## 1 Introduction  
In recent years, UAVs have been widely used in both military and civilian fields, such as urban penetration, battlefield reconnaissance, aerial photography, disaster area search and rescue, etc. [1, 2]. However, with the increasing diversification of missions and the complexity of flight environments, more and more users are reaching the limitations of single UAVs when performing missions [3]. Therefore, multiple UAV systems have gradually grown into a popular and challenging research topic [4]. As the most basic problem in the research of multi-UAV systems, the cooperative path planning technology of multiple UAVs directly affects the ability of UAVs to complete tasks smoothly, safely, and autonomously [5, 6]. Multi-UAV systems are usually deployed for more complex tasks, such as coordinated multi-UAV attack and detection missions, which require all UAVs to have the same and shortest arrival time [7]. In addition, since there are usually a variety of threats in flight environments where multiple UAV systems perform tasks, the planning of a safe path that must simultaneously avoid environmental threats and collisions between individual UAVs is a difficult problem [8]. Furthermore, ground-based navigation systems are often unable to detect the precise location and configuration information of all threats in complex environments [9]. Therefore, it is particularly difficult to coordinate the paths of all UAVs involved and adjust their existing paths in a timely and efficient manner according to real-time environmental information [10], especially for some tasks that require accurate arrival time and dynamic conflict avoidance simultaneously. The existing methods of solving the cooperative path planning problem of multiple UAVs include several collision avoidance methods and cooperative path generation methods [11]. Collision avoidance methods are often used to deal with local spatial conflicts. First, each UAV independently plans the shortest path while avoiding threats in the environment. During the path execution, each UAV regularly detects the position and speed of other UAVs around it. If there is a risk of collision, the UAVs adjust their paths in real time to avoid conflicts. Many local collision avoidance path planning algorithms based on collision avoidance methods have been proposed, such as the artificial potential field algorithm (APF) [12; 13], the centralized control barrier function algorithm (CCBF) [14], the distributed control barrier function algorithm (DCBF) [15], and the optimal reciprocal collision avoidance algorithm (ORCA) [16]. Since collision avoidance is only performed in a local range, these algorithms usually have high computational efficiency and the ability to dynamically and rapidly replan paths. However, as a local collision avoidance method, with the increase in the number of UAVs and threats, these algorithms may fall into local minima and lead to the failure of cooperative path planning. Additionally, since such methods focus on space conflict avoidance, the consistency of flight time is not considered. Cooperative path generation methods can be divided into two categories: coupling methods and decoupling methods [17]. The coupling method usually regards all UAVs as comprising an agent system and directly searches for the cooperative path of the agent system. Some popular coupling methods, such as increasing cost tree search (ICTS) [18] and conflict-based search (CBS) [19], have been extensively studied and many variant algorithms have been derived [20; 21; 22; 23]. The coupling method directly deals with the path planning problem of the agent system and can usually obtain the optimal solution for the system. However, it is well-known that even a simple variant of the path planning problem for multiple UAVs, such as a planned cooperative path with the sudden appearance of a threat, interferes with the implementation of a cooperative path that encounters both conflict-free space and path execution time consistency.