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Abstract—This paper deals with the design of a bio-inspired fish

like underwater vehicle. As the applications of underwater robots

grow, finding efficient propulsion techniques is of the utmost

importance. The current research has focused on the use of

biomimetic propulsion, which simulates the undulation of fish tail,

i.e. the sinusoidal oscillation. The objective is to mimic the

propulsion technique of the BCF mode carangiform swimming

style to swim efficiently over large distances at impressive speeds.

Beginning from the CAD construction in Solidworks, 3D motion

simulations in Matlab VRML and open-loop experimental and

simulation results are provided to illustrate the effectiveness of

the proposed methodology.

Index Terms – Biomimetic, Robotics, BCF, Kinematic Modeling,

Lagrange-Euler equations, Solidworks, MatlabVRML.

I. INTRODUCTION

he manifold contribution of bio-inspired robotics or bio-

mimetic [4] has been both continuously increasing

through the last decade. Biomimetics reflect the features and

capabilities of natural evolution of a system that could be

efficiently replicated or mimicked in a human engineered

system to the design of new technologies and the improvement

of conventional ones. One of the important focused

technologies has been the development of autonomous

underwater vehicles [5] as a greater part to the increasing

interest in unmanned underwater surveillance and monitoring.

Of particular interest are regions of the underwater

environment which are unexplored and dynamic as well as

underwater detection, pollution source tracking, underwater

archaeology, search and rescue, and so forth. A bio-inspired

approach in the design of underwater vehicles i.e. inspired

from nature has shown credibility for the design of vehicles

suitable to both vehicular morphology and methods of

locomotion. The study of underwater evolution of life and its

Dr. S K Panda is with the Electrical and Computer Engineering Department

National University of Singapore, Singapore 117576; (e-mail: eleskp@

nus.edu.sg).

Dr. Rajesh Kumar is with the Electrical Engineering Department Malviya

National Institute of Technology, Jaipur, India. (e-mail: rkumar@mnit.ac.in).

Abhra Roy Chowdhury is presently a Ph.D. scholar at the Electrical and

Computer Engineering Department National University of Singapore,( e-mail:

A0079791@ nus.edu.sg).

Bhuneshwar Prasad is presently a M.Sc. student at the Electrical and

Computer Engineering Department National University of Singapore, (e-mail:

bhuneshwar21@ nus.edu.sg).

Vinoth Kumar is presently a M.Sc. student at the Electrical and Computer

Engineering Department, National University of Singapore, (e-mail:

vinothkumarvishwanathan@ nus.edu.sg).

plethora of locomotion modes [2] has long been a subject of

interest to the Biological community. Aligning to the research

interest of the aforesaid, the Engineering community has taken

up the further task to construct mechanisms that shows or

replicates the behavior of swimming life-forms and their

motion. Majority of conventional design of autonomous

underwater vehicles used propellers as their principal mode of

propulsion. The propeller based locomotion although rendered

the initial answers to underwater locomotion but set issues on

high-maneuverability, efficiency and low power consumption.

The scientific community and researchers also found that

propeller-strikes produce greater amount of marine debris [8],

marine creature‟s mortality and shallow waters ecosystem

disturbances. Broadband noises produced from propellers have

severe acoustic effects on marine wildlife. Biomimicked or

Fish-like robots are expected to be quieter, more maneuverable

(lesser accidents), and possible more energy efficient (longer

missions). Undulating-finned robot can preserve undisturbed

condition of its surroundings for data acquisition and

exploration (stealth). Movement of fish through water without

creating ripples and eddies were more reasons to choose a bio-

inspired design for underwater locomotion.

Considering the propulsive features [5] of existing fish modes,

a novel propulsive mechanism that integrates fish-like

swimming with modular links and fin movements is proposed

in this paper. The robot will be able to implement speedy and

efficient fish-like swimming. This paper focuses on the

modeling, simulation and development studies of a BCF (Body

Caudal Fin) [1] [2] based prototype. The work in this paper

specifically identifies the usefulness of our model for purposes

of both speed and maneuverability. The construction of a

mechanical prototype for propulsion is demonstrated.

