Post on 01-May-2023
Proceedings Book40th International Symposium on Robotics
Edited by:
Luis Basañez - Raúl Suárez - Jan Rosell
Organized by: Asociación Española de Robótica y Automatización Tecnologías de la Producción – AER-ATP
International Federation on Robotics – IFR
Sponsors:
Institutional SponsorsMinisterio de Industria, Turismo y Comercio
Ministerio Ciencia e Innovación
ACC1Ó Generalitat de Catalunya
Ajuntament de Barcelona
Asociación Española de Normalización - AENOR
Global SponsorsAsea Brown Boveri, S.A. (ABB)
Adept Technology Ibérica, S.L.
Fanuc Robotics Ibérica, S.L.
Kuka Robots Ibérica, S.A.
Motoman Robotics Ibérica, S.L.
Schunk Intec, S.L.
Stäubli Española, S.A.
Published by:Asociación Española de Robótica y Automatización Tecnologías de la Producción – AER-ATP
Copyright © March 2009
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ContentsSESSION TU-M-1 - INDUSTRIAL ROBOTS IMPROVEMENTS
A Symmetric Parallel Schönflies-Motion Manipulator for Pick and Place.......................................................................... 21
O. Altuzarra, Ch. Pinto, V. Petuya, B. Sandru, M. Diez
University of the Basque Country, Spain
Open architecture controller for an ABB IRB2000 industrial robot.................................................................................... 29
J. L. González, R. Sanz, F. Gayubo, J. C. Fraile, J. P. Turiel
Fundación CARTIF, Spain
ILC Filter Design for Input-Delay Robot Manipulators....................................................................................................... 35
T.-J. Ha, J. S. Yeon, J. H. Park
Hangyang University, Korea
S.-W. Son, S. Lee
Hyundai Heavy Industries Co., Ltd., Korea
Analysis on Dynamic Characteristics of an Industrial Robot Wrist................................................................................... 41
P.-J. Kim, H.-C. Cho, S.-H. Lee, S.-H. Jung, J.-S. Hur
Hyundai Heavy Industries Co., Ltd., Korea
SESSION TU-M-2 - INTELLIGENT MANUFACTURING SYSTEMS
Obstacle Avoidance Algorithm for Safe Human-Robot Cooperation in Small Medium Enterprise Scenario..................... 49
N. Pedrocchi, M. Malosio, L. Molinari Tosatti, G. Ziliani
National Research Council, Italy
Distributed Flexible Transport System by Cooperation of Flexible AGVs......................................................................... 55
D. Herrero-Pérez
University Carlos III of Madrid, Spain
H. Martínez-Barberá
University of Murcia, Spain
Development of the Highly-Efficient End effecter of Robot Control Cell Production Systems for the
Productivity Improvement in Multi-product Production in Varying Volumes ..................................................................... 61
H. Yonezawa, T. Nishiki, N. Higuchi, Y. Sugano, H. Hayashi, K. Ida, T. Takagi, M. Noshino, W. Tokumoto,
M. Yamada, T. Fujita
IDEC Corporation, Japan
CAM/Robotics Integrated Postprocessing in Redundant Workcells by means of Fuzzy Control .................................... 67
J. Andres, L. Gracia, J. Tornero
Technical University of Valencia, Spain
SESSION TU-A-1 - SLAM
Map Fusion of Visual Landmark-based Maps ................................................................................................................. 75
M. Ballesta, O. Reinoso, A. Gil, L. Payá, M. Julià
Miguel Hernandez University, Spain
An Extension to ICP Algorithm and its Application to the Scan Matching Problem ......................................................... 81
L. Armesto
Technical University of Valencia, Spain
L. Domenech
Asociación de investigación en Diseño y Fabricación, Spain
J. Tornero
Technical University of Valencia, Spain
11
Visual Self-Localization for Small Mobile Robots with Weighted Gradient Orientation Histograms................................. 87
M. Hofmeister, M. Liebsch, A. Zell
University of Tübingen, Germany
A Mobile Robot For On-Line Registration of Indoor 3D Models ...................................................................................... 93
J. Pulido Fentanes, S. Marcos Pablos, Domínguez Quijada
