Exponential Convergence in Voronoi-based Coverage Control

Controllers for distributing mobile agents to cover a desired region have become popular in the motion-coordination literature, including numerous variations on the problem. In most cases, coverage controllers target asymptotic stability, in the Lyapunov sense, to the centroids of Voronoi cells. The popular cost function used exhibits multiple local minima and maxima, and the problem of computing the global minimum is known to be NP-hard. This paper provides explicit definitions for the rate of convergence of the network utilising a distributed coverage controller. In addition, under an assumption of strong local convexity, we provide an alternate stability proof that shows the controller exhibits exponential stability to local minima. An example is provided to illustrate conditions which strong local convexity holds.