Quasi-Infinite Horizon Nonlinear Model Predictive Control for Cooperative Formation Tracking of Underactuated USVs with Four Degrees of Freedom

To address the issues of external unknown disturbances and roll motion in the tracking control of underactuated unmanned surface vehicle (USV) formation, a cooperative formation control method based on nonlinear model predictive control (NMPC) algorithm and finite-time disturbance observer is proposed. Initially, a tracking error model for the USV formation is established within a leader–follower framework, utilizing a four-degree-of-freedom (4-DOF) dynamic model to simultaneously account for roll motion and trajectory tracking. This error model is then approximately linearized and discretized. To mitigate the initial non-smoothness in the desired trajectories of the follower USVs, a tracking differentiator is designed to smooth the heading angle of the leader USV. Thereafter, a quasi-infinite horizon NMPC algorithm is developed, in which a terminal penalty function is constructed based on quasi-infinite horizon theory. Furthermore, a finite-time disturbance observer is developed to facilitate real-time estimation and compensation for unknown marine disturbances. The proposed method’s effectiveness is validated both mathematically and in simulation. Mathematically, closed-loop stability is rigorously guaranteed via a Lyapunov-based proof of the quasi-infinite horizon NMPC design. In simulations, the algorithm demonstrates superior performance, reducing steady-state tracking errors by over 80% and shortening convergence times by up to 75% compared to a conventional PID controller. These results confirm the method’s robustness and high performance for complex USV formation tasks.