冗余度机器人雅可比矩阵求导方法及应用  

The Jacobian matrix derivation method of redundancy robots and its application

作　　者：洪磊[1] 孙汉旭[1] 贾庆轩[1] 陈钢[1] 

机构地区：[1]北京邮电大学自动化学院,北京100876

出　　处：《机械设计》2010年第2期33-36,62,共5页Journal of Machine Design

基　　金：国家高技术发展863计划资助项目(2004AA742101)

摘　　要：雅可比矩阵导数求解是进行冗余度机器人动力学优化分析的基础。基于旋量理论,提出了求解雅可比矩阵导数的改进方法。该方法利用运动旋量指数积易于求导的特点,避免了直接代入关节变量符号计算雅可比矩阵并依次求解关节变量偏导数的繁琐过程,在保持计算准确性的同时,极大地简化了雅可比矩阵求导运算。通过9自由度冗余度机器人优化关节力矩的拉抽屉操作实验,验证了算法的正确性和实用性。The derivative solution of Jacobian matrix is the basis for carrying out dynamics optimization analysis of redundancy robots. On the basis of screw theory, an improved method for solving the derivatives of Jacobian matrix was put forward. This method uses the characteristics of easy differentiation of utilizing the product of motion spinor index, thus avoided the tedious course of calculating the Jacobian matrix by substituting directly the joint variables symbols and of solving successively the partial derivatives of joint variables. At the same time of maintaining the calculation accuracy, the derivation operation of Jacobian matrix was greatly simplified. The correctness and practicability of this algorithm were testified through pulling drawer operation experiment on the optimized joint moment of 9-DOF redundancy robots.

关 键 词：冗余度 雅可比矩阵导数 运动旋量指数积 优化关节力矩 

分 类 号：TP242[自动化与计算机技术—检测技术与自动化装置]