Time-optimal synthesis for the Zermelo-Markov-Dubins problem: The constant wind case

We consider a combination of the classical Markov-Dubins problem and Zermelo's navigation problem. In particular, we consider the problem of characterizing minimum-time paths with prescribed positions and tangents for a vehicle with Dubins-type kinematics in the presence of uniform winds/currents. By utilizing optimal control theory, we characterize the structure of the optimal paths, and subsequently solve the time-optimal synthesis problem.