Trajectory tracking control with input saturation constraints for underactuated ships guided by a virtual ship

This study aims to address key challenges in trajectory tracking control for underactuated ships under complex sea conditions, such as managing unknown environmental disturbances, suppressing control input saturation, and avoiding the imaginary-part problem inherent in conventional fast terminal sliding mode control methods.

A comprehensive control strategy based on a virtual reference model and a novel sliding surface was proposed. By constructing a virtual ship system, the complex trajectory tracking problem of underactuated ship was decoupled and transformed into a precise speed tracking problem for the virtual ship. In the control loop, a global fast terminal sliding surface was introduced. To improve disturbance rejection ability, a nonlinear disturbance observer was integrated for real-time estimation of unknown, time-varying environmental disturbances. The estimated disturbance was introduced into the controller as a feedforward compensation term. In addition, to handle actuator saturation constraints, a saturation function was incorporated into the control law.

The simulation results show that, even in the presence of unknown time-varying external disturbances, the proposed controller still exhibits excellent robustness and tracking accuracy, while successfully avoiding the complex-domain computations required by traditional methods. Comparative analysis shows that, compared with an advanced second-order sliding mode controller and a conventional nonlinear sliding mode controller, the proposed method significantly improves convergence performance. In position tracking, the convergence accuracy improved by approximately 9.62% and 33.80%, respectively. In longitudinal velocity tracking, the error convergence accuracy improved even more significantly, reaching approximately 49.43% and 51.11% respectively.

The proposed global fast terminal sliding mode trajectory tracking controller demonstrates superior performance compared to second-order and conventional nonlinear sliding mode controllers, and offers a novel approach to the design of trajectory tracking controllers.