In this paper, we consider the task of tracking a maneuvering target both with a single nonholonomic agent and a swarm of nonholonomic agents. In order to achieve the tracking task, a decentralized continuous-time control scheme, which combines artificial potentials and sliding mode control techniques, is developed via constructive analysis. The effectiveness of the proposed control scheme is established analytically and demonstrated via a set of simulation results.
Issue Section:
Research Papers
References
1.
Astolfi
, A.
, 1996
, “Discontinuous Control of Nonholonomic Systems
,” Syst. Control Lett.
, 27
, pp. 37
–45
.10.1016/0167-6911(95)00041-02.
Balch
, T.
, and Arkin
, R. C.
, 1998
, “Behavior-Based Formation Control for Multirobot Teams
,” IEEE Trans. Rob. Autom.
, 14
(6
), pp. 926
–939
.10.1109/70.7367763.
Lawton
, J. R. T.
, Beard
, R. W.
, and Young
, B. J.
, 2003
, “A Decentralized Approach to Formation Maneuvers
,” IEEE Trans. Rob. Autom.
, 19
(6
), pp. 933
–941
.10.1109/TRA.2003.8195984.
Beard
, R. W.
, Lawton
, J.
, and Hadaegh
, F. Y.
, 2001
, “A Coordination Architecture for Spacecraft Formation Control
,” IEEE Trans. Control Syst. Technol.
, 9
(6
), pp. 777
–790
.10.1109/87.9603415.
Desai
, J. P.
, Ostrowski
, J. P.
, and Kumar
, V.
, 2001
, “Modeling and Control of Formations of Nonholonomic Mobile Robots
,” IEEE Trans. Rob. Autom.
, 17
(6
), pp. 905
–908
.10.1109/70.9760236.
Das
, A. K.
, Fierro
, R.
, Kumar
, V.
, Ostrowski
, J. P.
, Spletzer
, J.
, and Taylor
, C. J.
, 2002
, “A Vision-Based Formation Control Framework
,” IEEE Trans. Rob. Autom.
, 18
(5
), pp. 813
–825
.10.1109/TRA.2002.8034637.
Tanner
, H. G.
, Pappas
, G. J.
, and Kumar
, V.
, 2004
, “Leader-to-Formation Stability
,” IEEE Trans. Rob. Autom.
, 20
(3
), pp. 443
–455
.10.1109/TRA.2004.8252758.
Xie
, F.
, and Fierro
, R.
, 2009
, “Stabilization of Nonholonomic Robot Formations: A First-State Contractive Model Predictive Control Approach
,” J. Comput. Inf. Technol.
, 17
(1
), pp. 37
–50
.10.2498/cit.10011889.
Ogren
, P.
, Fiorelli
, E.
, and Leonard
, N. E.
, 2004
, “Cooperative Control of Mobile Sensor Networks: Adaptive Gradient Climbing in a Distributed Environment
,” IEEE Trans. Autom. Control
, 49
(8
), pp. 1292
–1302
.10.1109/TAC.2004.83220310.
Fax
, J. A.
, and Murray
, R. M.
, 2004
, “Information Flow and Cooperative Control of Vehicle Formations
,” IEEE Trans. Autom. Control
, 49
(9
), pp. 1465
–1476
.10.1109/TAC.2004.83443311.
Jadbabaie
, A.
, Lin
, J.
, and Morse
, A. S.
, 2003
, “Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules
,” IEEE Trans. Autom. Control
, 48
(6
), pp. 988
–1001
.10.1109/TAC.2003.81278112.
Orqueda
, O. A. A.
, Zhang
, X. T.
, and Fierro
, R.
, 2007
, “An Output Feedback Nonlinear Decentralized Controller for Unmanned Vehicle Co-Ordination
,” Int. J. Robust Nonlinear Control
, 17
(12
), pp. 1106
–1128
.10.1002/rnc.116713.
Dong
, W.
, and Farrell
, J. A.
