Suboptimal paths in the problem of a planar motion with bounded derivative of the curvature

Abstract

: We consider the planar motion of a car-like robot with a bounded derivative of the curvature, with given initial and final configuration (i.e. positions, tangent angles and curvatures). The tangent angle and the curvature of the path are assumed to be continuous. When the distance between the initial and the final point is much greater than the initial and final curvatures and the curvature's derivative, we show how to construct a suboptimal path (the cost is the path length). We admit a finite number of cusps in the path. Key-words: car-like robot, (sub)optimal path, clothoid, Maximum Principle of Pontryagin (R'esum'e : tsvp) Universit'e de Nice, Laboratoire de Math'ematiques U.R.A. du C.N.R.S., N168, Parc Valrose, 06108 Nice Cedex 2, France INRIA, Sophia Antipolis, 2004, Route des Lucioles 06565, Valbonne, France 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 6...