Calibration of robot base coordinate system based on spatial polyhedron anomaly projection
-
摘要: 针对不同类型、不同位置的工业机器人基坐标标定问题,提出一种基于空间多面体异点投影基坐标标定方法。所提出基坐标标定方法借助设计的标定台,分别获取主从工业机器人在空间中不同标定点的关节角度信息,将标定点与基坐标原点在空间中构建多空间多面体,并将空间多面体向主工业机器人所在的X-Y、X-Z和Y-Z面进行投影,根据投影图形获得远距离及不同类型工业机器人之间位姿变换矩阵。通过引入高斯白噪声误差模拟实际误差,结合理论分析及MATLAB软件进行仿真实验。实验结果表明改进后的基坐标标定方法具有极高的准确性、稳定性和标定精度。Abstract: In order to solve the problem of base coordinate calibration of industrial robots with different types and positions, the base coordinate calibration method based on the projection of different points of spatial polyhedron can be adopted.The proposed base coordinate calibration method relies on the designed calibration stage, the joint angle information of the master-slave industrial robot at different calibration points in space is obtained separately, Firstly, a multispace polyhedron is constructed in space by reference point and base coordinate origin, The spatial polyhedron is projected onto the x-Y, X-Z and Y-Z planes where the industrial robot resides, Finally, the position and pose transformation matrices between different types of industrial robots are obtained according to the projection graphics. By introducing the gaussian white noise error to simulate the actual error, combined with theoretical analysis and MATLAB software simulation experiment. Experimental results show that the improved base coordinate calibration method has high accuracy, stability and calibration precision.
-
表 1 各投影面利用及求解参数
投影平面 利用求解参数 求解参数 角度参数 位置参数 位置偏移参数1 位置偏移参数2 偏移角度 X-Y面 $ {\text{γ }} $ $ {p_x} $ $ {p_y} $ $ {p_{x1}} $ $ {p_{y1}} $ $ {\gamma _{\textit{z}} } $ X-Z面 $ \beta $ $ {p_x} $ $ {p_{\textit{z}} } $ $ {p_{x2}} $ $ {p_{\textit{z}1}} $ $ {\beta _y} $ Y-Z面 $ \alpha $ $ {p_y} $ $ {p_{\textit{z}} } $ $ {p_{y2}} $ $ {p_{\textit{z}2}} $ $ {\alpha _x} $ 表 2 实验1和2加入高斯白噪声角度值
实验 振幅 标定点位置 关节1/rad 关节2/rad 关节3/rad 关节4/rad 关机5/rad 关节6/rad 实验1 0.1 标定点P1 0.628 3 −1.570 8 0 0 1.570 9 0 标定点P2 −0.628 3 −1.570 7 0 0 1.570 8 0 标定点R1 −0.448 8 0 0 0 − − 标定点R2 0.448 8 0 0 0 − − 0.5 标定点P1 0.628 3 −1.571 1 0 0 1.571 1 0 标定点P2 −0.628 4 1.571 0 0 0 1.570 5 0 标定点R1 −0.448 8 0 0 0 − − 标定点R2 0.448 8 0 0 0 − − 实验2 0.1 标定点P1 1.047 2 −1.570 8 0 0 1.570 7 0 标定点P2 −1.047 2 −1.570 9 0 0 1.570 8 0 标定点R1 −0.628 3 0 0 0 − − 标定点R2 0.628 4 0 0 0 − − 0.5 标定点P1 1.047 0 −1.570 6 0 0 1.571 1 0 标定点P2 −1.047 2 −1.750 9 0 0 1.571 2 0 标定点R1 −0.618 3 0 0 0 − − 标定点R2 0.628 4 0 0 0 − − 表 3 PRY角度参数与位置参数
