Multi-robot Coverage and Exploration in Non-Euclidean Metric Spaces

Multi-robot coverage and exploration is a fundamental problem in robotics. A widely-used, efficient and distributable algorithm for achieving coverage of a convex environment with Euclidean metric is that proposed by Cortes, et al., which is based on the discrete-time Lloyd’s algorithm. It is significantly difficult to achieve the same in non-convex environments and with non-Euclidean metrics. In this paper we generalize the control law based on minimization of the coverage functional to spaces that are inherently non-Euclidean and are 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 exploration problems in highly non-convex indoor environments.