Higher-Order Non-Autonomous Optimal Area Coverage Control

We present an area coverage control algorithm for multi-agent systems with order-k Voronoi partitions. The system is non-autonomous due to the uncontrolled dynamics of external agents operating in the environment. Area coverage control is an optimal resource allocation problem in which optimal agents’ configurations are stationary points of a coverage metric, consisting of centroidal Voronoi tessellations. We consider time-evolving environments with order-k Voronoi partitions, where Voronoi cells are defined by k-nearest generator rules. This applies to scenarios in which it is necessary and/or desirable to assign $k\gt 1$ agents to the trajectories of each cell. We prove that the proposed non-autonomous feedback control, with feed-forward dictated by the environment’s drift, asymptotically converges the agents to optimal centroidal order-k Voronoi configurations. Theoretical predictions are illustrated in simulation.