The objectives and scopes show the target and boundary for

this project. Due to the complex nature of the mechanical

system, the paper focuses on developing a linear system model

using robot dynamics derivation. The simulation method is in

MATLAB Simulink, which is implemented by toolboxes Sim-

Mechanics and VRML. The prototype mechanical hardware

model was designed and developed using Solidworks. The

general approach that was used to complete is given as

following:

Develop a mathematical model of the Robot fish

based on the physical (CAD) data, dynamics

analysis and engineering assumptions.

Design, Modeling and Open-loop Control of a

BCF Mode Bio-mimetic Robotic Fish Abhra Roy Chowdhury, Bhuneshwar Prasad, Vinoth Kumar, Dr. Rajesh Kumar, Dr. S K Panda

T

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Develop a Solidworks model of the Robot-fish

design.

Export the Solidworks model to Matlab-Simulink

by use of Sim-Mechanics toolbox.

With the help of Virtual Reality Modeling

Language (VRML) in Matlab-Simulink develop a

3D Simulation of the prototype model.

Demonstrate the feasibility of building a flexible

bodied Robotic Fish (Robo-Fish) Propelled by a

single oscillating caudal fin and two pectoral fins

The paper is organized as follows. Section II reviews the

propulsive mechanism of the fish swimming. An overview of

the BCF swimming mode [2] in fishes is presented. In Section

III, the design characteristics and features of the prototype are

explained. The kinematics and dynamics modeling studies are

also presented. Further it presents the Solidworks design of the

mechanical prototype integrated with the MATLAB Sim-

Mechanics and its 3D Simulation using Virtual Reality

Modeling Language (VRML) toolbox. Then, Section IV shows

results from open loop experimental and simulation results are

presented on the four joints to produce the undulation of the

body motion. Conclusions and directions for future work are

discussed in Section V.

II. OVERVIEW OF BCF MODE FISH SWIMMING

Fishes have the ability to turn in less than a body length, and

from a standing start, fish can accelerate rapidly using only a

few flicks of their tails at the levels of more than 10 g's.

Locomotion in fishes is accomplished through a sequential

system of smaller muscles which contract in a wave along the

fish's body [1], [3]. Once they begin to move, fishes utilize

their sensory system to detect vortices created by their tails

and "push off' of the vortices which allows them to be very

efficient swimmers. This ability to take advantage of sensory

feedback allows them to avoid obstacles, make quick

maneuvers, and become as agile as possible in the underwater

environment efficiently.

The propelling process in fish motion is either undulatory

motion or oscillatory motion. In both ways body structures and

fin segments contribute the most in generating propulsion. Fish

swim either by using [2] [3]:

Body and/or caudal fin (BCF) locomotion,

Median and/or paired fin (MPF) locomotion,

Combination of both BCF and MPF[8] locomotion

There is a great variety of different types of fish propulsion

mechanisms. Two most generic categories of these are

periodic swimming and transient swimming. The latter is used

for rapid starts, escape maneuvers and turns. Periodic

swimming is used for steady, sustained locomotion. The

classification for fish periodic swimming was presented by

Breder et al.[9] in 1926. According to this classification there

are two main families of swimming: body and/or caudal fin

locomotion (BCF) and median and/or paired fin locomotion

(MPF). Fishes using BCF locomotion bend their bodies mainly

the posterior part into a backward-moving propulsive wave

that extends to caudal fin while fishes using MPF locomotion

use their other fins to propel themselves. Since 85% of fishes

use BCF locomotion, the focus of this paper is set on this type

of propulsion. At the basis of propulsion body and/or caudal

fin propulsion can be divided into 5 subgroups [2] [3]:

Anguilliform, Sub-carangiform, Carangiform, Thunniform and

Ostraciiform. Anguilliform swimming involves undulatory

motions, meaning that the transversal wave is moving through

whole body. Ostraciiform swimmer generates oscillatory

motions, in which the propulsive structure swivels without

exhibiting a wave formation. Sub-carangiform, carangiform

and thunniform motions are in between undulatory and

oscillatory motions sorted by the ratio of these two types. Two

of the most common types of fish bodies are carangiform, of

which the freshwater largemouth bass is one example.

