We consider the problem of controlling a group of vehicles to a formation. The approach mimics the development of dynamics of a system of particles subject to constraints. In particular, we use the notion of constraint forces to achieve and maintain a given formation. As opposed to the potential function approach used in the literature, the proposed constraint force approach directly compensates for only those parts of the applied forces, which act against the constraints. We develop a stable control algorithm that will achieve the formation while ensuring navigation of the group based on the desired trajectories, which are consistent with the constraints. Simulation results on an example are shown to corroborate the proposed method.
Issue Section:
Technical Papers
1.
Reynolds
, C. W.
, 1987, “Flocks, Herbs, and Schools: A Distributed Behavioral Model
,” Comput. Graph.
0097-8930, 21
, pp. 25
–34
.2.
Desai
, J. P.
, Ostrowski
, J. P.
, and Kumar V., 2001, “Modeling and Control of Formations of Nonholonomic Mobile Robots
,” IEEE Trans. Rob. Autom.
1042-296X, 17
, pp. 905
–908
.3.
Egerstedt
, M.
, and Hu
, X.
, 2001, “Formation Constrained Multiagent Control
,” IEEE Trans. Rob. Autom.
1042-296X, 17
, pp. 947
–951
.4.
Leonard
, N. E.
, and Fiorello
, E.
, 2001, “Virtual Leader, Artificial Potentials and Coordinated Control of Groups
,” Proceedings of the 40th IEEE Conference on Decision and Control
, pp. 2968
–2973
.5.
Lawton
, J. R.
, Beard
, R. W.
, and Young
, B. J.
, 2003, “A Decentralized Approach to Formation Maneuvers
,” IEEE Trans. Rob. Autom.
1042-296X, 19
, pp. 933
–941
.6.
Olfati-Saber
, R.
, and Murray
, R. M.
, 2002, “Distributed Cooperative Control of Multiple Vehicle Formations Using Structural Potential Functions
,” The 15th IFAC World Congress
.7.
Tanner
, H. G.
, Jadbabaie
, A.
, and Pappas
, G. J.
, 2003, “Stable Flocking of Mobile Agents, Part I: Fixed Topology
,” Proceedings of the 42th IEEE Conference on Decision and Control
, pp. 2010
–2015
.8.
Rimon
, E.
, and Koditschek
, D. E.
, 1992, “Exact Robot Navigation Using Artificial Potential Function
,” IEEE Trans. Rob. Autom.
1042-296X, 8
, pp. 501
–518
.9.
Dimarogonas
, D. V.
, Loizou
, S. G.
, Kyriakopoulos
, K. J.
, and Zavlanos
, M. M.
, 2006, “A Feedback Stabilization and Collision Avoidance Scheme for Multiple Independent Non-Point Agents
,” Automatica
0005-1098, 42
, pp. 229
–243
.10.
Olfati-Saberr
, R.
, 2006, “Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory
,” IEEE Trans. Autom. Control
0018-9286, 51
, pp. 401
–420
.11.
Eren
, T.
, 2004, “Rigid Formation of Autonomous Agents
,” Ph.D. thesis, Yale University.12.
Olfati-Saber
, R.
, and Murray
, R. M.
, 2002, “Graph Rigidity and Distributed Formation Stabilization of Multi-Vehicle Systems
,” Proceedings of the 41st IEEE Conference on Decision and Control
, pp. 2965
–2971
.13.
Rosenberg
, R. M.
, 1980, Analytical Dynamics of Discrete Systems
, Plenum
, New York
.14.
Goldstein
, H.
, 1953, Classical Mechanics
, Addison-Wesley
, Reading, MA
.15.
Witkin
, A.
, Gleicher
, M.
, and Welch
, W.
, 1990, “Interactive Dynamics
,” Comput. Graph.
0097-8930, 24
, pp. 11
–21
.16.
Udwadia
, F.
, and Kalaba
, R. E.
, 1996, Analytical Dynamics: A New Approach
, Cambridge University Press
, Cambridge, England
.17.
Horn
, R. A.
, and Johnson
, C. R.
, 1999, Matrix Analysis
, Cambridge University Press
, Cambridge, England
.18.
Krishna
, Y. S.
, Darbha
, S.
, and Rajagopal
, K. R.
, 2005, “Information Flow and Its Relation to the Stability of the Motion of Vehicles in a Rigid Formation
,” Proceedings of the American Control Conference
, pp. 1853
–1858
.19.
Tanner
, H. G.
, and Kumar
, A.
, 2005, “Formation Stabilization of Multiple agents using Decentralized Navigation Functions
,” Proceedings of Robotics: Science and Systems
, Cambridge
.20.
Chang
, D. E.
, Shadden
, S. C.
, Marsden
, J. E.
, and Olfati-Saber
, R.
, 2003, “Collision Avoidance for Multiple Agent Systems
,” Proceedings of the 42nd IEEE Conference on Decision and Control
, pp. 539
–543
.21.
Stipanovic
, D. M.
, Hokayem
, P. F.
, Spong
, M. W.
, and Šiljak
, D. D.
, 2007, “Cooperative Avoidance Control for Multiagent Systems
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 129
, pp. 699
–707
.Copyright © 2007
by American Society of Mechanical Engineers
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