## 1 Introduction  
Because of their low-cost, high-autonomy, super-flexibility, and especially absence of human risk, unmanned aerial vehicles (UAVs) have the potential to offer various capabilities for military and civilian applications. Recently, with the advances of dynamics [1; 2], navigation [3; 4], and sensors [5; 6], more civilian applications have been realized for UAVs, such as surveillance [7; 8], aerial photography [9; 10], search and rescue [11; 12], and others. For all of these applications with multiple UAVs, one critical technical problem is that the UAVs may collide with each other in the increasingly dense airspace. Although UAV collision does not cause the loss of human life, it still causes economic loss and seriously affects the task that UAVs are undertaking. Besides, with the occupancy of the airspace being denser, the ground station-based air traffic control cannot be sufficient to track every aircraft. As a result, it is essential to have an automatic UAV collision avoidance strategy to prevent unnecessary loss and guarantee the success rate of missions. Generally, for conventional flight, Traffic Alert and Collision Avoidance System (TCAS) or Global Positioning System (GPS)-based traffic display system is facilitated in manned aircraft to detect and alert possible collision in the near future. When two aircrafts are predicted to reach a certain distance, the system would alert the pilots to maneuver to avoid the collision. In terms of UAVs, relevant research is growing at a fantastic speed to realize the purpose of \"free flight\" [13], which has been the main issue for UAV mission implementation. Normally, assumptions that cooperative UAVs can communicate their positions, speed, heading, waypoints, and proposed trajectories are allowed [14; 15]. With the airspace density increasing, centralized methods are more computationally expensive to solve the UAVs' collision avoidance problem. Some proposed approaches change the UAVs' speed in a centralized way to avoid the predicted collision [16; 17]. However, the velocity amendment of the UAV is usually limited. Therefore, UAVs may still collide with each other if only velocity is adjusted. Based on the consideration above, some researchers adjust the heading direction of UAVs and keep a constant velocity to avoid collision [15; 18]. UAV collision avoidance methods are proposed by varying heading, velocity, or both [14; 19; 20]. However, the method sets the UAVs at constant altitude, which limits the practical use of the method. When it comes to methodology, many laws in other fields have been applied to avoid collision among UAVs. Methods based on potential field have been widely proposed [21; 22], while the idea of genetic methods [18; 19] is also popular to avoid collision. The _proportional navigation guidance law_ is used to solve the problem [23], which is one of the most-used strategies for missile engagement scenarios. Other strategies solving the problem are based on optimization algorithms, such as dynamic programming [24], Lyapunov Method [20], Markov Decision Process [25], radio signal strengths [26], rapidly-exploring random tree [27], and so on. In this paper, a 3D conflict avoidance problem for cooperative multiple UAVs sharing airspace is proposed. In the particular local airspace, it is assumed that the initial trajectory (a sequence of waypoints), real-time position, heading, and velocity of each UAV are shared as the sensors in the UAVs scan the environment at a fixed interval. Considering that conflict avoidance problem among UAVs is non-deterministic polynomial-time hard (NP-hard) [28], we transfer it to be discrete by sampling, which has been proven to have better performance in solving NP-hard problems [29]. We also consider the heading and position of each UAV at the next interval as the state condition. The rolling optimization algorithm (ROA) we propose predicts whether a collision may occur.