基于共形几何代数的6-DOF机器人运动学逆解  

Inverse Kinematics for 6-DOF Robot Based on Conformal Geometric Algebra

作　　者：冯春[1] 吴洪涛[2] 夏任波[1] 徐强[1] 代栋梁 

机构地区：[1]常州工学院机械与车辆工程学院,江苏常州213032 [2]南京航空航天大学机电学院,南京210016

出　　处：《机械设计与研究》2018年第1期69-75,共7页Machine Design And Research

基　　金：国家自然科学基金(51375230);江苏省自然科学青年基金资助项目(BK20140252);江苏省高校自然科学研究面上资助项目(14KJB510003);国家级大学生创新创业项目(201611055001);江苏省大学生创新创业项目(201611055001Z)

摘　　要：机器人运动学模型的建立普遍利用Denavit-Hartenberg（D-H）参数法，但是该代数方法的计算复杂度高。共形几何代数作为一种新的运算工具，具有几何直观性、简洁性，已经应用于机器人运动学。针对广泛应用的6自由度工业机器人，利用共形几何代数建立点、直线、圆周、平面和球体等几何对象，通过各对象之间的几何约束解决机器人运动学逆解。首先，以工业机器人典型的肩部、肘部和腕部结构为基础，定义3种结构形式；然后，利用已知的点以及相交约束关系建立直线、平面、圆周和球体等几何对象，通过它们的几何约束关系计算得到各个关节点并构造连杆直线；最后，构造旋转直线对象以及旋转平面并利用平行和垂直的几何约束关系计算各关节的旋转角，完成机器人逆解的计算。以常用的后3个关节轴线相交于1点和UniversalRobotUR3的6自由度关节机器人为例，利用该算法进行运动学逆解的验证，计算结果表明该算法的正确性。Denavit-Hartenberg （D-H） notation method is usually used to set up the kinematics model of a robot, but the method has high computational complexity. Conformal Geometric Algebra （CGA） is a new computation tool. It has properties of geometric intuitiveness, simplicity, and has been used to robot kinematics. For a wide range of applications of 6-DOF industrial robot, the paper demonstrates that the solution of the inverse kinematics in CGA relies on the constrain relationship of geometric objects like lines, circles, planes and spheres. First three kinds of robot configurations are defined based on the classical frame of industrial robot for shoulder, elbow and wrist style. Then the geometric objects such as lines, circles, planes and spheres are set up by the points and intersection relationship between＇ these objects, by which the joint points and the link lines could be obtained. Finally, the rotation angles are computed by the rotation line objects and rotation planes and the parallel and perpendicular constrain relationship, so the inverse kinematics of robot was completed. The correctness of the algorithm is verified by the robots with 6-DOF and with the last three joint axes intersecting to one point and the Universal Robot UR3, whose kinematics modes are set up by the proposed algorithm.

关 键 词：共形几何代数 6自由度 运动学正解 运动学逆解 工业机器人 

分 类 号：TP24[自动化与计算机技术—检测技术与自动化装置]