Decentralized Control of Connectivity for Multi-Agent Systems

In this paper we propose a decentralized algorithm to increase the connectivity of a multi-agent system. The connectivity property of the multi-agent system is quantified through the second smallest eigenvalue of the state dependent Laplacian of the proximity graph of agents. An exponential decay model is used to characterize the connection between agents. A supergradient algorithm is then used in conjunction with a recently developed decentralized algorithm for eigenvector computation to maximize the second smallest eigenvalue of the Laplacian of the proximity graph. A potential based control law is utilized to achieve the distances dictated by the supergradient algorithm. The algorithm is completely decentralized, where each agent receives information only from its neighbors, and uses this information to update its control law at each step of the iteration. Simulations demonstrate the effectiveness of the algorithm

[1]  George J. Pappas,et al.  Controlling Connectivity of Dynamic Graphs , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[2]  Stephen P. Boyd,et al.  Gossip algorithms: design, analysis and applications , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

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

[4]  P. S. Krishnaprasad,et al.  Equilibria and steering laws for planar formations , 2004, Syst. Control. Lett..

[5]  Felipe Cucker,et al.  Emergent Behavior in Flocks , 2007, IEEE Transactions on Automatic Control.

[6]  Paramvir Bahl,et al.  Distributed Topology Control for Wireless Multihop Ad-hoc Networks , 2001, INFOCOM.

[7]  Magnus Egerstedt,et al.  Connectivity graphs as models of local interactions , 2004, CDC.

[8]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.

[9]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

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

[11]  Stephen P. Boyd,et al.  Subgradient Methods , 2007 .

[12]  Sonia Martínez,et al.  Coverage control for mobile sensing networks , 2002, IEEE Transactions on Robotics and Automation.

[13]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

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

[15]  R. Murray,et al.  Robust connectivity of networked vehicles , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[16]  Mehran Mesbahi,et al.  On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian , 2006, IEEE Transactions on Automatic Control.

[17]  David Kempe,et al.  A decentralized algorithm for spectral analysis , 2008, J. Comput. Syst. Sci..

[18]  Petter Ögren,et al.  Cooperative control of mobile sensor networks:Adaptive gradient climbing in a distributed environment , 2004, IEEE Transactions on Automatic Control.

[19]  Sonia Martínez,et al.  Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions , 2006, IEEE Transactions on Automatic Control.

[20]  Daniel E. Koditschek,et al.  Exact robot navigation using artificial potential functions , 1992, IEEE Trans. Robotics Autom..

[21]  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).