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Curvature-Constrained Shortest Paths in a Convex Polygon

Abstract : Let B be a point robot moving in the plane, whose path is constrained to have curvature at most 1, and let P be a convex polygon with n vertices. We study the collision-free, optimal path-planning problem for B moving between two configurations inside P (a configuration specifies both a location and a direction of travel). We present an O(n2 log n) time algorithm for determining whether a collision-free path exists for B between two given configurations. If such a path exists, the algorithm returns a shortest one. We provide a detailed classification of curvature-constrained shortest paths inside a convex polygon and prove several properties of them, which are interesting in their own right. Some of the properties are quite general and shed some light on curvature-constrained shortest paths amid obstacles.
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Contributor : Sylvain Lazard <>
Submitted on : Tuesday, December 15, 2009 - 1:58:43 PM
Last modification on : Friday, February 26, 2021 - 3:28:03 PM
Long-term archiving on: : Monday, April 5, 2010 - 11:54:00 PM


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Pankaj K. Agarwal, Thérèse Biedl, Sylvain Lazard, Steve Robbins, Subhash Suri, et al.. Curvature-Constrained Shortest Paths in a Convex Polygon. SIAM Journal on Computing, Society for Industrial and Applied Mathematics, 2002, 31 (6), pp.1814-1851. ⟨10.1137/S0097539700374550⟩. ⟨inria-00100887⟩



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