## 4 Simulation and Results
### A Case Scenario
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(R_{\mathit{ef}}\) & \(R_{\mathit{el}}\) & **Velocity** & **\(\Delta\)f** & **_A_ & **_B_** \\ (**km**) & **(m)** & **(m/s)** & **(s)** & **(rad)** & **(rad)** \\ \hline
1.2 & 100 & \(30\) & \(1\) & \(-1.047\) & \(1.047\) \\  & & & \(w_{1}=w_{2}=w_{3}\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The assumptions of parameters and unmanned aerial vehicle (UAV) properties. Figure 8: The reachability tree of this multi-UAV scenario. Table 2 summarizes the amended waypoints of _UAV1_ and _UAV5_ (for the sake of simplicity, the data are recorded every two seconds). _UAV1_ starts to change its headings at 17:17:48 and returns to the original trajectories at 17:18:18, while _UAV5_ starts at 17:18:04 and ends at 17:18:24. Figure 9 depicts the relative distance of each pair of UAVs that are involved in a detected threat. From this figure, we can see that the minimum separation region of each UAV is never intruded upon, thanks to the favorable effect attained by the CA algorithm. Figure 10 illustrates the pitch angle profiles of _UAV1_ and _UAV5_ that amending their headings for the avoidance of corresponding threats in this scenario. At 17:17:48, _UAV1_ follows the control input that changes its pitch angle from 0 to 0.71 and climbs subsequently. At 17:17:58, _UAV1_ and _UAV2_ reach CPA and _UAV1_ begins to return to its original path. However, _UAV1_ climbs again at 17:18:02 because of the encounter with _UAV3_. At 17:18:18, _UAV1_ recoveries its course when both the involved threats are resolved. And meanwhile, the neighboring collision between _UAV4_ and _UAV5_ is avoided via the upward amendment of _UAV5_. Using this CA advisory, there is no domino effect between the two sub-scenarios. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**Time**} & \multirow{2}{*}{**ID**} & \multicolumn{3}{c}{**Ameded Trajectory**} & \multirow{2}{*}{**Time**} & \multirow{2}{*}{**ID**} & \multicolumn{2}{c}{**Ameded Trajectory**} \\  & & & **\(X\) (m)** & & **\(Y\) (m)** & & **\(Z\) (m)** & & **\(X\) (m)** & **\(Y\) (m)** & **\(Z\) (m)** \\ \hline
17:17:48 & _UAV1_ & 370.43 & 510.68 & 669.57 & 17:18:10 & _UAV1_ & 593.19 & 733.44 & 721.53 \\
17:17:50 & _UAV1_ & 387.85 & 528.10 & 686.68 & 686.68 & _UAV5_ & 628.79 & 779.87 & 572.48 \\ \hline
17:17:52 & _UAV1_ & 406.44 & 564.10 & 701.14 & & _UAV1_ & 614.07 & 754.32 & 716.18 \\
17:17:54 & _UAV1_ & 425.92 & 566.17 & 713.00 & & _UAV5_ & 614.12 & 754.47 & 578.76 \\ \hline
17:17:56 & _UAV1_ & 446.44 & 586.69 & 720.60 & & _UAV1_ & 633.94 & 774.19 & 705.67 \\
17:17:58 & _UAV1_ & 467.54 & 597.79 & 723.66 & & _UAV5_ & 599.14 & 728.52 & 580.34 \\ \hline
17:18:00 & _UAV1_ & 488.67 & 628.92 & 721.03 & & _UAV1_ & 651.64 & 791.89 & 689.14 \\
17:18:02 & _UAV1_ & 509.24 & 649.50 & 713.75 & & _UAV5_ & 584.16 & 702.58 & 578.76 \\ \hline
17:18:04 & _UAV1_ & 529.85 & 670.10 & 720.90 & & _UAV1_ & 667.72 & 807.97 & 669.57 \\
17:18:05 & _UAV5_ & 668.57 & 848.77 & 532.96 & & _UAV5_ & 569.50 & 677.18 & 572.48 \\ \hline
17:18:06 & _UAV1_ & 550.95 & 691.20 & 723.99 & 17:18:20 & _UAV5_ & 555.03 & 652.12 & 564.58 \\ \cline{2-2}  & _UAV5_ & 656.73 & 828.26 & 551.38 & 17:18:22 & _UAV5_ & 541.56 & 628.78 & 551.38 \\ \hline
17:18:08 & _UAV1_ & 572.14 & 712.39 & 725.25 & 17:18:24 & _UAV5_ & 529.72 & 608.28 & 532.96 \\ \cline{2-2}  & _UAV5_ & 643.26 & 804.93 & 564.58 & & & & \\ \hline \end{tabular}
\end{table} 
Table 2: _UAV1_ and _UAV5_ modified trajectories. Figure 9: Relative distance.