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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (7): 1316-1324    DOI: 10.3785/j.issn.1008-973X.2020.07.009
    
Kinematic calibration for robots based on relative accuracy
Chen-tao MAO1(),Zhang-wei CHEN1,*(),Xiang ZHANG2,3,Hong-fei ZU4
1. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China
2. School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310000, China
3. Hangzhou Econ Technologies, Hangzhou 310011, China
4. School of Mechanical Engineering and Automation, Zhejiang Sci-tech University, Hangzhou 310000, China
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Abstract  

A kinematic calibration method for structure parameters based on the relative accuracy was proposed by using the robust minimax optimization theory in order to meet the requirements of high relative accuracy for industrial robots in the application fields of laser cutting, arc welding and so on. The relative orientation accuracy between two successive configurations was guaranteed by minimizing the worst relative positioning errors corresponding to the three target spheres, and a nonlinear optimization problem with constraints was established. Then the original problem was approximated by using a quadratic sequence programming method, and a primal-dual subgradient algorithm was introduced to search the local optimal solution quickly under inequality constraints. The structural parameter errors of the robot introduced in the process of manufacturing and assembly were identified. The compensation and verification were conducted. The experimental results showed that the relative positioning and orientation accuracies of the six-axis robot IRB2600 increased by 67.98% and 24.32%, and the seven-axis robot IRB14000 improved by 90.61% and 74.61%, respectively.

Key words： kinematic calibration      relative accuracy      minimax optimization      industrial robot     
Received: 03 January 2020      Published: 05 July 2020
CLC:  TP 241  
Corresponding Authors: Zhang-wei CHEN     E-mail: mct@zju.edu.cn;chenzw@zju.edu.cn
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Chen-tao MAO
Zhang-wei CHEN
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Hong-fei ZU
Cite this article:

Chen-tao MAO,Zhang-wei CHEN,Xiang ZHANG,Hong-fei ZU. Kinematic calibration for robots based on relative accuracy. Journal of ZheJiang University (Engineering Science), 2020, 54(7): 1316-1324.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2020.07.009     OR     http://www.zjujournals.com/eng/Y2020/V54/I7/1316


基于相对精度指标的机器人运动学校准

针对工业机器人在激光切割、弧焊等应用领域对相对精度的指标要求，结合鲁棒的极小极大优化理论，提出基于相对精度指标的运动学结构参数校准方法. 通过最小化3个靶球对应的最差相对定位误差，保障前、后两位型间的相对定向精度，构建包含约束的非线性优化问题；使用二次序列规划方法对原问题进行近似，通过主二元子梯度算法在满足不等式约束的条件下快速搜索局部最优解，实现对由于部件制造和装配等环节引入机器人结构参数误差的辨识. 进行补偿并精度验证后的实验结果表明，六轴机器人IRB2600的相对定位及定向精度分别提升了67.98%和24.32%，七轴机器人IRB14000分别提升了90.61%和74.61%.


关键词： 运动学校准,  相对精度,  极小极大优化,  工业机器人 
Fig.1 End-points of robots and its DOF analysis
位型数 n g M 位型数 n g M
2 5 6 6 4 7 12 0
3 6 9 3 k 3+k 3k 12?3k
Tab.1 DOF analysis of virtual mechanical system corresponding to different numbers of configurations
Fig.2 Linearization of distance errors between two end-points
序号 ${a_i}/{\rm{mm}}$ ${d_i}/{\rm{mm}}$ ${\theta _i}/(^\circ )$ ${\alpha _i}/(^\circ) $
1 150 445 0 ?90
2 900 0 ?90 0
3 150 0 0 ?90
4 0 938 0 90
5 0 0 180 90
6 0 200 0 0
Tab.2 Nominal DH parameters for robot IRB2600
Fig.3 Measurement process of end-points for IRB2600
Fig.4 Relative positioning accuracy before calibration
方法 精度指标 优化方法 约束条件 姿态处理
本文方法 相对 SQP，主二元 有 最小化最差情况
文献[7]方法 相对 高斯牛顿，SVD 无 无
文献[10]方法 绝对 高斯牛顿 无 最小化位姿误差
文献[11]方法 绝对 高斯牛顿，LM 无 无
Tab.3 Comparison on different calibration methods
方法 Δd1)/% Δo/%
[0, 0.2] mm [0, 0.4] mm [0, 0.002] rad [0, 0.004] rad
注：1) 表示只列出3个靶球对应指标中最差的一项.
校准前 17.43 33.90 16.79 61.07
本文方法 51.03 82.81 44.63 92.53
文献[7]方法 50.63 80.59 29.62 82.32
文献[10]方法 51.07 81.03 38.26 86.30
文献[11]方法 49.21 79.66 28.34 76.73
Tab.4 Frequency distribution of relative accuracy in different specific intervals on IRB2600
Fig.5 Relative positioning accuracy after calibration
方法 RMSd1)/mm Δdmax /mm RMSo /rad Δomax /rad
注：1) 表示只列出3个靶球对应指标中最差的一项.
校准前 1.195 1 3.726 7 0.003 9 0.009 2
本文方法 0.293 2 1.193 4 0.002 5 0.007 4
文献[7]方法 0.318 4 1.413 8 0.003 1 0.008 5
文献[10]方法 0.312 8 1.488 1 0.002 9 0.008 4
文献[11]方法 0.332 3 1.589 7 0.003 3 0.009 0
Tab.5 Relative accuracy with different methods on IRB2600
方法 Δd1)/% Δo/%
[0, 0.3] mm [0, 0.6] mm [0, 0.005] rad [0, 0.01] rad
注：1) 表示只列出3个靶球对应指标中最差的一项.
校准前 3.37 7.01 2.30 12.48
本文方法 71.39 94.79 63.96 99.84
文献[7]方法 57.07 86.89 13.17 34.85
文献[10]方法 65.82 92.18 30.10 86.08
文献[11]方法 65.74 92.16 29.96 85.70
Tab.6 Frequency distribution of relative accuracy in different specific intervals on IRB14000
方法 RMSd1)/mm Δdmax /mm RMSo /rad Δomax /rad
注：1) 表示只列出3个靶球对应指标中最差的一项.
校准前 5.560 9 13.519 0.023 3 0.044 5
本文方法 0.296 0 1.270 1 0.004 8 0.011 3
文献[7]方法 0.396 4 1.494 8 0.014 2 0.025 3
文献[10]方法 0.334 4 1.258 7 0.007 4 0.014 9
文献[11]方法 0.334 7 1.260 0 0.007 4 0.014 9
Tab.7 Relative accuracy with different methods on IRB14000
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