Global tracking control of underactuated ships with off-diagonal terms

We propose a methodology to design a controller that forces the position and orientation of underactuated ships, of which the sway axis is not actuated, and the mass and damping matrices are not assumed to be diagonal as often required in the literature, to globally track a reference trajectory. The reference trajectory is not required to be generated by a ship model. Our new result is facilitated by an introduction of changing the ship outputs, several coordinate transformations, backstepping technique, and utilizing the ship dynamic structure. Numerical simulations illustrate the result.