On the Equivalence of Multi-Agent 2D Coverage Control and Leader-Follower Consensus Network
Xiaotian Xu, Alexander Davydov, Yancy J. Diaz-Mercado · 2023
Coverage control algorithms seek to spatially distribute agents in a domain of coverage, e.g., to minimize proximity to all points. Leader-follower consensus network algorithms use local coordination rules to influence the behavior of a multi-agent system (MAS) as a whole through explicit control of a subset of agents (called leaders) and neighbor interactions. In this paper, the equivalence of these two classes of distributed algorithms for swarm robotics, that were once considered inherently different, is established. We present a swarm robotics application, where the real agents (i.e., the robots) in the domain of coverage are followers; and virtual agents (i.e., the leaders) are introduced based on the domain of coverage. The dynamics of followers are shown to be in the form of a weighted, state-dependent consensus protocol and the dynamics of the leaders (dependent on the evolution of the domain) are provided. Formulating a standard coverage algorithm (i.e., Lloyd’s algorithm) over 2D polygonal domains as a leader-follower consensus protocol makes the structure of the ensemble-level dynamics for the MAS explicit with respect to neighbor interaction. The resultant weighted graph Laplacian may contribute to the future investigation on the performance guarantees of a MAS tracking a time-varying domain. The equivalence of the two classes of algorithms is validated in simulation.