Absolute Position Accuracy Calibration Algorithm for Robots Based on Joint Geometric Error

doi:10.12068/j.issn.1005-3026.2025.20230303

Abstract

Abstract:

An industrial robot kinematic model with joint geometric error parameters and a calibration algorithm is proposed. Firstly， based on the DH model， six geometric error parameters are introduced for each joint to establish a more comprehensive error calibration model. The solutions of forward and inverse kinematic for the model are realized. Then， a differential kinematic Jacobian matrix containing 45 parameters， including joint errors， base coordinate errors， and tool coordinate errors is established. An iterative algorithm based on a small sample test set is used to solve the error parameters. Finally， experimental verification is carried out using a laser tracker on the SIASUN SR10C robot. The calibrated error parameters are then compensated into the model. Results show that， after calibration compensation， the maximum position error of the robot decreases by approximately 80%， the average position error decreases by approximately 80%， and the error variance decreases by approximately 97%， demonstrating that this method can significantly improve the absolute position accuracy and determinacy of industrial robots.

Key words: industrial robot, absolute position accuracy, kinematic model, geometric error, calibration

CLC Number:

TP 242

Liang LIANG, Cheng-dong WU, Shi-chang LIU. Absolute Position Accuracy Calibration Algorithm for Robots Based on Joint Geometric Error[J]. Journal of Northeastern University(Natural Science), 2025, 46(4): 1-7.

Figures/Tables 13

Fig.1 Diagram of robot kinematic coordinate system

Fig.2 Diagram of joint coordinate system with geometric error

Fig.3 Diagram of error kinematics inverse solution process

Fig.4 Diagram of joint geometric error calibration process

Fig.5 Schematic diagram of experimental platform

Table 1 Parameters of experiment platform

设备	主要参数	参数值
机器人	额定载荷/kg	10
	工作范围/mm	1 393
	重复定位精度/mm	0.05
	减速器	LHSG， LHD系列
机器人控制器	处理器	E3845，4核， 1.91 GHz
	操作系统	Real Time Linux
	算法运算周期/ms	4
激光跟踪仪	测量范围/m	2~80
	精度/(mm·m^-1)	0.095+0.005
	分辨率/μm	0.5

Fig.6 Curves of joint angle values in the each test set

Fig.7 Spatial distribution diagram of test results (measuring coordinate)

Table2 List of calibration results

项目	$o x$ /mm	$o y$ /mm	$o z$ /mm	$α$ ×10³/rad	$β$ ×10³/rad	$γ$ ×10³/rad
关节1	0	0	0	0	0	0
关节2	0.116	0	0	0.080	-0.370	0
关节3	0	0	0.599	0.098	1.120	-0.060
关节4	0	0.221	0.015	0.520	0	0
关节5	-0.234	0	-0.068	0	0.150	0.260
关节6	0	0.020	-0.068	0	0	0.090
基坐标	4 418.2	-418.2	1 100.9	-0.9	-4.6	-3 085.0
工具坐标	0.294	-0.169	-0.100	—	—	—

Table2 List of calibration results

项目	$o x$ /mm	$o y$ /mm	$o z$ /mm	$α$ ×10³/rad	$β$ ×10³/rad	$γ$ ×10³/rad
关节1	0	0	0	0	0	0
关节2	0.116	0	0	0.080	-0.370	0
关节3	0	0	0.599	0.098	1.120	-0.060
关节4	0	0.221	0.015	0.520	0	0
关节5	-0.234	0	-0.068	0	0.150	0.260
关节6	0	0.020	-0.068	0	0	0.090
基坐标	4 418.2	-418.2	1 100.9	-0.9	-4.6	-3 085.0
工具坐标	0.294	-0.169	-0.100	—	—	—

Fig.8 Error of position measurement values compared to theoretical values before and after calibration

Fig.9 Probability distribution of position measurement error before and after calibration

Fig.10 Error between measured and theoretical position values for the validation set

Fig.11 Probability distribution of position measurement error before and after calibration

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