# A Hierarchical Mission Planning Method for Simultaneous Arrival of Multi-UAV Coalition
## 1 Introduction
[17], the UAVs use resources in a balanced manner to improve the system's robustness in the dynamic and uncertain environment. However, the works cited above assume that only the UAV performing a search task can send a bid to form a coalition, they do not consider the overlapping coalitions, which will decrease the mission performance. For the cooperative task allocation and rendezvous problems, [PERSON] et al. [18] proposed a global optimization algorithm inspired by the biological features of the hill Myna and desert Sparrow, the algorithm can be applied to ad-hoc networks in various applications. For the overlapping coalitions problem, [PERSON] et al. [19] proposed two distributed coalition formation algorithms for multi-UAV based on the contract net protocol, the sequence of UAVs and pop-up tasks are considered in the dynamic environment with limited communication range. The studies cited above do not take into account the obstacles and no-fly-zones in the environment, which significantly limits the application of the coupled task allocation and path planning algorithm. To maximize the system performance, the paths for the UAVs in the same coalition should satisfy simultaneous arrival as well as some other constraints, such as the kinematic constraint of a UAV and collision avoidance with obstacles. For the simultaneous arrival problem (also called rendezvous problem), the velocity-based [20; 21] method has been used. The simultaneous arrival problem of multiple UAVs is addressed by a velocity control approach [20], the UAVs communicate with each other to make a consensus on the estimated time of arrival. A distributed optimization algorithm based on game theory [21] was proposed for a UAV rendezvous problem, each UAV adjusts its velocity according to the states of its neighbors in a predefined time interval. However, this method is easy to cause velocity saturation [22] and a large amount of communication is required. Some other studies [7; 23] assume all the UAVs fly at the same and constant speed, so the simultaneous arrival for multi-UAV can be achieved by planning paths of equal length. In our previous work, a cooperative particle swarm optimization (CPSO) algorithm is proposed to generate Pythagorean hodograph (PH) paths of equal length for each UAV. However, the task sequence of UAVs is not considered. In this paper, the focus is on the coupled task allocation and path planning problems for multi-UAV performing simultaneous arrival tasks. Considering the target's resource requirement, simultaneous arrival, time-dependent values of targets, resource consumption of UAVs and collision avoidance with obstacles. A hierarchical mission planning method is proposed to solve the coupled task allocation and path planning problem for a multi-UAV performing a multi-task, which is also the contribution of this paper. The method consists of three phases. In the first phase, the PH curve is calculated as the estimated path for each UAV, which can provide a more accurate input for the task allocation process. Then, a task allocation algorithm is proposed to form a coalition for each target considering the task sequence of UAVs and the resource requirement of targets. Finally, the path planning process generates the flyable and safe paths for the fixed-wing UAVs in the same coalition to realize the simultaneous arrival. The rest of this paper is organized as follows: In Section 2, a description of the multi-UAV cooperative attacking problem is given. Section 3 describe the task allocation method for multi-UAV. In Section 4, path planning method to achieve simultaneous arrival is presented. Experimental results are shown in Section 5. In Section 6, the conclusions are given.