| Curvature-Constrained Shortest Paths in a Convex Polygon (Extended Abstract) (1998) | |||||||||||||||||
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| ) Pankaj K. Agarwal Therese Biedl y Sylvain Lazard z Steve Robbins x Subhash Suri -- Sue Whitesides k 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(n 2 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. Center for Geometric Computing, Computer Science Depar... | |||||||||||||||||
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