# A polynomial-time algorithm for computing shortest paths of bounded curvature amidst moderate obstacles

1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
2 ISA - Models, algorithms and geometry for computer graphics and vision
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In this paper, we consider the problem of computing shortest paths of bounded curvature amidst obstacles in the plane. More precisely, given two prescribed initial and final configurations (specifying the location and the direction of travel) and a set of obstacles in the plane, we want to compute a shortest $C^1$ path joining those two configurations, avoiding the obstacles, and with the further constraint that, on each $C^2$ piece, the radius of curvature is at least 1. In this paper, we consider the case of moderate obstacles (as introduced by Agarwal et al.) and present a polynomial-time exact algorithm to solve this problem.
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https://hal.inria.fr/inria-00099509
Contributor : Sylvain Lazard <>
Submitted on : Tuesday, December 15, 2009 - 3:01:39 PM
Last modification on : Saturday, January 27, 2018 - 1:30:41 AM
Long-term archiving on : Monday, April 5, 2010 - 11:52:14 PM

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### Citation

Jean-Daniel Boissonnat, Sylvain Lazard. A polynomial-time algorithm for computing shortest paths of bounded curvature amidst moderate obstacles. International Journal of Computational Geometry and Applications, World Scientific Publishing, 2003, 13 (3), pp.189-229. ⟨10.1142/S0218195903001128⟩. ⟨inria-00099509⟩

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