Reachability by paths of bounded curvature in a convex polygon

Ahn, Heekap; Cheong, Otfried; Matoušek, Jiřǐ; Vigneron, Antoine E.

Reachability by paths of bounded curvature in a convex polygon

Type

Article

Authors

Ahn, Heekap
Cheong, Otfried
Matoušek, Jiřǐ
Vigneron, Antoine E.

KAUST Department

Visual Computing Center (VCC)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Computer Science Program
Geometric Algorithms Group

Date

2012-01

Abstract

Let B be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most 1, and let P be a convex polygon with n vertices. Given a starting configuration (a location and a direction of travel) for B inside P, we characterize the region of all points of P that can be reached by B, and show that it has complexity O(n). We give an O(n2) time algorithm to compute this region. We show that a point is reachable only if it can be reached by a path of type CCSCS, where C denotes a unit circle arc and S denotes a line segment. © 2011 Elsevier B.V.

Citation

Ahn, H.-K., Cheong, O., Matoušek, J., & Vigneron, A. (2012). Reachability by paths of bounded curvature in a convex polygon. Computational Geometry, 45(1-2), 21–32. doi:10.1016/j.comgeo.2011.07.003

Acknowledgements

Work by Cheong was supported by Mid-career Researcher Program through NRF grant funded by the MEST (No. R01-2008-000-11607-0). Work by Ahn was supported by the National IT Industry Promotion Agency (NIPA) under the program of Software Engineering Technologies Development.