Fundación CARTIF, Spain
E. Zalama, J. Gómez García-Bermejo, J. R. Perán González
Universidad de Valladolid, Spain
SESSION TU-A-2 - VISION
Robotic Quality Assurance using 3D Laser Rotating Scanner.........................................................................................101
A. Picón, A. Bereciartua, J. A. Gutiérrez, J. Pérez
ROBOTIKER-TECNALIA, Spain
Tracking based on Hue-Saturation Features with a Miniaturized Active Vision System ..................................................107
J. A. Corrales, P. Gil, F. A. Candelas, F. Torres
University of Alicante, Spain
Hybrid Collaborative Stereo Vision System for Mobile Robots Formation Navigation .....................................................113
F. Roberti, J. M. Toibero, C. Soria
Universidad Nacional de San Juan, Argentina
R. F. Vassallo
Universidades Federal do Espirito Santo, Brasil
R. Carelli
Universidad Nacional de San Juan, Argentina
Robotics Platform Integrating Visual Recognition and RFID for Classification and Tracking Applications ......................119
C. Cerrada, J. J. Escribano, J. L. Bermejo, I. Abad, J. A. Cerrada, R. Heradio
UNED, Spain
SESSION WE-M-1 - MODELLING AND CONTROL
On Evolving a Robust Force-Tracking Neural Network-Based Impedance Controller.....................................................127
J. de Gea, Y. Kassahun
University of Bremen, Germany
F. Kirchner
DFKI (German Reserach Center for Artificial Intelligence), Germany
Safe Avoidance of Online-detected Obstacles for Robot Manipulators...........................................................................133
L-P. Ellekilde, H. G. Petersen
University of Southern Denmark, Denmark
Real Time Distributed Control of parallel robots using redundant sensors .....................................................................139
I. Cabanes, A. Zubizarreta, M. Marcos, Ch. Pinto
University of the Basque Country, Spain
Force Amplifier Mechanism for Small Manipulator...........................................................................................................145
Y. Aiyama, T. Kudou
University of Tsukuba, Japan
Searching a valid hand configuration to perform a given grasp ......................................................................................151
R. Suárez, J.-A. Claret
Universitat Politècnica de Catalunya, Spain
The Role of Simulation Tools in the Teaching of Robot Control and Programming........................................................157
A. Romeo
Universidad de Zaragoza, Spain
12
SESSION WE-M-2 - HUMAN ROBOT INTERACTION
Haptic Interaction with a Virtual Hand in Collaborative Tasks..........................................................................................165
Héctor A. Moreno, Roque Saltaren, M. Ferre, R. Aracil
Universidad Politécnica de Madrid, Spain
Robotics Teleoperation Using Bilateral Control by State Convergence and a Haptic System of Assistance ..................171
C. Peña
Universidad Politécnica de Madrid / Universidad de Pamplona, Spain / Colombia
R. Aracil, R. Saltaren, M. Ferre
Universidad Politécnica de Madrid, Spain
A Multimodal Teleoperation Framework: Implementation and Experiments ....................................................................177
E. Nuño
Technical University of Catalonia / University of Guadalajara, Spain / México
L. Basañez, L. Palono, A. Rodríguez
Technical University of Catalonia, Spain
Control Strategies for Human-Robot Interaction using EOG ...........................................................................................183
E. Iañez, J. M. Azorín, E. Fernandez, J. M. Sabater
Universidad Miguel Hernández de Elche, Spain
An augmented reality interface for training robotics through the web..............................................................................189
C. A. Jara, F. A. Candelas, P. Gil, M. Fernández, F. Torres
University of Alicante, Spain
A Power Assist Device for handling Heavy loads.............................................................................................................195
