Reachability by paths of bounded curvature in a convex polygon

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.

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

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.

Elsevier BV

Computational Geometry


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