Multi-robot coverage and exploration on Riemannian manifolds with boundaries

Multi-robot coverage and exploration are fundamental problems in robotics. A widely used, efficient and distributable algorithm for achieving coverage of a convex environment with Euclidean metrics is that proposed by Cortes which is based on the discrete-time Lloyd’s algorithm. This algorithm is not directly applicable to general Riemannian manifolds with boundaries that are non-convex and are intrinsically non-Euclidean. In this paper we generalize the control law based on minimization of the coverage functional to such non-Euclidean spaces punctured by obstacles. We also propose a practical discrete implementation based on standard graph search-based algorithms. We demonstrate the applicability of the proposed algorithm by solving efficient coverage problems on a sphere and a torus with obstacles, and exploration problems in non-convex indoor environments.