Zermelo-Markov-Dubins problem and extensions in marine navigation

This note accounts for optimal control techniques applied to marine navigation for seismic acquisition. More precisely, the goal is to gain time in turns and alignment maneuvers. A model for the kinematics of the marine vessel and sea current is proposed, then extended to include the evolution of the shape of the towed underwater cables during the maneuver. Two minimum time problems are stated, depending on whether the shape of the streamers is in the model or not. The simpler case is the so-called Zermelo-Markov-Dubins problem, recently studied in the literature. It generalizes the classical Dubins problem. The complete model is not standard, and preliminary analysis of controllability and of properties of minimum time trajectories are given.