Non-autonomous State-Feedback to Stabilize the Error Dynamics in Time-Varying Area Coverage Control Problems

Abstract

We propose a state-feedback control scheme for area coverage problems using a group of agents operating in a time varying environment. The coverage metric defining the optimal control problem encodes a time-varying risk density that models an evolving environment in which the agents operate. The evolution of the environment is caused by the presence of mobile external objects (targets). Maximum coverage can be accomplished by deploying more (less) agents to the part of the area marked with a high (low) risk density, resulting into non-uniform agents' distributions that adapt to the environment. The workspace is partitioned according to a Voronoi tessellation with respect to a distance that quantifies robots' sensing performances. For every initial configuration of the group of agents in the workspace, the proposed non-autonomous state-feedback controller asymptotically drives the agents to time varying centroids of the Voronoi tessellation, therefore positioning them in the optimal configuration with respect to the performance measured by the coverage metric. The proposed control scheme is illustrated by simulations.