## 5 Experimental Validation
### Experiments in the Real Environment
#### 5.2.2 Landing Line Experiments
(**d**) plan the trajectory. (**e**) fly close to the position for landing. small distance in the \(y\)-axis direction, and the tracking error is relatively small. In the \(z\)-axis direction, the FPLIR firstly rises and then gradually approaches the power line, so the error also gradually decreases. Table 7 lists the root mean square error (RMSE), maximum error, and landing error of position tracking along the \(x\)-, \(y\)-, and \(z\)-axes. It can be seen that the RMSE in all three directions is less than \(1.2\times 10^{-1}\) m, and the landing errors are \(1.5\times 10^{-3}\) m, \(6.18\times 10^{-2}\) m, and \(-1.62\times 10^{-3}\) m, respectively. Therefore, the FPLIR can achieve good trajectory tracking and meet the position error requirements when landing on the line. Compared with the data in Figure 13, there is an increase in the relative error between the actual trajectory and the reference trajectory due to the positional drift of the VIO. The landing line speed of the FPLIR was limited to reduce the risk during the experiment. As shown in Figure 1(a), the speed of the FPLIR changed smoothly and the motion was stable during the landing line. The speed change in the \(y\)-axis direction was small due to the small slope of the power line, so the FPLIR hardly needed to adjust its position in the \(y\)-axis direction. The smaller speed adjustment in the \(z\)-axis direction proved that the combination of the rough and precise landing line strategy was able to achieve the accuracy requirements of landing while consuming less energy. Additionally, according to the data in Table 8, the RMSEs for the actual trajectory and the reference trajectory of the FPLIR in the \(x\)-, \(y\)- and \(z\)-directions were \(9.57\times 10^{-2}\) m/s, \(3.64\times 10^{-2}\) m/s and \(7.26\times 10^{-2}\) m/s, respectively, which demonstrates that it can track the trajectory stably. At the same time, the velocities of the FPLIR at the landing line were \(-1.145\times 10^{-2}\) m/s, \(4.27\times 10^{-3}\) m/s and \(-1.78\times 10^{-2}\) m/s in the x-, y-, and z-directions, respectively, thus meeting the requirements of the landing line velocity. The above data indicate that the proposed method allows the FPLIR to land on the power line safely and steadily, and the errors in positions and velocities meet the actual requirements. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Title** & **X (m)** & **Y (m)** & **Z (m)** \\ \hline RMSE & \(1.139\times 10^{-1}\) & \(4.45\times 10^{-2}\) & \(1.171\times 10^{-1}\) \\ Error at landing & \(1.5\times 10^{-3}\) & \(6.18\times 10^{-2}\) & \(-1.62\times 10^{-3}\) \\ Maximum error & \(3\times 10^{-1}\) & \(2.3\times 10^{-1}\) & \(1.27\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Position errors between the planned and actual trajectories. Figure 19: Landing trajectory and position tracking error. The design of the landing method for the FPLIR developed in this paper does not share similarities with other landing methods for the purpose of comparison. Therefore, we compared the landing results with those of a pipeline inspection robot [15], and the results are shown in Tables 9 and 10. Compared with the pipeline inspection robot, the average absolute position error (Mean Absolute Error, MAE) in the X- and Y-axis directions of the FPLIR decreased by 25.48% and 42.98%, respectively, while the Z-axis direction remained almost the same. The velocity at landing approached zero. These two points indicate that our landing method has better stability and safety. Since the pipeline inspection robot does not use trajectory planning, the final state of the robot cannot be constrained. Furthermore, the control effect of the PID controller is weaker than that of the MPC control, resulting in lower landing accuracy.