Observer Based Path Following for Underactuated Marine Vessels in the Presence of Ocean Currents: A Local Approach - With proofs

Abstract: In this article a solution to the problem of following a curved path in the presence of a constant unknown ocean current disturbance is presented. The path is parametrised by a path variable that is used to propagate a path-tangential reference frame. The update law for the path variable is chosen such that the motion of the path-tangential frame ensures that the vessel remains on the normal of the path-tangential reference frame. As shown in the seminal work [20] such a parametrisation is only possible locally. A tube is defined in which the aforementioned parametrisation is valid and the path-following problem is solved within this tube. The size of the tube is proportional to the maximum curvature of the path. It is shown that within this tube, the closed-loop system of the proposed controller, guidance law, and the ocean current observer provides exponential stability of the path-following error dynamics. The sway velocity dynamics are analysed taking into account couplings previously overlooked in the literature, and is shown to remain bounded. Simulation results are presented.