# Curvature-constrained shortest paths in a convex polygon

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

### Duke Authors

### Cited Authors

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

### Published Date

- January 1, 1998

### Published In

- Proceedings of the Annual Symposium on Computational Geometry

### Start / End Page

- 392 - 401

### Citation Source

- Scopus