## 4 Results and Discussion

Table 3: Position of each player at the end of the game. Figure 2: The position of each player changing with time in (**a**) x-axis, (**b**) y-axis, and (**c**) z-axis. **Example 2. ** The maximum unit mass thrusts of the pursuer, the evader, and the defender are \(T_{\rm P}=0.09\times\rm g\), \(T_{\rm E}=0.01\times\rm g\), and \(T_{\rm D}=0.02\times\rm g\), respectively, and the game time is 159.81193 s. The positions and velocities of the pursuer, the evader and the defender in the initial time are shown in Table 2. The pursuer does not consider the impact of the defender when performing orbital maneuvers. As shown in Figure 6, the defender successfully intercepts the pursuer at the terminal moment. Figure 7 shows the distance between the defender and the pursuer during the game. According to Figure 7, the distance becomes shorter and shorter in the entire game, which is caused by the pursuer's not considering the impact of the defender. At the terminal moment, the distance between the defender and the pursuer is 0.4004 km, which is shorter than the safety distance 0.5 km. Figure 4: The curves of the control variable of each player with time in (**a**) x-axis, (**b**) y-axis, and (**c**) z-axis. Figure 5: The curves of zero-control miss distance with time in (**a**) x-axis, (**b**) y-axis, and (**c**) z-axis. Figure 6: The position of each player changing over time in (**a**) x-axis, (**b**) y-axis, and (**c**) z-axis. Figure 8 shows the control variable of each player changing with time in the game. As shown in the figure, the control curve of the pursuer overlaps with that of the evader in the whole procedure, the reason being that the pursuer only considers the evader when performing orbital maneuvers. Comparing Example 1 with Example 2, it can be seen that with the control strategy based on the fuzzy comprehensive evaluation, the pursuer can successfully bypass the defender, and finally capture the evader. The pursuer, for not considering the impact of the defender, is eventually intercepted by the defender. The maximum unit mass thrusts of the pursuer, the evader, and the defender are \(T_{\rm P}=0.14\times\mathrm{g}\), \(T_{\rm E}=0.01\times\mathrm{g}\), and \(T_{\rm D}=0.14\times\mathrm{g}\), respectively. The maneuverability of the defender and that of the pursuer are the same, and the game time is 177.87788 s. The positions and velocities of the pursuer, the evader, and the defender in the initial time are shown in Table 4. The pursuer adopts the control strategy based on the fuzzy comprehensive evaluation. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Pursuer** & **Evader** & **Defender** \\ \hline \(X/\mathrm{km}\) & 0 & 8 & 18 \\ \(Y/\mathrm{km}\) & 0 & 9 & 24 \\ \(Z/\mathrm{km}\) & 30 & 12 & 0 \\ \(V_{X}/\big{(}\mathrm{km}\cdot\mathrm{s}^{-1}\big{)}\) & 0 & 0 & 0 \\ \(V_{Y}/\big{(}\mathrm{km}\cdot\mathrm{s}^{-1}\big{)}\) & 0 & 0 & 0 \\ \(V_{Z}/\big{(}\mathrm{km}\cdot\mathrm{s}^{-1}\big{)}\) & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Positions and velocities of the initial time. Figure 8: The control variable of each player changing over time in (**a**) x-axis, (**b**) y-axis, and (**c**) z-axis. Figure 7: The distance between the pursuer and the defender changing over time. Figure 9 shows the curves of the positions of the three players changing with time in directions of \(X\), \(Y\), \(Z\). As shown in Figure 9, the defender successfully intercepts the pursuer at the end of the game. Figure 10 shows the curves of the control variable of each player changing with time in the directions of \(X\), \(Y\), \(Z\). At 160 s or so, the pursuer starts to change the control strategy to evade the defender. However, because of the same maneuverability of the defender and the pursuer, the pursuer does not successfully bypass the interception of the defender. Table 5 shows the position of each player at the terminal moment.