Flatness of the Generic Under-Actuated 6-Degrees-of-Freedom Unmanned Surface Vessel

The flatness of the under-actuated unmanned surface vessel with circular hull-shape (``the hovercraft") has long been known. We resolve the long-standing open problem: whether the generic under-actuated 6-degrees-of-freedom (dof) unmanned surface vessel (gUSV) admits a feedback linearization. Lie symmetries of the gUSV are used to construct a dynamic feedback linearization, explicit flat outputs and flat parametrization, for all hydrodynamic parameter values. In this generic case the dynamic compensator has order 6, in contrast to the hovercraft vessel whose dynamic compensator has order 4.