, 2009
, “Decentralized Cooperative Control of Multiple Nonholonomic Dynamic Systems With Uncertainty
,” Automatica
, 45
(3
), pp. 706
–710
.10.1016/j.automatica.2008.09.01514.
Masoud
, A. A.
, 1995
, “A Boundary Value Problem Formulation of Pursuit-Evasion in a Known Stationary Environment: A Potential Field Approach
,” IEEE International Conference on Robotics
, pp. 2734
–2739
.15.
Kim
, D.-H.
, and Oh
, J.-H.
, 1998
, “Globally Asymptotically Stable Tracking Control of Mobile Robots
,” IEEE International Conference on Control Applications
, Vol. 2
, pp. 1297
–1301
.16.
Fierro
, R.
, and Lewis
, F. L.
, 1995
, “Control of a Nonholonomic Mobile Robot: Backstepping Kinematics Into Dynamics
,” IEEE Conference on Decision and Control
, Vol. 4
, pp. 3805
–3810
.17.
Kube
, R. C.
, and Bonabeau
, E.
, 2000
, “Cooperative Transport by Ants and Robots
,” Rob. Auton. Syst.
, 30
(1/2
), pp. 85
–101
.10.1016/S0921-8890(99)00066-418.
Yamaguchi
, H.
, 1999
, “A Cooperative Hunting Behavior by Mobile-Robot Troops
,” Int. J. Robot. Res.
, 18
(8
), pp. 931
–940
.10.1177/0278364992206666419.
Raffard
, R. L.
, Tomlin
, C. J.
, and Boyd
, S. P.
, 2004
, “Distributed Optimization for Cooperative Agents: Application to Formation Flight
,” IEEE Conference on. Decision and Control
, Vol. 3
, pp. 2453
–2459
.20.
Gazi
, V.
, and Ordonez
, R.
, 2007
, “Target Tracking Using Artificial Potentials and Sliding Mode Control
,” Int. J. Control
, 80
(10
), pp. 1626
–1635
.10.1080/0020717070145530721.
Yao
, J.
, Ordonez
, R.
, and Gazi
, V.
, 2007
, “Swarm Tracking Using Artificial Potentials and Sliding Mode Control
,” J. Dyn. Syst., Meas., Control
, 129
(5
), pp. 749
–754
.10.1115/1.276451122.
Saaj
, C. M.
, Lappas
, V.
, and Gazi
, V.
, 2006
, “Spacecraft Swarm Navigation and Control Using Artificial Potential Field and Sliding Mode Control
,” IEEE International Conference on Industrial Technology
, Mumbai, India
, pp. 2646
–2652
.23.
Lee
, D.
, 2010
, “Passive Decomposition and Control of Nonholonomic Mechanical Systems
,” IEEE Trans. Rob.
, 26
(6
), pp. 978
–992
.10.1109/TRO.2010.208243024.
Defoort
, M.
, Floquet
, T.
, Kokosy
, A.
, and Perruquetti
, W.
, 2008
, “Sliding-Mode Formation Control for Cooperative Autonomous Mobile Robots
,” IEEE Trans. Ind. Electron.
, 55
(11
), pp. 3944
–3953
.10.1109/TIE.2008.200271725.
Khatib
, O.
, 1986
, “Real-Time Obstacle Avoidance for Manipulators and Mobile Robots
,” Int. J. Rob. Res.
, 5
(1
), pp. 90
–98
.10.1177/02783649860050010626.
Rimon
, E.
, and Koditschek
, D. E.
, 1992
, “Exact Robot Navigation Using Artificial Potential Functions
,” IEEE Trans. Rob. Autom.
, 8
(5
), pp. 501
–518
.10.1109/70.16377727.
Utkin
, V. I.
, 1992
, Sliding Modes in Control and Optimization
, Springer-Verlag
, Berlin, Heidelberg
.28.
Utkin
, V. I.
, Guldner
, J.
, and Shi
, J.
