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Deals with the problem of motion planning for a car-like robot (i.e. nonholonomic mobile robot whose turning radius is lower bounded). The main contribution is the introduction of a new metric in the configuration space R/sup 2/*S/sup 1/ of such a system. This metric is defined from the length of the shortest paths in the absence of obstacles. The authors study the relations between the new induced topology and the classical one. This study leads to new theoretical issues about sub-Riemannian geometry and to practical results for motion planning. In particular they prove an inclusion relation of neighbourhoods in both topologies, which is the basis of an efficient obstacle avoidance local method.>
Laumond et al. (Wed,) studied this question.