Multi-Robot Coverage Control With Bounded Suboptimality Guarantees

We consider a coverage control problem, where a team of robots move in a convex domain to minimize a standard coverage cost. One prevalent approach to solve this problem is to use a gradient based controller (e.g., Lloyd’s algorithm), which stabilizes the local minima of such a coverage cost function. However, to the best of our knowledge, there are no formal results on how suboptimal these local minima can be. In this letter, we first show the existence of arbitrarily bad local minima. We then prove that a local search based approximation algorithm, which was originally developed for other location optimization problems (k-means/medians), can be adapted to the coverage control problem to stabilize configurations with bounded suboptimality in a decentralized manner. We also support our theoretical results with experiments on robots.