Carangiform swimmers generally have rapidly oscillating tail.

In this type of locomotion the majority of movement is

concentrated in the very rear of the body and tail. The other

type is thunniform, of which the tuna is an example. Here, the

tail itself tends to be large and crescent shaped. These two

body types are not extremely different, and both are efficient

swimmers. Present paper tries to include the features of both

the swimming forms to develop a new prototype.

III. SYSTEM MODEL

The BCF mode carangiform style [5] of locomotion is

approximated using a 4-link (including the pectorals attached

to the head) mechanism with four actuated joints. The first link

as “head” functions as the “body” and is roughly two-thirds of

the weight of the entire robot. The “tail” of the robot is formed

by the second link connected to the caudal fin and pectorals by

the third and fourth link. Our mechanism is a reasonable

approximation to BCF carangiform locomotion, and therefore

small modifications of this model should have general use in

the analysis of carangiform swimming. In specific the methods

and techniques presented in this paper are applicable to the

posterior of the body with any degree of articulation or even

full flexibility.

The dynamics of any rigid body [6] can be completely

described by the translation of the centroid and the rotation of

the body about its centroid. The dynamics equations for the

four link system described are derived by defining the inertia

torques of each link and the reaction torques from the

connecting links. This leads to the ability to derive the actuator

torques necessary to produce the tail motion that is desired.

The links are interdependent in two major respects:

The torque produced on or by a link produces a

reaction torque on the other links.

The motion of the links changes the shape of the

linkage, which changes the inertia seen by previous

links

The approach used in this paper is developing a linearized

dynamic model of the Robo-Fish system. The two major

sections of the present paper Robo-Fish system model are:

1. Denavit-Hartenberg (DH) Kinematics Mode [7]: The

dynamics due to translation and rotation along the joints and

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the hydrodynamic (non-linear) forces on the Robotic Fish

system.

2. Lagrangian Dynamics Model [7]: The dynamics due to

kinetic and potential energy generated along each link and

inertia of the free-flow water entrained in the Robo-Fish

System.

When describing the kinematics and dynamics of the mode

shown in Fig.1, the interlink actuator-shaft constitutes the

inertial frame of reference. A local coordinate frame is

assigned to each DOF, both the constrained and the

constraining, of the link segments. The coordinate frames are

assigned according to the Standard Denavit-Hartenberg

notation.

Link and Joint Parameters

Joint angle (θi): the angle of rotation from the X i-1

axis to the Xi axis about the Z i-1 axis. It is the joint

variable if joint i is rotary.

Joint distance (di): the distance from the origin of the

(i-1) coordinate system to the intersection of the Z i-1

axis and the Xi axis along the Z i-1 axis. It is the joint

variable if joint i is prismatic.

Link length (ai): the distance from the intersection of

the Z i-1 axis and the Xi axis to the origin of the ith

coordinate system along the Xi axis.

Link twist angle (αi): the angle of rotation from the Z

i-1 axis to the Zi axis about the Xi axis.

Reference Frames:

FI Inertial frame of manipulator-base system.

FB Base Frame located at the centre of mass of the

base.

Fi Coordinate frame of the ith

link of the manipulator.

Vectors:

rB Position of frame F0 relative to and projected onto

frame FB.

rI Position of frame F0 relative to and projected onto

frame F0.

di Position of frame Fi relative to and projected onto

frame F0.

ri Position of point on link i relative to frame F0.

ρi Position of point on link i relative frame Fi.

b Position of point on the base relative frame FB.

bB Position of point on the base relative to frame FI.

vi Velocity of point on link i relative to frame FI.

vB Velocity of point on the base relative to frame FI.

Link parameters have been identified for the assigned frames,

according to the Standard Denavit-Hartenberg convention.

Table 1 summarizes the link parameters.

