## 4 Experimental Verification
### Experimental Validation  
To verify the actual error compensation effect of the ISBOA-BP neural network model on the rock-drilling robotic arm, 50 sets of data were randomly selected from the robotic arm's motion space and compensated using the trained model. The experimental results are presented in Figure 12. Figure 12a-c show the positioning error compensation results of the robotic arm's end in the XYZ directions, respectively, while Figure 12d illustrates  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Total Tolerance (mm)** & \
\begin{tabular}{c} **Average Absolute** \\ **Error (mm)** \\ \end{tabular} &
\begin{tabular}{c} **Standard Deviation** \\ **(mm)** \\ \end{tabular} \\ \hline Uncompensated & [52.381, 354.211] & 190.792 & 89.525 \\ BP & [1.697, 85.965] & 33.791 & 13.608 \\ GA-BP & [1.228, 54.572] & 30.085 & 10.724 \\ PSO-BP & [0.954, 48.331] & 29.943 & 10.471 \\ SBOA-BP & [1.132, 37.742] & 29.139 & 9.864 \\ ISBOA-BP & [0.803, 36.427] & 28.831 & 9.423 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Analysis of compensation results for each algorithm.  
Figure 11: Adaptation curves of the four algorithms.  
the total positioning error of the robotic arm. The statistical results before and after error compensation are summarized in Table 3.  
As shown in Figure 12, the robotic arm exhibits significant positioning errors in all directions before compensation, failing to meet the required accuracy standards. Moreover, the positioning errors along different axes show varying distribution characteristics: the x- and y-direction errors tend to shift positively, while the z-direction errors shift negatively. This variation arises from the differing impact of error sources on the positioning accuracy in the x-, y-, and z-directions. Notably, the positioning errors along the z-axis are considerably larger than those along the other axes. This is primarily because the z-axis is perpendicular to the ground, and gravity's effect on the connecting rods and joints becomes more pronounced, especially when the end-effector is extended farther, exacerbating this error. After compensation, both the magnitude of the error and its fluctuation range in each direction are significantly reduced, resulting in a more consistent and reasonable error distribution. As shown in Table 3, the maximum positioning errors of the robotic arm in  
Figure 12: Position error before and after compensation. (**a**) Errors in x-direction. (**b**) Errors in y-direction. (**c**) Errors in z-direction. (**d**) Total position errors.  
the x-, y-, and z-directions are reduced from 166.243 mm, 184.063 mm, and 297.178 mm to 16.974 mm, 26.443 mm, and 32.986 mm, respectively. Similarly, the average absolute errors decrease from 92.282 mm, 73.824 mm, and 129.112 mm to 7.321 mm, 12.305 mm, and 11.755 mm, respectively. The maximum total positioning error of the arm is reduced from 350.901 mm to 36.095 mm, and the average absolute positioning error decreases from 187.972 mm to 28.317 mm, indicating an improvement in the positioning accuracy of the rock-drilling arm by 84.94%. These results collectively demonstrate the effectiveness of the neural network-based error compensation method proposed in this paper.