Curvature-constrained shortest paths in a convex polygon

Published

Journal Article

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. 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 straight-line segment. Some of the properties are quite general and shed some light on curvature-constrained shortest paths amid obstacles.

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; Biedl, T; Lazard, S; Robbins, S; Suri, S; Whitesides, S

Published Date

  • September 1, 2002

Published In

Volume / Issue

  • 31 / 6

Start / End Page

  • 1814 - 1851

International Standard Serial Number (ISSN)

  • 0097-5397

Digital Object Identifier (DOI)

  • 10.1137/S0097539700374550

Citation Source

  • Scopus