  This paper discusses dynamical systems for disk-covering and sphere-packing
problems. We present facility location functions from geometric optimization
and characterize their differentiable properties. We design and analyze a
collection of distributed control laws that are related to nonsmooth gradient
systems. The resulting dynamical systems promise to be of use in coordination
problems for networked robots; in this setting the distributed control laws
correspond to local interactions between the robots. The technical approach
relies on concepts from computational geometry, nonsmooth analysis, and the
dynamical system approach to algorithms.
