Coordination and geometric optimization via distributed dynamical systems

2003/05/29 by Jorge Cortes, Francesco Bullo, Cortes, Jorge +1 · 1 citation
Mathematics · #05B40 #37N35 #49J52 #68W15 #93D20 #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #math.DS #math.OC #msc:05B40 #msc:37N35 #msc:49J52 #msc:68W15 #msc:93D20

paper · pdf · doi:10.48550/arxiv.math/0305433

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

arxiv created 2003/05/29 · arxiv updated 2009/11/30

Abstract

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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