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

Jean-Daniel Boissonnat (1) , Sylvain Lazard (2)

1 PRISME - Geometry, Algorithms and Robotics
2 ISA - Models, algorithms and geometry for computer graphics and vision

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.

Mots clés: non-holonomic robot; motion planning; shortest paths; mobile robot; planification de trajectoires; plus courts chemins; robotique mobile; géométrie algorithmique; computational geometry; système mécanique non holonome

Domaines: Autre [cs.OH]

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, 2003, 13 (3), pp.189-229. ⟨10.1142/S0218195903001128⟩. ⟨inria-00099509⟩