Global tracking control of underactuated ships with nonzero off-diagonal terms in their system matrices

A methodology is proposed to design a controller that forces position and orientation of underactuated ships to globally track a reference trajectory. The ships under consideration are not actuated in the sway direction, and the mass and damping matrices are not assumed to be diagonal, as often required in the literature. It is not required that the reference trajectory be generated by a ship model. The paper also addresses the tracking problem with constant bias of environmental disturbances. The new result is facilitated by the introduction of change to the ship position, several nonlinear coordinate changes, the backstepping technique, and utilizing the ship dynamic structure.