# Navigation Path Extraction and Experimental Research of Pusher Robot Based on Binocular Vision
## 3 Results and Analysis
### Angular Deviation Evaluation  
The angular deviation (\(\theta\)) referred to the positive (+\(\theta\), the left side of the specified working route), negative (\(-\theta\), the right side of the specified working route) or zero (0\(\theta\), at the specified working route) deviation, relative to the actual advancing direction of the pusher robot and the specified working route. The actual working angle deviation was determined by the position connection of the laser ranging module installed in the middle and tail of the pushing robot. \(\theta\) was used to evaluate the robustness of the system proposed in this study to changes in angular bias. The pusher robot started at the beginning of each row in different directions from \(-45\) to \(+45\), relative to the guide path. Due to the relatively narrow lateral field of view of the camera (90\({}^{\circ}\)), the system would not have been able to generate coordinates for the navigation path when the angular deviation exceeded \(\pm 45^{\circ}\). Therefore, in this test on angular deviation, the range between \(-45^{\circ}\) and \(+45^{\circ}\) was mainly studied. In the angle deviation test of path extraction and the motion control system, the working area of 1 dairy cow barn was randomly selected, the pushing robot at one end of the working area placed, and a different initial angle from the specified working route (\(+45^{\circ}\), \(+15^{\circ}\), \(-45^{\circ}\) and \(-15^{\circ}\)) maintained. The pusher robot was set up to operate autonomously along the extraction navigation path with a working distance of 50 m. Figure 20 shows the resulting angular deviation from different values of \(\theta\). In [PERSON]'s research [32], the stability threshold was set at \(\pm 5^{\circ}\), based on the nature of the terrain of the orchard. Based on this basis, the stability threshold in this study was also set to \(\pm 5^{\circ}\). It was found from Figure 9 that, despite the different \(\theta\) values, through the path extraction and the adjustment of the motion control system, the pusher robot could perform effective direction correction, so that the change of \(\theta\) gradually became smaller. When the initial angles were \(+45^{\circ}\) and \(-45^{\circ}\), the angle adjustment of the pusher robot was relatively large, and the stability threshold was reached after driving distances of 35 and 34 m, respectively, and continued to be more stable. When the initial angles were \(+15^{\circ}\) and \(-15^{\circ}\), the angle adjustment of the pusher robot was relatively smooth, and entered the stable threshold after traveling 13 and 14 m, respectively. Compared with larger initial angles (\(\theta\) = \(+45^{\circ}\) and \(-45^{\circ}\)), the system could quickly adjust the deviation of smaller initial angles (\(\theta\) = \(+15^{\circ}\) and \(-15^{\circ}\)), allowing the robot to enter a stable state more quickly. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Operating Area**} & \multicolumn{4}{c}{**Lateral Deviation (cm)**} \\ \cline{2-5}  & **Maximum** & **Average** & **Standard Deviation** & **RMSE** \\ \hline
1 & 7.8 & 3.4 & 2.2 & 4.3 \\
2 & 8.1 & 4.1 & 2.9 & 5.1 \\
3 & 6.1 & 2.2 & 1.8 & 3.1 \\
4 & 8.9 & 4.8 & 3.3 & 5.5 \\
5 & 7.3 & 2.8 & 2.1 & 3.7 \\ Average & 7.6 & 3.5 & 2.5 & 4.3 \\ \hline \end{tabular}
\end{table} 
Table 1: Statistical results of lateral errors in different operating areas. The above test results showed that a larger starting \(\theta\) initially showed much difficulty in path tracking. However, as the robot moved forward, it tended to correct the path in successive frames, until it finally achieved the correct path. The sharp peaks observed for a starting \(\theta\) of 45\({}^{\circ}\) could have occurred as a result of the camera not being able to capture one fence sufficiently, thus generating noisy work path coordinates. A quicker stability achievement was observed for a starting \(\theta\) of 15\({}^{\circ}\).