of a VRT can be

found based upon the simple slug model detailed in [114, 115]. The average thrust

from a VRT is given by Equation C.1. A list of the notation can be found at the end

of this section.

T = ρπ3

16Ls

2Ds2f 2 (C.1)

The ratio of LsDs

is called the formation number, n. The optimum value of n has been

found to be ≈ 4 [115, 116]. For a given output thrust and frequency, Equation C.1

can be re-arranged to �nd Ls and Ds as shown in Equations C.2 and C.3. Figure C.2

shows the slug length and diameter to give an output thrust of 10mN over a range of

input frequencies. The thrust value was chosen on the basis of the thrust output of the

propellers investigated in Section 4.4.

Ls =√n

4

√16T

ρf 2π3(C.2)

Ds =

√1

n4

√16T

ρf 2π3(C.3)

The next stage in the VRT design is to calculate the dimensions of the cavity shown

in Figure C.3. The ori�ce diameter is equal to the diameter of the slug. The disk is a

234


plate which is attached to both the membrane and the actuator and is used to de�ect

the membrane.

Figure C.3: Helmholtz Cavity Based VRT

The cavity and disk diameters and the membrane de�ection can be found by one of

two methods. With the �rst method, the cavity and disk diameters are �xed and the

required membrane de�ection can be calculated using Equation C.4 [114]. The second

method has the membrane de�ection set along with a ratio of cavity diameter to disk

diameter. The two diameters are then calculated using Equations C.5 and C.6 [114].

δ =2Ls

3

n2(Dc2 +Dd

2)(C.4)

Dc =

√2Ls

3

n2δ ∗ (1 + 1ratio2

)(C.5)

Dd =Dc

ratio(C.6)

Once the dimensions of the cavity, disk and de�ection have been found, the next task

is to calculate the input force required from the actuator. This is done by calculating

the exit velocity of the slug, shown in Equations C.7 - C.10 [115], and using Newtons'

second law to calculate the force as shown in Equations C.11 and C.12. Once the exit

velocity of the slug of water has been calculated, the acceleration can found, assuming

that the water starts with zero initial velocity. The intermediate velocity, Up, is the

velocity of the slug before it leaves the ori�ce.

Um = 2δf (C.7)

235


Up = UmDc

2

Do2 (C.8)

Re =UpDo

ν(C.9)

Ue = Up(1 +8√π

1√Re

√Ls√Do

) (C.10)

a =Ue − Ue(0)

Tp2

(C.11)

F = ma

F =πDo

2

4Lsρa

(C.12)

The required input force is independent of the cavity and membrane dimensions due to

Equation C.8 which normalises the intermediate velocity. The input force for a range

of cavity:disk diameter ratios is shown in Figure C.4. The input power can then be

found in terms of the work done. The distance the work is done over is the distance

the disk travels and the time is Tp2.

Figure C.4: Input Force for a Range of Cavity:Disk Diameter Ratios for the VCM

W = F∆s (C.13)

P =W

t

P =FδTp2

(C.14)

236


The model shows that as the ratio of cavity:disk diameter increases, so does the required

input force.

Table C.1: Notation for Appendix C.3Tp Time Interval F Forcea Acceleration W Work Done

∆S Distance Work Done Over t Timeρ Density of Water P PowerT Average Thrust Ls Length of SlugDs Diameter of Slug f Frequencyn Formation Number Do Diameter of Ori�ceDc Cavity Diameter Dd Disk Diameterδ Membrane De�ection Um Membrane VelocityUe Exit Velocity Up Intermediate Velocity

C.4 Motor/Propeller Selection

The following procedure enables the thrust produced by a given motor/propeller com-

bination to be determined. The process is undertaken for a single motor power then

repeated over the complete range [219].

1. Select a motor speed and associated power output.

2. Using the propeller diameter, calculate the power coe�cient.

The power coe�cient, KP = Pρn3D5 , is a non dimensional term relating the output

power of the propeller to its characteristics. P is the power, n is the rotational

speed of the motor and D is the diameter of the propeller.