P. González de Santos, E. García, J. F. Sarria, R. Ponticelli, J. Reviejo
Institute of Industrial Automation - CSIC, Spain
SESSION WE-A-1 - NEW ROBOT APPLICATIONS
Advanced HMI for robot programming: An Industrial application for the ceramic industry ..............................................203
G. Veiga
University of Coimbra, Portugal
R. Cancela
Motofil Robotics / University of Aveiro, Portugal / Portugal
Use of CAD/CAM/ROB integration for Scaled Orography Modelling. A case study: Mijares River.................................209
J. Andrés, L. Gracia, J. Tornero
Technical University of Valencia, Spain
Welding Process Control for Rapid Manufacturing: Two Different Approaches Using Tin and Stainless Steel ..............213
G. Muscato, G. Spampinato, L. Cantelli
Università degli Studi di Catania, Italy
Evolution of the Robotics in the NDT Inspection .............................................................................................................219
R. Alberdi, M. Aguado, J. L. Rembado
Tecnatom, S.A., Spain
SESSION WE-A-2 - AERIAL ROBOTS
TG2M: Trajectory Generator and Guidance Module for the Aerial Vehicle Control Language AVCL...............................225
A. Barrientos, J. Colorado, P. Gutiérrez
Universidad Politécnica de Madrid, Spain
Development of an Adaptive Wing System for the Aquila Disseminative Multilayered Unmanned Aerial System..........233
A. Khan, R. Molfino
University of Genova, Italy
13
RF-based Particle Filter localization for Wildlife Tracking by using an UAV.....................................................................239
P. Soriano, F. Caballero
University of Seville, Spain
A. Ollero
University of Seville / Centro Avanzado de Tecnologías Aeroespaciales, Spain / Spain
Method based on a particle filter for UAV trajectory Prediction under uncertainties........................................................245
R. Conde, J. A. Cobano
Universidad de Sevilla, Spain
A. Ollero
Universidad de Sevilla / Centro Avanzado de Tecnologías Aeroespaciales, Spain
SESSION TH-M-1 - MOBILE ROBOT NAVIGATION
Comparative Study of Localization Techniques for Mobile Robots based on Indirect Kalman Filter...............................253
R. González, F. Rodríguez, J. L. Guzmán, M. Berenguel
Universidad de Almería, Spain
Adaptive Extended Kalman Filtering for Mobile Robot Localization.................................................................................259
R. Caballero
Universidad Tecnológica de Panamá, Panamá
D. Rodríguez-Losada, F. Matia
Universidad Politécnica de Madrid, Spain
Stereo Image Registration Based on RANSAC with Selective Hypothesis Generation...................................................265
R. Cupec.
University of Osijek, Croatia
A. Andreja Kitanov, I. Petrovic
University of Zagreb, Croatia
Manoeuvres for Autonomous Mobile RoboT Navigation using the Optical Flow and Time-to-Contact Techniques................271
P. Nebot, E. Cervera
Jaume I University, Spain
Control Structure a Mobile Robot for Maintenance of Material Flow Systems ................................................................277
T. Brutscheck, M. Bücker, B. Kuhlenkötter
Dortmund University of Technology, Germany
Speaker Localization and Tracking in Mobile Robot Environment Using a Microphone Array ........................................283
I. Markovic, I. Petrovic
University of Zagreb, Croatia
SESSION TH-M-2 - PLANNING IN ROBOTICS
An Hybrid Architecture for Multi-Robot Integrated Exploration .......................................................................................291
M. Juliá, A. Gil, L. Payá, O. Reinoso
Miguel Hernández University, Spain
A Constraint-based Probabilistic Roadmap Planner .......................................................................................................297
A. Pérez, A. Rodríguez, J. Rosell, L. Basañez
Technical University of Catalonia, Spain
Error Adaptive Tracking for Back Stepping Controllers: Application to Mobile Robots ...................................................303
