基于齐次变换矩阵数值解的6自由度并联机构位姿正解解算  

Forward kinematics of the 6-DOF parallel mechanism based on homogeneous transformation matrix numerical solution

作　　者：刘玉梅[1,2] 曹晓宁[1] 王秀刚[1] 王帆[1] 徐振[1] 卢海隔[1] 

机构地区：[1]吉林大学交通学院,吉林长春130022 [2]长春轨道客车股份有限公司,吉林长春130062

出　　处：《哈尔滨工程大学学报》2013年第7期894-898,共5页Journal of Harbin Engineering University

基　　金：吉林省科科技厅重点资助项目(20080356);长春市科技支撑计划资助项目(2010018);吉林大学研究生创新基金资助项目(20121076);中国博士后科学基金特别资助项目(2012T50275)

摘　　要：为提高6自由度并联机构位姿正解求解速度,提出了一种基于齐次变换矩阵数值解的位姿正解解算方法.结合齐次空间变换矩阵前3阶顺序主子矩阵的正交特性及各液压缸杆长约束条件,建立了以齐次变换矩阵12个元素为未知量的非线性方程组的数学模型,得出了雅克比矩阵解析总表达式,采用牛顿拉夫逊法算法逐次迭代得到齐次变换矩阵数值解,再根据齐次变换矩阵与位姿转化关系求解对应位姿.结合实例,利用位姿正解仿真解算模型对所提出的位姿正解方法准确性及高效性进行了验证.结果表明:以齐次变换矩阵元素为变量的位姿正解解算方法比以位姿为变量的传统计算方法速度快.In order to increase the solving speed of forward kinematics for 6-DOF parallel mechanism, the forward kinematics solution method based on homogeneous transformation matrix numerical solution was proposed in this pa- per. By combining the orthogonality of the first three-order sequence master matrix of the homogeneous transforma- tion matrix with the hydraulic cylinder rod length constraints, the mathematical model of nonlinear equations taking the 12 elements of the homogeneous transformation matrix as unknown variables was established, and the Jacobian matrix analytical expression was summarized. The homogeneous transformation matrix numerical solution was ob- tained by means of the successive iteration of Newton-Raphson algorithm, and then the corresponding pose was solved according to the relationship between the homogeneous transformation matrix elements and the position varia- bles. The accuracy and high effectiveness of the solution method in this paper was validated using the forward kine- matics simulation model with examples. The results showed that the forward kinematics solution method taking the homogeneous transformation matrix elements as unknown variables is faster than the traditional calculation method takin~ the oose as unknown variables.

关 键 词：6自由度并联机构 齐次变换矩阵 位姿正解 牛顿拉夫逊法 

分 类 号：TP249[自动化与计算机技术—检测技术与自动化装置]