Curvature-constrained shortest paths in a convex polygon (extended abstract)

Abstract

Let B be a point robot moving in the plane, whose path is constrained to have curvature at most1, 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(n²log n) time algorithm for determining whether a collision-free path exists for Bbetween 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.