Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke





.......................

.......................


Publications [#235406] of Pankaj K. Agarwal

Papers Published

  1. Agarwal, PK; Biedl, T; Lazard, S; Robbins, S; Suri, S; Whitesides, S, Curvature-constrained shortest paths in a convex polygon, in Fourteenth Annual Symposium on Computational Geometry, Proceedings of the Annual Symposium on Computational Geometry (1998), pp. 392-401
    (last updated on 2017/12/11)

    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.

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320