# Research of Calibration Method for Industrial Robot Based on Error Model of Position
## 5 Robot Calibration Experiment  
The experimental object of this paper is IRB120 industrial robot. The measurement system is shown in Figure 4. The measuring instrument is Leica AT960 MR absolute laser tracker as shown in Figure 5, which can measure the end position of the robot with laser \begin{table}
\begin{tabular}{c c} \hline
**Identification Condition** & **Redundancy Parameter** \\ \hline \(\alpha_{i}\
eq 0\) & None \\ \(\alpha_{i}=0\delta a_{i}\
eq 0\) & \(\Delta d_{i}\) \\ \(\alpha_{i}=0\delta a_{i}=0\) & \(\Delta d_{i}\), \(\Delta\theta_{i}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Redundancy identification of robot kinematics parameters. receiving target ball as shown in Figure 6. The software SpatialAnalyzer (SA) can be used for data acquisition connecting Leica AT960 MR, data processing, and exporting the data of the robot end position based on its own coordinate system. Using the coordinate conversion method mentioned in Section 2.3, the data in AT960 MR coordinate system and the data in the RBCS are fitted with the least square method. The transformational matrix between the coordinate system of AT960 MR and the robot base can be obtained by Matlab software. So the data in laser tracker coordinate system can be converted to the RBCS. The measured robot end pose in AT960 MR and the robot end pose displayed in the robot controller are unified into the same coordinate system for comparison. The first step of calibration experiment is modeling. First, the kinematics model of the robot is determined. The MDH model of the ABB IRB120 robot is expressed in Figure 7,  
Figure 4: Experimental scenario. Figure 5: Leica laser tracker. Figure 6: Target ball. and the MDH parameters are expressed in Table 2.  
The nominal transformation model parameters can be obtained by calibrating the robot DCP coordinate system and the RBCS as shown in Tables 3 and 4:  
According to the analysis of redundancy parameters in Section 3.1, the error of redundancy parameters in the kinematics model of robot is \(\Delta d_{2}\), \(\Delta d_{6}\) and \(\Delta\theta_{6}\), and the redundancy parameters in the transformation model of RBCS are \(\Delta z\) and \(\delta z\). So there are 28 discernible parameters in this calibration experiment. Fifty groups of robot pose data are taken as calibration points in robot workspace, and the error of robot parameters is computed. The parameters errors of the identified error models are expressed in Tables 5-7. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(x\) (mm) & \(y\) (mm) & \(z\) (mm) & \(Rx\) (\({}^{\circ}\)) & \(Ry\) (\({}^{\circ}\)) & \(Rz\) (\({}^{\circ}\)) \\ \hline \(-\)27.31 & \(-\)19.82 & 25.71 & \(-\) & \(-\) & \(-\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Nominal parameters of robot DCP coordinate transformation model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(Axis\)\(i\) & \(\theta_{i}\) & \(\mathbf{d}_{i}\) & \(\mathbf{a}_{i}\) & \(\mathbf{\alpha}_{i}\) & \(\mathbf{\beta}_{i}\) \\ \hline \(1\) & \(\theta_{1}\) & 290 & 0 & \(-\)90 & \(-\) \\ \(2\) & \(\theta_{2}-90\) & 0 & 270 & 0 & 0 \\ \(3\) & \(\theta_{3}\) & 0 & 70 & \(-\)90 & \(-\) \\ \(4\) & \(\theta_{4}\) & 302 & 0 & 90 & \(-\) \\ \(5\) & \(\theta_{5}\) & 0 & 0 & \(-\)90 & \(-\) \\ \(6\) & \(\theta_{6}\) & 72 & 0 & 0 & \(-\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Nominal parameters of robot MDH model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(x\) (mm) & \(y\) (mm) & \(z\) (mm) & \(Rx\) (\({}^{\circ}\)) & \(Ry\) (\({}^{\circ}\)) & \(Rz\) (\({}^{\circ}\)) \\ \hline \(-\)1384.05 & 1448.6 & \(-\)391.47 & 1.6 & 1.8 & 60.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Nominal parameters of robot base coordinate transformation model. Figure 7: ABB IRB 120 MDH model. The calibrated parameter error is substituted into the model by the compensation method proposed in Section 3.3.