F. Diaz-del-Rio, D. Cagigas, J. L. Sevillano, S.
Vicente, D. Cascado
Universidad de Sevilla, Spain
Simultaneous Task Subdivision and Assignment in the FRACTAL Multi-robot System ..................................................309
C. Rossi, L. Aldama, A. Barrientos
Universidad Politécnica de Madrid, Spain
14
A Dynamic Model-Based Acceleration Setting Method for Industrial Robots Trajectories ..............................................315
J. -Y. Kim, D.-H. Kim, S.- R. Kim
Hyundai Heavy Industries Co., Ltd., Korea
Path planning using sub-and-super-harmonic functions .................................................................................................319P. Iñiguez
Rovira i Virgili University, Spain
J. Rosell
Technical University of Catalonia, Spain
SESSION TH-A-1- SERVICE ROBOTICS
An Underwater Robotic System for Sea-bottom Reclamation ........................................................................................327
R. Molfino, M. Zoppi
University of Genova, Italy
Decentralized Control for Robot Teams in Unknown Environments ................................................................................333
R. Falconi, C. Melchiorri
University of Bologna, Italy
“HUMI” - a mobile Robot for Humanitarian Demining ......................................................................................................339
P. Kopacek
Vienna University of Technology, Austria
Robot Technology to Support Workplace Ergonomic Adaptation ...................................................................................345
J. de Nó, P. González de Santos
Instituto de Automatica Indusrial - CSIC, Spain
Developing a strategic research agenda for robotics in Europe .....................................................................................351
R. Bischoff, T. P. Guhl
KUKA Roboter GmbH, Germany
O. Schwandner
Fraunhofer-Institute für Produktionstechnik und Automatisierung (IPA), Germany
SESSION TH-A-2 - COGNITIVE ROBOTICS
Improved Vibration based Terrain Classification using Temporal Coherence .................................................................359
P. Komma, C. Weiss, A. Zell
University of Tübingen, Germany
A cognitive System based on Emotions for Autonomous Robots ...................................................................................365
I. Chang
Universidad Tecnológica de Panamá, Panamá
M. Álvarez, R. Galán
Universidad Politécnica de Madrid, Spain
An Evolutionary Approach to Maximum Likelihood Estimation for Generative Stochastic Models ..................................371
R. C. Kelley, M. Nicolescu, M. Nicolescu, S. Louis
University of Nevada, USA
3D Internet Simulation of the Collective Behaviour of Robot Swarms ...........................................................................377
F. P. Bonsignorio
Heron Robots s.r.l., Italy
15
Hybrid Collaborative Stereo Vision Systemfor Mobile Robots Formation Navigation
F. Roberti†, J.M. Toibero†, C. Soria†, R.F. Vassallo‡ and R. Carelli†
†Instituto de Automática, Universidad Nacional de San Juan, Av. San Martín Oeste 1109 - J5400ARL- ARGENTINA (e-mail: froberti@inaut.unsj.edu.ar)
‡Dpto. de Enghenaria Elétrica, Universidade Federal do Espirito Santo Av. Fernando Ferrari 514, Vitória, ES, BRASIL
Abstract: This paper presents the use of a hybrid collaborative stereo vision system (3D-distributed visual sensing using different kind of vision cameras) for the autonomous navigation of a wheeled robot team. It is proposed a triangulation-based method for the 3D-posture computation of an unknown object by considering the collaborative hybrid stereo vision system, and this way to steer the robots team to a desired position relative to such object while maintaining a given robot formation. Experimental results with real mobile robots are included to validate the proposed vision system.
1. INTRODUCTION
Artificial vision systems have been widely used as external sensors in mobile robotics applications due to the large amount of information that they can offer. For this reason, they become nowadays in the most used sensors in tasks such as surveillance, search, exploration, rescue, mapping and even they have been used for autonomous navigation (Soria et al., 2007; Carelli et al., 2006b; Okamoto y Grassi, 2002; Vassallo et al., 2005). Moreover, the use of two or more cameras simultaneously gives to the system the 3D perception, allowing it to successfully perform different tasks in completely unknown environments. Additional advantages could be obtained by including onmidirectional cameras into the system (Correa y Okamoto, 2005). These cameras allow increasing the horizontal visual field to 360º but loosing image resolution. Another choice is to combine catadioptric cameras with perspective-transformation cameras constructing a new hybrid stereo vision system, which have the advantages of both mentioned kind of vision cameras (Adorni et al., 2001; Sturm, 2002). It is a well known fact that most of the previously mentioned tasks could be done more efficiently by considering two o more robots working cooperatively (Carelli et al., 2006a; Das et al., 2002; Roberti et al., 2007; Toibero et al., 2008). A similar situation could be thought for the stereo vision system, where each camera is on a different robot introducing a new collaboration degree between the robots in the team. Hence, the robots not only execute a cooperative task but also help to perform an environment information recollection which is necessary to carry out this task. This concept of vision sensors distribution among the different robots in the team not only reduces the computational effort by dividing image processing tasks, but also allows introducing a reconfigurable stereo vision system able to be adapted to the requisites imposed by the robot surroundings (Zhu et al.., 2004; Cervera, 2005).
