## 3 Experiment and Application
### Engineering Application: Multi-UAVs Cooperative Path Planning
#### 3.2.4 Simulation Validation  
The planning space was set as 100 km \(\times\) 100 km \(\times\) 500 m, including six peaks. The parameters of the original digital terrain model were set to a = 0.1, b = 0.01, c = 1, d = 0.1, e = 0.2, f = 0.4, and g = 0.02. The height of the peak, horizontal coordinates of the highest point, and slope parameters are listed in Table 8. Multi-UAV cooperative path planning was conducted under a known mission assignment scheme. In the simulation experiment, the path sub-population was initialized in accordance with the number of UAVs. The numbers of individuals in the sub-population, iterations, and path points were 50, 100, and 10, respectively. The weight coefficients of all cost functions corresponded to 0.4, 0.2, 0.1, 0.2, and 0.1. The flight speed range of the UAV was 40-60 m/s. **Case 1:** Three UAVs begin from the starting point and arrived at the designated target point to perform tasks. The coordinates of the starting and target points are presented in Table 9. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number** & **Altitude (m)** & **Center Location (x,y)/(kcm)** & **Slope** \\ \hline
1 & 130 & (56,82) & (10,10) \\
2 & 150 & (75,20) & (10,10) \\
3 & 300 & (50,45) & (12,12) \\
4 & 100 & (22,20) & (8,8) \\
5 & 150 & (20,70) & (8,8) \\
6 & 150 & (77,73) & (10,10) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Model parameters of peaks. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number** & **Start Point** & **Target Point** \\ \hline
1 & (1,1,0) & (100,30,70) \\
2 & (1,30,0) & (100,40,70) \\
3 & (1,60,0) & (100,50,70) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Coordinates of the starting and target points of all UAVs (case 1). Figure 7: The specific flow of the multi-UAVs cooperative path planning based on APO. The three-dimensional path planning and contour map of each UAV are displayed in Figure 8a,b. The cost and synthetic path cost convergence curves of each UAV are plotted in Figure 8c,d. Figure 8 illustrates that all UAVs could effectively avoid the threat and reach the target point. The cost function values of each UAV gradually converge with the increase in iteration times, thereby verifying the effectiveness of the algorithm. Through a simulation, the flight time intervals (unit: s) and range (unit: km) of each UAV are presented in Table 10. The time intersection is [1849.0089, 2554.5307]. The time synergy requirement can be satisfied by setting different flight speeds for all UAVs. **Case 2:** Four UAVs fly to two target points. The coordinates of the starting and the target points are listed in Table 11.  
The planned path diagrams of UAVs are obtained as depicted in Figure 9a,b. The path cost convergence and synthetic cost curves of each UAV are plotted in Figure 9c,d. Through a simulation, the flight time intervals (unit: s) and range (unit: km) of each UAV are presented in Table 12. The time intersection is [1961.975, 2417.0379]. The planned paths and voyages are close and can effectively avoid obstacles. If the UAVs are close to one another, then collisions can be avoided by setting different flight altitudes. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number** & **Range (km)** & **Flight Time (s)** \\ \hline
1 & 110.9405 & [1849.0089, 2773.5134] \\
2 & 102.1812 & [1703.0205, 2554.5307] \\
3 & 102.259 & [1704.3164, 2556.4746] \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Range and flight time of each aircraft (case 1). Figure 8: The result of case 1. (**a**) 3D UAV cooperative path map; (**b**) contour map of cooperative path; (**c**) convergence curve of each UAV; (**d**) path cost convergence curve. **Case 3:** Six UAVs fly to six target points. The coordinates of the starting and the target points are listed in Table 13.  
The result of case 3 was obtained as depicted in Figure 10. Through a simulation, the flight time intervals (unit: s) and range (unit: km) of each UAV are presented in Table 14. The time intersection is [1924.111, 2481.215].