# Analytic Time Reentry Cooperative Guidance for Multi-Hypersonic Glide Vehicles
## 5 Simulation and Result Analysis
### Time Cooperative Guidance Simulation Experiment of Multi-Hypersonic Vehicle for a Moving Target  
This section carries out cooperative guidance simulation experiments for simple moving targets. The initial state of the three aircraft is set in Table 2, and the expected cooperative flight time is set to 800 s. The experiment assumes that each aircraft can sense the real-time position of the target. After the initial 400 s of the flight simulation, the target begins to move in the horizontal plane in the following manner:  
\[\left\{\begin{array}{l}\theta(t)=32-0.01*(t-400)\\ \phi(t)=20+0.01*(t-400)\end{array}\right. \tag{33}\]  
Figure 21: Velocity histories of the bank angle.  
Figure 20: Velocity histories of the AOA.  
where \(\theta(t)\) and \(\phi(t)\) are the real-time latitude and longitude of the target point, respectively.  
Figures 22-24 show the cooperative guidance experimental results of the proposed algorithm for simple moving targets. It can be seen that the altitude and velocity terminal constraints are well satisfied at the expected cooperative time. Figure 23 shows the three-dimensional reentry trajectory of the three aircraft and the trajectory of the target. The aircraft can reach the vicinity of the moving target at the expected time and reach the final handover area to prepare for the subsequent terminal guidance phase.  
Figures 25 and 26 show the changes in the control quantity of the simulation experiment in this section. It can be seen that the changes in the control quantity can meet the constraints and meet the design expectations. The reverse sign strategy of the bank angle plays a role, and the number of bank angle reversals in this section is fewer, which reduces the pressure of the actuator when the aircraft pursues the moving target.  
In summary, the analytical time cooperative reentry guidance algorithm proposed in this paper has certain theoretical significance for the cooperative guidance problem of moving targets such as Equation (33).  
Figure 23: 3D reentry trajectory.  
Figure 22: Time histories of the altitude.  
Figure 24: Time histories of the velocity.  
Figure 25: Velocity histories of the AOA.  
Figure 29 shows the terminal position obtained by the experiment. The green pentagram in Figure 29 is the expected target point, and the circle is the range of terminal position error that it is set to 30 km. It can be seen that the terminal error of 120 simulations is less than 30 km, which is within the allowable range of the set terminal error. In this paper, the experiment set the terminal target longitude of 32\({}^{\circ}\), latitude of 20\({}^{\circ}\), and the longitude error and the latitude error are not exceeded, while the landing point is more concentrated. The size interval distribution of the terminal error value shown in Figure 30 shows that more than 80% of the landing points are within 20 km, and the average terminal error of 120 simulation experiments is 17.73 km. Figure 31 shows the moment when the extreme point of the path constraint appears in the Monte Carlo simulation experiment. It can be seen that in the presence of disturbance, the trajectory heat flux rate, dynamic pressure, and overload obtained by the algorithm still exceed the upper limit of the constraint, and a safe reentry trajectory can be obtained.  
In summary, the improved time-resolved hypersonic vehicle reentry guidance algorithm proposed in this paper has good robustness.  
Figure 30: Monte Carlo experiment drop point distribution.  
Figure 29: Monte Carlo experiment drop point distribution.