Generalized Equations of Motion

In the present work to obtain the dynamic equations of the

DOF base, the Lagrange-Euler formulation [7] is used which is

given by

τ i

eqn. …. (1)

Where, The Lagrange function is defined as

L = K – P eqn. …. (2)

Table 1. Identified link parameters for the Robo-fish model.

Fig.1: Relative orientations and locations of local coordinate frames at the CM of the head and the Inertial Frame of reference.

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Where

K: Total kinetic energy of robot

P: Total potential energy of robot

q: Joint variable of i-th joint

q : First time derivative of joint variables

τ: Generalized force (torque) at i-th joint

The right hand side of the equation is external forces or

torques acting on the base such as thruster control jets or

momentum gyros equations of motion.

eqn. …. (3)

Where,

eqn. …. (4)

D is the Inertia matrix

eqn. …. (5)

eqn. …. (6)

h is the Coriolis-centripetal matrix

eqn. …. (7)

c is the Gravity matrix.

τ is the generalized Force (torque) vector, and q is the

generalized angular coordinate. The above manipulator

dynamic equations have been developed in three dimensions

for an „n‟ link manipulator on a 6 degree of freedom base,

assuming that there is gravity acting on the system. In matrix

form torques are given by the dynamic equation form as

D(q)q + h(q,q ) + c(q) = τ

eqn. …. (8)

Where M is the Inertia matrix, V is the Coriolis-centripetal

matrix, G is the Gravity matrix.

(A) Solidworks Model Design

Solidworks, as the mainstream software in virtual prototype

field, combines multi-body dynamics modeling with large

displacements as well as multi functioning tools. It also

supports data exchange with other geometric modeling

software during product development. Solidworks has a more

powerful geometric modeling function. By utilizing

Solidworks, a kinematics model of Robot-fish, with

coordinated motion of multiple propulsive mechanisms, is

established as shown in Fig. 2 and further imported into

MATLAB through a common data exchange interface with the

XML format.

(B) Sim-Mechanics Model of the Robo-Fish

After the Robo-fish Assembly is exported to the Physical

Modeling XML format, the Sim-Mechanics toolbox Model is

generated.

Fish Environment – Ground – Head – Root Body – Interlinks -

Caudal fin inside a subsystem, called Robo-fish assembly,

representing the entire Sim-mechanics assembly. Fig.3

(C) 3D Simulation using VRML (Virtual Reality Model)

Model

Simulink 3D Animation allows us to visualize the dynamic

system simulations in a 3D virtual reality environment. It

provides an interface between MATLAB and Simulink and

virtual reality graphics represented in Virtual Reality Modeling

Language (VRML). By changing the position, rotation, size,

and other properties of objects in the virtual world, enabling us

to observe the dynamic behavior of the system.

The V-Realm Builder GUI offers a hierarchical, tree-style

view of objects that make up the virtual world. The

characteristics of the Robo-Fish can be driven from Simulink.

This model computes the position and the pitch of the Robot-

Fish.

In the Simulink diagram, the VR Sink is updated with two

inputs. The first input is Robot-Fish rotation. The rotation is

defined by a four-element vector. The first three numbers

define the axis of rotation. In present work, it is [0 0 1] for the

Z-axis. The yaw of the Robot-Fish is expressed by the rotation

about the Z-axis. The last digit is the rotation angle around the

Fig.2: Solidworks model of Robo-fish

.

Fig.3: Robot-Fish Complete model in Sim-Mechanics

.

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Z-axis, in radians. In the Simulink model, we have to connect

the line going to the Scope block labeled Display Yaw to the

Robot-Fish rotation input. The second input is plane

translation. This input describes the plane‟s position in the

virtual world. This position consists of three coordinates, x, y,

z. The connected vector must have three values. In this model

underwater environment is in the x-y plane. In the Simulink

model, the line going to the Scope block labeled Display

Position to the Robot-Fish translation input is connected. Once

the signals are connected the Scope blocks are removed. The

actual simulated model in VRM appears as shown in the Fig.4.

