Distributed combinatorial rigidity control in multi-agent networks

Ryan K. Williams, Andrea Gasparri, Attilio Priolo, Gaurav S. Sukhatme

Abstract: In this paper, we propose a distributed control law to maintain the combinatorial rigidity of a multi-agent system in the plane, when interaction is proximity-limited. Motivated by the generic properties of rigidity as a function of the underlying network graph, local link addition and deletion rules are proposed that preserve combinatorial rigidity through agent mobility. Specifically, redundancy of network links over local sub-graphs allows the determination of topological transitions that preserve rigidity. It is shown that local redundancy of a network link is sufficient for global redundancy, and thus applying minimal communication, and computation that scales like O(n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ), the generic topological rigidity of a network can be preserved.