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

In this paper a solution to the problem of following a curved path in the presence of a constant unknown ocean current disturbance is presented. We introduce a path variable that represents the curvilinear abscissa on the path which is used to propagate the path-tangential reference frame. The proposed dynamic update law of the path variable is non singular and the guidance law is designed such that the vessel can reject constant unknown ocean currents by using an ocean current observer. It is shown that the closed-loop system composed of the guidance law, controller and observer provides globally asymptotically stable and locally exponentially stable path following errors. The sway velocity dynamics is analyzed and, under adequate hypothesis on the path curvature, it is shown that the dynamics are well behaved and that the guidance law to exist. Simulations are presented to verify the theoretical findings.