Underactuated ships follow smooth paths: Full state-feedback

A method is proposed to design a global controller that forces an underactuated ship to follow a reference path under constant disturbances induced by wave, wind and ocean-current. The controller guarantees the ship to be on the path and its total velocity to be tangential to the path with an adjustable forward speed. The ship under consideration is not actuated in the sway axis, while the mass and damping matrices are not assumed to be diagonal. Nonlinear damping terms are also included to cover both low- and high-speed applications. The new result is facilitated by choosing an appropriate body-fixed frame origin, designing a suitable filter of sway velocity, several nonlinear coordinate changes, backstepping technique, and utilizing the ship dynamic structure. Numerical simulations illustrate the result.