Industrial robot de-redundant measurement and error compensation considering uncertainty

doi:10.3785/j.issn.1008-973X.2025.09.021

Journal of ZheJiang University (Engineering Science)

2025, Vol. 59

Issue (9): 1975-1985 DOI: 10.3785/j.issn.1008-973X.2025.09.021

Industrial robot de-redundant measurement and error compensation considering uncertainty

Zexuan SI1,2(

),Jun ZHANG1,2,Yuting LIU1,2,He LV1,Shijie GUO1,2,*(

)

1. School of Mechanical Engineering, Inner Mongolia University of Technology, Hohhot 010051, China
2. Inner Mongolia Key Laboratory of Robotics and Intelligent Equipment Technology, Hohhot 010051, China

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Abstract

Problems in industrial robot kinematic calibration were addressed. These included measurement redundancy caused by positioning error similarity at sampling points, and kinematic parameter compensation affected by measurement uncertainty. A parameter calibration method combining de-redundant trajectory measurement and measurement uncertainty was proposed. Firstly, the spatial positioning error variation function was measured to characterize the Cartesian space similarity between the joint and the end effector, and a spatial de-redundant measurement trajectory for the ball bar instrument with multi-joint synchronous driving was constructed. Secondly, an improved moth-flame optimization algorithm (MFO) with enhanced encirclement and search strategy was developed to enhance the accuracy and efficiency of inverse kinematics and error parameter identification. Thirdly, a dynamic correction strategy for identification parameters based on measurement parameter uncertainty was formulated, and a nested optimization method for kinematic compensation parameters was established. Finally, the error compensation test results showed that based on the results of de-redundant measurement and identification, the accuracy of the robot was improved by 49.8% after error compensation without considering uncertainty, and by 53.5% after error compensation considering uncertainty. The processing test showed that after the error compensation considering the uncertainty, the size error of the impeller workpiece was reduced by 32.3% on average and the shape and position error was reduced by 38.9% on average, compared with the impeller workpiece processed before compensation.

Key words： industrial robot de-redundant measurement parameter identification measurement uncertainty error compensation

Received: 10 December 2024 Published: 25 August 2025

CLC:

TH 115

Fund: 国家自然科学基金资助项目(52365064，52365058)；内蒙古关键技术攻关项目(2021GG0255)；内蒙古自治区高等学校创新团队发展计划支持项目(NMGIRT2213)；内蒙古自治区直属高校基本科研业务费项目(ZTY2023005，JY20230043)；内蒙古自治区高等学校青年科技英才支持计划项目(NJYT23043)；内蒙古自然科学基金资助项目(2023LHMS05018，2023LHMS05017)；内蒙古自治区“英才兴蒙”工程团队项目(2025TEL02).

Corresponding Authors: Shijie GUO E-mail: 1075385743@qq.com;sjguo@imut.edu.cn

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Cite this article:

Zexuan SI,Jun ZHANG,Yuting LIU,He LV,Shijie GUO. Industrial robot de-redundant measurement and error compensation considering uncertainty. Journal of ZheJiang University (Engineering Science), 2025, 59(9): 1975-1985.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.09.021 OR https://www.zjujournals.com/eng/Y2025/V59/I9/1975

工业机器人去冗余测量与考虑不确定度的误差补偿

针对工业机器人运动学标定过程中采样点定位误差相似性导致的测量冗余、运动学参数补偿受测量不确定性影响的问题，提出去冗余轨迹测量与虑及测量不确定度的参数校准方法. 通过测量空间定位误差变差函数进行关节-末端执行器笛卡尔空间相似性表征，构建多关节同步驱动的球杆仪空间去冗余测量轨迹；构建包围与搜索策略改进的飞蛾火焰优化算法(MFO)，以提升运动学逆解及误差参数辨识的精度与效率；建立基于测量参数不确定度的辨识参数动态修正策略，构建运动学补偿参数嵌套寻优方法. 误差补偿试验结果表明，基于去冗余测量与辨识结果，进行未考虑不确定度的误差补偿后，机器人定位精度提升49.83%，进行考虑不确定度的误差补偿后，相对于补偿前，机器人定位精度提升53.47%. 加工试验表明，进行考虑不确定度的误差补偿后，所加工叶轮工件相较于补偿前加工的叶轮工件，尺寸误差平均减小32.3%，形位误差平均减小38.9%.

关键词： 工业机器人, 去冗余测量, 参数辨识, 测量不确定度, 误差补偿

Fig.1 Industrial robot and its joint coordinate system

Tab.1 Robot kinematics modeling parameters

Tab.2 Error model parameters comparison

Tab.3 Influence rates of error parameters

Tab.4 Robot parameter table with errors

Fig.2 Comparison of iterative curves of algorithms

Tab.5 Random error parameters

Fig.3 Variation function values of positioning error

Fig.4 Mean and variance curves of sampling point error

Fig.5 Measurement trajectory diagram

Fig.6 Moth flame identification algorithm flow chart

Fig.7 Nested compensation algorithm flow chart

Fig.8 De-redundant trajectory measurement site

Fig.9 Uncertain interval scatter plot of sampling points

Fig.10 Iterative comparison of algorithms with different population numbers

Tab.6 Identification and parameter correction values

Fig.11 Comparison of effects before and after measurement trajectory compensation of ball bar instrument

Tab.7 Comparison of trajectory error and efficiency of manipulator considering and not considering uncertainty compensation

Fig.12 Processing inspection and comparison


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