机器人运动学标定中的轴拟合方法改进及精度分析

Improvement and Accuracy Analysis of the Axis Fitting Method in Robot Kinematics Calibration

轴旋转法中轴线拟合精度决定着标定后机器人的绝对定位精度,本文采用两种轴线拟合方法并分析其拟合精度。第一种是传统的拟合方法,将测量点拟合为圆,用过圆心的法向量作为机器人轴线。第二种是改进的拟合方法,利用测量点拟合球和平面,得到拟合球和平面的截交圆。为了避免传统方法中过圆心法向量微小的误差带来大的几何参数标定误差,采用双截交圆圆心的连线作为机器人轴线。通过与激光跟踪仪自带软件拟合结果比较,拟合的截交圆圆心具有更高的精度。分别采用第一、第二轴轴线向量,第一轴轴线向量以及第二轴轴线向量在第一轴垂直面上的投影作为机器人基坐标系的方向向量,构建将测量点从测量系统转换到机器人系统中的转换矩阵,通过对两种转换矩阵转换后的测量点差值比较,直接采用第二轴轴线作为基坐标系方向向量的转换矩阵具有较大的测量点转换误差。

The central axis fitting accuracy of the axis rotation method determines the absolute positioning accuracy of the calibrated robot.In this study,two kinds of axis fitting methods are used,and their fitting accuracies are analyzed.The first kind is the traditional fitting method,which fits the measuring point as a circle and uses the normal vector through the center of the circle as the axis of the robot.The second kind is the improved fitting method,which uses the measuring point to fit the sphere and plane,and obtains the intersecting circle of the fitted sphere and plane.In order to avoid the large geometric parameter calibration error caused by the small error of the over-center normal vector in the traditional method,the line of the center of the double intersecting circle is used as the axis of the robot.Compared with the fitting results of the laser tracker software,the fitted center of the intersecting circle has higher accuracy.The axis vectors of the first and the second axes are used,the axis vector of the first axis and the projection of the axis vector of the second axis on the vertical plane of the first axis are respectively used as the direction vector of the robot base coordinate system,and the conversion matrix of the measurement point from the measurement system to the robot system is constructed.By comparing the measurement point difference after conversion of the two conversion matrices,the conversion matrix using the second axis directly as the base coordinate system direction vector has a large measurement point conversion error.