基于等效运动链的并联机器人运动学标定方法

doi:10.3901/JME.2022.14.071

机械工程学报 ›› 2022, Vol. 58 ›› Issue (14): 71-84.doi: 10.3901/JME.2022.14.071

• 特邀专栏：大型构件视觉测量与机器人加工 • 上一篇下一篇

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基于等效运动链的并联机器人运动学标定方法

夏纯, 张海峰, 李秦川, 柴馨雪

浙江理工大学机机械与自动控制学院杭州 310018

收稿日期:2021-06-16 修回日期:2021-12-26 出版日期:2022-07-20 发布日期:2022-09-07
通讯作者: 柴馨雪(通信作者)，女，1988年出生，博士，讲师。主要研究方向为基于几何代数的机构学理论。E-mail：chaixx@zstu.edu.cn
作者简介:夏纯，女，1995年出生。主要研究方向为机构运动学标定。E-mail：xiac9454xc@163.com;张海峰，男，1996年出生。主要研究方向为并联机器人运动控制。E-mail：zhanghf5688@163.com;李秦川，男，1975年出生，博士，教授。主要研究方向为并联机器人机构学和应用技术。E-mail：lqchuan@zstu.edu.cn
基金资助:
国家自然科学基金(51935010，52005448)和浙江省自然科学基金(LQ19E050015)资助项目。

Novel Kinematic Calibration Method of Parallel Mechanisms Using the Equivalent Kinematic Chains

XIA Chun, ZHANG Haifeng, LI Qinchuan, CHAI Xinxue

School of Mechanical Engineering & Automation, Zhejiang Sci-Tech University, Hangzhou 310018

Received:2021-06-16 Revised:2021-12-26 Online:2022-07-20 Published:2022-09-07

摘要/Abstract

摘要： 为了解决并联机器人结构复杂难以准确求解误差模型的问题，提出一种基于等效运动链的并联机器人运动学标定方法。首先通过并集和交集算子求解动平台上的运动空间解析表达式，构建与动平台运动空间等效的虚拟串联运动链，并对其进行误差模型，再将末端误差补偿到等效运动链的末端，最后通过并联机器人运动学反解计算出误差补偿后动平台末端位姿对应的驱动值，并将其补偿到并联机器人的驱动关节中。以2-UPR-RPU并联机器人和冗余驱动的2-UPR-2-RPU并联机器人为例，二者的运动空间都等效于一个RPR串联运动链，对虚拟串联RPR运动链进行误差建模，并对误差模型进行仿真与标定试验验证。试验结果表明，标定后的2-UPR-RPU并联机器人和冗余驱动的2-UPR-2-RPU并联机器人位置误差和姿态误差平均值下降明显，均验证了该方法的正确性。所提方法将并联机器人的误差建模转化为等效的串联运动链的误差建模，直接将等效运动链补偿的末端位姿代入并联机器人的运动学反解即可得到驱动关节的补偿值，无需进行并联机器人的运动学正解，具有计算简单的优点。

关键词: 并联机器人, Grassmann-Cayley代数, 等效运动链, 误差建模, 运动学标定

Abstract: The error modeling of parallel robot is difficult to solve accurately because of the complex structure. In order to solve this problem, a kinematic calibration method based on equivalent kinematic chains is proposed. Firstly, the analytic expression of the twist space on the moving platform is obtained through the join and meet operators. The virtual serial kinematic chain equivalent to the twist space of the moving platform is established, and the error model can be constructed for the equivalent virtual serial kinematic chain. The end error is compensated to the end of the equivalent kinematics chain. Finally, the corresponding driving values of the end pose of the moving platform after the error compensation is calculated by the inverse kinematics of the parallel mechanisms, and compensated to the driving joints of the parallel mechanisms. Taking the 2-UPR-RPU parallel robot and 2-UPR-2-RPU redundant actuated parallel robot as examples. The twist space of the both is equivalent to an RPR serial kinematic chain. The error modeling of the virtual serial RPR kinematic chain is established, and it is verified by simulation and calibration experiments. The experimental results show that both the average position error and the average orientation error of 2-UPR-RPU and2-UPR-2-RPU parallel robots are dropped sharply, which verifies the correctness of the proposed method. This method transforms the error modeling of parallel robots into the error modeling of the equivalent serial kinematic chain. The compensation value of the driving joint can be obtained by solving inverse kinematic equations of parallel robot without any forward kinematics, which has the advantage of simple calculation.

Key words: parallel robots, grassmann-cayley algebra, equivalent kinematic chains, error modeling, kinematic calibration

中图分类号:

TD156

夏纯, 张海峰, 李秦川, 柴馨雪. 基于等效运动链的并联机器人运动学标定方法[J]. 机械工程学报, 2022, 58(14): 71-84.

XIA Chun, ZHANG Haifeng, LI Qinchuan, CHAI Xinxue. Novel Kinematic Calibration Method of Parallel Mechanisms Using the Equivalent Kinematic Chains[J]. Journal of Mechanical Engineering, 2022, 58(14): 71-84.

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基于等效运动链的并联机器人运动学标定方法

Novel Kinematic Calibration Method of Parallel Mechanisms Using the Equivalent Kinematic Chains

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