3. From the propeller chart of KP vs J (provided by the manufacturer), calculate

the speed.

J = VanD

is the advance ratio which is a relationship between the motion of the

�uid and the propeller [220]. Va is the advance velocity.

4. Using the value of J calculate the thrust from the propeller chart of KT vs J .

KT = Tρn2D4 is the non-dimensional thrust coe�cient and arises due to the axial

thrust produced by the �uid on the propeller. T is the thrust.

5. Compare the thrust value with the drag value.

The thrust should be greater than the drag otherwise the vehicle will not move.

6. Repeat for the whole motor speed range.

237

Appendix D

MK VI Compass Calibration Curve

Figure D.1: Non-Linear Distortion Curve for Digital Compass for MK VI Prototype

238

Appendix E

Kalman Filter

This Appendix details the equations for a discrete time Kalman Filter and the corre-

sponding 'C' code implementation. The for are taken from [135].

E.1 General Equations

x−k = Axk−1 +Buk−1 (E.1a)

P−k = APk−1AT +Q (E.1b)

Kk = P−k HT (HP−k H

T +R)−1 (E.1c)

xk = x−k +Kk(zk −Hx−k ) (E.1d)

Pk = (I −KkH)P−k (E.1e)

E.2 Implementation for Position and Velocity Esti-

mates

The speci�c instance of the Kalman �lter detailed here is for the estimation of position

and velocity for a Bounded PD controller using only noisy position data. The following

notational substitutions and expansions have been used:

239


A =

[A1 A2

A3 A4

]xk = B =

[B1

B2

]

xk−1 = C =

[C1

C2

]x−k = D =

[D1

D2

]

P−k = E =

[E1 E2

E3 E4

]Pk = G =

[G1 G2

G3 G4

]

H =[H1 H2

]I =

[1 0

0 1

]

Kk =

[K1

K2

]Pk−1 =

[P1 P2

P3 P4

]

Q =

[Q1 Q2

Q3 Q4

]

E.2.1 Step 1

Using Equation E.1a:

D = AC (E.2a)[D1

D2

]=

[A1 A2

A3 A4

][C1

C2

](E.2b)

Therefore:

D1 = A1C1 + A2C2 (E.3a)

D2 = A3C1 + A4C2 (E.3b)

E.2.2 Step 2

Using Equation E.1b:

E = (APAT ) +Q (E.4a)[E1 E2

E3 E4

]=

([A1 A2

A3 A4

][P1 P2

P3 P4

][A1 A3

A2 A4

])+

[Q1 Q2

Q3 Q4

](E.4b)

240


Therefore:

E1 = Q1 + [A1(A1P1 + A2P3) + A2(A1P2 + A2P4)] (E.5a)

E2 = Q2 + [A3(A1P1 + A2P3) + A4(A1P2 + A2P4)] (E.5b)

E3 = Q3 + [A1(A3P1 + A4P3) + A2(A3P2 + A4P4)] (E.5c)

E4 = Q4 + [A3(A3P1 + A4P3) + A4(A3P2 + A4P4)] (E.5d)

E.2.3 Step 3

Using Equation E.1c:

K =EHT

(HEHT ) +R(E.6)

Let V = EHT and w = (HEHT ) +R, so:[V1

V2

]=

[E1 E2

E3 E4

] [H1 H2

](E.7)

w =[H1 H2

] [E1 E2

E3 E4

][H1

H2

]+R (E.8)

Therefore:

V1 = E1H1 + E2H2 (E.9a)

V2 = E3H1 + E4H2 (E.9b)

w = (H1(H1E1 +H2E3) +H2(H1E2 +H2E4)) +R (E.9c)

Hence:

K =

[V1WV2W

](E.10)

K1 =E1H1 + E2H2

(H1(H1E1 +H2E3) +H2(H1E2 +H2E4))(E.11a)

K2 =E3H1 + E4H2

(H1(H1E1 +H2E3) +H2(H1E2 +H2E4))(E.11b)