In this paper it is considered the use of a collaborative hybrid stereo vision system (3D distributed visual sensing using different types of vision cameras) for the autonomous navigation of a mobile robots team. It is proposed a triangulation-based method for the posture computation of an unknown object in the tridimensional space by using the hybrid collaborative stereo vision system steering the robots team to a desired goal position relative to such object (Soria et al., 2007) while maintaining an a priori known robot formation (Roberti et al., 2007).
Other previously published papers consider reconfigurable stereo vision systems. In the work of (Zhu et al., 2004) it is introduced a reconfigurable vision system composed by two onmidirectional cameras and it is proposed its use to perform a human being following task within a surveillance scope. In the work of (Cervera, 2005) the vision system is integrated exclusively by perspective transformation cameras and exposes its use in object-manipulation tasks by considering a mobile manipulator. Different from these papers, this work proposes the construction of a hybrid collaborative vision system and its use for the autonomous navigation of a robot team.
The remainder of this paper is organized as follows: Section 2 summarizes the different vision systems models employed along the paper and presents the proposed hybrid stereo vision system. Sections 3 and 4 deal with the control strategies considered for the autonomous robot team navigation. Section 5 exposes the experimental results obtained and finally, Section 6 states conclusions and describe future related works.
2. VISION SYSTEMS MODELS
A vision camera transforms a 3D space into a 2D projection on the image plane, where the vision sensor is located. This
113
projection causes the lost of the depth perception, which means that each point on the image plane corresponds to a ray in the 3D space.
2.1 Perspective projection camera model
Several projection models for the representation of the image formation process have been proposed. The most used is the perspective projection model or “pin-hole” model. In this model, a coordinate system Z,Y,X,O PPPP attached to the
camera is defined in such a way that the X and Y axes define a base for the image plane and the Z axis is parallel to the optic axis. The origin of the framework Z,Y,X,O PPPP is
located at the focus of the camera lens. From Fig.1.a, a fixed point P in the 3D space with coordinates T
PPP ZYXPon the framework attached to the perspective camera will be projected on the image plane as a point with coordinates
TPP
P vu given by,
TPP
P
PP YXZf
(1)
where fP is the focal length of the camera expressed in pixels.
2.2 Omnidirectional vision system
Omnidirectional vision systems allow obtaining 360º field-of-view images. These images could be obtained by using a single camera rotating around its own Y-axis, by using multiple cameras, each one oriented in a different direction or by using a catadioptric system (Yagi, 1999). Central catadioptric cameras combine convex reflective surfaces and perspective cameras with the aim of attaining a 360º field-of-view with a single image. These vision systems are formed by mounting a camera in front of a convex mirror in such a way that the camera sees the image reflected by the mirror (Baker and Nayar, 1998), as Fig.1b shows. The catadioptric camera used in this work was built with a conventional perspective projection color CCD camera and a hyperbolic mirror, by aligning the camera optic axis with the mirror axis, and making the optic centre of the camera coincident with the focus F’ of the hyperbola (Svoboda et al. 1998).
Fig.1.a) Perspective projection camera model and 1.b) Catadioptric vision system
Fig.2. Stereo vision system
In the framework Z,Y,X,O OOOO attached to the
perspective camera of the catadioptric system, the equation that describes the hyperbolic mirror geometric is,
12
22
2
2
byx
aez with 22 bae (2)
2.3 Hybrid stereo vision system
Both vision systems briefly described in the above Sections could be combined with the aim of constructing a stereo vision system in order to obtain depth perception (Adorni et al., 2001). With this stereo vision system, it will be possible to get the 3D coordinates of an object without any previous knowledge about it. The structure of the proposed vision system is shown in Fig. 2. In this figure the coordinates of the relevant points are,
TO 200 eF ; T
OOOO ZYXP
TPPP
P ZYXP ;T
mmmmO ZYXP
TOO
O vu ; T
PPP vu
(3)
where 0F is the focus of the hyperbolic mirror expressed in the omnidirectional vision system framework, 0P is the interest point P expressed in the omnidirectional vision system framework, 0Pm is the point where the ray PFcrosses the mirror expressed in the omnidirectional vision system framework, 0 is the projection of 0Pm on the omnidirectional image plane, PP is the interest point Pexpressed in the perspective projection camera framework, and P is the projection of P on the perspective projection camera image plane.
