# Research of Calibration Method for Industrial Robot Based on Error Model of Position
## 5 Robot Calibration Experiment
After measurement, the robot pose error before and after compensation is obtained as shown in Figure 8. The results of compensation analysis are expressed in Table 8.  
Comparing Tables 7 and 8, the compensation effect of 50 groups of calibration points is better than that of 100 groups of sampling points. This is because the position error of the robot end is not only related to the parameter error of the robot kinematics model, but also influenced by many other factors. In addition, the error caused by measurement disturbance is unavoidable in the process of measurement. Therefore, in the process of identifying parameter errors, a group of optimal solutions are obtained according to the position error characteristics of all 50 groups of calibration points. In the 100 groups of sampling points except the calibration points, some of them differ greatly from the position error characteristics of the calibration points, and the calibration results have comparatively poor compensation effect on these sampling points. Therefore, the overall calibration effect is not as good as the compensation for the calibration point. In order to verify the correlation between calibration effect and the distribution of calibration points, add the following experiments: Take the point [300, 300, 300] in the RBCS as the center, respectively establish three kinds of cube space with the size of 600 mm, 450 mm, and 300 mm, defined as areas a, b, and c respectively. Fifty groups data of robot's \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mathbf{\Delta x}\) (mm) & \(\mathbf{\Delta y}\) (mm) & \(\mathbf{\Delta z}\) (mm) & \(\mathbf{\Delta Rx}\) (\({}^{\circ}\)) & \(\mathbf{\Delta Ry}\) (\({}^{\circ}\)) & \(\mathbf{\Delta Rx}\) (\({}^{\circ}\)) \\ \hline
0.0746 & 0.0849 & \(-\)0.0687 & \(-\) & \(-\) & \(-\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parameters error of DCP coordinate system error model of robot. \begin{table}
\begin{tabular}{c c c c c} \hline \hline _Axis i_ & \(\mathbf{\Delta\theta}\) (\({}^{\circ}\)) & \(\mathbf{\Delta d}\) (mm) & \(\mathbf{\Delta a}\) (mm) & \(\mathbf{\Delta a}\) (\({}^{\circ}\)) & \(\mathbf{\Delta\beta}\) (\({}^{\circ}\)) \\ \hline
1 & \(-\)0.0616 & \(-\)0.1641 & 0.0745 & \(-\)0.0883 & \(-\) \\
2 & \(-\)0.0398 & \(-\) & \(-\)0.2474 & 0.0695 & 0.0701 \\
3 & 0.0801 & 0.1487 & 0.2094 & \(-\)0.0962 & \(-\) \\
4 & 0.0997 & 0.1345 & \(-\)0.1471 & \(-\)0.1321 & \(-\) \\
5 & 0.0157 & 0.0745 & \(-\)0.0677 & 0.1027 & \(-\) \\
6 & \(-\) & \(-\) & 0.0224 & \(-\)0.0754 & \(-\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameters error based on end pose recognition. Figure 8: Position error curve of robot before and after compensation. pose are measured in the three areas, respectively, and ensure that the pose of sampling points are evenly distributed in each space, as shown in Figure 9.  
The sampling points in the b and c areas are taken as calibration points to the position error identification algorithm. The calculated parameters errors results are compensated respectively to the sampling points in area a. Calculating and comparing the errors before and after calibration, the experimental results are shown in Figure 10 and Table 9.  
From the above results, it can be seen that the more uniform the selected calibration points are distributed in a certain space, the better effect of the calibration solution is. In comparison, these literature [14; 15; 16] all use the laser tracker as the measuring instrument to improve the absolute positioning accuracy of the robot. Literature [14] improved the accuracy by about one time. Literature [15] uses different calibration methods to reduce the maximum error by about 60%, but the experiment only measured the data of 20 points, and the optimized maximum positioning deviation is still 1.30 mm. Literature [16] measures 1000 points in a certain working space, which can reduce the mean value of absolute positioning accuracy from 0.981 to 0.292, and the error is reduced by about 70%.