From geometric optimization and nonsmooth analysis to distributed coordination algorithms

We investigate the coordination of groups of autonomous robots performing spatially-distributed sensing tasks. We present facility location functions from geometric optimization and study their differentiable properties. We then design distributed coordination algorithms and analyze them as nonsmooth gradient flows. The resulting control laws correspond to basic interaction behaviors between the robots. The technical approach relies on concepts from computational geometry, nonsmooth analysis, and the dynamical system approach to algorithms.