# Cooperative Guidance Law for the Mother-Cabin of the Anti-UAV Cluster Mother-Son Missile
## 4 Simulations  
This section verifies the designed cooperative guidance law. Taking the cooperative interception of UAV clusters by three mother-son missiles as an example, it is required that the three mother-cabins reach the \"release point\" at the same time with zero LOS and the same speed. The communication topology \(G\) between the three missiles is shown in Figure 4. The maximum overload in the LOS direction of the missile is 5 g, the maximum overload in the normal direction of the LOS is 10 g, g = 9.8 m/s\({}^{2}\), and the simulation step length is 0.01 s.  
Guidance law parameters are set as follows: parameter setting of controller (9): \(\alpha_{i}=0.8\), \(V_{m}=500\) Parameter setting of controller (15): \(k_{1}=1\), \(k_{2}=5\), \(\beta_{i}=0.2\). Disturbance observer (19) parameters: \(\lambda_{0i}=1.5\), \(\lambda_{1i}=2\), \(\lambda_{2i}=3\), \(\mu_{0i}=3\), \(\mu_{1i}=4\), \(\mu_{2i}=5\), \(L_{i}=1\), where \(i=1,2,3\). Two scenarios are used to verify the performance of the guidance law, target non-maneuver and circular maneuver, and different initial states of the missiles and targets are set. Note: the \"targets\" here represents the \"release points\", and the \"missiles\" here represents the \"mother-cabins\". Scenario 1: The targets do not maneuver, and the initial state of the missiles and targets is shown in Table 1.  
The simulation results are shown in Figure 5. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Initial Position/m** & **Initial Speed/m-s\({}^{-1}\)** & **Initial Heading Angle/\({}^{\circ}\)** \\ \hline Missile 1 & (\(-1000\), \(2100\)) & 520 \\ Missile 2 & (\(0\), \(1900\)) & 500 \\ Missile 3 & (\(0\), \(1100\)) & 470 \\ Target 1 & (\(25\),\(000\), \(1800\)) & 200 \\ Target 2 & (\(27\),\(000\), \(1600\)) & 200 \\ Target 3 & (\(25\),\(000\), \(1400\)) & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Initial state setting of missiles and targets. Figure 4: Communication topology of three missiles. Figure 3: Multi-missile cooperative guidance structure. As can be seen from Figure 5a,b, except for missile 2 needing to complete a quick turn at the initial phase for heading angle adjustment, all three missiles can obtain a smooth trajectory under the action of the controller and can impact the targets simultaneously in  
Figure 5: Simulation results of target non- 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. 38.28 s, with misses of less than 0.5 m. As can be seen from Figure 5c,d, due to the large difference in the initial time-to-go, the three missiles need to quickly adjust their speed in the initial phase. However, after approximately 2 s, the convergence process becomes very smooth, and the time-to-go and speed converge to the same only at the time of impact. This allows the controller to meet the guidance requirements with only a small, continuous, and smooth output. As can be seen from Figure 5b,e,f, the overload in the normal LOS direction of the missiles is saturated in the initial phase so that the missiles can quickly adjust to the desired attitude. Then, the controller only needs to adjust the output in a small range according to the motion state of the missile-target. The subsequent output after approximately 2 s is small and there is no chattering, which ensures a relatively flat trajectory. The LOS and the LOS rate can both converge to zero in approximately 20 s.  
In conclusion, Figure 5 shows that the missiles can quickly meet the zero LOS constraint while ensuring a smoother trajectory, which creates good conditions for the seeker to detect the cluster target. The controller adjusts the speed slowly and steadily to ensure that the output of the controller is small and continuous.