Objective When multiple unmanned vehicle systems conduct cooperative target tracking with a specific formation, the existence of obstacles in the marine environment will bring collision risk and affect the movement of unmanned vehicles. Although the traditional collision avoidance method can achieve collision avoidance, it is easy to disrupt the original tracking formation. At the same time, the traditional formation change method does not consider the influence of the target state on the tracking formation, so it is difficult to adapt to the target tracking scene. To solve these problems, an adaptive target tracking formation transformation control method based on the hyperbolic tangent (Tanh) function is proposed.

Methods Firstly, the concept of collision detection is introduced according to the overlapping relationship between formation and obstacles, and then three formation transformation strategies are designed based on the collision detection results, namely, contraction, rotation and their combination transformation. Then, considering that the Tanh function can map the positive real part of the function to the range of 0 to 1, and its transformation curve is relatively smooth, the Tanh function is introduced and the critical distance and safe distance of formation transformation are combined to design the adaptive transformation law of formation. According to the different strategies and transformation degrees, this method can flexibly realize multiple tracking formations. The transformation law can smooth the formation transformation process. Then, considering the formation of the tracking formation and the synchronization with the target movement, the consistency deviation model is established based on the expected formation and target speed, and the distributed kinematics controller is designed by using the inverse step method, which realizes the stable tracking of the target and improves the response speed of the system. At the same time, the dynamic controller is designed based on the super twisting sliding mode method, and the stability of the closed-loop system is proved at last.

Results Taking the system composed of four USVs as an example, the proposed algorithm is verified by simulation experiments under the integrated scenarios of telescopic, rotating, telescopic and rotating combination and dense obstacles respectively. The simulation results show that the USV formation can track the corresponding formation transformation according to the distribution of obstacles, and the tracking errors of position, heading and speed are significantly reduced, and the output of longitudinal control force and turning control moment is smoother compared with the artificial potential field method.

Conclusion The design method not only meets the need of formation change of USV target tracking formation in the environment of obstacles, but also realizes the stable formation change, ensuring the safety of multi-USV system and the integrity of tracking formation.