# Cooperative Guidance Law for the Mother-Cabin of the Anti-UAV Cluster Mother-Son Missile
## 4 Simulations
In the initial phase, the output of the two controllers is saturated so that the missiles can adjust to the desired attitude as quickly as possible, allowing them to better cope with the possible subsequent maneuvering of the targets. The subsequent output is small and there is no chattering, which can save energy and ensure flight stability. Scenario 2: The targets do a circular maneuver with an acceleration of 2 m\({}^{2}\cdot\) s\({}^{-1}\). The initial state of the missiles and targets is shown in Table 2.  
The simulation results are shown in Figure 6.  
As can be seen from Figure 6a,b, except for missile 3 needing to complete a quick turn at the initial stage due to the heading angle adjustment, the three missiles can obtain a smooth trajectory under the action of the controller and can impact the target simultaneously in 38.70 s, with misses less than 1 m. Figure 6c,g shows that the output characteristics of the controller and the convergence characteristics of the missile state are similar to those when the targets are not maneuvering. It can be seen that after adjusting the initial state of the missiles, targets, and the maneuvering situation of the targets, the designed guidance law still performs well. Table 3 shows that under the two targets maneuvering conditions, the misses of each missile are less than 1 m, that is, allowing each mother-cabin to fly to the \"release point\" with a small deviation. In addition to the convergence of the LOS to zero, which satisfies the detection conditions of the seeker for the UAV cluster, it is also necessary to pay attention to the heading angle of the mother-cabins at the \"release point\". When the target is not maneuvering, the heading angle of each missile can converge to zero. When the target is maneuvering in a circular pattern with an acceleration of 2 m\({}^{2}\cdot\) s\({}^{-1}\), the heading angles of the three missiles are all maintained at a value of approximately \(-9^{\circ}\) to respond to the targets' maneuvering. It can be assumed that the initial velocity of the son-interceptors is aligned with the targets after release and is capable of completing the follow-on interception. \begin{table}
\begin{tabular}{c c c} \hline
**Initial Position/m** & **Initial Speed/m\(\cdot\)s\({}^{-1}\)** & **Initial Heading Angle\({}^{\circ}\)** \\ \hline Missile 1 & (\(-\)500, 2200) & 500 \\ Missile 2 & (800, 1800) & 530 \\ Missile 3 & (0, 1000) & 480 \\ Target 1 & (28,000, 1600) & 200 \\ Target 2 & (25,000, 1500) & 200 \\ Target 3 & (23,000, 1300) & 200 \\ \hline \end{tabular}
\end{table} 
Table 2: Initial state setting of missiles and targets. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Targets** & **Missiles** & **Misses/m** & **Intercept Time/s** & **Missile Heading Angle/\({}^{\circ}\)** \\ \hline \multirow{3}{*}{Non-maneuver} & Missile 1 & 0.16 & & 0 \\  & Missile 2 & 0.37 & 38.28 & 0 \\  & Missile 3 & 0.08 & & 0 \\ \hline \multirow{3}{*}{circular maneuver} & Missile 1 & 0.47 & & \(-9.13\) \\  & Missile 2 & 0.34 & 38.70 & \(-9.18\) \\ \cline{1-1}  & Missile 3 & 0.63 & & \(-9.20\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Guidance results. Figure 6: Simulation results of the target circular maneuver. (**a**) Missile-target trajectory; (**b**) missile-target relative distances; (**c**) overload on the LOS direction; (**d**) speed convergence curve; (**e**) overload on the normal direction of LOS; (**f**) LOS convergence curve; (**g**) LOS rate convergence curve. Combining Figures 5 and 6 with Table 3, it can be seen that the designed multi-missile cooperative guidance law is well-suited to the mother-cabin guidance in this operational pattern, with the advantages of a smooth trajectory and a small, non-chattering controller output.