基于旋转矩阵正交性的转向架6自由度平台位姿正解解算  

Forward kinematics solution of bogie 6-DOF platform based on the orthogonality of rotation matrix

作　　者：王秀刚[1] 苏建[1] 曹晓宁[1] 徐振[1] 卢海隔[1] 田宗举[1] 

机构地区：[1]吉林大学交通学院,长春130022

出　　处：《吉林大学学报（工学版）》2013年第5期1241-1246,共6页Journal of Jilin University:Engineering and Technology Edition

基　　金：吉林省科技厅重点项目(20080356);长春市科技支撑计划项目(2010018);吉林大学研究生创新基金项目(20121091;20121076);吉林大学青年科技创新基金项目(450060487415)

摘　　要：利用齐次变换矩阵中旋转矩阵的正交特性及牛顿迭代实现了转向架空间姿态模拟平台的运动学正解解算。根据旋转矩阵元素之间的正交关系及各液压缸杆长约束条件,建立了以齐次变换矩阵各元素为未知量、方程数等于未知量数的非线性方程组的数学模型,并运用牛顿拉夫逊法进行近似求解,再根据齐次变换矩阵元素与位姿变量对应函数关系求解相应位姿,避免了牛顿拉夫逊法算法迭代求解过程中三角函数反复运算,提高了位姿正解解算速度。本文研究的转向架6自由度平台位姿正解解算方法为转向架空间姿态模拟的实现提供了依据,同时为其余形式的6自由度平台位姿解算提供了理论基础和技术支持。The paper employed the orthogonality of rotation matrix of homogeneous transfer matrix and Newton iteration to obtain the solution of forward kinematics of the space attitude simulation bogie. First, according to the orthogonal relationship between the elements of the rotation matrix and the length constraints of the hydraulic cylinder rods, the mathematical model with nonlinear equations was established. In this model, the elements of the homogeneous transformation matrix were taken as the unknowns, and the number of equations was equal to the number of the unknowns. Then, the approximate solution was obtained with Newton-Raphson method. Finally, the corresponding position and pose were solved on the basis of the relationship between the elements of the homogeneous transformation matrix and the position variables. The method avoids the iterative calculation of trigonometric function with Newton-Raphson method, improving the speed to solve the forward kinema＊ics. Also, the method of forward kinematics of the bogie 6-DOF platform provides ＊he possibility of realizing the space attitude simulation of bogie. It provides the theoretical basis and technical support for the pose solution of other forms of 6-DOF platform.

关 键 词：铁路运输 空间姿态模拟平台 位姿正解 齐次变换矩阵 牛顿迭代 

分 类 号：U260[机械工程—车辆工程]