Coordination and geometric optimization via distributed dynamical systems

Details Coordination and geometric optimization via distributed dynamical systems Coordination and geometric optimization via distributed dynamical systems

2003-05-29

arxiv.org/abs/math/0305433v1

Mathematics

Optimization and Control

31 pages, 8 figures, includes index of symbols. More information on http://motion.csl.uiuc.edu

Scientific paper

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.

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