## 1 Introduction  
Unmanned aerial vehicles (UAVs) are widely used in both civilian and military fields, including search and rescue [1], environmental monitoring [2], surveillance and attacks [3], and so on. Based on the multi-agent theory and applications [4; 5; 6], a group of UAVs flying in a formation [7] rather than a single UAV can obtain higher combating effectiveness, deliver greater coverage, and will have wider applications in the future. Regarding the multi-agent formation problem, some important studies exist. [PERSON] described a theoretical framework for the design and analysis of the distributed flocking algorithm for the multi-agent self-organizing flocking problem, two constraint-free algorithms, and one constrained algorithm considering the obstacles proposed. For generating regular polygon formation of a multi-robot, each robot is represented as an electric charge. The formation can be realized based on the attractive forces of a virtual center and the repulsive forces between different robots; the collision avoidance with obstacles can be achieved based on the potential field theory [8; 9]. [PERSON] et al. [10] propose a distributed formation control algorithm to form different formation shapes for multiple rectangular agents. An artificial potential function is used and a repulsive function is used to avoid collision. To make the UAVs reach a predetermined rendezvous state simultaneously, path-planning for multi-UAV formation rendezvous becomes one of the key technologies in UAV formation flying. Recently, many researchers have been looking into the problem of cooperative path-planning of multiple UAVs [11; 12; 13]. To solve the problem of multi-UAV rendezvous, the velocity control method is used [14; 15]. [PERSON] et al. [14] use the consensus algorithm based on the estimated time of arrival, where velocity control and a wandering maneuver are applied to avoid collisions with other UAVs. Unfortunately, this method requires a large amount of communication. Regarding the cooperative timing problem among multiple UAVs, the path and velocity of each UAV are determined by the coordination functions and coordination variable; however, this may lead to velocity saturation [16]. Some other researchers use the trajectory control method [17; 18; 19] to realize multi-UAV rendezvous, which assumes that each UAV flies at a constant and equal velocity. For multiple UAVs performing many-to-one tasks, two wandering maneuvers [18] based on Dubins curve are proposed to achieve simultaneous arrival. A simple method based on basic geometry [19] is proposed to generate paths of equal length in a remote-sensing problem, where each UAV first calculates the Dubins longest path. Because a Dubins curve consists of arcs of the minimal turning radius and straight lines, the discontinuous curvature of Dubins curve leads to a large tracking error for UAV. A three-step method is proposed [20] to generated feasible UAV paths to achieve simultaneous arrival; the connection of the arc and line in Dubins path is replaced with the clothoid arc. The method consists of (i) generating flyable paths using Dubins path with clothoid arcs, (ii) satisfying the collision avoidance constraint, and (iii) generating paths of equal length. However, this method requires a large amount of computation because of the iteration strategy. According to the existing literature on cooperative path-planning of UAVs, the commonly used paths are as follows: Dubins paths [14; 21], clothoid paths [20; 22], B-spline paths [18; 23], and Pythagorean hodograph (PH) paths [16; 24]. The Dubins path is the shortest path, but it has discontinuous curvature; the other three paths have continuous curvature. Regarding the clothoid path, there is no closed-form solution and iteration is required for a solution. For the B-spline path, the curvature at any point on the curve has no closed-form solution and it is difficult to meet the maximum-curvature constraint of UAVs.