# Kinematics Model Optimization Algorithm for Six Degrees of Freedom Parallel Platform
## 3 Results
### Physical Test  
In order to further verify the correctness and stability of the MPR-NR algorithm running in the parallel platform system, a kinematics positive solution experiment based on the physical platform was designed in this research. For parallel platforms, the kinematics inverse solution is relatively simple. The parallel platform can be moved to a specified attitude by adjusting the length of each group of robotic arms to achieve a closed-loop attitude. The experimental process is designed as follows: The parallel platform is adjusted to the specified attitude in the workspace through the attitude closed-loop control method. Record the arm length information fed back by each servo driver when reaching the target attitude. The length information of the manipulator is imported into the MPR-NR algorithm of the MATLAB platform to calculate the kinematics positive solution. Compare the calculation results with the attitude of the parallel platform physical setting. Through this method, the closed loop from the attitude of the parallel platform to the length of each group of manipulators and then to the attitude of the algorithm simulation can be completed. Then compare the attitude of the parallel platform calculated by the MPR-NR kinematics forward solution algorithm with the attitude of the real object. It can be confirmed whether the algorithm can run as theoretically expected. The experimental process is shown in Figure 6.  
Figure 5: The relationship between stopping conditions and solution accuracy: (**a**) \(D(L_{k})\) and \(D(X_{k})\) relationship diagram; (**b**) \(D(L_{k})\) and iteration number relationship diagram. Figure 6: Flowchart of physical test experiment. In the host computer of the parallel platform control center, set the target attitude of the parallel platform in the workspace as \( \begin{bmatrix}0^{\circ}&0^{\circ}&5^{\circ}&12\text{ mm}&-4\text{ mm}&40\text{ mm}\end{bmatrix} \). The unit of displacement in the MATLAB algorithm is meter, and the unit of angle is radian. Therefore, unit conversion is required when comparing parameters. The converted target attitude value is \( \begin{bmatrix}0&0&0.0870&0.012&-0.004&0.040\end{bmatrix} \). Click the run button in the host computer and wait for each driver to complete the length adjustment of the mechanical arm. Make the parallel platform run to the set target attitude. The length information of each robot arm when the upper computer of the control center performs in the closed-loop attitude is shown in Figure 7.  
It can be seen from Figure 7 that when the parallel platform performs joint closed-loop control and moves to the end point, the lengths of the six sets of robotic arms are \( \begin{bmatrix}339.5&336.5&336.6&329.2&345.1&334.5\end{bmatrix} \). Input the length information of each group of manipulators into MATLAB. Using the MPR-NR algorithm to complete the kinematics forward solution, the attitude of the parallel platform corresponding to the length value of the group of manipulators can be obtained. The reference values of the pose parameters and the calculated values obtained by the MPR-NR algorithm are shown in Table 5. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Attitude Parameter** & **Reference Value** & **Calculation Value** \\ \hline \(\alpha\) & 0 & \(-1.68\times 10^{-4}\) \\ \(\beta\) & 0 & \(5.83\times 10^{-5}\) \\ \(\gamma\) & 0.0870 & 0.0896 \\ \(x\) & 0.0120 & 0.0120 \\ \(y\) & \(-0.0040\) & \(-0.0040\) \\ \(z\) & 0.0400 & 0.0398 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Attitude parameter reference value and MPR-NR algorithm calculation value. Figure 7: Set the target attitude and read the arm length. Comparing the attitude reference value in Table 5 with the attitude calculation value data obtained by the MPR-NR algorithm, it can be seen that the calculation result of the algorithm has a small gap with the set reference attitude. It can be shown that the operation of the MPR-NR algorithm is in line with expectations.