An explicit shortest path generation scheme for point stabilization of the car-like robot in free space

Abstract

This paper proposes a shortest path generation scheme for point stabilization of the car-like robot. An implicit shortest point stabilization algorithm has been suggested conceptually by Vendittelli. As an extension, we present an algorithm which is more explicit and faster than previous one. Our scheme provides exact equations for practical implementation. Moreover, its computation time is remarkably lower than the previous one for the case in which the final point changes frequently. We provide a proof of the optimality and validate the performance of our algorithm through the simulation and experiment. where v(t) ,ω (t) are a linear and an angular velocity. These two velocities are control inputs to the robot. We assume minimum turning radius as 1 and |v(t )=1 | which means that the robot can go both forward and backward with constant speed. Now, we say(x(t0) ,y (t0) ,θ (t0)) as an initial posture and (x(tf) ,y (tf) ,θ (tf)) as a final posture, where t0 and tf are an initial and a final time. We also denote (xf ,y f) as a final point.