# Short Landing for Flying-Wing Unmanned Aircraft with Thrust Vector
## 6 Simulation Verification and Discussion
### Robustness against Model Mismatch  
The proposed short-landing technique must consider various uncertainties and modeling errors to ensure flight safety. Examples of these uncertainties include thrust-induced uncertainties [41], ground-effect uncertainties [25], uncertainties due to the interaction between lift fans and wings, inertial parameter uncertainties, and uncertainties in thrust loss induced by the increase in nozzle pitch angle [42]. To test the robustness of the proposed technique, an MC simulation was conducted with 500 simulations, where model parameters were perturbed in the nonlinear model, as shown in Table 5.  
During the MC simulation, it was observed that, although the angle-of-attack command value was set to 6 degrees, the steady-state angle-of-attack response was between 3 and 9 degrees. This shows that the flight boundary protection method proposed in Section 6.2 is effective in protecting the flight boundary. Figure 25a illustrates the steady-state angle-of-attack response for the 500 simulations conducted during the MC simulation.  
To prevent the throttle command value from going beyond its trim boundary, an additional angle-of-attack command is generated by the flight boundary protection method when the throttle command value exceeds 0.6, as shown in Figure 25b.  
To assess the effect of the additional angle-of-attack command on the success rate of short landings, 500 MC simulations were performed without flight envelope protection and using the perturbation range of parameters from Table 5. A landing was considered unsuccessful if the distance error between the touchdown point and the intended touchdown point exceeded 5 m, or if the aircraft failed to land. Among the 500 simulations, 127 short landings failed due to early touchdown or excessive pitch oscillations during the approach, as illustrated in Figure 23. The success rate of short landings was found to be 74.6%, and Figure 26 illustrates the angle-of-attack response of successful landings.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Explanation** & **Bias Range** \\ \hline \(M\) & Mass & \(\pm 1\) kg \\ \(cgx\), \(cgy\), \(cgz\) & Centre of gravity & \(\pm 5\)\% \\ \(q_{thr}\) & Dynamic pressure & \(\pm 15\)\% \\ \(C_{L\alpha}\) & Lift coefficient derivative & \(\pm 20\)\% \\ \(C_{l\beta}\) & Roll moment coefficient derivative & \(\pm 20\)\% \\ \(C_{l\alpha}\), \(C_{m\beta}\), \(C_{nbr}\) & Roll, pitch, and yaw control derivatives & \(\pm 20\)\% \\ \(T\) & Engine thrust & \(-20\)–\% \\ \(T_{f}\) & Lift fan force & \(-20\)–\% \\ \(I_{xx}\), \(I_{yy}\), \(I_{zz}\) & Moment of inertia & \(\pm 20\)\% \\ \(C_{lp}\), \(C_{mq}\) & Damping moment coefficient derivatives & \(\pm 50\)\% \\ \(C_{D0}\) & Drag coefficient & \(0\)–\(20\)\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Model parameters bias.  
Figure 24: Sink rate control under the wind gust.  
The flight trajectories of the MC simulation with the flight boundary protection based on the additional angle-of-attack command are shown in Figure 27. The UAV follows a curved trajectory and achieves a short landing, even with parameter uncertainties. In addition, there is no oscillation or divergence in the landing trajectory during the MC simulation, thus demonstrating the robustness of the proposed control strategy. Moreover, the distance errors in all cases were less than 4 m, as shown in Figure 28b. This improvement enhances the likelihood of successful landings. To evaluate the landing accuracy, the circular error probability (CEP) is introduced. The calculated result of the CEP is 0.94 m, as depicted in Figure 28a. The mean and variance of the landing distance error are 0.947 and 0.512, respectively, as shown in Figure 28b. According to the flying quality requirement in Reference [43], high-precision landing was achieved.  
Figure 26: Angle-of-attack response of successful landing without the flight boundary protection.  
Figure 25: States response of the MC simulation: (**a**) angle-of-attack response and (**b**) throttle response.