Optimal Synthesis in the Reeds and Shepp Problem with Onesided Variation of Velocity

We consider a time-optimal problem for the Reeds and Shepp model describing a moving point on a plane, with a onesided variation of the speed and a free final direction of velocity. Using Pontryagin Maximum Principle, we obtain all possible types of extremals and, analyzing them and discarding nonoptimal ones, construct the optimal synthesis.