# Kinematics Model Optimization Algorithm for Six Degrees of Freedom Parallel Platform
## 1 Introduction  
Multi-degree-of-freedom parallel platforms are widely used in intelligent manufacturing and industrial production, and the research on parallel platforms has also been a research hotspot in recent years. Among them, the dynamics of the parallel platform studies the relationship between the force on the moving platform and the force on each manipulator [1]. Commonly used dynamic modeling methods for parallel platforms include Newton-Euler method [2], [PERSON] method [3], spiral theory and virtual work principle [4; 5; 6], etc. The dynamic model can be used to design the inverse dynamics controller of the parallel platform, so as to improve the transient, dynamic, and steady-state performance of the parallel platform [7; 8; 9].  
The movement of the parallel platform in space is realized by changing the length of the six groups of parallel manipulator arms, which is an indirect control [10]. In order to realize arbitrary adjustment of the pose of the parallel platform, it is necessary to establish a mapping relationship between the pose of the parallel platform and the length of each manipulator, that is, a kinematics problem. The kinematics problem of the parallel platform consists of two problems of forward kinematics and inverse kinematics [11; 12]. At present, there are many solutions for the kinematics solution of the parallel platform. [PERSON] et al. proposed a control scheme for a five-degree-of-freedom parallel platform based on neural network technology [13]. [PERSON] et al. present various solutions in Real-Time Solving of Kinematics Problems in Parallel Mechanisms [14; 15; 16]. Among them, the kinematics forward solution has a large amount of computation, which makes it difficult to carry out real-time control of the parallel platform in the workspace. In order to avoid this problem,the expected trajectory of the parallel platform in the workspace is usually mapped to the joint space of the manipulator through the inverse kinematics solution. Then, in the joint space, the closed-loop control of the length of the manipulator is performed according to the mapping value, thereby indirectly realizing the trajectory tracking of the parallel platform. However, there are the following deficiencies in such a control method [17; 18; 19]:  
1. The movement trajectory of each robot arm is calculated by interpolation before movement. For the situation that has deviated from the preset trajectory, no correction can be made, and the control accuracy is not high.
2. During the movement of the parallel platform, the convergence speed of each robot arm is different. The length closed-loop control of each manipulator independently according to the mapping value will lead to large process errors in the platform shake and working space.
3. It is difficult to realize the speed control of the parallel platform in the working space.  
Therefore, this study proposes a kinematics forward solution algorithm based on multivariate polynomial regression to address the difficulty caused by the fact that the kinematics forward solution has a large amount of computation. The optimization goal of controllable solution accuracy and high efficiency is achieved. Through the comparison of simulation experiments, it is concluded that the multivariate polynomial regression method can guarantee the accuracy. The calculation time consumption and the number of iterations is far less than the conclusion of the traditional Newton iterative algorithm.