In this paper we propose distributed algorithms to automatically deploy a group of robotic agents and provide coverage of a discretized environment represented by a graph. We present a discrete coverage algorithm which converges to a centroidal Voronoi partition while requiring only pairwise “gossip” communication between the agents. Our theoretical analysis is based on a dynamical system on partitions of the graph’s vertices. We also establish bounds on the computational requirements of the algorithm and demonstrate its functionality with simulations.

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