The Shortest path synthesis for non-holonomic robots moving forwards

Abstract

: We calculate the partition of the configuration space IR 2 \\Theta S 1 of a car-like robot, only moving forwards, with respect to the type of the length optimal paths. This kind of robot is subject to kinematic constraints on its path curvature and its orientation. Starting from the results on shortest paths by [Dub57] and [BCL92], we give new optimality conditions on these paths, and compute the partition for any horizontal plane of the configuration space. Key-words: Optimal control, Synthesis problem, Non-holonomic robot, Bounded radius of curvature, Dubins shortest paths (R'esum'e : tsvp) LAAS 7 avenue du Colonel Roche -- 31077 Toulouse Phone : +33 61 33 63 47 -- Fax : +33 61 33 64 55 E-mail : soueres, jpl@laas.fr This work is partly supported by Esprit Project PROMotion 6546 Unite de recherche INRIA Sophia-Antipolis 2004 route des Lucioles, BP 93, 06902 SOPHIA-ANTIPOLIS Cedex (France) Telephone : (33) 93 65 77 77 -- Telecopie : (33) 93 65 77 65 Synth`ese des Plus co...