Coverage Control on the Special Euclidean Groups*

In this paper, we investigate a coverage strategy for a multi-robot system across a domain of interest for applications involving pose-sensitive event services. The resulting problem is modeled as a coverage control problem on the special Euclidean groups. Based on the geometry inherent to the unimodular Lie groups, the geodesic-based Voronoi cell of a robot in charge of a subdomain and the locational cost function representing the coverage quality are defined. The controller for driving a team of planar robots to a critical point of the locational cost is derived and augmented by a control barrier certificate for the purpose of collision avoidance. The performance of the proposed controller is compared with the situation where the orientations of the robots are ignored during the coverage process using the standard Lloyd’s algorithm for both homogeneous and heterogeneous (in terms of robots’ relative mobility and safe radii) multi-robot teams.