Global partial-state feedback and output-feedback tracking controllers for underactuated ships

New global partial-state feedback and output-feedback control schemes for tracking control of an underactuated surface ship without sway force available are presented. For the case of partial-state feedback, we do not require measurements of the ship sway and surge velocities, while, for the case of output-feedback, none of the ship velocities are required for feedback. The reference trajectory to be tracked can be a curve including a straight-line. Global nonlinear coordinate changes are introduced to transform the ship dynamics to a system affine in the ship velocities to design observers to globally exponentially estimate unmeasured velocities. The controllers' development is based on Lyapunov's direct method and backstepping technique, and utilizes the passive property of ship dynamics and their interconnected structure. Numerical simulations are provided to illustrate the effectiveness of the proposed controllers.