The Markov-Dubins problem in the presence of a stochastic drift field

We consider the problem of navigating a small Dubins-type aerial or marine vehicle to a prescribed destination set in minimum expected time and in the presence of a stochastic drift field induced by local winds or currents. First, we present a deterministic control law that is independent of the local winds/currents and their statistics. Next, by employing numerical techniques from stochastic optimal control, we compute an optimal feedback control strategy that incorporates the stochastic variation in the wind when driving the Dubins vehicle to its destination set in minimum expected time. Our analyses and simulations offer a side-by-side comparison of the optimal deterministic and stochastic optimal feedback control laws for this problem, and they illustrate that the deterministic control can, in many cases, capture the salient features of structure of the stochastic optimal feedback control.