  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.
