## 3 Comprehensive Calibration of the Coal Gangue Sorting System
### System Comprehensive Calibration Experiment  
The traditional calibration method of conveyor belt does not consider the angle deflection error between the conveyor belt coordinate system and the robot coordinate system. In this paper, by improving the traditional conveyor belt calibration method, a more accurate transformation relationship matrix between the two coordinate systems is obtained and the influence of the two calibration methods on the system error is compared through experiments.  
As shown in Figure 7, the camera is calibrated to get the internal parameters of the camera and the position of the read target point in the camera coordinate system \(P_{i}^{V}\).  
The end probe of the robot is moved to the initial point O to obtain the coordinate position O\({}_{0}\) of the O point in the robot coordinate system. The conveyor belt is controlled to move an equal distance four times with each movement comprising 150 mm, which is the corresponding encoder variation.  
\[\Delta L_{C}=\frac{\Delta L_{R}}{Factor_{c}} \tag{16}\]  
The position under the robot coordinate after each movement is measured as shown in Figure 8: O\({}_{1}\) (\(-\)161.588, 199.710, \(-\)890.267), O\({}_{2}\) (\(-\)14.956, 201.710, \(-\)890.468), O\({}_{3}\) (\(-\)130.944, 204.840, \(-\)890.266), O\({}_{4}\) (277.788, 207.460, \(-\)889.244), and O\({}_{5}\) (423.932, 210.140, \(-\)891.460).  
Using the above two calibration methods, the data of two groups of positions in the robot coordinate system after movement are obtained respectively, as shown in Table 1.  
According to the data shown in Table 1, the maximum cumulative deviation of the calibration method in this paper is 3.839 mm in the specified operating space, which is far lower than the 13.841 mm obtained with the traditional calibration method. The deviation error caused by the calibration method in this paper is obviously smaller than that caused by the traditional calibration method. The system calibration accuracy is effectively improved, and the calibration method is simple and practical.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Serial** \\ **Number** \\ \end{tabular} } & \multicolumn{3}{c}{**Actual Coordinates**} & \multicolumn{3}{c}{**Coordinates Obtained by the**} & \multicolumn{3}{c}{**Coordinates Obtained by**} & \multicolumn{3}{c}{**Comprehensive**} & \multicolumn{3}{c}{**Traditional**} \\  & & & & **Calibration Method in this Work** & **Traditional Calibration Method** & **Error** & **Error** & **Error** \\ \hline \hline \multirow{2}{*}{1} & \(\mathbf{x}\) & \(\mathbf{y}\) & \(\mathbf{z}\) & \(\mathbf{x}\) & \(\mathbf{y}\) & \(\mathbf{z}\) & \(\mathbf{x}\) & \(\mathbf{y}\) & \(\mathbf{z}\) & \\ \hline \multirow{2}{*}{2} & \(1\) & \(-161.588\) & \(199.710\) & \(-890.267\) & \(-161.588\) & \(199.710\) & \(-890.267\) & \(-11.588\) & \(199.710\) & \(-890.267\) & 0 & 0 \\  & \(2\) & \(-149.456\) & \(201.710\) & \(-890.468\) & \(-13.738\) & \(202.960\) & \(-890.267\) & \(-11.588\) & \(199.710\) & \(-890.267\) & 1.757 & 3.9222 \\  & \(3\) & \(130.944\) & \(208.480\) & \(-890.266\) & \(133.962\) & \(205.640\) & \(-890.267\) & \(138.412\) & \(199.710\) & \(-890.267\) & 3.312 & 9.0602 \\  & \(4\) & \(277.788\) & \(207.460\) & \(-899.244\) & \(208.812\) & \(208.434\) & \(-890.267\) & \(287.230\) & \(199.710\) & \(-890.267\) & 3.338 & 12.258 \\  & \(5\) & \(433.932\) & \(210.140\) & \(-891.460\) & \(434.392\) & \(213.760\) & \(-890.267\) & \(441.952\) & \(199.710\) & \(890.267\) & 3.839 & 13.841 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Data and error of two calibration methods.  
Figure 8: Conveyor belt calibration experiment.  
Figure 7: Target point.