Metric induced by the shortest paths for a car-like mobile robot

Deals with the computation of the shortest path metric for a nonholonomic car-like robot. Bounds on the length d_RS(o,c) of the shortest path linking the configuration o=(0,0,0) to any configuration c=(x,y,θ) (|x|+|y|^1/2+|θ|)/3⩽d_rs (o,c)⩽12(|x|+|y|^1/2+|θ|)^⊙ are derived: sufficiently close to o. The analytical shape of the ball computed with this metric in the configuration space R²×S¹ of the system is provided. Such a study has both theoretical and practical issues in motion planning, leading to computational complexity results while allowing an efficient potential field method for obstacle avoidance to be designed