Consensus of Open Multi-agent Systems over Dynamic Undirected Graphs with Preserved Connectivity and Collision Avoidance

We address the consensus problem with collision avoidance for multi-agent systems under limited sensing ranges, in the case where new interconnections and agents may be added at any time. The graph topology is represented by a dynamic undirected graph, assumed to be connected only at an initial time, and the open multi-agent system is modeled via a multidimensional impulsive switched representation. We propose a barrier-Lyapunov-function-based consensus control law that guarantees inter-agent collision-avoidance and connectivity maintenance and, relying on the edge-agreement framework, we establish almost-everywhere asymptotic stability of the consensus manifold. The obtained results are also readily applicable to closed multi-agent systems with edge addition. A numerical simulation illustrates the effectiveness of the proposed approach.