241


E.2.4 Step 4

Using Equation E.1d:

B = D + (K(z − (HD))) (E.12a)[B1

B2

]=

[D1

D2

]+ (

[K1

K2

](z − (

[H1 H2

] [D1

D2

]))) (E.12b)

Therefore:

B1 = D1 +K1(z − (H1D1 +H2D2)) (E.13a)

B2 = D2 +K2(z − (H1D1 +H2D2)) (E.13b)

(E.13c)

E.2.5 Step 5

Using Equation E.1e:

G = (I −KH)E (E.14a)[G1 G2

G3 G4

]=

([1 0

0 1

]−

[K1

K2

] [H1 H2

])[E1 E2

E3 E4

](E.14b)

Therefore:

G1 = E1 −K1H1E1 −K1H2E3 (E.15a)

G2 = E2 −K1H1E2 −K1H2E4 (E.15b)

G3 = E3 −K2H2E3 −K2H1E1 (E.15c)

G4 = E1 −K2H2E4 −K2H1E2 (E.15d)

E.2.6 Step 6

Once the main equations have been run, the parameters need to be updated as follows:

C = B and P = G.

242


E.3 Implementation for Data Fusion

If sensor data is available for both position and velocity, the Kalman Filter can be used

to combine the readings to get more accurate estimates. The di�erence between this

implementation and the one described in the previous section is that the observation

model is now a square matrix instead of a vector. Equations in a form suitable for

translation into `C' code are shown below:

D1 = A1C1 + A2C2 (E.16a)

D2 = A3C1 + A4C2 (E.16b)

E1 = Q1 + [A1(A1P1 + A2P3) + A2(A1P2 + A2P4)] (E.17a)

E2 = Q2 + [A3(A1P1 + A2P3) + A4(A1P2 + A2P4)] (E.17b)

E3 = Q3 + [A1(A3P1 + A4P3) + A2(A3P2 + A4P4)] (E.17c)

E4 = Q4 + [A3(A3P1 + A4P3) + A4(A3P2 + A4P4)] (E.17d)

V1 = E1H1 + E2H2 (E.18a)

V2 = E1H3 + E2H4 (E.18b)

V3 = E3H1 + E4H2 (E.18c)

V4 = E3H3 + E4H4 (E.18d)

W1 = R1 + [H1(E1H1 + E3H2) +H2(E2H1 + E4H2)] (E.18e)

W2 = R2 + [H3(E1H1 + E3H2) +H4(E2H1 + E4H2)] (E.18f)

W3 = R3 + [H1(E1H3 + E3H4) +H2(E2H3 + E4H4)] (E.18g)

W4 = R4 + [H3(E1H3 + E3H4) +H4(E2H3 + E4H4)] (E.18h)

243


K1 =−(W3V2 −W4V1)

(W1W4 −W2W3)(E.19a)

K2 =(W1V2 −W2V1)

(W1W4 −W2W3)(E.19b)

K3 =−(W3V4 −W4V3)

(W1W4 −W2W3)(E.19c)

K4 =−(W1V4 −W2V3)

(W1W4 −W2W3)(E.19d)

B1 = D1 + [K1(Z1 − (H1D1 +H2D2)) +K2(Z2 − (H3D1 +H4D2))] (E.20a)

B2 = D2 + [K3(Z1 − (H1D1 +H2D2)) +K4(Z2 − (H3D1 +H4D2))] (E.20b)

G1 = −E1(H1K1 +H3K2 − 1)− E3(H2K1 +H4K2) (E.21a)

G2 = −E2(H1K1 +H3K2 − 1)− E4(H2K1 +H4K2) (E.21b)

G3 = −E1(H1K3 +H3K4)− E3(H2K3 +H4K4 − 1) (E.21c)

G4 = −E2(H1K3 +H3K4)− E4(H2K3 +H4K4 − 1) (E.21d)

