## 1 Introduction  
In August 2018, the U.S. Department of Defense released _the Unmanned Systems Integrated Roadmap 2017_-2042, which reemphasized that the development of autonomous technology is of great importance for improving the efficiency and performance of unmanned systems as well as soldiers [1]. The development of UAVs is an essential part of studying unmanned military systems [2], of which UAV autonomous clusters have become an important direction for the future [3]. Moreover, UAV clusters have begun to play a key role in targeted attacking in the future battlefield with advantages including \"defeating the most enemy with the least resources\", a flexible and straightforward delivery mode, and ease of avoiding enemy's Air Defense Radar System (ADRS). With this attacking strategy, the successful attack rate can be improved because attacking UAVs require expensive and high precision strike weapons; furthermore, it is difficult for the enemy to find, defend against, and destroy UAVs quickly. Therefore, studying the stable formation method of large-scale UAV clusters has practical implications for military operation. At present, there are five commonly used plane formation methods: the leader-follower method [4; 5; 6; 7; 8; 9; 10], the behavior-based method [11; 12; 13; 14; 15; 16], the virtual structure method [17; 18; 19; 20; 21; 22; 23; 24; 25; 26], the graph theory method [27; 28; 29; 30; 31; 32; 33], and the consistency method [34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45]. However, these methods do not consider the stability of UAV formation planes when they are destroyed or decayed by the enemy on the battlefield. If the \"Leading goose\" UAV in the formation or a UAV on a certain critical node faces such a situation, formations using the methods above will be disrupted. The UAV cluster formations can be disrupted by strong electromagnetic communication or enemy fire attacks. To address these issues with ideal and mature formation methods, this paper studied the bionic mechanism of the maturely evolved flocks and compared the characteristics of the classical models proposed by scholars worldwide. For example, [PERSON] established an essential but straightforward cluster model--the Vicsek model (VM) [46; 47]--based on the assumption that the individual field of view (FOV) is 360\({}^{\circ}\), which is not realistic given that this range for most creatures is limited. Considering the limited FOV, [PERSON] et al. [48] established the RFVN model by upgrading the VM. The Couzin model also considered the FOV issue in studying cluster motion modeling [49]. However, the RFVN model assumes that the direction of FOV is consistent with the individual's moving direction, which is inconsistent with the actual biological perception mode. Therefore, based on the RFVN model, [PERSON] et al. [49] introduced the limited FOV and the strategy of random line-of-sight (LOS) to establish the Random LOSVM (RLosVM). Furthermore, based on the above models [3], [PERSON] and [PERSON] et al. proposed a fixed neighborhood region (FNR) model and a fixed number of neighbors (FNN) model according to the topological distance interaction rules of the starling movement. In the FNN model, when one individual refers to the motion state of another in the perception range, its sight may be blocked by others in the formation, making it unable to obtain information about its neighbors effectively. After improving the FNN model, the MFNN model was built, with which individuals can dynamically sense the motion of the nearest \"neighbor\" in all directions. In addition, [PERSON] and [PERSON] et al. believed that the VM only considers the information of the previous moment when updating, but the individuals in the actual cluster motion have \"memories\". This means that the individual decision-making considers not only neighbors' information at the current time, but also previous ones. Therefore, they introduced the fractional calculus idea to the VM and established the fractional order VM (FOVM).