实验 振幅 位置点 RPY角度参数/rad 位置参数/m $ \alpha $ $ \beta $ $ \gamma $ Px Py Pz 实验1 0.1 P1 −3.141 5 0.000 1 0.628 3 1.173 1 0.852 3 1.300 0 P2 3.141 5 0.000 1 −0.628 3 1.173 1 −0.852 3 1.300 0 R1 0 0 0.448 8 0.630 7 −0.303 7 0.300 0 R2 0 0 −0.448 8 0.630 6 0.303 7 0.300 0 0.5 P1 −3.141 6 0.000 1 0.628 3 1.172 8 0.852 0 1.300 2 P2 −3.141 3 −0.000 5 −0.628 4 1.173 0 −0.852 4 1.300 2 R1 0 0 0.448 8 0.630 7 −0.303 7 0.300 0 R2 0 0 −0.448 8 0.630 7 0.303 7 0.300 0 实验2 0.1 P1 3.141 6 −0.000 1 1.047 2 0.725 0 1.255 8 1.300 0 P2 −3.141 5 −0.000 1 −1.047 2 0.725 0 −1.255 7 1.300 1 R1 0 0 0.628 3 0.566 3 −0.411 5 0.300 0 R2 0 0 −0.628 4 0.566 3 0.411 5 0.300 0 0.5 P1 −3.141 1 0.000 5 1.047 0 0.725 3 1.255 8 1.300 0 P2 3.141 3 0.000 3 −1.047 2 0.724 9 −1.255 5 1.300 1 R1 0 0 0.628 3 0.566 3 −0.411 5 0.300 0 R2 0 0 −0.628 4 0.566 3 0.411 5 0.300 0 表 4 各投影面参数
实验 振幅 X-Y面 X-Z面 Y-Z面 $ {\gamma _{\textit{z}} } $/rad $ {P_{x1}} $/m $ {P_{y1}} $/m $ {\beta _y} $/rad $ {P_{x2}} $/m $ {P_{{\textit{z}} 1}} $/m $ {\alpha _x} $/rad $ {P_{y2}} $/m $ {P_{{\textit{z}} 2}} $/m 实验1 0.1 1.570 8 4.000 0 −1.000 0 0.000 1 4.000 0 1.000 0 0.000 0 −1.000 1 1.000 2 0.5 1.570 7 3.999 9 −0.999 7 0.000 1 4.000 0 1.000 2 0.000 1 −1.000 0 1.000 1 实验2 0.1 1.570 7 5.999 9 −4.000 1 0.000 0 6.000 0 1.000 1 0.000 1 −4.000 0 1.000 0 0.5 1.570 9 5.999 6 −3.999 8 0.000 3 5.999 7 1.000 1 0.000 2 −4.000 2 1.000 2 表 5 误差值
实验 振幅 erot/rad etran/m 实验1 0.1 0.00010 0.00014 0.5 0.00017 0.00022 实验2 0.1 0.00014 0.00014 0.5 0.00054 0.00036 -
[1] 徐意. 工业机器人协同运动控制技术的研究与实现[D]. 武汉: 华中科技大学, 2019. [2] 纪慧君, 苗鸿宾, 李孟虔, 等. 双机器人基坐标系标定方法的研究[J]. 制造技术与机床, 2021(11): 72-76. doi: 10.19287/j.cnki.1005-2402.2021.11.014 [3] 吴潮华. 多工业机器人基座标系标定及协同作业研究与实现[D]. 杭州: 浙江大学, 2015. [4] 燕浩, 程小虎, 杨正蒙, 等. 基于手眼关系与基坐标关系的协作焊接机器人标定[J]. 机械工程与自动化, 2020(4): 27-30. [5] Luo R C, Hao W. Automated tool coordinate calibration system of an industrial robot[C]. 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2018: 5592-5597. [6] 任瑜, 郭志敏, 张丰, 等. 基于非线性优化的机器人坐标系标定方法[J]. 传感器与微系统, 2020, 39(1): 6-8. doi: 10.13873/J.1000-9787(2020)01-0006-03 [7] Wu L, Ren H L. Finding the kinematic base frame of a robot by hand-eye calibration using 3d position data[J]. IEEE Transactions on Automation Science and Engineering, 2017: 314-324. [8] Ni J, Shi H, Wang M. Disturbance observer-based cooperative learning tracking control for multi-manipulators[C]. 2020 7th International Conference on Information, Cybernetics, and Computational Social Systems(ICCSS), 2020: 229-234. [9] 侯仰强, 王天琪, 李天旭, 等. 焊接机器人系统标定技术研究现状[J]. 焊接, 2017(12): 17-22,69-70.