# A Hierarchical Mission Planning Method for Simultaneous Arrival of Multi-UAV Coalition
## 5 Simulation Results
### General Scenario  
A general scenario is presented to show the whole process of the multi-UAV mission planning, where six UAVs needed to attack two targets. A square region with the size of \(3200\) m \(\times\) 3200 m was used. At the initial time, the information of the targets is known as shown in Table 1. The UAVs were required to form two coalitions that satisfy the resource requirement of the targets. The UAVs in the same coalition were required to arrive to their target simultaneously. The initial information of the six UAVs are shown in Table 2. The parameters used in the mission planning method are shown in Table 3.  
At the initial time, the task allocation algorithm was used to form coalitions for the two targets. In the first allocation round, the UAV \(U_{5}\) was selected as the manager UAV, the target \(T_{1}\) was first to be assigned. The coalition \(C_{1}=[U_{5},U_{4},U_{2}]\) was formed to attack the target \(T_{1}\) simultaneously. As the target \(T_{1}\) was the first assigned target, the CPSO algorithm was used to generate simultaneous arrival paths for these UAVs as shown in Figure 2a. The path lengths of the three UAVs in the coalition \(C_{1}\) from their initial location to the target \(T_{1}\) were 1862.5 m, 1863.8 m and 1862.7 m, respectively. Then, the \begin{table}
\begin{tabular}{c c c c} \hline
**Targets** & **Initial Location (m)** & **Resource Requirement** & **Initial Value** \\ \hline Target 1 & \((1500,1600)\) & \((4,2)\) & 100 \\ Target 2 & \((2000,1000)\) & \((5,4)\) & 90 \\ \hline \end{tabular}
\end{table} 
Table 1: The initial information of the targets. \begin{table}
\begin{tabular}{c c c} \hline
**UAVs** & **Initial Location (m)** & **Heading Angle (rad)** & **Initial Resource** \\ \hline UAV 1 & \((0,0)\) & \(pi/6\) & \((2,1)\) \\ UAV 2 & \((1500,0)\) & \(pi/6\) & \((1,0)\) \\ UAV 3 & \((3000,0)\) & \(3\cdot 4/pi\) & \((3,2)\) \\ UAV 4 & \((500,2200)\) & \(pi/6\) & \((2,2)\) \\ UAV 5 & \((2000,2000)\) & \(pi/6\) & \((1,1)\) \\ UAV 6 & \((3000,3000)\) & \(-3\cdot 4/pi\) & \((2,1)\) \\ \hline \end{tabular}
\end{table} 
Table 2: The initial information of the unmanned aerial vehicles (UAVs). \begin{table}
\begin{tabular}{c c c} \hline
**Parameters** & **Notation** & **Value** \\ \hline Descent rate of target’s reward & \(\beta\) & 0.05 \\ The minimum turning radius of the UAV & \(R_{\min}\) & 50 m \\ Weight value of the target reward in Equation (6) & \(w_{1}\) & 0.8 \\ Weight value of the cost in Equation (6) & \(w_{2}\) & 0.2 \\ Weight value in Equation (25) & \(w\) & 0.8 \\ Velocity of the UAVs & \(V\) & 50 m/s \\ Population size of the PSO algorithm & \(M_{p}\) & 50 \\ Acceleration coefficient of the PSO algorithm & \(c_{1}\) & 2 \\ Acceleration coefficient of the PSO algorithm & \(c_{2}\) & 2 \\ \hline \end{tabular}
\end{table} 
Table 3: Control parameters in the proposed mission planning method. UAVs in the coalition \(C_{1}\) updated their resources according to Equation (19). The ETAs for the three UAVs are shown in Figure 3a. It can be seen that, the three UAVs could arrive simultaneously to the target \(T_{1}\). In the second allocation round, the UAV \(U_{3}\) was selected as the manager UAV to assign the target \(T_{2}\). The coalition \(C_{2}=[U_{3},U_{4},U_{1}]\) was formed to attack the target \(T_{2}\). As the target \(T_{2}\) was not the first assigned target. The modified CPSO algorithm was used to generate simultaneous arrival paths for the UAVs in the coalition \(C_{2}\). The generated paths for these UAVs are shown in Figure 2a. The path lengths of the UAVs from their initial locations to the target \(T_{2}\) were 3008.03 m, 3008.7 m and 3008.31 m, respectively. It can be seen that the UAV \(U_{4}\) had to perform the target \(T_{1}\) before \(T_{2}\), this was considered in the modified CPSO algorithm. The ETAs for the UAVs in the coalition \(C_{2}\) are shown in Figure 3b. These UAVs could arrive simultaneously to the target \(T_{2}\). Using the proposed algorithms, the formed coalitions could obtain the maximum system utility in Equation (6).