The objective of this Section is to find the equation system that allows getting the 3D coordinates of the interest point P in the framework attached to the perspective projection camera. Initially, it is necessary to express the point 0Pm as a function of the 0P-coordinates, finding the expression of the ray PF in the omnidirectional vision system framework,
eZezYyeZezXx
2/22/2
OO
OO (4)
F
P
Pm
OP
pZ
pY
fP fO
PO
OO F’
pX
OZ
OX-OY
P
YP
XP
ZP
PXPY
PZ
uP
vPOP
fP
114
and introducing (4) in (2), a second order equation in z, that represent the z-coordinates of the two points where the ray PF crosses the hyperbole, is obtained
1/2
22
2/ 22
OO
2
OO
22 beZ
ezYeZ
ezXaez (5)
Operating and reorganizing (5),
02 CzBzA (6)with
2O
2
2O
2O
2 21
eZbYX
aA ; 2
O2
2O
2O
2 242
eZbYXe
aeB
and 12
42
O2
2O
2O
2
2
2
eZbYXe
aeC .
Then, (6) can be solved by using
AACBBz
242
2,1 (7)
The value will be the z-coordinate of the point 0Pm. By introducing in (4), the 3D coordinates of the point 0Pm can be gotten as functions of 0P 3D coordinates,
eZeXX 2/2 OOm (8.1)eZeYY 2/2 OOm (8.2)
mZ (8.3)Now, the pin-hole model of the perspective camera in the omnidirectional system,
Tmm
m
OO YXZf
(9)
can be used to get the projection of the point 0Pm in the omnidirectional image. Next, by introducing (8.1), (8.2) and (8.3) in (9) the equations that relate the projection of the interest point P after its reflection on the mirror with its 3D coordinates in the framework attached to the omnidirectional vision system can be obtained,
OO
OOO
O
OO 2
2;
22
YeZfe
vXeZfe
u (10)
By taking into account that PP and 0P are the same interest point represented in two different coordinate systems, it is possible to relate them by
TPRP OP (11)
where 33ijrR and 13
itT are the rotation matrix and the translation vector that represent the relative position between both frameworks. Equation (11) can be split in the following three equations,
3O132O121O11P tZrtYrtXrX
3O232O221O21P tZrtYrtXrY
3O332O321O31P tZrtYrtXrZ(12)
Now, XP, YP, X0 and Y0 in (12) can be replaced using (1) and (10), obtaining the following three-equation system of three variables ( , Z0, ZP),
313212111PP
PO13O12O11 trtrtrZ
fu
Zrvrur
323222121PP
PO23O22O21 trtrtrZ
fv
Zrvrur
333232131PO33O32O31 trtrtrZZrvrur
(13)
where O
O
22
feeZ
.
The three-equation system (13) allows getting the z-coordinate of the interest point P in both coordinate systems (Z0, ZP) and parameter. Then, by using (1) and (10), the complete 3D position of the point in both frameworks can be obtained. As it is usual in stereo vision systems, it is necessary to know the extrinsic parameters (R and T), the focal length of the perspective projection camera fP, and the coordinate of the interest point on the image planes (O and P ), which are measured directly from the images using some image processing method. Although the feature extraction and the points’ correspondence between images are very interesting problems, they are not addressed and it is considered that O and P are obtained by some image processing technique.
