## 4 Simulation and Results
### A Case Scenario  
To verify the feasibility of the proposed algorithms, our simulation experiments are performed on a manually generated scenario of five UAVs (with the corresponding trajectories Tr1, Tr2, Tr3, Tr4 and Tr5), illustrated in Figure 7. This scenario includes the following characteristics:  
1. It is a fairly complex scenario with multiple UAVs. Indeed, among the first three trajectories, Tr1 imposes sequent threats to both Tr2 and Tr3; moreover, an encounter emerges between Tr4 and Tr5, which further increases the complexity of the scenario. 2. It involves the interrelationship (also called domino effect) between neighboring threats. For instance, a new secondary threat between _UAV_3 and _UAV_5 may emerge in the process of resolving their respective previous threat. 3. It resolves successive threats via a compositive CA trajectory, i.e., _UAV_1 is detected to encounter _UAV_2 and _UAV_3 separately in a short continuous time period and the two successive conflicts can be considered overall rather than one by one. In the above scenario, each UAV is assumed to be heading towards its own target position along the straight line. Simulations start with the initial information about the position and velocity of the UAVs in a scenario. For the local area, the UAV states have been treated as broadcast information with efficient real-time communication. The assumptions and the parameter setup values are given in  
Figure 6: The CA reachability tree. Figure 7: Five-UAV scenario with the generated optimal resolution. Table 1. The proposed algorithms are coded in C++ and the simulation is performed on an EliteBook laptop with a processor Intel i5 of 2.6 GHz and 4 GB of RAM. In this causal analysis, the cost of various feasible CA trajectories assists the decision making of solution selection. After executing the proposed CA system, the optimal strategy, that Tr1 synthetically amends upward and _UAV5_ climbs, is implemented. The entirety of the reachable states of this multi-UAV scenario are displayed in Figure 8. From the proposed multi-threat resolution point of view, solo _UAV1_ climbs (Tr11) or _UAV2_ descends (Tr21) to resolve the first threat (see state a). However there would generate a secondary threat with Tr3 if trajectory Tr11 is applied (see state b). Then _UAV1_ could climb again and a composite CA trajectory (Tr111) is generated (see state d). Meanwhile, _UAV3_ could descend (Tr31) to resolve the new encounter (see state e). For resolving the threat between _UAV4_ and _UAV5_, _UAV4_ amends downward (Tr41) or _UAV5_ turns upward (Tr51). In state d, there would be no domino effect between the neighboring UAVs (see state h and state i), while a new threat would appear between the descending _UAV3_ and climbing _UAV5_ (see state k) and have to be resolved through the following heading change (see state p and state q). On the other branch, the first threat is resolved by the amendment of Tr2 (see state c), and two options are considered to solve the encounter between _UAV1_ and _UAV3_ (see state f and state g). In state f, the collision between _UAV4_ and _UAV5_ could be avoided directly without domino effect (see state l and state m). However in state g, a new threat (see state n) would appear between the descending _UAV3_ and climbing _UAV5_ and it could be resolved by one of the involved trajectories (see state r and state s). Since the cost criterion is taken into consideration in the decision-making process, it is clear that state i (_UAV1_ climbs twice for the sequent threats with _UAV2_ and _UAV3_, and _UAV5_ amends upward to avoid the collision with _UAV4_) is the best one of the feasible scenarios. The amended trajectories of _UAV1_ and _UAV5_are represented in Figure 7.