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This paper presents a definition of convexity useful for describing local optimality in configuration spaces, proves that finding convex regions is relatively easy, and presents an algorithm for approximating the free configuration space using a set of such convex regions. The paper examines simple but interesting systems: serial planar arms with revolute joints, and a Reeds-Shepp car. The paper experimentally explores an approach for finding good (although not necessarily optimal) trajectoriesdoi:10.1109/iros.2015.7354072 dblp:conf/iros/BalkcomKLWZ15 fatcat:zxlp6547yfgyzcyoecrueq3g7q