## 3 Results
### Experiments of Quadrotor Trajectory Tracking  
The UAV flight demonstration on the RNN-LSTM maneuverability model is important for verifying the accuracy of the synchronous control in time and space. Two different UAV flights were carried out. The planned trajectories were designed and converted into the corresponding sets of control instructions by the maneuverability model. Then, the sets of control instructions were used to control the UAV flight, and the corresponding actual flight data were collected. Later, the evaluation focused on the consistency of the actual real-time flight data (velocity, acceleration, position, and time) with the planned trajectory data. The planned trajectory of the straight flight is a process in which the UAV linearly increases its acceleration from an actionless state and then linearly decreases to zero. Figure 8 shows the comparison of the variables between the actual flight and the planned straight flight trajectory. It can be seen that the actual acceleration, velocity, and coordinate values collected at each moment are basically the same as the planned trajectory. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{4}{c}{**Root Mean Square (LSTM (BP))**} \\ \cline{2-5}  & **ROLL** & **PIT** & **THR** & **YAW** \\ \hline \(0^{\circ}\) & 1.39 (3.91) & 1.94 (4.42) & 0.51 (0.51) & 0.33 (0.34) \\ \(45^{\circ}\) & 2.62 (5.66) & 2.21 (5.24) & 1.81 (1.71) & 0.94 (0.98) \\ \(90^{\circ}\) & 1.91 (7.22) & 3.42 (6.45) & 0.42 (0.41) & 0.70 (0.69) \\ \(135^{\circ}\) & 1.53 (6.32) & 1.87 (8.86) & 0.76 (0.84) & 0.54 (0.53) \\ \(180^{\circ}\) & 2.28 (4.88) & 1.94 (4.24) & 0.67 (0.67) & 0.55 (0.55) \\ \(225^{\circ}\) & 1.83 (4.71) & 1.74 (3.11) & 1.17 (1.15) & 0.47 (0.49) \\ \(270^{\circ}\) & 2.14 (5.37) & 3.00 (7.42) & 0.25 (0.27) & 0.30 (0.27) \\ \(315^{\circ}\) & 1.60 (3.76) & 2.05 (5.34) & 0.51 (0.46) & 0.41 (0.40) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The errors of the BP and RNN-LSTM models in different directions. Figure 7: The contrast values of the RNN-LSTM prediction and the actual flight in different directions: (**a**) the x-axis positive direction; (**b**) the y-axis negative direction; (**c**) the x-axis positive and y-axis negative direction; and (**d**) the x-axis negative and y-axis positive direction. According to the coordinate values of the actual flight obtained in Figure 8d, the speed at each moment is calculated by the change in coordinate points. Since the deviation in the UAV positioning is \(\pm\)15 cm, the actual coordination curve of the UAV has fluctuated within a certain numerical range, which is shown in Figure 8c,d. Then, the velocity calculated by only two coordinate points fluctuates greatly. Therefore, a mean filter with a window size of 50 sample points (equal to 2 s) was used to smooth the coordinates. Figure 8b shows the curve of the calculated velocity varying with time by filtering. If the accelerations are not monotonically increasing or decreasing in high-speed conditions, the velocity in the window was averaged to a lower value. This is the reason for why the maximum velocity value is much smaller than the theoretical value at this moment of 3.84 s. The final velocity of the UAV in the experiment is around 0, which is basically consistent with the planned trajectory. Due to the error accumulation, the deviation between the actual flight coordinate position and the preset position is larger when the actual flight position is farther from the initial position. The deviation between the final flight distance of the experiment and the preset path is approximately 0.7 m, and its error is within 6%. Compared with other control algorithms, our proposed open-closed loop hybrid strategy not only reduces system oscillation and overshoot, but also shows better consistency between the preset and actual velocity [16; 17; 18]. The quadrilateral flight, which is made up of four continuous straight flights, was implemented to further evaluate the accuracy of the strategy.