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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Communication dans un congrès
Symposium on Computational Geometry - SCG 1998, Jun 1998, Mineapolis, United States. ACM, pp.392-401, 1998, SCG '98 Proceedings of the fourteenth annual symposium on Computational geometry. 〈10.1145/276884.276928〉
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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. Symposium on Computational Geometry - SCG 1998, Jun 1998, Mineapolis, United States. ACM, pp.392-401, 1998, SCG '98 Proceedings of the fourteenth annual symposium on Computational geometry. 〈10.1145/276884.276928〉. 〈hal-00827890〉

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