## 1 Introduction  
To conduct the cooperative target hunting by multi-AUV in an underwater environment, the AUVs not only need to take into account basic problems (such as searching, path planning) but also need to cooperate in order to catch the targets efficiently [1]. The target hunting by multi-AUV has attracted much attention due to its complexity and significance [2; 3]. Today, much research has been done on the multi-AUV hunting issue, and there are some approaches proposed that apply to this issue. [PERSON] et al. [4] presented a hunting approach derived from the virtual structure. The advantage of the virtual structure approach is that the formation can be maintained very well while maneuvering. [PERSON] et al. [5] considered formation control of a team of mobile robots based on the virtual structure. The main advantage of this approach is that it is fairly easy to prescribe the coordinated behavior for the whole formation group and add a type of robustness to formation by using formation feedback. However, the disadvantage of the virtual structure is that requiring the formation to act as a rigid virtual structure limits the class of potential applications. Recently, some research has dealt the hunting process with simple obstacles. [PERSON] [6] proposed a method based on making troop formations for enclosing the target and presented a smooth time-varying feedback control law for coordinating motions for multi-robots. [PERSON] [7] has applied the improved reinforcement algorithm in the multi-robot hunting problem. However, in these studies, the hunting target is usually static. For the shortcomings mentioned above, [PERSON] [8] proposed a cooperative hunting strategy with dynamic alliance to chase moving target. This method can shorten the completion time to some extent. [PERSON] [9] proposed a new hunting method with new definition concepts of occupy, overlapping angle and finally calculated an optimized path for hunting multi-robots, but the environment is too open, and the initial location of hunting robots is too close to a moving target. Some work has been reported to adapt the leader-following algorithm to achieve target hunting. For example, [PERSON] et al. [10] presented a bio-inspired neural network model with formation strategy to complete the hunting task. [PERSON] et al. [11] proposed a leader-following formation control method for mobile robots with a directed tree topology. [PERSON] et al. [12] have used leader-following formation algorithm to guide multi-agent cooperation for hunting task. These algorithms are easy to understand and implement, since the coordinated team members only need to maneuver according to the leader. However, the leader-following algorithm is no explicit feedback from the followers to leader, and the failure of the leader leads to the failure of the whole formation team. There are many neural network approaches proposed for target hunting. For examples, [PERSON] et al. [13] proposed a simple ant colony optimization meta-heuristic (SACOdm) algorithm to solve the path planning problem of autonomous mobile robots. The SACOdm methods determine the robots' path based on the distance from the source to the target nodes, where the ants remember the visited nodes. [PERSON] et al. [14] proposed a hunting algorithm based on a bioinspired neural network. The hunting AUVs' paths are guided through the bio-inspired neural network and the results show that it can achieve the desired hunting result efficiency. [PERSON] [15] has proposed a method based on diffusion adaptation with network to research intelligent predators hunting for fish schools. Although neural networks can complete the hunting task, they often need to perform large amount of calculation, incurring prohibitive computational cost. Therefore, the neural network algorithm is not suitable for real-time system. Potential field algorithms were proposed for real-time target hunting and became the most widely studied distributed control methods [16].