244

Appendix F

MK VI Software Flowchart

Figure F.1: Flowchart for the MK VI Software

245

Appendix G

SIMULINK Model

246


FigureG.1:Top

Levelof

SIMULINKModel

247

Appendix H

Discrete PIDγ Controller Derivation

A modi�ed version of the standard form of the continuous time PIDγ controller is given

by:

C = kp +kiTis

+kdTds

1 + γTds(H.1)

This leads to the transfer function:

U = CE (H.2a)

U =kpTis(1 + γTds) + ki(1 + γTds) + kdTiTds

2

Tis+ TiTdγsE (H.2b)

U =kpTis+ kpTiTdγs

2 + ki + kiTdγs+ kdTiTds2

tis+ TiTdγs2E (H.2c)

U =(kpTiTdγ + kdTiTd)s

2 + (kpTi +KiTdγ)s+ kiTiTdγs2 + Tis

E (H.2d)

∴U =a1s

2 + a2s+ a3a4s2 + a5s

E, (H.2e)

248


With coe�cients:

a1 = kpTiTdγ + kdTiTd (H.3a)

a2 = kpTi + kiTdγ (H.3b)

a3 = ki (H.3c)

a4 = TiTdγ (H.3d)

a5 = Ti, (H.3e)

To convert to discrete time, the Bilinear Z-Transform, or Tustin Approximation, is

used:

s =2

T

1− Z−1

1 + z−1=

2− 2z−1

T + Tz−1(H.4)

Substituting this into the continuous time transfer function leads to:

U =a1(

2−2z−1

T+Tz−1 )2 + a2(2−2z−1

T+Tz−1 ) + a3

a4(2−2z−1

T+Tz−1 )2 + a5(2−2z−1

T+Tz−1 )E (H.5a)

U =a1(2− 2z−1)2 + a2(2− 2z−1)(T + Tz−1) + a3(T + Tz−1)2

a4(2− 2z−1)2 + a5(2− 2z−1)(T + Tz−1)E (H.5b)

U =a1(4− 8z−1 + 4z−1) + a2(2T − 2Tz−2) + a3(T

2 + 2T 2z−1 + T 2z−2)

a4(4− 8z−1 + 4z−2) + a5(2T − 2Tz−2)E (H.5c)

U =4a1 − 8a1z

−1 + 4a1z−2 + 2a2T − 2a2Tz

−2 + a3T2 + 2a3T

2z−1 + a3T2z−2

4a4 − 8a4z−1 + 4a4z−2 + 2a5T − 2a5Tz−2E

(H.5d)

U =(4a1 + 2a2T + a3T

2) + (2a3T2 − 8a1)z

−1 + (4a1 − 2a2T + a3T2)z−2

(4a4 + 2a5T )− 8a4z−1 + (4a4 − 2a5T )z−2E (H.5e)

∴U =b1 + b2z

−1 + b3z−2

b4 + b5z−1 + b6z−2E, (H.5f)

249


With coe�cients:

b1 = 4a1 + 2a2T + a3T2 (H.6a)

b2 = 2a3T2 − 8a1 (H.6b)

b3 = 4a1 − 2a2T + a3T2 (H.6c)

b4 = 4a4 + 2a5T (H.6d)

b5 = −8a4 (H.6e)

b6 = 4a4 − 2a5T, (H.6f)

This can then be re-arranged into the form of a di�erence equation as shown below:

U =b1 + b2z

−1 + b3z−2

b4 + b5z−1 + b6z−2E (H.7a)

b4U + b5z−1U + b6z

−2U = b1E + b2z−1E + b3z

−2E (H.7b)

b4u[n] + b5u[n− 1] + b6u[n− 2] = b1e[n] + b2e[n− 1] + b3e[n− 2] (H.7c)

u[n] = −b5b4u[n− 1]− b6

b4u[n− 2] +

b1b4e[n] +

b2b4e[n− 1] +

b3b4e[n− 2], (H.7d)

H.1 Addition of Low Pass Filter

The transfer function of a basic low-pass �lter is given by:

