## 4 Results
The differences between the proposed method with \({}^{W}\)\(T_{\text{T}}\) calibrated in adjacent regions (blue lines vs. yellow lines) are caused by the calibration uncertainties of the TCP frame, which is merely 1.08 mm between \(\Omega_{1}\) and \(\Omega_{2}\) and 1.1 mm between \(\Omega_{3}\) and \(\Omega_{4}\) in total distance. The statistical result of the experiment is demonstrated in Table 4.  
Figure 10: Experimental results of robot compensation. (**a**) Positioning error of \(\Omega_{1}\) (**b**) Positioning error of \(\Omega_{2}\); (**c**) Positioning error of \(\Omega_{3}\); (**d**) Positioning error of \(\Omega_{4}\). As seen in the results, the method in Ref. [28] is able to effectively reduce the maximum error in \(\Omega_{1}\) from 10.6342 mm to 0.9507 mm, resulting in an improvement of accuracy by 91.06%. Similarly, the accuracy in \(\Omega_{2}\), \(\Omega_{3}\) and \(\Omega_{4}\) increased by 91.76%, 91.02% and 88%, respectively. Despite the significant improvement in error compensation of about 90% in each region, it still falls short of meeting the requirements of a drilling accuracy of 0.25 mm. In comparison, when using the method proposed in this paper with \({}^{\text{W}}\)T\({}_{\text{T}}\) calibrated in the corresponding region, the maximum errors in \(\Omega_{1}\), \(\Omega_{2}\), \(\Omega_{3}\) and \(\Omega_{4}\) are reduced to 0.21 mm, 0.23 mm, 0.2 mm and 0.22 mm, respectively. As opposed to the method in Ref. [28], the accuracy is further improved by 77.91%, 75.08%, 61.33% and 77.3%, which meets the accuracy requirements of the drilling task. However, when the TCP frames are calibrated in the adjacent region, the maximum errors in \(\Omega_{1}\), \(\Omega_{2}\), \(\Omega_{3}\) and \(\Omega_{4}\) rise to 0.7061 mm, 0.5798 mm, 0.3565 mm and 0.6618 mm, proving that the division strategy of the region is reasonable. Other scientists also developed different compensation methods for robots with a large orientation variation. The comparison can be seen in Table 5. In reference [30], [PERSON] divided the joint space into two 3-dimensional subspaces and created spatial grids to compensate for both positioning and orientation errors. However, the positioning accuracy after compensation was still 0.334 mm, which did not meet the requirements for the drilling task. On the other hand, Electroimpact [3] developed high-accuracy robots with an accuracy of 0.18 mm by using optical encoders on each joint and integrating a real-time compensation algorithm into the CNC system. However, this method has the limitations of requiring hardware modification and the real-time compensation algorithm being only accessible to a limited group of companies. In comparison, the method proposed in this paper offers a high accuracy compensation method that is suitable for all robots. With the aim of further studying the similarity characteristics of positioning errors, the spatial distances and orientation deviations between each desired drilling position and [_TDR_] in \(\Omega_{1}\) and \(\Omega_{2}\) are calculated, and the regression line is fitted, as shown in Figure 11. Through the comparison of regression functions in Figure 11a,b, it is apparent that in \(\Omega_{1}\), the effect of orientation on error similarity is significantly higher than that of spatial distance; that is, the more similar the orientation is, the smaller the residual error is. On the other hand, Figure 11c shows that in \(\Omega_{2}\), the residual error decreases with the increase of spatial distance, which indicates that the similarity of error does not increase with the decrease of distance in Cartesian space, but the accuracy enhances with the descends of orientation deviation, which further proves that the influence of orientation deviation on robot positioning error is greater than that of spatial distance.