Bounded Controllers for Decentralized Formation Control of Mobile Robots with Limited Sensing
Keywords:Formation control, mobile robot, local potential function, nonholonomic mobile robot.
AbstractThis paper presents a constructive method to design bounded cooperative controllers that force a group of N mobile robots with limited sensing ranges to stabilize at a desired location, and guarantee no collisions between the robots. The control development is based on new general potential functions, which attain the minimum value when the desired formation is achieved, and are equal to infinity when a collision between any robots occurs. Smooth and p times differential jump functions are introduced and embedded into the potential functions to deal with the robot limited sensing ranges. Formation tracking is also considered.
P. K. C.Wang, Navigation Strategies for Multiple Autonomous Mobile Robots Moving in Formation, J. Robot. Syst., Vol. 8, No. 2, pp. 177-195, 1991. http://dx.doi.org/10.1002/rob.4620080204
A. K. Das, R. Fierro, V. Kumar, J. P. Ostrowski J. Spletzer, and C. J. Taylor, A Vision Based Formation Control Framework, IEEE Transactions on Robotics and Automation, vol. 18, pp. 813-825, 2002. http://dx.doi.org/10.1109/TRA.2002.803463
N. E. Leonard and E. Fiorelli, Virtual Leaders, Artificial Potentials and Coordinated Control of Groups, Proceedings of IEEE Conference on Decision and Control, Orlando, FL, pp. 2968-2973, 2001. http://dx.doi.org/10.1109/cdc.2001.980728
R.T. Jonathan, R.W. Beard and B.J. Young, A Decentralized Approach to Formation Maneuvers, IEEE Transactions on Robotics and Automation, vol. 19, pp. 933-941, 2003. http://dx.doi.org/10.1109/TRA.2003.819598
T. Balch and R. C. Arkin, Behavior-Based Formation Control for Multirobot Teams, IEEE Transactions on Robotics and Automation, vol. 14, pp. 926-939, 1998. http://dx.doi.org/10.1109/70.736776
M. A. Lewis and K.-H. Tan, High Precision Formation Control of Mobile Robots Using Virtual Structures, Autonomous Robots, vol. 4, pp. 387-403, 1997. http://dx.doi.org/10.1023/A:1008814708459
R. Skjetne, Moi, S., and T. I. Fossen, Nonlinear Formation Control of Marine Craft, Proceedings of IEEE Conference on Decision and Control, Las Vegas, NV, pp. 1699-1704, 2002. http://dx.doi.org/10.1109/cdc.2002.1184765
D. M. Stipanovica, G. Inalhana, R. Teo and C. J. Tomlina, Decentralized Overlapping Control of a Formation of Unmanned Aerial Vehicles, Automatica, vol. 40, pp. 1285 -1296, 2004. http://dx.doi.org/10.1016/j.automatica.2004.02.017
D.B. Nguyen and K.D. Do, Formation control of mobile robots, International Journal of Computers, Communications and Control, Vol. I, No. 3, pp. 41-59, 2006. http://dx.doi.org/10.15837/ijccc.2006.3.2294
K.D. Do and J. Pan, Nonlinear formation control of unicycle-type mobile robots, Robotics and Autonomous Systems, In Press, Available online 1 November 2006.
H. G. Tanner and A. Kumar, Towards Decentralization of Multi-Robot Navigation Functions, Proceedings of IEEE International Conference on Robotics and Automation, Barcelona, pp. 4143-4148, 2005. http://dx.doi.org/10.1109/robot.2005.1570754
H. G. Tanner and A. Kumar, Formation Stabilization of Multiple Agents Using Decentralized Navigation Functions, Robotics: Science and Systems I, S. Thrun, G. Sukhatme, S. Schaal and O. Brock (eds), MIT Press, pp. 49UË 56, 2005.
E. Rimon and D. E. Koditschek, Robot Navigation Functions on Manifolds with Boundary, Advances in Applied Mathematics, vol. 11, pp. 412-442, 1990. http://dx.doi.org/10.1016/0196-8858(90)90017-S
V. Gazi and K. M. Passino, A Class of Attraction/Repulsion Functions for Stable Swarm Aggregations, International Journal of Control, vol. 77, pp. 1567-1579, 2004. http://dx.doi.org/10.1080/00207170412331330021
H. G. Tanner, A. Jadbabaie and G. J. Pappas, Stable Flocking of Mobile Agents, Part II: Dynamics Topology, Proceedings of IEEE Conference on Decision and Control, Hawaii, pp. 2016-2021, 2003.
S. S. Ge and Y. J. Cui, New Potential Functions For Mobile Robot Path Planning, IEEE Transactions on Robotics and Automation, vol. 16, pp. 615-620, 2000. http://dx.doi.org/10.1109/70.880813
P. Ogren, M. Egerstedt, and X. Hu, A Control Lyapunov Function Approach to Multi-agent Coordination, IEEE Transactions on Robotics and Automatation, vol. 18, pp. 847-851, 2002. http://dx.doi.org/10.1109/TRA.2002.804500
P. Ogren, E. Fiorelli and N. E. Leonard, Cooperative Control of Mobile Sensor Networks: Adaptive Gradient Climbing in a Distributed Environment, IEEE Transactions on Automatic Control, vol. 49, No. 8, pp. 1292-1302. http://dx.doi.org/10.1109/TAC.2004.832203
H. Khalil, Nonlinear systems, Prentice Hall, 2002.
A. Wells, Theory and Problems of Lagrangian Dynamics, New York, 1967.
D. Liberzon, Switching in Systems and Control, Birkauser, 2003. http://dx.doi.org/10.1007/978-1-4612-0017-8
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