Y =kf

Tfs+ 1(H.8)

The discretised form is found by substituting Equation H.4 as follows:

250


Y =kf

Tf (2−2z−1

T+Tz−1 ) + 1(H.9a)

Y =kfT + kfTz

−1

(2Tf + T ) + (T − 2Tf )z−1(H.9b)

∴Y =c1 + c1z

−1

c2 + c3z−1, (H.9c)

With coe�cients:

c1 = kfT (H.10a)

c2 = 2Tf + T (H.10b)

c3 = T − 2Tf , (H.10c)

Combining the low-pass �lter with the controller leads to:

U =b1 + b2z

−1 + b3z−2

b4 + b5z−1 + b6z−2c1 + c1z

−1

c2 + c3z−1E (H.11a)

U =b1c1 + b1c1z

−1 + b2c1z−1 + b2c1z

−2 + b3c1z−2 + b3c1z

−3

b4c2 + b4c3z−1 + b5c2z−1 + b5c3z−2 + b6c2z−2 + b6c3z−3E (H.11b)

U =b1c1 + (b1c1 + b2c1)z

−1 + (b2c1 + b3c1)z−2 + b3c1z

−3)

b4c2 + (b4c3 + b5c2)z−1 + (b5c3 + b6c2)z−2 + b6c3z−3E (H.11c)

∴U =d1 + d2z

−1 + d3z−2 + d4z

−3

d5 + d6z−1 + d7z−2 + d8z−3E, (H.11d)

With coe�cients:

251


d1 = b1c1 (H.12a)

d2 = c1(b1 + b2) (H.12b)

d3 = c1(b2 + b3) (H.12c)

d4 = b3c1 (H.12d)

d5 = b4c2 (H.12e)

d6 = b4c3 + b5c2 (H.12f)

d7 = b5c3 + b6c2 (H.12g)

d8 = b6c3, (H.12h)

The new transfer function can be rearranged to the following di�erence equation:

u[n] = −d6d5u[n−1]− d7

d5u[n−2]− d8

d5u[n−3]+

d1d5e[n]+

d2d5e[n−1]+

d3d5e[n−2]+

d4d5e[n−3]

(H.13)

u[n] = h1u[n−1] +h2u[n−2] +h3u[n−3] +h4e[n] +h5e[n−1] +h6e[n−2] +h7e[n−3]

(H.14)

With coe�cients:

252


h1 = −d6d5

(H.15a)

h2 = −d7d5

(H.15b)

h3 = −d8d5

(H.15c)

h4 =d1d5

(H.15d)

h5 =d2d5

(H.15e)

h6 =d3d5

(H.15f)

h7 =d4d5, (H.15g)

253

Appendix I

Linearisation

There are two sources of non-linearities in the plant; the hydrodynamic drag, Equa-

tion I.1, and the actuator saturation, Equation I.2. The hydrodynamic drag can be

linearised using a �rst order Taylor series expansion around an equilibrium point. The

saturation term cannot be so easily dealt with but as the aim was only to obtain an

approximation of the CLTF bandwidth, it was decided to ignore it.

2.6506ν3 + 4.1527|ν3|ν3 = τ3 (I.1)

−0.08 ≤ τ3 ≤ 0.08 (I.2)

A six-step method of linearization by Taylor series expansion is outlined in [221]. An

abbreviated version is detailed below. The non-linear model described in Equation I.1

can be expressed as:

f(τ3, ν3, ν3) = 2.6506ν3 + 4.1527|ν3|ν3 − τ3 = 0 (I.3)

Selecting the equilibrium point (ν3 = 0) for the output velocity as ν3 = νo and the

thrust force at this point as τ3 = τo. At this point, f(τo, νo, 0) = 0 and a Taylor

expansion can be performed as shown in Equation I.4.

f(τ3, ν3, ν3) ∼= f(τo, νo, 0) +∂f

∂τ3

∣∣∣∣τ3=τoν3=νo

(τ3− τo) +∂F

∂ν3


(ν3− νo) +∂f

∂ν3


(ν3− νo)

(I.4)

254


Evaluated at the equilibrium points, Equation I.4 yields:

f(τ3, ν3, ν3) ∼= 0 + (−1)(τ3 − τo) + 8.3054νo(ν3 − νo) + 2.6506(ν3 − νo) (I.5)

Re-arranging and changing the model's variables so that τ3 = (τ3 − τo), ν3 = (ν3 − νo)and ˙ν3 = (ν3 − νo) leads to the linearised ordinary di�erential equation shown in

Equation I.6.

