# Cooperative Multi-UAV Collision Avoidance Based on a Complex Network
## 4 Simulation and Results
### A Case Scenario  
Figure 4a shows the UAV trajectory under the first key node selecting method, which is barely based on degree. In this scenario, the first time a TA appears is when \(UAV_{1}\) and \(UAV_{9}\) collide with each other. After the analysis of the CA system, we discovered that when avoiding the imminent collision, some potential collisions may occur. Therefore, when the TA issues a warning at 18:15:22 for the first time, the system selects \(UAV_{1}\) as the key node and instructs \(UAV_{1}\) to descend to avoid a conflict. As the simulation step progresses, \(UAV_{1}\) and \(UAV_{9}\) burst into each other's collision volumes. This time, \(UAV_{1}\) becomes the key node, and a climb instruction is sent to \(UAV_{1}\) to avoid collision. The result in Figure 4b demonstrates the conflict resolution maneuver and that the difference in this method arises because the key node in the same scenario is different. When selecting the key node by the node contracting method, the system selects the \(UAV_{9}\) as the key node and instructs \(UAV_{9}\) to descend to avoid conflict. These UAVs form a decentralized CA situation. This can be explained by the fact that the robustness of the network in this area has been minimized. The intuitive image is that three UAVs have spread out and no cross routes have appeared, thus avoiding the domino effect. Table 2 summarizes the trajectory of \(UAV_{1}\) and \(UAV_{9}\) (the waypoints are recorded every 4 s for simplicity) in the same scenario under two different key node selecting methods. The UAV starts to change its angle at 18:15:23 and returns to the original trajectory at 18:17:23. From this simulation, the results indicate that the CA system can facilitate the UAV cluster to effectively avoid collision in both scenarios. The figure illustrates the relative distance of each pair of UAVs that are involved in a collision scenario involving nine UAVs and four conflicts among them. It is noteworthy that the distance between \(UAV_{i}\) and \(UAV_{j}\) is defined by \(d_{ij}\). Evidently, the separation of each pair of UAV is never intruded upon, according to Figure 5. For instance, in Scenario 1, \(UAV_{1}\) encounters \(UAV_{6}\) and \(UAV_{9}\), and the distances between them are always larger than the separation distance even at the closest point such that the safety flight is guaranteed, and it is the same in Scenario 2. Figure 4: Trajectory (**a**) with key node selecting based on degree and (**b**) with key node selecting based on the node contraction method. Because the algorithm implements a single-machine change in direction, when the UAV does not reach the pre-set CA altitude, the relative distance of the UAV will be reduced slightly; however, it will not collide because it is at the predicted moment of collision. The UAV has already flown to a safe altitude; therefore, although a close trend may occur during CA, the UAV can maintain a safe relative distance in the subsequent flight path. Figure 6 depicts the situation during the final CA of the UAV group. The connection represents the potential threat between the UAVs. The connection method is the same as the logic of building the network. It is related to the relative distance between nodes and the relative speed between the nodes. The network node can identify key nodes and subsequently select the most appropriate CA direction according to the network properties. We defined a new amount to measure the effect of UAVs when selecting key nodes using different methods. We defined this amount as the residual threat factor. The meaning of this quantity is the measure of the sum of threats to the UAVs in a certain area centered on the critical node after a conflict avoidance maneuver. That is, it evaluates the safety of the UAV in a certain area centered on the point after performing CA maneuver. Therefore, the threat coefficients of the UAVs in the area are added, and different key node selections are compared.