IV. SIMULATION RESULTS AND DISCUSSION

The project implementation is carried out in MATLAB. The

yaw-axis servomotor is a Hitec HS5085MG (3.6Kg-cm) and

Hitec HS485HB (4.8Kg-cm) used in the head joint. The work

in this paper has addressed the construction of a fin-actuated

(bio-inspired) fishlike underwater vehicle demonstrating the

Solidworks (mechanical model), MATLAB Sim-Mechanics,

VRML (3D motion) and Simulink to emulate the same. Also

the kinematic and dynamic modeling studies are explained and

tackled. Information about the design and construction of the

prototype is also elaborated. The inspiration and motivation of

this paper is described by the remarkable swimming abilities

of BCF mode carangiform style of swimming.

Out of various activities, some cases are considered for the

open-loop implementation. The controller implementation is

done on PIC dsPIC33F. The Simulink Model of the Robo-fish

is shown in Fig.5

For a given set of angles that generate the undulation of

motion in the open loop the output response has been observed

as shown in Fig.6. After feeding the desired set of trajectory

angles, the trajectory equation velocity (qd) and acceleration

(qdd) are calculated for particular time between initial and final

time. After obtaining angles, velocity and acceleration, D-H

matrix is formed (the dynamic sub-system).

By substituting these in Lagrangian equation, the torque at the

4 body joints are calculated acting on each servo actuator

(Motor sub-system).The tracking controller shown here is PD

(Proportional + Derivative) with appropriate tuned gains for a

stable system response. In all the above four cases it is seen

that the torques effect on the joint angle variation is a smooth

fixed pattern. The angular motion as shown in Fig.7 posses a

steady state position in short time periods (for all the four

joints) after the initial actuation signal has been rendered. All

the four joints (therefore links) attain steady state and settle in

that position, and moves linearly in one direction. When

torque is applied to the first joint, the first joint oscillates and

the second follows it with a delay.

Similarly for the other joints the system motion works. The

angular velocity also reduces to a stable margin Fig.8 after the

actuators have encountered the given torque generated by

desired trajectory angles on the dynamics of the body. As the

four joints have been distributed throughout the entire length

of the Robo-fish as shown in the mechanical design and

following the simulation results, the smooth and steady motion

of the entire body is therefore inferred.

Fig.4: Robot-fish VRML simulation

.

Fig.6: Robot-Fish open-loop simulation output (torque)

.

Fig.5: Computed Torque control model of Robot-fish in Simulink

.

Fig.7: Robot-Fish angular position output (4 joints)

.

Time (sec)

.

Time (sec)

.

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All the four joints (therefore links) attain steady state and settle

Based on the steady simulation results the experiments

validating the same were undertaken for different body-motion

configurations to emulate the undulation of the Robo-fish in

open environment (here Air) shown in Fig 9.

V. CONCLUSIONS AND FUTURE WORK

The manufactured prototype is a 45 cm. long, 6 DOF fishlike

underwater robot with a horizontal caudal fin (tail). The

system uses DC servomotors as actuators and is controlled by

micro-controller dsPIC33F. The future work primarily focuses

on developing a closed loop control algorithm and its

implementation .Up-gradation of the servos to BLDC and

hydrodynamic analysis has to be performed in the subsequent

stages of the development of this project. This paper describes

the modeling method of a Bio-Inspired Robo-Fish. Simulations

and Experiments have been carried out to verify the model of

the robotic fish. Future work will focus on the more accurate

fluid force and optimization of the robotic fish. The 3D

dynamic model derived within the framework of multi-body

dynamics has to be compared with experimental measurements

from the tests performed to verify the efficacy of the

established model. In addition, the discrepancy between the

simulations and the experiments is also due to the un-modeled

factors and mechanical limitations on the robot nonlinearities

present in the system.

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Fig.8: Robot-Fish angular velocity (4 joints) output

.

Fig.9: The Open-loop experimental setup showing the driving of the

Robo-fish to perform various fundamental maneuvers via delivery

of appropriate trajectory

.

Time (sec)

.