Containment Control in Mobile Networks

In this paper, the problem of driving a collection of mobile robots to a given target destination is studied. In particular, we are interested in achieving this transfer in an orderly manner so as to ensure that the agents remain in the convex polytope spanned by the leader-agents, while the remaining agents, only employ local interaction rules. To this aim we exploit the theory of partial difference equations and propose hybrid control schemes based on stop-go rules for the leader-agents. Non-Zenoness, liveness and convergence of the resulting system are also analyzed.

[1]  H.G. Tanner,et al.  On the controllability of nearest neighbor interconnections , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[2]  Vijay Kumar,et al.  Controlling formations of multiple mobile robots , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[3]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[4]  Vijay Kumar,et al.  Leader-to-formation stability , 2004, IEEE Transactions on Robotics and Automation.

[5]  G. Ferrari-Trecate,et al.  Analysis of Coordination in multiple Agents Formations through Partial Difference Equations , 2004 .

[6]  Jacques-Louis Lions,et al.  Mathematical Analysis and Numerical Methods for Science and Technology: Volume 5 Evolution Problems I , 1992 .

[7]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[8]  Giancarlo Ferrari-Trecate,et al.  Analysis of coordination in multi-agent systems through partial difference equations , 2006, IEEE Transactions on Automatic Control.

[9]  Magnus Egerstedt,et al.  Connectivity graphs as models of local interactions , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[10]  M. Egerstedt,et al.  Leader-based multi-agent coordination: controllability and optimal control , 2006, 2006 American Control Conference.

[11]  R. O. Saber.  A Unified Analytical Look at Reynolds Flocking Rules , 2003 .

[12]  C. DeWitt-Morette,et al.  Mathematical Analysis and Numerical Methods for Science and Technology , 1990 .

[13]  H. Sussmann,et al.  A maximum principle for hybrid optimal control problems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[14]  A. Bensoussan,et al.  Difference equations on weighted graphs , 2005 .

[15]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[16]  Magnus Egerstedt,et al.  Conflict Resolution for Autonomous Vehicles: A Case Study in Hierarchical Control Design , 2002 .

[17]  George J. Pappas,et al.  Flocking in Fixed and Switching Networks , 2007, IEEE Transactions on Automatic Control.

[18]  Béla Bollobás,et al.  Modern Graph Theory , 2002, Graduate Texts in Mathematics.

[19]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[20]  M. Egerstedt,et al.  On the regularization of Zeno hybrid automata , 1999 .

[21]  R. Olfati-Saber.  A Unified Analytical Look at Reynolds Flocking Rules , 2003 .

[22]  Magnus Egerstedt,et al.  Hierarchical Containment Control in Heterogeneous Mobile Networks , 2006 .

[23]  Mehdi Gati,et al.  Analysis of coordination in multi-agent systems through partial difference equationsߞPart I: T , 2005 .