The control problem of avoidance-path-following is a critical consideration in the research of unmanned surface vehicle (USV) navigation control, and it holds great significance for the navigation safety of USVs. A guidance and control scheme based on finite-distance convergence is proposed in this paper. First, the requirements for the USV to avoid obstacles from the perspective of path-following lateral error are analyzed. Then, a new performance function with finite-distance convergence is proposed to constrain the lateral error. Based on this, a heading guidance law and a backstepping controller are designed to ensure that the lateral error converges to a steady-state value within the prescribed navigation distance and that the stability is maintained, satisfying the requirements of obstacle avoidance for the USV. In addition, an adaptive velocity command is designed to adjust the velocity with the lateral error, which, to a certain extent, avoids the saturation of the heading actuator caused by the large lateral error. Finally, it is proven through theory and simulation that the control algorithm can guide the USV to achieve avoidance-path-following within a limited distance and to avoid obstacles effectively.

For the guidance problem of trajectory tracking in multiple unmanned surface vehicles (USVs), a trajectory tracking guidance method with collision avoidance based on a novel guiding vector field is proposed. Firstly, within the framework of the virtual leader–follower method for formation control, a tracking error model for followers is developed based on the motion model of USVs. Secondly, considering the limitations of conventional trajectory tracking guidance methods in addressing various initial error conditions, a novel guiding vector field is developed for the design of the heading guidance law to enhance tracking performance. Then, a multi-USV collision avoidance strategy is proposed for formation navigation safety. The trigger conditions, actions and release conditions for collision avoidance are established in this strategy. USVs could avoid collision in time by following the commands outlined in the strategy, especially in complex situations where multiple USVs are simultaneously at risk of colliding with each other. And the theoretical proof is completed. Furthermore, the heading and velocity guidance laws are designed by combining the guidance vector field and the collision avoidance strategy. It is demonstrated that the tracking errors of the system are uniformly bounded based on Lyapunov stability theory. Finally, the effectiveness of the method is verified through simulation.