## 1 Introduction  
There are many studies in collision avoidance that could be sorted out into two main domains, i.e., tactical and strategic [1]. The first is the geometric algorithm, which analyzes the relative motion of aircraft in geometric space and implements passive collision avoidance under the procedure of detection-avoidance [2; 3; 4; 5]. The other is the track planning algorithm, which actively plans the conflict-free flight path from the current position to the destination based on the perception detection of obstacles under the constraint of minimum safety separation distance. The geometric algorithm is widely researched. [PERSON] [3] and [PERSON] [4] proposed a novel collision cone approach for irregularly shaped moving objects with unknown trajectories. [PERSON] [5] improved the 3D analytical algorithm by proposing a cylindrical safety bubble that allows different minimum separations of the vertical and horizontal planes with respect to the nominal trajectory to be achieved. The performances of such system, using active obstacle detection through radar, have been discussed in the paper [6]. Geometric algorithm is intuitive with low computing cost and always provides an optimal solution in 3D environments whether the aircraft cooperates or not. But most of the current Genetic Algorithm (GA) only focus on pairwise encounters. For multiple conflict resolution, more complicated algorithm should be considerable, the calculation amount of checking each threat repeatedly becomes inconsiderably massive. [PERSON] [7] presented an aggregate collision cone approach to allow arcrafts to detect and avoid collisions with more threats simultaneously. But there are only three aircrafts in experiments [8]. The geometric algorithm to be used, furthermore, is also dependent, to some extent, from the available sensors onboard, as emphasized in the paper [9]. The main aspects of the track planning algorithm include the potential field method [10; 11; 12], linear programming, discretized space domain and stochastic theory methods, and so on. [PERSON] [11] improved the artificial potential field by combining the Lyapunov theorem to make the disturbing balance points divergent so that the Unmanned Aerial Vehicle (UAV) can avoid the minimum point. [PERSON] [12] modified the artificial potential fields by combining a priority system to prevent the special case of an aircraft circling its destination. The artificial potential field has the advantage of rapid respondent speed, small computation capacity and real-time property. However, there exist some problems, such as the unreachable goal and the existence of a local minimum point value, and these do not apply to the fixed-wing aircraft due to continuous adjustment and an unstable state [13]. To plan an optimal trajectory for collision avoidance, [PERSON] [14] developed an algorithm of modified Grossberg neural network (GNN) to get the trajectories outside of the danger zone based on current sensor information and mission objectives. GNN has been used earlier in robot applications and is implementable in UAVs that have limited capabilities. [PERSON] [15] developed an algorithm of rapidly exploring random trees (RRT), [PERSON] [16] proposed an algorithm of mixed integer linear programming (MILP), and [PERSON] [17], [PERSON] [18], [PERSON] [19] applied ant colony optimization algorithm (ACO). These algorithms have obvious defects of limited application; they apply mostly to an immovable obstacle and cannot solve a dynamic obstacle. In addition, they require massive iterative calculation, which suits of-line route planning but not real-time planning. To solve the multi-aircraft conflict, [PERSON] [20] proposed a consensus algorithm to solve the rendezvous problem by attaining a consensus on the estimated time of arrivals. However, it could not manage dynamic obstacles. [PERSON] [21] proposed a satisficing decision theory by applying the game theory, but it lacks efficiency and suits a 2D model of airspace.