Summary
In this paper, a new leaderless cooperative formation control strategy is proposed for a group of autonomous mobile robots. Through the local state and input transformations, the formation control problem can be recast as the cooperative control design problem for a class of general canonical systems with arbitrary but finite relative degree. A set of less-restrictive sufficient conditions on group communication topology to ensure the success of cooperative control design has been established. The system stability is rigorously proved by studying the convergence of products of row stochastic matrices. The proposed design does not require either that collaborative robots have a fixed communication/control structure (such as leader/follower or nearest neighbor) or that their sensor/communication graph be strongly connected. Detailed simulation results are provided to illustrate the effectiveness of the proposed method.
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References
R. Arkin. Behavior-Based Robotics. MIT Press, 1998.
T. Balch and R. C. Arkin. Behavior-based formation contorl for multirobot teams. IEEE Trans. on Robotics and Automation, 14:926–939, 1998.
R. B. Bapat and T. E. S. Raghavan. Nonnegative Matrices and Applications. Cambridge University Press, Cambridge, 1997.
P. Bhatta and N. E. Leonard. Stabilization and coordination of underwater gliders. In Proc. 41st IEEE Conf. Decision and Control, 2002.
J. P. Desai, J. Ostrowski, and V. Kumar. Controlling formations of multiple mobile robots. In IEEE Conference on Robotics and Automation, pages 2864–2869, Leuven, Belgium, May 1998.
J. Alexander Fax and R. M. Murray. Finite-horizon optimal control and stabilization of time-scalable systems. In Proc. 39th IEEE Int. Conf. on Decision and Control, Sydney, Australia, 2000.
D. Fox, W. Burgard, H. Kruppa, and S. Thrun. A probabilistic approach to collaborative multi-robot localization. Autonomous Robots, 8(3), 2000.
D. Freedman. Markov Chains. Springer-Verlag, New York, 1983.
V. Gazi and K. M. Passino. Stability analysis of swarms. IEEE Trans. on Automatic Control, 48:692–697, 2003.
R. A. Horn and C.R. Johnson. Matrix Analysis. Cambridge University Press, Cambridge, 1985.
A. Jadbabaie, J. Lin, and A. S. Morse. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. on Automatic Control, 48:988–1001, 2003.
W. Kang, N. Xi, and A. Sparks. Theory and applications of formation control in a perceptive referenced frame. In IEEE Conference on Decision and Control, pages 352–357, Sydney, Australia, Dec. 2000.
H. K. Khalil. Nonlinear Systems, 3rd edition. Prentice Hall, Upper Saddle River, New Jersey, 2003.
J. R. T. Lawton, R. W. Beard, and B. J. Young. A decentralized approach to formation maneuvers. IEEE Trans. on Robotics and Automation, to appear, 2003.
N. E. Leonard and E. Fiorelli. Virtual leaders, artificial potentials and coordinated control of groups. In IEEE Conference on Decision and Control, pages 2968–2973, Orlando, FL, Dec. 2001.
Z. Lin, M. Brouchke, and B. Francis. Local control strategies for groups of mobile autonomous agents. IEEE Trans. on Automatic Control, 49:622–629, 2004.
P. K. Menon and G. D. Sweriduk. Optimal strategies for free-flight air traffic conflict resolution. J. of Guidance, Control and Dynamics, 22:202–211, 1999.
H. Minc. Nonnegative Matrices. John Wiley & Sons, New York, NY, 1988.
L. Moreau. Leaderless coordination via bidirectional and unidirectional timedependent communication. In Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, Dec 2003.
R. Olfati and R. M. Murray. Distributed cooperative control of multiple vehicle formations using structural potential functions. In 15th Triennial World Congress, Barcelona, Spain, 2002.
L. E. Parker. Alliance: An architecture for fault-tolerant multi-robot cooperation. IEEE Trans. on Robotics and Automation, 14:220–240, 1998.
Z. Qu. Robust Control of Nonlinear Uncertain Systems. Wiley-Interscience, 1998, New York.
Z. Qu, J. Wang, and R. A. Hull. Cooperative control of dynamical systems with application to mobile robot formation. In The 10th IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems: Theory and Applications, Japan, July 2004.
Z. Qu, J. Wang, and R. A. Hull. Products of row stochastic matrices and their applications to cooperative control for autonomous mobile robots. In Proceedings of 2005 American Control Conference, Portland, Oregon, 2005.
W. Ren and R. W. Beard. Consensus of information under dynamically changing interaction topologies. In Proceedings of the American Control Conference, Boston, Jun 2004.
C. W. Reynolds. Flocks, herds, and schools: a distributed behavioral model. Computer Graphics (ACM SIGGRAPH 87 Conference Proceedings), 21(4):25–34, 1987.
R. O. Saber and R. M. Murray. Agreement problems in networks with directed graphs and switching topology. In Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, Dec 2003.
R. O. Saber and R. M. Murray. Consensus protocols for networks of dynamic agents. In Proceedings of the American Control Conference, Denver, CO, Jun 2003.
D. Swaroop and J. Hedrick. String stability of interconnected systems. IEEE Trans. on Automatic Control, 41:349–357, 1996.
T. Vicsek, A. Czirok, E. B. Jacob, I. Cohen, and O. Shochet. Novel type of phase transition in a system of self-driven particles. Physical Review Letters, 75:1226–1229, 1995.
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Qu, Z., Wang, J., Hull, R.A. (2007). Leaderless Cooperative Formation Control of Autonomous Mobile Robots Under Limited Communication Range Constraints. In: Grundel, D., Murphey, R., Pardalos, P., Prokopyev, O. (eds) Cooperative Systems. Lecture Notes in Economics and Mathematical Systems, vol 588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48271-0_6
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