Objective In cooperative target tracking missions involving multiple unmanned surface vehicles, maintaining a prescribed formation is often challenged by the presence of obstacles in the marine environment, which increases the risk of collision and disrupts vehicle motion. Traditional collision avoidance methods can prevent collision avoidance but tend to disrupt the original tracking formation. Meanwhile, conventional formation transformation methods typically neglect the influence of the target state on the tracking formation, limiting their adaptability in dynamic tracking scenarios. To address these problems, this study proposes an adaptive formation transformation and control method for target tracking based on the hyperbolic tangent (Tanh) function.

Methods  First, collision detection is formulated based on the overlap between formation and obstacles, and then three formation transformation strategies are designed based on the collision detection results, namely, contraction, rotation and a combined transformation. Then, considering that the Tanh function can map the positive real values to the range of 0 to 1 with a smooth transformation curve, it is introduced to integrate the critical distance and safe distance in order to define an adaptive formation transformation law. According to different strategies and transformation degrees, this method enables flexible realization of multiple tracking formations, while smoothing the formation transformation process. Then, to ensure coordinated tracking and synchronization with the target’s motion, a consistency deviation model is established based on the expected formation and target velocity. A distributed kinematics controller is designed using the inverse step method, which enables stable target tracking and enhances the system’s response speed. In addition, a dynamic controller based on the super-twisting sliding mode method is implemented, and the stability of the closed-loop system is rigorously verified.

Results  Taking a system of four USVs as an example, the proposed algorithm is validated through simulation experiments under the integrated scenarios involving telescopic, rotational, combined telescopic-rotational, and dense obstacle conditions. The results show that the USV formation can adaptively track the desired formation transformations according to the obstacle distribution. The proposed approach significantly reduces tracking errors in position, heading and speed, while producing smoother outputs for both longitudinal control forces and turning control moments compared with the artificial potential field method.

Conclusion The proposed design method not only meets the requirements for formation transformation in USV cooperative target tracking under obstacle-rich environments, but also realizes the stable formation transformation, ensuring the safety of multi-USV system and the integrity of tracking formation.