# Research and Verification of Trajectory Tracking Control of a Quadrotor Carrying a Load
## 4 Simulation Verification
Each channel of the controller is compared and simulated using the neural network adaptive integral backstepping algorithm and the existing adaptive integral backstepping algorithm. In Figures 4 and 5, the neural network adaptive integral backstepping algorithm can track the desired curve quickly and stably, and the tracking effect is closer to the desired curve than the adaptive integral backstepping algorithm and the backstepping algorithm. Among them, the green dashed line is the trajectory curve of the hanging load, while a quadrotor and its load are given for one sampling moment during the simulation. From Figures 6 and 7, it can be seen that the control effect of the adaptive integral backstepping algorithm does not differ much from that of the algorithm proposed in the paper after being affected by weaker wind disturbances, but the calculation of the average error still shows that the algorithm proposed in this paper is slightly better. However, when the system is subjected to strong wind disturbance, it is obvious from the figure that the actual trajectory of the algorithm in this paper fits better with the expected trajectory, and the error fluctuation is smaller and more stable. Table 2 below shows the comparison of the average error of different algorithms on the \(X\)-axis under different intensity interference. It is obvious from the table that the average error of the algorithm proposed in this paper is the smallest, and its performance is significantly improved compared to the integral backstepping algorithm and the backstepping algorithm. In the table, _Bks_ represents the backstepping algorithm, _Adp_ represents the adaptive integral backstepping algorithm, and _Rbf_ represents the neural network adaptive integral backstepping algorithm. Figure 4: Space trajectory tracking of a quadrotor carrying a load system: (**a**) weak interference; (**b**) strong interference. Figure 5: The spatial top view of a quadrotor carrying a load system: (**a**) weak interference; (**b**) strong interference. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Interference** & **Bks** & **Adp** & **Rbf** \\ \hline Weak & 0.1062 m & 0.0536 m & 0.0489 m \\ \hline Strong & 0.1878 m & 0.1156 m & 0.0962 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: \(X\) position average error. In Figures 8 and 9, the pink curve represents the backstepping algorithm, the red curve represents the adaptive integral backstepping algorithm, and the blue curve represents the algorithm proposed in this article. It can be seen from the figure, all three methods can be stabilized quickly, but from the perspective of local scaling, the adaptive integral backstepping method and backstepping method produce larger overshoot, generate larger fluctuations, and take a longer time. The neural network adaptive integral backstepping algorithm can be stabilized quickly and with less overshoot. From the error point of view, the error fluctuation of the adaptive integral backstepping method is larger, which indicates that the addition of a neural network can better ensure the stable tracking of the trajectory in the case of external disturbances of different intensities. Table 3 below shows the comparison of the average error of different algorithms on the \(Y\)-axis under different interference intensities. It is obvious from the table that the average error of the algorithm proposed in this paper is the smallest, and its performance is significantly improved compared to the integral backstepping algorithm and the backstepping algorithm. Figure 6: \(X\)-axis change of a quadrotor carrying a load system: (**a**) weak interference; (**b**) strong interference. Figure 7: \(X\)-axis error of a quadrotor carrying a load system: (**a**) weak interference; (**b**) strong interference.