, 1999
, Sliding Mode Control in Electromechanical Systems
, CRC Press
, Boca Raton, FL
.29.
Olfati-Saber
, R.
, 2006
, “Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory
,” IEEE Trans. Autom. Control
, 51
(3
), pp. 401
–420
.10.1109/TAC.2005.86419030.
Olfati-Saber
, R.
, and Murray
, R. M.
, 2002
, “Distributed Cooperative Control of Multiple Vehicle Formations Using Structural Potential Functions
,” Proceedings of the IFAC World Congress
, Barcelona, Spain
.31.
Egerstedt
, M.
, and Hu
, X.
, 2001
, “Formation Constrained Multi-Agent Control
,” IEEE Trans. Rob. Autom.
, 17
(6
), pp. 947
–951
.10.1109/70.97602932.
Reif
, J. H.
, and Wang
, H.
, 1999
, “Social Potential Fields: A Distributed Behavioral Control for Autonomous Robots
,” Rob. Auton. Syst.
, 27
, pp. 171
–194
.10.1016/S0921-8890(99)00004-433.
Guldner
, J.
, and Utkin
, V. I.
, 1994
, “Stabilization of Nonholonomic Mobile Robots Using Lyapunov Functions for Navigation and Sliding Mode Control
,” IEEE Conference on Decision and Control
, Lake Buena Vista, FL
, pp. 2967
–2972
.34.
Guldner
, J.
, Utkin
, V. I.
, Hashimoto
, H.
, and Harashima
, F.
, 1995
, “Tracking Gradients of Artificial Potential Fields With Non-Holonomic Mobile Robots
,” American Control Conference
, Seattle, WA
, pp. 2803
–2804
.35.
Guldner
, J.
, and Utkin
, V. I.
, 1996
, “Tracking the Gradient of Artificial Potential Fields: Sliding Mode Control for Mobile Robots
,” Int. J. Control
, 63
(3
), pp. 417
–432
.10.1080/0020717960892185036.
Gazi
, V.
, and Passino
, K. M.
, 2003
, “Stability Analysis of Swarms
,” IEEE Trans. Autom. Control
, 48
(4
), pp. 692
–697
.10.1109/TAC.2003.80976537.
Gazi
, V.
, and Passino
, K. M.
, 2004
, “Stability Analysis of Social Foraging Swarms
,” IEEE Trans. Syst., Man, Cybern., Part B
, 34
(1
), pp. 539
–557
.10.1109/TSMCB.2003.81707738.
Gazi
, V.
, and Passino
, K. M.
, 2004
, “A Class of Attraction/Repulsion Functions for Stable Swarm Aggregations
,” Int. J. Control
, 77
(18
), pp. 1567
–1579
.10.1080/0020717041233133002139.
Gazi
, V.
, 2005
, “Swarm Aggregations Using Artificial Potentials and Sliding Mode Control
,” IEEE Trans. Rob.
, 21
(6
), pp. 1208
–1214
.10.1109/TRO.2005.85348740.
Gazi
, V.
, Fidan
, B.
, Hanay
, Y. S.
, and Köksal
, M. İ.
, 2007
, “Aggregation, Foraging, and Formation Control of Swarms With Non-Holonomic Agents Using Potential Functions and Sliding Mode Techniques
,” Turk. J. Elec. Eng. & Comp. Sci.
, 15
(2
), pp. 149
–168
.41.
Brockett
, R. W.
, 1983
, “Asymptotic Stability and Feedback Stabilization
,” Differential Geometric Control Theory
, R. S.
Millman
and H. J.
Sussmann
, eds., Birkhauser
, Boston, MA
, pp. 181
–191
.42.
Liu
, S.
, Tan
, D.
, and Liu
, G.
, 2005
, “Vision-Based Formation Control of Mobile Robots With Relative Motion States
,” IEEE International Conference on Robotics and Biomimetics (ROBIO)
, pp. 72
–76
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