Distributed combinatorial rigidity control in multi-agent networks

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(n₂), the generic topological rigidity of a network can be preserved.