Math @ Duke

Publications [#235449] of Pankaj K. Agarwal
Papers Submitted
 Agarwal, PK; Biedl, T; Lazard, S; Robbins, S; Suri, S; Whitesides, S, Curvatureconstrained shortest paths in a convex polygon,
SIAM Journal on Computing, vol. 31 no. 6
(2002),
pp. 18141851 [doi]
(last updated on 2018/08/20)
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 collisionfree, optimal pathplanning 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 collisionfree 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 curvatureconstrained shortest paths inside a convex polygon and prove several properties of them, which are interesting in their own right. For example, we prove that any such shortest path is comprised of at most eight segments, each of which is a circular arc of unit radius or a straightline segment. Some of the properties are quite general and shed some light on curvatureconstrained shortest paths amid obstacles.


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