Remark. Note that (13) has been found considering hyperbolic shape mirror and its application is restricted for this kind of catadioptric vision systems. Nevertheless, it can be generalized for any mirror shape if it is considered the general projection model (Geyer and Daniilidis, 2000). In this case, (13) becomes,
313212111
OO12O11
13PP
PO12O11
trtrtr
Zml
vrurrZ
fu
mlvrurl
323222121
OO22O21
23PP
PO22O21
trtrtr
Zml
vrurrZ
fv
mlvrurl
333232131
OO32O31
33PO32O31
trtrtr
Zml
vrurrZ
mlvrurl
(14)
where l and m are parameters of the general projection
model; 2O
2O
2O ZYX , ZP and Z0 are the unknown
variables of the three-equation system (14)
3. FORMATION CONTROL
The coordinated navigation for the robots team is achieved by considering the formation control proposed by (Roberti et al,2007), which allows the robots to reach a specific formation, and to maintain it while the robots navigate in the workspace. This formation controller is based on a decentralized leader-following technique, i.e., the leader robot navigates under its own control law sensing the followers’ posture (relative to its own reference framework). With this information the leader
115
computes the control actions to be send to each follower in order to successfully accomplish the navigation objective under formation. Follower robots are considered as unicycle-like robots navigating with linear velocity v and orientation on the coordinate system Y,X,O LLL attached to the leader
robot. By considering the robot as the punctual object C, the following equation set can describe this movement
'cossinsencos
vdvydvx
(15)
where v’ y are the leader robot linear and angular velocities (and hence, the velocities that rule its associated framework movement); is the follower robot angular velocity; d-distance and -angle define the follower robot position with respect to the leader robot according to Fig. 3.
In order to compute an error between the actual positions of each robot and its desired positions in the formation, let
Tiii yxL be the position vector of the i-th robot, and
Tdidii yxd
L be the i-th desired position, with i=1,2,..,n
both vectors are defined on the framework Y,X,O LLL
attached to the leader robot, as Fig.4 shows. For each case, the n position vectors can be arranged in the global vectors:
TTn
LT2
LT1
LL and TTLT2
LT1
LLndddd .
The difference between the actual and the desired robot’s position is,
dLLL ~
. (16)The formation error is defined as follows,
hhhhhhh dddLL ;;~ (17)
where h is the output variable, which captures information on the actual conditions of the robots team and dh represents
the desired output variable. The function h L must be defined in such a way that it is continuous and differentiable, and the Jacobian matrix J that relates h with L ,
Jh LL ; nnx22L
LL hJ , (18)
has full rank. Vector L has two different components, that
is lsLLL , where s
L is the time variation of L
due to the velocities of the follower robots; and lL is the
Fig.3. Robot kinematic model
Fig.4. Actual and desired positions
time variation of L due to the velocities of the leader robot. Now, the first equation of (18) can be written as:
lsJh LLL . (19)The control objective is to guarantee that the multi-robot system asymptotically reaches the desired formation defined by hd. Formally, the designed control system must satisfy that 0h t
t
~lim . First, from (19) a vector of reference
velocities for the robots is defined as,
lhfKhJ d1
rL
h~
LL ~(20)
where K is a diagonal and positive definite matrix, hfh
~~ is a
continuous saturation function applied to the output error, such that 0~~
~ hfh hT for all 0h~ ; for example hfh
~~ can
be selected as h~tanh . Vector rL represents the velocities
of the follower robots on the framework attached to the leader robot that allows them to reach the desired formation and keep it while following the leader. It can be proved that the following commands for linear and angular velocities
riiici fk ~ (21)
iiciv ~cosLr (22)
guarantee that the follower robots will asymptotically achieve the reference velocities defined in (20). In (21) and (22), k i
is a positive constant; irii~ is the angular error
between the i-th robot and the heading of its reference velocity; ri is the time derivative of the reference velocity heading for the i-th robot; if ~ is a continuous saturation function applied to the angular error, such that 0~~
ii ffor all 0~
i .
4. LEADER ROBOT NAVIGATION CONTROL
The leader robot navigates accordingly to the control laws proposed by (Soria et al., 2007). This controller generates the linear and angular velocity commands (v’c and c) in order to set its position (and consequently, the whole team) in front of an unknown object. Such commands are obtained by computing the robot-object relative posture. This posture is defined by the distance and the angles and , as can be seen in Fig.5.
The control objective is to maintain the robot at certain fixed distance d behind the object with = d considering only the robot-object information provided by the vision camera.
