采用解耦的牛顿迭代法进行六自由度平台运动正解分析  

The Decoupling Newton Iterative Method Is Used to Study the Positive Solution of the Motion of the 6-DOF Platform

作　　者：罗文超 朱玉玉[1] LUO Wenchao;ZHU Yuyu(Southwest University of science and technology,School of Information Engineering,Mianyang Sichuan 621010,China)

机构地区：[1]西南科技大学信息工程学院,四川绵阳621010

出　　处：《机械设计与研究》2022年第5期68-72,共5页Machine Design And Research

基　　金：四川省科技计划重点研发项目(2021YFG0374)。

摘　　要：典型六自由度平台由于6个控制杆采用并联结构,存在耦合度高的特点。牛顿迭代法在对这种六自由度平台求正解时会构造6个六元非线性方程,在求解此方程组的过程中会构造一个6×6的雅克比矩阵,求解复杂且耗时。文中设计的一种解耦六自由度平台是在典型并联六自由度平台的基础上分别对x,y以及偏航角方向进行解耦,从而构成的一个串并联六自由度平台。牛顿迭代法计算该解耦六自由度平台的正解时,只需构造3个三元非线性方程和一个3×3的雅克比矩阵,降低了求解复杂度。牛顿迭代法在设计的解耦六自由度平台的正解速度较典型并联结构六自由度平台提升了75.7%,提高了六自由度平台的实时性。The typical six degrees freedom platform has the characteristics of heavy coupling because the six control rods adopt a parllel structure.When solving the forward kinematics of a 6-DOF plaform using the Newton iterative method,six non-linear equations with six unknowns need to be solved by constructing a 6×6 Jacobian matrix,and the solution of which is complex and time-consuming.The decoupling 6-DOF platform designed in this paper is achieved by decoupling the X,Y and yaw angle directions of a typical parallel 6-DOF platform,respectively.When Newton iterative method is used to obtain the forward kinematics of the decoupled 6-DOF platform,only three nonlinear equations with three unknowns needs to be solved with a 3×3 Jacobian matrix,which reduces the complexity of solving process.The forward kinematics solution of speed of the Newton iterative method in the decoupled 6-DOF platform is 75.7%higher than that of the typical 6-DOF platform,and the real-time performance of the 6-DOF platform is improved.

关 键 词：牛顿迭代法 并联结构 解耦六自由度平台 正解速度优化 实时性 

分 类 号：TP23[自动化与计算机技术—检测技术与自动化装置]