Nonlinear tracking control of underactuate ships based on a unified kinematic and dynamic model

This paper proposes a nonlinear tracking control method for underactuated ships based on a unified kinematic and dynamic model. There are several literatures using backstepping-based controllers, which usually results in the complicated control structures and the restriction on the reference trajectories. To obtain a controller with much simpler structure and less restriction on the reference trajectory, the kinematics and dynamics are combined into a single unified model and then backstepping-like linearization method is employed based on this model. Whereas the torque input for translation motion can be directly obtained, the torque input for rotational motion is designed in such a way that the pseudo yaw angle command is first designed and then the actual yaw angle is made to follow its pseudo command. The resulting position and yaw angle tracking errors are shown to remain globally uniformly ultimately bounded through stability analysis. Furthermore, the choice of the control gains is less restrictive than the previous similar methods, and more general reference trajectory can be followed by the proposed controller, as demonstrated in the numerical simulations.