2008/12/08 by Laura Krick, Mireille E. Broucke, Bruce A. Francis · 14 citations
Computer Science · Engineering · #Distributed Control Multi-Agent Systems #Robotic Locomotion and Control #Control and Stability of Dynamical Systems
paper · doi:10.1080/00207170802108441
Abstract This article considers the design of a formation control for multivehicle systems that uses only local information. The control is derived from a potential function based on an undirected infinitesimally rigid graph that specifies the target formation. A potential function is obtained from the graph, from which a gradient control is derived. Under this controller the target formation becomes a manifold of equilibria for the multivehicle system. It is shown that infinitesimal rigidity is a sufficient condition for local asymptotical stability of the equilibrium manifold. A complete study of the stability of the regular polygon formation is presented and results for directed graphs are presented as well. Finally, the controller is validated experimentally. Keywords: cooperative controlmultiagent formationsgraph rigidity Acknowledgements The authors thank Manfredi Maggiore for a helpful discussion on centre manifold theory. Notes Note 1. The notation e i is used to refer both to the edge i and as an error vector pointing in the direction of edge i in the framework.