## 5 Results
### Effectiveness Analysis of Trajectory Planning  
To verify the effectiveness of the mission-planning results, the proposed method is simulated in comparison with particle swarm optimization (PSO) by taking failure cases I and IV as examples. For failure case I, the orbital semimajor axis is optimized by fixing the payload mass and apogee height; for failure case IV, the payload mass is optimized by fixing the target orbit parameters.  
This paper uses the PSO algorithm with improved global search performance by [PERSON] [22]. Ignoring the adjustment of the launch vehicle to the motion plane after the failure, the initial pitch angle and the slope of the two pitch angles according to the time averaging are the particle positions, and the squared sum of the perigee altitude deviation, apogee altitude deviation, and payload mass deviation is the value of the fitness function. The number of populations is set to 30, and the maximum number of iterations is 200. Comparative simulation results after optimization can be obtained, as shown in Figures 12-17.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Perigee** & **Apogee** & **Payload** & **Semimajor** & **Eccentricity** & **Orbit Inclination** \\  & **Altitude/km** & **Altitude/km** & **Mass/kg** & **Axis Error/m** & **Error** & **Error/\({}^{\circ}\)** \\ \hline I & 410 & 500 & 9.00 & 85.76 & \(4.85\times 10^{-5}\) & \(3.94\times 10^{-5}\) \\ II & 410 & 490 & 4.99 & 147.84 & \(-4.44\times 10^{-5}\) & \(2.85\times 10^{-7}\) \\ III & 157 & 400 & 7.50 & 61.49 & \(-6.18\times 10^{-5}\) & \(7.84\times 10^{-5}\) \\ IV & 370 & 400 & 5.37 & 26.60 & \(-6.73\times 10^{-5}\) & \(3.78\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Feasibility results of mission decision making and trajectory planning.  
Figure 12: Engine thrust.  
Figure 13: Flight trajectory and terminal orbit.  
Figure 14: Perigee altitude.  
Figure 15: Apogee altitude.  
Figure 16: Mass.  
Figure 17: Pitch angle.  
The results show that, under the same fault condition, the mission loss obtained by the proposed method is slightly larger than that of the PSO, but the calculation cost is far less than that of the PSO. Theoretically, the optimal results will be obtained when the population size, particle dimension of the PSO, and the number of iterations are large enough; the degradation gradients used in this paper to simplify the neural network modeling process limit the optimality of the method. However, this paper uses the RBFNN, the TDOS, and the ATU-IGM to generate guidance commands, which make the control angle and states smoother and can better meet the actual flight requirements; the PSO guidance commands obtained by parameterizing the control have obvious parameterization characteristics (for example, the linearized model adopted by the PSO in this paper) and are not only different from the actual flight commands but also easy to make the states fluctuate greatly, as shown in Figures 15 and 17.  
In summary, it can be seen that the proposed method is almost at the same level with the traditional numerical solution method in terms of the accuracy of mission planning and trajectory planning, but mission adaptability and solution efficiency have been greatly improved. The population size and initial guesses greatly influence the convergence and computational speed of the PSO method. In contrast, the proposed method in this paper uses the RBFNN for mission decision making, which simplifies the calculation process, and the ATU-IGM for trajectory planning to generate the guidance instructions in analytic form. Therefore, the timeliness of mission planning is effectively ensured.