Distributed Coverage Control on Surfaces in 3D Space

This paper addresses the problem of deploying a group of networked robots on a non-planar surface embedded in 3D space. Two distributed coverage control algorithms are presented that both provide a solution to the problem by discrete coverage of a graph. The first method computes shortest paths and runs the Lloyd algorithm on the graph to obtain a centroidal Voronoi tessellation. The second method uses the Euclidean distance measure and locally exchanges mesh cells between approximated Voronoi regions to reach an optimal robot configuration. Both methods are compared and evaluated in simulations and in experiments with five robots on a curved surface.