Curvature-Constrained Shortest Paths in a Convex Polygon

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 forB moving between two configurations insideP (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 forB 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 Department, Duke University, Box 90129, Durham, NC 27708–0129, USA; [email protected]; http://www.cs.duke.edu/ ̃pankaj/. Supported in part by National Science Foundation research grant CCR–93–01259, by Army Research Office MURI grant DAAH04–96–1–0013, by a Sloan fellowship, by a National Science Foundation NYI award and matching funds from Xerox Corporation, and by a grant from the U.S.-Israeli Binational Science Foundation. ySchool of Computer Science, McGill University, 3480 University Street, Montreal, Qc, H3A 2A7, Canada; [email protected]. zSchool of Computer Science, McGill University; [email protected]. Supported in part by an INRIA postdoctoral award. xSchool of Computer Science, McGill University; [email protected]. Supported by an FCAR scholarship. {Department of Computer Science, Washington University Campus Box 1045, One Brookings Drive, St. Louis, MO 63130-4899, USA; [email protected];http://www.cs.wustl.edu/ ̃suri/. Research partially supported by NSF Grant CCR-9501494. kSchool of Computer Science, McGill University; [email protected]. Supported by NSERC and FCAR research grants.