# Visual-Based Positioning of Aerial Maintenance Platforms on Overhead Transmission Lines
## 4 Results
### Laboratory Validation  
A scale model 1:8 of a three-phase distribution system with power-lines, approximating a straight line and without interruption was used in the laboratory validation. The model was wrapped with camouflage at the bottom to simulate the different objects which could be found in a transmission grid environment. The UAV movement was simulated by a KUKA robotic arm model KR-6. Laboratory experiments were conducted in the _Centro Integrado de Manofuctura y Automatizacion_ (CIMA) at the Universidad Tecnica Federico Santa Maria, located in Valparaiso, Chile. The procedure can be summarized in six main steps:  
1. The positioning system was mounted in the clamp of robotic arm to simulate the UAV attitude. 2. The parameter reference separation by the acquisition an image set (30 images) at a fixed attitude in off-line mode was proposed. 3. The operator set up the robot height with respect to wires of the model, and the path to be followed by the robot. 4. The robotic arm automatically moved on the pre-determined path, recording a video sequence. 5. Visual data were analyzed in MATLAB programming environment (MathWorks, Natick, MA, USA). The robotic arm position provided by the software from the manufacturer was used as the reference in each experiment. 6. The estimated placement of the camera was shown in a graphical user interface (GUI). Three experiments were carried out to prove the algorithm behavior: straight line path, circular path, and circular variable path. Figure 6 shows schematics of experiments developed in indoor tests. The first experiment consisted of moving the positioning system in a straight line path at three different heights, maintaining the camera plane fixed and parallel to the power-lines plane, as shown in Figure 7a. A database with 600 visual images was analyzed to investigate the behavior of the positioning system in each trail. It is possible to observe that the camera positioning (magenta dots) converges to the reference (blue dots) in Figure 7a for each studied height. In terms of the root medium squared error (RMSE), our approach was within this tolerance limit for this type of applications [57, 58]. Furthermore, The algorithm accuracy was higher than 90.35% in the three-phase system detection, as shown in Table 2a. The second experiment consisted of moving the positioning system in a circular path. The camera plane rotated around the power-lines plane, as shown in Figure 7b. The second set of data acquired from the visual sensor allowed analyzing the accuracy and reliability of relative positioning from five different radii by processing more than 1000 visual images in each trail. Results of absolute positioning are shown in Figure 7b where the blue line is the height reference and the magenta line is the camera positioning and the statistical analysis is tabulated in Table 2b. Moreover, the algorithm accuracy was higher than 78.5% in the three-phase system detection. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{(**a**)} \\ \hline
**Height mm** & 650 & 850 & 1050 & \\ \hline
**Analyzed frames** & 600 & 600 & 600 & \\
**True positives** & 543 & 575 & 573 & \\
**Accuracy \%** & 90.35 & 95.67 & 95.53 & \\
**RMSE mm** & 18.94 & 13.81 & 10.30 & \\ \hline \multicolumn{5}{c}{(**b**)} \\ \hline
**Radius mm** & 550 & 650 & 850 & 950 \\ \hline
**Analyzed frames** & 1003 & 1143 & 1247 & 1174 \\
**True positives** & 882 & 898 & 1144 & 984 \\
**Accuracy \%** & 87.93 & 78.5 & 91.7 & 83.7 \\
**RMSE mm** & 47.74 & 55.77 & 63.69 & 58.44 \\ \hline \multicolumn{5}{c}{(**c**)} \\ \hline
**Radius mm** & 550 & 650 & 850 & 950 \\ \hline
**Analyzed frames** & 1003 & 1143 & 1247 & 1174 \\
**True positives** & 973 & 1061 & 1128 & 1093 \\
**Accuracy \%** & 96.9 & 92.7 & 90.4 & 93 \\
**RMSE mm** & 58.81 & 60.97 & 59.32 & 47.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Laboratory results. Statistical analysis of different developed experiments: (**a**) straight line path; (**b**) circular path; and (**c**) circular variable path.