基于共形几何代数的串联机器人误差建模方法  

Error modelling method of series robots based on conformal geometric algebra

作　　者：张睿 张海峰 柴馨雪 ZHANG Rui;ZHANG Hai-feng;CHAI Xin-xue(School of Mechanical Engineering and Automation,Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]浙江理工大学机械与自动控制学院,浙江杭州310018

出　　处：《机电工程》2022年第3期281-290,共10页Journal of Mechanical & Electrical Engineering

基　　金：国家自然科学基金资助项目(51935010,52005448);浙江省自然科学基金资助项目(LQ19E050015)。

摘　　要：针对机器人绝对定位精度相对较低,无法满足高端制造领域的精度要求等问题,提出了一种基于共形几何代数(CGA)的串联机器人误差建模方法。首先,在CGA的框架下,通过计算相邻关节点的CGA运动算子及其共轭形式,得到了机器人末端坐标系的坐标轴投影及原点坐标表示,建立了串联机器人运动学模型;然后,通过微分运算建立了误差模型,并运用Levenberg-Marquardt算法辨识出了其几何参数误差;最后,根据辨识出的误差参数计算了末端误差,并将其补偿到串联机器人的末端位姿中完成了运动学标定实验,并通过该方法对JAKA Zu3六自由度串联机器人进行了误差建模与运动学标定实验。理论分析及研究结果表明:经运动学标定实验后,JAKA Zu3串联机器人的平均位置误差由2.9331 mm下降到0.6152 mm,平均姿态误差由0.0297 rad下降到0.0057 rad,标定效果明显,该结果验证了该方法的正确性,证明其可以作为一种误差建模和运动学标定的有效途径。Aiming at the problem that the absolute positioning accuracy of robots was relatively low and could not meet the precision requirements of high-end manufacturing field,a series robot error modeling method based on conformal geometric algebra(CGA)was proposed.Based on the framework of conformal geometry algebra,firstly the kinematics model of serial robot was established by calculating the CGA motion operator of adjacent nodes and its conjugate form,and the projection of the terminal coordinate system and the representation of the origin coordinates were obtained.Then the error model was established based on differential operation,and the geometric parameter errors were identified by Levenberg-Marquardt algorithm.Finally,the terminal errors were calculated according to the identified error parameters and were compensated to the terminal pose of the serial robot.The error modeling and kinematics calibration of Jaka ZU36-DOF serial robot were carried out by this method.The theoretical analysis and research results show that the average position error of JAKA Zu3 robot decreases from 2.9331 mm to 0.6152 mm and the average attitude error decreases from 0.0297 rad to 0.0057 rad after the kinematic calibration experiment.The calibration effect is obvious,which proves the correctness of the method and can be used as the effective approach for error modeling and kinematic calibration.

关 键 词：串联机器人 运动学标定 共形几何代数 误差建模 

分 类 号：TH112[机械工程—机械设计及理论] TP24[自动化与计算机技术—检测技术与自动化装置]