Optimal Synthesis of the ZermeloMarkovDubins Problem in a Constant Drift Field
We consider the optimal synthesis of the ZermeloMarkovDubins problem, that is, the problem of steering a vehicle with the kinematics of the IsaacsDubins car in minimum time in the presence of a drift field. By using standard optimal control tools, we characterize the family of control sequences that are sufficient for complete controllability and necessary for optimality for the special case of a constant field. Furthermore, we present a semianalytic scheme for the characterization of an optimal synthesis of the minimum-time problem. Finally, we establish a direct correspondence between the optimal syntheses of the MarkovDubins and the ZermeloMarkovDubins problems by means of a discontinuous mapping.
optimal synthesis markovdubins problem zermelos navigation problem non-holonomic systems