Disturbance compensating predictive control for path following of underactuated surface vessels with roll constraints

When underactuated surface vessels (USVs) sail on the sea, strong disturbances from wind, wave and current probably lead to large roll motion, which severely affects the stability of path following. The roll motion, produced by steering, can offset the roll motion generated by waves, and then the rudder roll stabilization can be realized. However, the path following performance is affected by strong coupling between the control of heading and rudder roll stabilization. In order to handle with the condition, a robust controller with roll constraints is designed to follow the straight path based on the predictive control strategy, and then the coordinate control of heading and rudder roll stabilization can be realized. By defining the error dynamics of path following in the Serret-Frenet frame and dividing the rudder angle envelope, the switched affine model is established combing with heading and roll dynamics. The disturbance observer is used to estimate the disturbances and unmodeled errors, and the real time feedforward compensation is designed to improve the system robustness. Meanwhile, the non-minimum phase characteristic of the USV system is analyzed, and it is transferred into a new minimum phase system based on the output re-definition method, which means reselecting the weighted matrix of the objective function in the predictive control. The analytical predictive control law is obtained using the state space prediction and receding horizon, and the linear programming is used to ensure the roll angle in the specified range. The simulation results have shown a good performance of the proposed control law. The coordinate convergences of heading and heading angle errors are ensured with the satisfaction of roll constraints.