Path following of under-actuated ships based on backstepping and predictive control method.

To deal with the sideslip angle caused by the current disturbances or transverse motion for path following of under-actuated ships, a nonlinear observer established by an exponential function is introduced in the backstepping approach which converts the path following into heading control. Then, the model predictive control (MPC) method is used as a heading controller, addressing the rudder optimization. A linear extended state observer technology was exploited to estimate yaw rate, external disturbances, and internal uncertainties, which could avoid measuring the high-order state used in the MPC controller and promote the accuracy of the MPC internal model. Moreover, an inverse tangent function is applied to develop a new method for switching the reference heading angle to reduce rudder amplitude when the ship is choosing the next waypoint. Finally, the validity and reliability of the design method were verified through comparative computer simulation experiments.