TCP calibration method based on spherical uniform distribution for welding robot
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摘要: 当前焊接机器人工具中心点(TCP, tool center point)采用固定参考点法标定时，存在机器人位姿选择的随机性和分布的不均匀性，为解决这一问题，提出了一种基于球面均匀分布的TCP标定方法. 以机器人自带的“六点法”为初步标定基础，创建初始测量点位形；在离线仿真环境下，采用力学斥力迭代法构建以固定参考点为球心呈球面均匀分布的虚拟点，逐组计算使虚拟机器人第六轴末端中心处于各虚拟点处，剔除其中关节角超限、连杆之间发生碰撞的情形；最后调节实际机器人到筛选后的各测量点位形，应用最小二乘球面拟合法求解最终的TCP标定结果. 结果表明，该方法使机器人姿态在各测量点绕固定参考点均匀分布，最大限度增大了各测量点之间机器人位姿的差异度，可有效提高标定精度和稳定性.Abstract: In the current fixed reference point method for calibration of welding robot tool center point (TCP), there are problems of randomness of robot posture selection and non-uniformity of distribution. For this reason, a method of TCP calibration based on spherical uniform distribution is proposed. Based on the “six-point method”, the initial measurement configuration is created at first. Then, in the off-line simulation environment, the mechanical repulsion iteration method is used to construct the virtual points with spherical uniform distribution with the fixed reference point as the center of the sphere. The end center of the virtual robot sixth axis was located at each virtual point by group calculation, and the situations of joint angle over limit and link collision are eliminated. Finally, the actual robot is adjusted to the selected measurement configurations for the final TCP calibration, and the result is solved by the least square spherical fitting method. The results show that this method can make the robot posture evenly distributed around the fixed reference point at each measuring point, and maximize the difference degree of robot posture, it is verified that this method can effectively improve the calibration accuracy.
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图 3 固定参考点球面均匀分布虚拟点的创建
Figure 3. Virtual points creation with uniform distribution on the spherical surface of a fixed reference points. (a) virtual points creation randomly on the unit sphere; (b) virtual points uniform distribution on the unit sphere; (c) virtual points mapping from the unit sphere to the reference sphere; (d) virtual points final distribution on the reference sphere formed by vector rotation transformation.
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图 6 离线编程创建并筛选理想测量点位形
Figure 6. Creating and selecting ideal measuring points by off-line programming
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图 7 标定结果精度分析
Figure 7. Accuracy analysis of calibration results. (a) absolute deviation of tool position calibration Pm components; (b) absolute error curve of
$\Delta $ components.表 1 空间点不同区域分布的球面拟合误差分析
Table 1 Spherical fitting error analysis of spatial points in different regions
分布系数a, b 条件数cond( ${{{A}}^T}{{A}}$ )位置误差 $\Delta {P_{\rm{r}}}$ 半径误差 $\Delta r$ 0.2 614.787 9 53.914 1 53.801 8 0.4 135.264 1 0.187 9 0.108 8 0.6 112.448 5 0.111 1 0.047 5 0.8 73.595 1 0.081 0 0.027 5 1.0 55.638 1 0.080 7 0.023 7 
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表 2 8个实际测量点位形的机器人末端位姿数据
Table 2 Robot end position and pose data of eight actual measurement points
位形组 末端坐标系原点位置坐标(mm) 末端坐标系姿态 ZYX欧拉角θ/(°) $x$ $y$ ${\textit{z}}$ $\alpha $ $\beta $ $\gamma $ ${P_1}$ 845.94 36.33 929.00 172.16 5.69 178.81 ${P_2}$ 844.32 −203.71 754.63 151.85 63.13 111.52 ${P_3}$ 1156.84 −273.80 837.78 −160.67 8.48 114.83 ${P_4}$ 892.07 264.87 626.98 −100.54 71.36 −45.25 ${P_5}$ 967.25 272.23 861.60 170.38 43.32 −132.83 ${P_6}$ 994.18 −169.04 959.54 −177.80 19.47 146.93 ${P_7}$ 918.90 −205.95 524.97 70.66 55.97 14.60 ${P_8}$ 1080.09 90.62 1020.30 167.39 2.66 −166.33
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表 3 TCP位置标定试验结果
Table 3 Experimental results of TCP position calibration
序号 均匀分布组(1 ~ 10组)TCP位置标定Pm值(mm) 非均匀分布组(11 ~ 20组)TCP位置标定Pm值(mm) ${P_{mx}}$ ${P_{my}}$ ${P_{mz}}$ ${P_{mx}}$ ${P_{my}}$ ${P_{mz}}$ 1 −3.63 0.94 325.77 −3.77 0.09 326.07 2 −3.77 1.33 324.71 −4.68 1.87 324.25 3 −3.44 1.54 325.01 −5.60 −0.73 324.32 4 −3.81 1.23 325.26 −4.93 1.53 324.37 5 −3.73 1.10 324.67 −4.78 −0.74 326.46 6 −3.69 1.12 325.36 −2.31 0.21 325.17 7 −3.78 1.10 325.89 −4.12 2.30 326.76 8 −3.47 1.46 325.80 −5.98 0.98 324.73 9 −3.78 1.35 324.80 −4.75 −0.04 324.68 10 −3.91 1.34 324.72 −3.80 1.45 324.46
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[1] Hong Y X, Du D, Pan J L, et al. Seam-tracking based on dynamic trajectory planning for a mobile welding robot[J]. China Welding, 2019, 28(4): 46 − 50.
