# Kinematics Model Optimization Algorithm for Six Degrees of Freedom Parallel Platform
## 4 Discussion and Conclusions  
In this study, a spatial geometric model was established for a six-degree-of-freedom parallel platform. The Jacobian matrix of the parallel platform was further studied, and the forward solution algorithm of Newton iterative kinematics was deduced. In order to improve the real-time performance of the forward motion solution of the parallel platform,  
Figure 8: MPR-NR positive solution error.  
a kinematics forward solution algorithm based on multivariate polynomial regression (MPR) was proposed.  
Through simulation experiments, the following conclusions can be drawn: The MPR algorithm has the characteristics of fast solution speed and controllable calculation time but uncontrollable solution accuracy. The MPR algorithm has a certain accuracy, but with the expansion of the sample space, the accuracy drops significantly, and so it cannot meet the high-precision control requirements. The MPR algorithm can improve the solution accuracy by increasing the degree of polynomials, but the calculation amount will increase geometrically. On the basis of the above, this paper combines the advantages of the two algorithms and further combines the two algorithms into a polynomial regression-Newton iterative algorithm (MPR-NR). The MPR-NR algorithm uses the MPR algorithm to obtain a preliminary solution and then uses the Newton iteration method to improve the solution accuracy. The simulation proves that the MPR-NR algorithm can greatly reduce the number of iterations and improve the real-time performance of the algorithm while maintaining the same accuracy as the Newton iterative algorithm. Finally, the MPR-NR is deployed to the host computer of the control center to verify the correctness and stability of the new algorithm.  
In this research, the kinematics of the parallel platform was deeply studied, and the space geometry model of the parallel platform was established. On this basis, the inverse kinematics solution of the parallel platform was analyzed and solved. The forward solution algorithm of Jacobian matrix and Newton iterative kinematics of the parallel platform was realized. In the study, we proposed a multivariate polynomial regression (MPR) kinematics forward solution algorithm. Aiming at the shortcomings of the above algorithms, an algorithm combining multivariate polynomial regression and Newton iteration method (MPR-NR) was proposed. The proposed algorithm has controllable solution accuracy and high efficiency. Through the comparison of simulation experiments, it is concluded that the calculation time and iteration times of the MPR-NR method are much smaller than that of the Newton iterative algorithm under the premise of ensuring accuracy. The feasibility and correctness of the algorithm in the host computer of the control center are verified by physical tests. Finally, the MPR-NR algorithm was successfully transplanted to the host computer of the parallel platform control center.  
Conceptualization, W.Z. and B.Y.; methodology, Z.Y. and Q.G.; software, M.L.; validation, Q.G.; formal analysis, M.L. and Q.G.; investigation, B.Y. and S.L.; resources, M.L. and Z.Y.; data curation, Q.G.; writing--original draft preparation, M.L., Z.Y. and L.Y.; writing--review and editing, Z.Y., M.L., W.Z. and L.Y.; visualization, Z.Y., S.L. and M.L.; supervision, B.Y.; project administration, W.Z.; funding acquisition, W.Z. All authors have read and agreed to the published version of the manuscript.  
Support by the Sichuan Science and Technology Program, 2021 YQ0003.  
Not applicable.  
The data presented in this study are available upon request from the corresponding author. The data are not publicly available due to the fact that the experiment, at current stage, is not at the level to be published.  
The authors declare no conflict of interest.