ИСТИНА

We consider a time-optimal problem for the Reeds and Shepp model describing a moving point on a plane, with a free final direction of velocity. Using Pontryagin maximum principle, we obtain all types of extremals and, analyzing them and discarding nonoptimal ones, construct the optimal synthesis. What is more, for some trajectories which are not globally-optimal, but may be locally-optimal, we use secondorder optimality conditions for the pure bang-bang extremals to have information about their local optimality.