## 7 Numerical Simulation and Results  
### Test 1: Calculating Trajectories  
The first test consists of using the proposed framework to compute trajectories for UAVs that visit the DPs whose location was calculated as per Section 6.1. The first trial uses the same map and DPs shown in Figure 4. The calculated trajectories that minimize distance are shown in 2D in Figure 9 and in 3D in Figure 10. When minimizing distance, the distance of the longest path is minimized. It can be observed that all DPs are successfully visited and that the no-fly zones are avoided. The flight profile for the green UAV is plotted in Figure 11. The UAV flies the path counter-clockwise starting at the yellow dot. The UAV takes off and climbs to the minimum flying altitude to reach the starting point. This takeoff is not shown in the flight profile. The UAV then flies at constant altitude and visits the first two DPs. On the speed diagram, one can see that the UAV hovers at the DPs to download the data from the sensors. The UAV then immediately climbs to the altitude of the next two DPs and flies to the third DP reaching steady speed. This may be easier to see on the 3D diagram. After hovering at the third DP, the UAV accelerates, but does not have a sufficient distance to reach steady speed and must decelerate to stop at DP 4. After DP 4, the UAV flies and stops at a high altitude above DP 5. It then descends until it reaches the proper altitude to download the sensor data. After downloading the data, the UAV returns to the starting point at constant altitude. The recovery of the UAV is not shown on the flight profile. The statistics for the three paths are listed in Table 2.  
Figure 10: Same paths as in Figure 9, but shown in 3D.  
Figure 9: Paths minimizing distance for three UAVs visiting 15 DPs covering the 70 sensors.  
The second trial uses the same scenario, but consists of minimizing time instead of distance. Figure 12 shows the paths calculated by the proposed framework. Here, the blue and green UAVs fly a much longer trajectory than the red UAV, but they fly their trajectory at constant altitude whereas the red UAV climbs considerably to visit the two DPs located in the middle of the island. As mentioned in Section 5.1, the vertical speed of the UAV is much slower than its horizontal speed. So overall, the three UAVs have similar flying times. The overall duration of the mission is 788.8 s as listed in Table 3 which is much shorter than that of the previous test. In a third test, paths that minimize energy are calculated. This resulted in paths very similar to those minimizing the flying time.  
In the third trial, a more complex scenario is shown. The same map is used but 100 sensors are randomly placed with a wireless range of 170 m. The locations of the DPs are then calculated. Initially, the proposed framework calculates 66 DPs, but following the removal of extra DPs at Algorithm 2, 55 DPs remain. The paths for three UAVs that minimize distance are then calculated and plotted in Figure 13. A similar test is run on a different map with again 100 sensors randomly positioned, but this time, the objective function minimized is the flying time of the UAVs. The calculated paths are shown in Figure 14. On that figure, one may see loops such as for the green trajectory, however, the path is in three dimensions and these loops result in shorter flying times.  
Figure 14: Paths minimizing distance for three UAVs visiting 40 download points covering 100 sensors.  
Figure 12: Path minimizing time for three UAVs visiting 15 download points covering the 70 sensors.  
Figure 13: Paths minimizing distance for three UAVs visiting 55 download points covering 100 sensors.