## 1 Introduction  
The advances of intelligent autonomous systems have led UAV swarm technology and its application to the current scientific research hotspot [1, 2]. Cooperative task assignment stands out as an essential component and a precondition of task accomplishment and autonomous control of UAV swarm systems [3]. Cooperative task assignment is to assign a considerable number of different types of subtasks and their order to each UAV in the swarm while meeting the task requirements with UAV capabilities and the multiple constraints involved. In the past few decades, there have been several main sorts of assignment algorithms for UAV swarm cooperative task assignment: the heuristic algorithm and the market-based algorithm, for example [4]. Heuristic algorithms generally search a certain range of solution space in an acceptable time by simulating natural phenomena to obtain feasible solutions to optimization problems. Common methods include the genetic algorithm [5, 6, 7, 8], the particle swarm optimization algorithm [9], the ant colony algorithm [10, 11], and the wolf swarm algorithm [12]. For UAV swarms with distributed architecture, heuristic algorithms always need to obtain global information. This process consumes lots of communication and computing resources as well as time to achieve global consensus; it is not suitable to apply heuristic algorithms. Compared with heuristic algorithms, market-based approaches (such as contract network protocol), distinctively characterized by distributed computing of swarms, requires only local information of the swarm and have the advantages of flexibility, robustness, and high operation speed [13] and, hence, are more suitable for distributed UAV swarms. Meanwhile, with strong scalability, market-based approaches can well handle cooperativetask assignments with complex constraints such as limited communication [14] and time windows [15] and have been applied to dynamic task assignments [16; 17; 18]. The algorithms adopted are a part of the assignment approaches for the task assignment in complex and changeable combat scenarios, which are usually modeled as constraints or objectives from different perspectives. The crucial topics to be investigated in this field include cooperative task assignment with the trajectory coupled [19; 20] as well as under dynamic resistant circumstances [21; 22; 23]. In [24], a scheme to assign tasks in UAV swarms based on the contract network protocol (CNP) is presented, in which an A* algorithm is applied in flight path planning and path length estimation with a no-fly zone and threat considered. Under this scheme, the coupling between task assignment and flight path planning can be solved. However, their work does not take into consideration either pop-up missions or UAV faults. A study [25] has proposed a novel model for UAV coalition and an algorithm derived from basic geometry that generates a path derived from the original Dubins curve for application in remote sensing missions of fixed-wing UAVs. Another study [26] proposed an unmanned air vehicle (UAV) swarm task and a resource dynamic assignment algorithm based on the task sequence mechanism. By establishing a task sequence, each UAV strictly separates the necessary task time and synchronization waiting time. For the newfound targets, each UAV quickly determines its available time period. According to the available time and task resources, an auction algorithm and a consensus algorithm are used to decompose the task assignment into the initial distributed assignment phase and the swarm consensus phase to develop real-time conflict-free task solutions for UAV swarms. However, their work does not take into account the communication topology and time constraints. In [27], a CNP-based approach to a multi-UAV task assignment is proposed, in which a flight path planning method based on PH curves is combined with cooperative particle swarm optimization (PSO), cooperative variables, and cooperative functions to achieve attack synchronization on certain targets.