2.6506 ˙ν3 + 8.3054νoν3 = τ3 (I.6)

Equation I.6 can be evaluated at any given equilibrium point, νo. For the purpose of

this analysis, the equation needed to be converted to the s-domain and into the form

of a transfer function as shown in Equation I.7.

U(s)

E(s)=

0.3773

s2 + (3.1334νo)s(I.7)

The transfer function can then be inserted into the Simulink model in place of the non-

linear plant. The linearised plant should be linearised around an equilibrium point

which matches the non-linear model as closely as possible. This will be a di�erent

point if the saturation block is removed. Once an equilibrium point was chosen, the

saturation block was removed and the frequency response investigated. Figure I.1

shows the responses of the linearised system at equilibrium points relating to thruster

forces between 0N − 0.08N at 0.005N intervals.

Figure I.1 shows that one of the responses (green) matched the non-linear response (red)

very closely. This related to an equilibrium point of νo = 0.0035ms−1 and τo = 0.005N .

At these values, the transfer function for the linearised plant becomes Equation I.8.

This was then be used in the frequency analysis to calculate the CLTF bandwidth.

U(s)

E(s)=

0.3773

s2 + 0.011s(I.8)

I.1 Frequency Response

The closed loop bandwidth, ωBW is de�ned as the frequency range of input signals that

the closed loop system can successfully track without severe attenuation. The cut-o�

point for increased attenuation is −3dB. This point can be found by considering the

Bode plot of the closed loop transfer function, the general form of which is shown

255


in Equation I.9, where G is the transfer function of the plant and C is the transfer

function of the controller. The bode plot itself is shown in Figure I.2.

Y (s)

R(s)=

GC

1 +GC(I.9)

From Figure I.2, ωBW was found to be 0.155Hz. The sampling rate of the digital

controller, ωs, should be at least twice the bandwidth, according to the Nyquist sam-

pling theorem, meaning ωs ≥ 0.31Hz. In practice this is often not good enough and

ωs ≈ 4 to 30∗ωBW [212, 213]. The sampling frequency should therefore be in the range

0.31Hz ≤ ωs ≤ 4.65Hz. Higher sampling frequencies can be used and may improve

the response.

256


Figure I.1: Step Responses for Varying Linearization Equilibrium Points

Figure I.2: Bode Plot of Closed Loop System

257

Appendix J

Controller Outputs for Simulations

and Experiments

Figure J.1: Control Output for Figure 7.5

258




259



Figure J.5: Control Output for Figure 7.18, 10% Uncertainty

260


Figure J.6: Control Output for Figure 7.18, 50% Uncertainty


261




262



Figure J.11: Control Output for Figure 8.1, Bounded PD Controller

263


Figure J.12: Control Output for Figure 8.1, PIDγ Controller

Figure J.13: Control Output for Figure 8.2, Bounded PD Controller

264


Figure J.14: Control Output for Figure 8.2, PIDγ Controller

Figure J.15: Control Outputs for Figure 8.13

265

Appendix K

Surge and Sway Controller Simulation

`Ideal-World' Results

Figure K.1: Responses for Individual DOF for Horizontal Position Control in `Ideal-World'

266


Figure K.2: 2D Position and Orientation in `Ideal-World'

267

Appendix L

Additional Vertical Motion

Experiment Results

Figure L.1: Vertical Motion Experiment Using Bounded PD Controller on the MK VIPrototype with a Disturbance

268

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