This paper unifies and extends several different existing strategies for multi-robot coverage control, including ones based on Voronoi partitions, probabilistic models, and artificial potential fields. We propose a cost function form for coverage problems that can be specialized to fit different distributed sensing and actuation scenarios. We show that controllers based on Voronoi partitions can be approximated arbitrarily well by simpler methods that do not require the computation of a Voronoi partition. The performance of three different controllers designed with the new approach is compared in simulation. We also formally delineate two classes of multi-agent problems: consensus problems and non-consensus problems. We show that coverage control is a non-consensus problem and that it requires the optimization of a nonconvex cost function.
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