WX
WY
d
LYLX
v
v’
x
y
WO
| d|C
Ld1
Ld2
LX
LY yd2
xd2yd1
xd1
y1
y2
x1
x2
L2
L1
116
Fig.5. Robot-object relative posture
This way, some characteristic problems due to odometry errors can be avoided. Nevertheless, the vision system must be fast and precise, guaranteeing the controller quality. Being
d~ and d
~ , then the control objective could be specified as
twith0~;0~ (23)
The robot-object relative position evolution will be given by their time derivatives. Where the distance error variation is given by the difference between the velocity projections of the robot (v’) and the object (vT) on the line 3
L O P (Fig.5),
cos'cos~ vvT . (24)
Analogously, the -angle variation has three terms: the leader robot angular velocity and the rotational effect produced by the linear velocities of both: the robot and the objective. This could be written as
sin'sin~ vvT . (25)
Next, it is proposed the following controller which satisfies the control objective (23),
cos)~(cos
'fv
v Tc (26)
sin'sin)~( vvf Tc (27)
where )~(,)~( ff are continuous saturation functions such that 0xfx for all 0x . For this paper,
)~tanh()~( kf and )~tanh()~( kf , being k ,, k and positive constants. The -distance and the angles
necessaries for the control laws computation could be obtained from the (not vertically aligned) unknown object corner positions P1 and P2 as is shown in Fig.5,
22P1P
22P1P2
1 yyxx (28)
2P1P2P1P1 /tan yyxx (29)
2P1P
2P1P1tan2 xx
yy(30)
where (xP1,yP1) and (xP2,yP2) are de coordinates of the points P1 and P2 obtained through the hybrid stereo vision system.
5. EXPERIMENTAL RESULTS
In order to validate the proposed method for reconstructing the 3D position of an unknown object, a collaborative sensing experiment using the hybrid stereo vision system was carried out. The experimental setup is a mobile robots team consisting of two mobile robots Pioneer (manufactured by Mobile Robots Inc.). The leader robot has the catadioptric vision system and the follower robot has the conventional perspective projection camera. In the experiment, the team of robots must autonomous navigate maintaining a desired formation until they reach a desired posture relative to a static unknown object (vT = 0). In Fig. 6, the complete structure of the proposed control system is showed.
By using the hybrid collaborative stereo vision system, the team gets the posture of the unknown object relative to the leader robot, necessary in (26) and (27); and with the catadioptric vision system, the leader robot obtains the posture of the follower robot relative to its own framework, required in (20), (21) and (22). Additionally, the posture of the follower robot allows the leader to determine the matrix R and the vector T that define the relative posture between both vision systems, needed in (13).
Fig.6. Proposed control system
Figures 7, 8 and 9 show the results of the experiment. Figure 7 shows the evolution of the distance error d
~ ;whereas Fig. 8 shows the evolution error d
~ ; and the trajectories described by the robots are shown in Fig. 9.
Fig.7. Catadioptric Vision System: Robot-object position error
Leader controller
Followerrobot
Formationcontroller
d
Ld
L
O
P
v’c
c
vT vc
c
-
-
v’
-d
H
Leader robot
Perspective camera
Omnidirectional camera
Unknown Object
LY
LX
Leader Robot
v’
yP1
yP2
xP2
xP1
P1 P2P3
117
Fig.8. Catadioptric Vision System: Robot-object angular error
Fig.9. Trajectories described by the robots
6. CONCLUSIONS
In this paper, it has been presented a collaborative hybrid stereo vision system, i.e., a stereo vision system composed by a perspective transformation camera and a catadioptric camera, each one mounted on different mobile robots. This way, both robots collaborates on the environment information extraction needed to satisfy the proposed control objectives. Also, the stereo vision system can be re-configured with the aim of obtaining the best quantity and the better environment information quality. Furthermore, experimental results that clearly show the good performance of this vision system when applied to the mobile robot navigation have been presented.
Future works on this subject, will address the implementation of collaborative vision systems with more than two cameras, the proposal for new algorithms to compute the best vision system configuration and consequently the desired position of each robot into the desired formation. Furthermore, the consideration of Scale Invariant Features Transform (SIFT) algorithms for the image features extraction and for the determination of correspondence between the points on different images would add robustness to the vision system.
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