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Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (8): 1457-1465    DOI: 10.3785/j.issn.1008-973X.2020.08.002
    
Prediction and compensation of robot deformation under pressure force of pressure foot
Ying-jie GUO(),Fan GU,Hui-yue DONG*(),Hai-jin WANG
Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China
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Abstract  

The industrial robot deforms under the pressure force of the pressure foot, resulting that the pressure foot slides on the workpiece surface. A robot stiffness model under the constraint of pressure foot was proposed, and the robot deformation was predicted and compensated with the model, in order to solve the above problem and improve robot positioning accuracy. The kinematics model of robot was established based on the modified Denavit-Hartenberg method. On this basis, the coupling relationship between the translational deformation of the robot end and the pressure force of the pressure foot was studied, the robot stiffness model under the constraint of pressure foot was established, and the numerical values of six joint stiffness of the robot were obtained through the joint stiffness identification experiment based on the L-M algorithm. The stiffness model was used to predict the translational deformation of the robot end at different hole positions under certain pressure force, and the theoretical hole positions were compensated off-line. Experimental results show that the average position error of the robot decreases from 0.22 mm to 0.05 mm in robotic drilling with the proposed compensation method, satisfying the requirement of positioning accuracy.



Key wordsindustrial robot      stiffness model      pressure foot      joint stiffness identification      error compensation     
Received: 28 August 2019      Published: 28 August 2020
CLC:  TP 242.2  
Corresponding Authors: Hui-yue DONG     E-mail: zju_gyj@zju.edu.cn;donghuiyue@zju.edu.cn
Cite this article:

Ying-jie GUO,Fan GU,Hui-yue DONG,Hai-jin WANG. Prediction and compensation of robot deformation under pressure force of pressure foot. Journal of ZheJiang University (Engineering Science), 2020, 54(8): 1457-1465.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2020.08.002     OR     http://www.zjujournals.com/eng/Y2020/V54/I8/1457


压脚压紧力作用下的机器人变形预测和补偿

针对工业机器人在压脚压紧力作用下由于结构变形所引起的压脚沿工件表面滑移的问题,提出压脚约束下的机器人刚度模型,并基于该模型对机器人变形进行预测和补偿,以提高机器人制孔的定位精度. 基于改进的Denavit-Hartenberg方法建立机器人运动学模型;在此基础上,通过研究机器人末端平移变形与压脚压紧力之间的相互耦合关系,建立压脚约束下的机器人刚度模型,通过基于L-M算法的关节刚度辨识实验获得机器人6个关节刚度的具体数值;应用该刚度模型预测一定压脚压紧力作用下不同孔位的机器人末端平移变形,并对理论孔位信息进行离线补偿. 试验结果表明,在采用上述方法补偿机器人滑移变形后,机器人制孔的平均位置误差由原先的0.22 mm降低到0.05 mm,满足机器人自动化制孔定位精度要求.


关键词: 工业机器人,  刚度模型,  压脚,  关节刚度辨识,  误差补偿 
i ai?1 / mm αi?1/(°) di / mm θi/(°)
1 0 0 1045 0
2 500 90 0 90
3 1300 0 0 0
4 ?55 90 1025 0
5 0 ?90 0 0
6 0 90 290 ?180
Tab.1 MOD_DH parameters of KUKA KR600 robot
Fig.1 Link coordinate system of KUKA KR600 robot
Fig.2 MOD_DH model of robot with Matlab simulation
Fig.3 Diagram of pressure force of pressure foot
Fig.4 Schematic diagram of sliding movement and sliding friction
Fig.5 Flowchart of L-M algorithm
Fig.6 Experimental system for joint stiffness identification
位姿 θ1 /(°) θ2 /(°) θ3 /(°) θ4 /(°) θ5 /(°) θ6 /(°)
1 0.64 119.15 ?34.44 68.03 0.92 119.85
2 0.45 118.01 ?35.21 34.76 1.42 152.13
3 0.38 118.90 ?34.98 18.30 1.90 169.56
4 0.25 119.65 ?33.11 69.97 0.41 125.88
5 2.10 119.43 ?32.76 121.23 3.04 65.74
Tab.2 Five different poses of robot
P / MPa F0 / N P / MPa F0 / N
0.2 798.4 0.5 1996.8
0.3 1181.6 0.6 2325.0
0.4 1608.6 ? ?
Tab.3 Five different pressure forces of pressure foot
Fig.7 Schematic diagram of sliding compensation process
组别 位姿 实际滑移/mm 理论滑移/mm
θ1/(°) θ2/(°) θ3/(°) θ4/(°) θ5/(°) θ6/(°)
1 ?51.18 85.00 ?7.05 ?85.00 49.95 ?99.25 0.24 0.28
2 ?49.36 86.27 ?14.49 ?77.03 49.40 ?102.94 0.20 0.24
3 ?47.69 86.15 ?21.44 ?67.37 50.83 ?101.28 0.19 0.21
4 ?45.80 83.41 ?2.40 ?92.21 53.61 ?95.40 0.23 0.25
5 ?43.80 87.20 ?16.84 ?67.88 51.61 ?121.12 0.20 0.22
6 ?42.21 94.21 ?9.60 ?85.02 42.88 ?99.00 0.23 0.24
Tab.4 Deformation value of slide under six groups of robot poses
Fig.8 Experimental system for compensation of pressure foot’s sliding movement
Fig.9 Robot end deflection values in different poses
组别 x0y0z0)/mm x1y1z1)/mm [(x1?x02+(y1? y02]1/2/mm
1 (1294.89,?1256.59,2052.25) (1294.92,?1256.54,2052.25) 0.06
2 (1293.29,?1177.33,1957.45) (1293.30,?1177.31,1957.45) 0.02
3 (1293.18,?1112.40,1854.43) (1293.13,?1112.39,1854.43) 0.05
4 (1437.22,?1143.03,2086.54) (1437.18,?1143.04,2086.54) 0.04
5 (1380.01,?1026.21,1972.66) (1379.98,?1026.25,1972.67) 0.05
6 (1342.29,?952.12,2187.55) (1342.22,?952.09,2187.55) 0.08
Tab.5 Robot position errors after compensation
Fig.10 Position errors before and after compensation
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