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A Geometric Proof on Shortest Paths of Bounded Curvature  

Ahn, Hee-Kap (세종대학교 컴퓨터공학과)
Bae, Sang-Won (한국과학기술원 전산학과)
Cheong, Otfried (한국과학기술원 전산학과)
Publication Information
Journal of KIISE:Computer Systems and Theory / v.34, no.4, 2007 , pp. 132-137 More about this Journal
Abstract
A point-wise car-like robot moving in the plane changes its direction with a constraint on turning curvature. In this paper, we consider the problem of computing a shortest path of bounded curvature between a prescribed initial configuration (position and orientation) and a polygonal goal, and propose a new geometric proof showing that the shortest path is either of type CC or CS (or their substring), where C specifies a non-degenerate circular arc and S specifies a non-degenerate straight line segment. Based on the geometric property of the shortest path, the shortest path from a configuration to a polygonal goal can be computed in linear time.
Keywords
Shortest path; Dubins path; curvature; geometry; reachability;
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