## 5 Evaluation and Discussion of the Kinematic Calibration Method Using Optimal Measurement Pose
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \(i\) & \(\mathbf{d}x_{Ai}\) & \(\mathbf{d}y_{Ai}\) & \(\mathbf{d}z_{Ai}\) & \(\mathbf{d}x_{Bi}\) & \(\mathbf{d}y_{Bi}\) & \(\mathbf{d}z_{Bi}\) & \(\mathbf{d}h_{i}\) \\ \hline
1 & \(-0.5\) & \(-0.2\) & \(-1\) & \(-0.4\) & \(0.2\) & \(0.6\) & \(0.6\) \\
2 & \(0.1\) & \(-0.3\) & \(-0.7\) & \(0.4\) & \(0.2\) & \(-0.3\) & \(-0.1\) \\
3 & \(0\) & \(-0.4\) & \(-0.3\) & \(-0.1\) & \(-0.3\) & \(0.7\) & \(0.1\) \\
4 & \(0.3\) & \(1.1\) & \(-0.2\) & \(-0.1\) & \(-0.7\) & \(0.2\) & \(-0.2\) \\
5 & \(-0.4\) & \(0.3\) & \(-0.7\) & \(-1.3\) & \(0.8\) & \(0.7\) & \(0.3\) \\
6 & \(-0.9\) & \(-0.2\) & \(1.1\) & \(0.4\) & \(-0.4\) & \(-0.3\) & \(-0.2\) \\ \hline \end{tabular}
\end{table} 
Table 6: Preset values of kinematic parameter errors (unit: mm). Figure 6: The process of measurement poses selection using improved DETMAX algorithm and traditional DETMAX algorithm. The optimal measurement poses are used for calibration. During the calibration process, the variation of kinematic parameter errors during the iteration process are shown in Figure 8. Due to space constraints, only seven kinematic parameter errors related to the first hardpoint are given in the figure. After three iterations, the error value tends to be stable and the convergence speed of the calibration is fast. The identification results of all kinematic parameter errors are shown in Table 7. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(i\) & \(\mathbf{d}\mathbf{x}_{Ai}\) & \(\mathbf{d}\mathbf{y}_{Ai}\) & \(\mathbf{d}\mathbf{z}_{Ai}\) & \(\mathbf{d}\mathbf{x}_{Bi}\) & \(\mathbf{d}\mathbf{y}_{Bi}\) & \(\mathbf{d}\mathbf{z}_{Bi}\) & \(\mathbf{d}\mathbf{h}_{i}\) \\ \hline \(1\) & \(-0.476\) & \(0.134\) & \(-0.032\) & \(0.275\) & \(-0.432\) & \(-0.882\) & \(-0.476\) \\ \(2\) & \(-0.221\) & \(-0.275\) & \(-0.380\) & \(1.121\) & \(0.277\) & \(-0.232\) & \(-0.221\) \\ \(3\) & \(-1.012\) & \(-0.708\) & \(-0.307\) & \(-0.200\) & \(-0.710\) & \(1.104\) & \(-1.012\) \\ \(4\) & \(-0.381\) & \(0.426\) & \(-0.162\) & \(-0.128\) & \(-1.343\) & \(0.410\) & \(-0.381\) \\ \(5\) & \(0.184\) & \(0.246\) & \(-0.287\) & \(-0.686\) & \(0.791\) & \(-0.430\) & \(0.184\) \\ \(6\) & \(0.597\) & \(-0.324\) & \(0.708\) & \(0.195\) & \(0.678\) & \(-0.288\) & \(0.597\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Identification results of kinematic parameter errors. Figure 8: The variation of kinematic parameter errors during the calibration. Figure 7: Results of the observability index \(O_{1}\) corresponding to 1000 sets of random poses. After obtaining the identification results of the kinematic parameter errors, the theoretical kinematic parameters are modified, and a new kinematic model is established based on the modified parameters. Then, set 150 primary mirror pose targets, and evaluate the result of the calibration. The results obtained by using the proposed calibration method and traditional calibration method were compared. The errors of the 150 poses of the primary mirror are shown in Figure 9. Figure 9a shows the position error, and Figure 9b shows the attitude error. The results in Figure 9 show that the proposed calibration method using the optimal measurement poses achieves significantly higher accuracy than the traditional calibration method, both in position accuracy and attitude accuracy. The above results verify the effectiveness of the proposed calibration method. The errors of the proposed calibration method and the traditional calibration method are listed in Table 8. Compared with the traditional method, the mean position error obtained by the proposed method decreases by 78.4%, and the mean attitude error decreases by 70.6%. The number \(n\) of measurement poses in the above calibrations is 20. The number of measurement poses in calibration has been increased, and the results are shown in Figure 10. When using traditional methods, the integrated error decreases significantly as the number of measurement poses increases.