# A Hierarchical Mission Planning Method for Simultaneous Arrival of Multi-UAV Coalition
## 5 Simulation Results
### General Scenario
The UAV \(U_{4}\) was selected to be the part of the two coalitions \(C_{1}\) and \(C_{2}\). The UAV \(U_{6}\) had not been assigned any target, which denotes that the UAV \(U_{6}\) was always at its base. It can be seen from Figure 2a that the paths for these UAVs could avoid collision with the obstacles. The curvature of each UAV's path is shown in Figure 2b, which demonstrated that these paths had continuous curvature and satisfied the maximum curvature constraint. Figure 3: (a) The ETA for the target \(T_{1}\); (b) the ETA for the target \(T_{2}\). Figure 2: (a) The mission planning results for two targets; (b) curvature of each UAV’s path. It can be seen from Figures 4 and 5 that when the straight line and PH curve were used in the path estimation process, respectively, the task allocation methods generated different allocation strategies. When the straight line was used in the path estimation process, the generated coalitions were \(C_{1}=[U_{1},U_{3}]\) and \(C_{2}=[U_{2},U_{4}]\) for the target \(T_{1}\) and \(T_{2}\), respectively. That was because the UAV \(U_{1}\) was closer to target \(T_{1}\) than target \(T_{2}\) when the straight line was used in the path estimation. However, when there are obstacles in the environment, the path planning process should generate paths avoiding collision with obstacles, which will have a large deviation from the path estimation process using straight line. When path estimation using the PH curve was used in the mission planning method, it produced a more reasonable allocation strategy, the generated coalitions were \(C_{1}=[U_{3},U_{4}]\) and \(C_{2}=[U_{1},U_{2}]\) for the target \(T_{1}\) and \(T_{2}\), respectively. Table 6 summarizes the results of these two path estimation methods for this study case. In Table 6, the mission time denotes the total time to perform all the targets, the system utility was calculated by Equation (6). It can be seen that, the mission time using the straight line in the path estimation was longer than that using the PH curve, which also led to a lower system utility. In order for a deeper comparison of performance differences of the two path estimation methods, the performance of the two path estimation methods with increasement in the number of targets was compared by Monte Carlo simulation. In the set of simulation, there were six UAVs in the team, and the number of targets varied from 10 to 30. For each simulation, obstacles were taken into consideration. The location of UAVs and targets were randomly generated in a bounded region. Each target needed three different types of resources, each required resource was a random integer between three and five. Each UAV also carried three types of resources, and each type of resource was randomly generated between 20 and 30. Using two different path estimation methods, the comparison results of average mission completion time and system utility are shown in Figure 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Figure \#** & **Path Estimation** & **Mission Time (s)** & **System Utility** \\ \hline
4a & Straight line & 51.7 & 1.3 \\
5a & PH curve & 35.6 & 26.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance of different path estimation methods. Figure 5: (a) Mission planning results (Pythagorean hodograph (PH) curve is used in the path estimation process); (b) curvature of each UAVs’ path. Figure 6a shows the average mission time using the two path estimation methods when the number of targets increased. The vertical axis denotes the average mission completion time of 100 runs. The horizontal axis indicates the number of targets. When the PH curve was used in the path estimation process, it could obtain a smaller mission completion time compared to the path estimation using the straight line. That was because the deviation between the estimated path and the actual path was smaller, when the PH curve was used in the path estimation process.