## 2 Related Works  
In this section, we review the related works, including the formation control algorithms of the multi-robot system. [PERSON] [17] studied the nonlinear model predictive about the control formation problem of USVs in the environment with obstacles. Based on the decentralized geometric control strategy in the leader-follower structure, the underactuation of USVs, and environmental obstacles, a formation controller for real-time optimization nonlinear predictive control method was designed to realize formation and obstacle avoidance. [PERSON] [18] presented a design of cooperative controllers for several agents based on the constraint of sensing ranges and collision avoidance. Then, [PERSON] [19] discussed the formation control of underactuated ships limited to collision avoidance and communication. An elliptic collision avoidance method was proposed, and the nonlinear coordinate transformation and additional control were introduced to control the underactuated ship. Simultaneously, the potential energy function was used in the controller design with collision avoidance between the ships. [PERSON] et al. [20] proposed a neural-network-based leader-follower underdrive UAV formation controller based on the uncertainty of leader dynamics and environmental interference. The uncertainty dynamics of the leader were approximated only by the sight distance and angle measured by the local sensor, and a control law that does not rely on an accurate model was designed. After that, an observer-based distributed formation controller was proposed. The formation controller based on neighbor information was designed using a neural network, back-stepping, and graph theory, and used to estimate the speed information [14]. Since then, to overcome problems such as model uncertainty, ocean noise, and unpredictable speed of leaders and followers, adaptive control, neural networks, high-gain observers, and minimum learning parameter algorithms have been combined into the backstepping design, a new adaptive output feedback control scheme has been proposed, which realizes the leader-follower formation based only on position and heading angle, and only two parameters need to be learned online [21; 22]. [PERSON] et al. [23] proposed a distributed adaptive cooperative formation control strategy based on a virtual leader, designed a navigation system and an adaptive neural network synchronization controller that can calculate a specified trajectory, and solved the problem of model uncertainty to achieve stable formation. [PERSON] et al. [24] studied the formation control of USVs in a leader-follower structure, considering model uncertainty and dynamic disturbance of the environment. [PERSON] [25] proposed a leader-follower formation tracking controller for USVs affected by torque limitation and environmental noise. The saturation function was used to reduce the risk of driver saturation. The radial basis function and adaptive robust control technology were used to improve the robustness of the controller in a disturbance environment. On this basis, the formation method was developed into the three-dimensional formation control of underactuated underwater vehicles based on the neural network, and the nonlinear saturation observer was introduced to estimate the speed of the follower [26]. [PERSON] et al. [27] considered the autonomous navigation of the leader-follower USV formation in a complex environment, and the predictive control based on the limited control set realized the USV team to reach the destination in a certain formation with internal collision avoidance under the condition of no prior knowledge of the environment and predefined trajectory. In other respects, [PERSON] et al. [28] studied the leader-follower formation control problem of fully actuated ships and proposed a navigation formation control method, which uses control, navigation, and synchronization algorithms to ensure that each individual can converge and stay in the assigned formation position to achieve formation. [PERSON] et al.