## 1 Introduction  
As a disruptive technology that changes the way society works and lives in the future, unmanned system technology has received a lot of attention and rapid development in academia and industry, among which the application of intelligent decision making robots in resource exploration, environmental monitoring, biological research, etc., has became a hotspot for research [1, 2, 3]. When operating in unknown waters, the operation efficiency and detection range of a single autonomous underwater vehicle (AUV) are limited by the size of the platform, while multiple AUVs operating in formation can not only improve the search efficiency, but also achieve cooperative positioning with a short communication time delay to ensure the accuracy of underwater navigation and operational safety, while the robots in the formation can occupy the coordinates around the target in a many-to-one manner to complete the capture task. Therefore, it is important to study the mission-planning of AUV formations in different environments. In the unknown underwater environment, the AUV formation completes the capture of underwater targets in two stages: search and capture. Since the terrain obstacles can affect the safety of the formation, the array-shaped obstacles formed by submarine gullies and bulges make the AUV formation unable to maintain the original structure; therefore, whether the robots can complete the formation change independently according to the distribution of obstacles during operation has a great impact on the safety of cooperative operation. Formation transformation [4; 5] is mainly divided into static and dynamic: static formation transformation generally refers to fixed-formation transformations when obstacle distribution is not considered. [PERSON] [6] applied nonlinear control theory and graph theory methods to study formation control strategies for mobile robots, using double rows or a columnar parade through obstacle areas, but such schemes cannot adaptively adjust the formation according to environmental information, have low flexibility and high time and energy costs, and have large limitations. [PERSON], [PERSON] et al. [7; 8] virtually tracked linear formations using an improved artificial potential field method, but the linear structure has a high repetition rate in its detection range and low efficiency in cooperative detection. [PERSON], [PERSON] et al. [9; 10] proposed a controller based on a neural network model, which can better maintain the formation of AUVs, but did not discuss the case of traversing large obstacle domains. The dynamic formation transformation can select the optimal formation autonomously based on the environmental information. [PERSON] et al. [11] proposed an optimal efficiency model for evaluating multi-robot formation transformation for obstacle domains, choosing formation convergence time and path length as evaluation criteria, respectively, but the two models are difficult to balance in practical applications [12]. After searching for a target, whether the robots in the formation can quickly complete the assignment of capture positions and dynamically path-plan has a great impact on the efficiency of the capture operation. [PERSON] [13] resolved the Multiple Traveling Sales Person (MTSP) problem using a genetic algorithm (GA), but Euclidean distance was the only cost function. [PERSON] [14] and [PERSON] [15] both proposed a self-organizing neural-network-based task assignment method, but did not consider the robot's own load energy consumption. The path-planning algorithms such as A* [16; 17; 18], neural network [19; 20; 21], ant colony [22; 23; 24] and reinforcement learning [25; 26; 27; 28], etc., are more mature. [PERSON], [PERSON] et al. [29; 30] proposed a bionic neural wave network (BNWN) algorithm to complete the path-planning in a multi-AUVs collaborative target capture process; however, the computational effort is large and the real-time performance is difficult to guarantee.