[2] 余卓骅, 胡艳梅, 何银水. 薄板机器人自动焊接焊枪三维偏差的有效提取[J]. 焊接学报, 2019, 40(11): 49 − 53. doi: 10.12073/j.hjxb.2019400287 Yu Zhuohua, Hu Yanmei, He Yinshui. Effective three-dimensional deviation extraction of the welding torch for robotic arc welding with steel sheets[J]. Transactions of the China Welding Institution, 2019, 40(11): 49 − 53. doi: 10.12073/j.hjxb.2019400287
[3] Deniz C, Cakir M. High precise and zero-cost solution for fully automatic industrial robot TCP calibration[J]. Industrial Robot: An Industrial Journal, 2019, 46(5): 650 − 659. doi: 10.1108/IR-03-2019-0040
[4] Ruther M, Lenz M, Bischof H. The narcissistic robot: robot calibration using a mirror[C]//11th International Conference on Control Automation Robotics and Vision. IEEE, 2010: 169-174.
[5] Gordic Z, Ongaro C. Calibration of robot tool centre point using camera-based system[J]. Serbian Journal of Electrical Engineering, 2016, 13(1): 9 − 20. doi: 10.2298/SJEE1601009G
[6] Cai Y, Gu H, Li C. Easy industrial robot cell coordinates calibration with touch panel[J]. Robotics and Computer-Integrated Manufacturing, 2018, 50: 276 − 285. doi: 10.1016/j.rcim.2017.10.004
[7] Borrmann C, Wollnack J. Enhanced calibration of robot tool centre point using analytical algorithm[J]. International Journal of Materials Science and Engineering, 2015, 3(1): 12 − 18.
[8] 张华君, 夏超, 叶永龙. Staubli激光切割机器人工具标定[J]. 轻工机械, 2013, 31(2): 7 − 11. doi: 10.3969/j.issn.1005-2895.2013.02.003 Zhang Huajun, Xia Chao, Ye Yonglong. Tool calibration of staubli laser cutting robot[J]. Light Industry Machinery, 2013, 31(2): 7 − 11. doi: 10.3969/j.issn.1005-2895.2013.02.003
[9] 侯仰强, 王天琪, 李亮玉, 等. 基于双机器人协调焊接标定算法[J]. 焊接学报, 2017, 38(2): 92 − 96. Hou Yangqiang, Wang Tianqi, Li Liangyu, et al. Study of calibration algorithm based on dual-robot coordinate welding[J]. Transactions of the China Welding Institution, 2017, 38(2): 92 − 96.
[10] 李福运. 工业机器人TCP自标定精度叠加方法的设计与应用[J]. 机械, 2017, 44(8): 50 − 53. doi: 10.3969/j.issn.1006-0316.2017.08.012 Li Fuyun. The designation and application of TCP self-calibration precision superposition method on industrialrobot[J]. Machinery, 2017, 44(8): 50 − 53. doi: 10.3969/j.issn.1006-0316.2017.08.012
[11] 朱晓鹏, 张轲, 涂志强, 等. 基于球面拟合法的机器人与变位机位姿关系标定[J]. 焊接学报, 2013, 34(1): 41 − 44. Zhu Xiaopeng, Zhang Ke, Tu Zhiqiang, et al. Calibration of relative position and orientation between robot and positioner based on spheres fitting method[J]. Transactions of the China Welding Institution, 2013, 34(1): 41 − 44.
[12] 陈庆诚, 朱世强, 王宣银. 基于旋量理论的串联机器人逆解子问题求解算法[J]. 浙江大学学报(工学版), 2014, 48(1): 8 − 14. Chen Qingcheng, Zhu Shiqiang, Wang Xuanyin. Inverse kinematics sub-problem solution algorithm for serial robot based on screw theory[J]. Journal of Zhejiang University(Engineering Science), 2014, 48(1): 8 − 14.
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