Abstract: Relocalization-based eye-hand calibration algorithm was proposed to solve the problems of manual errors and quadratic errors in hand-eye calibration in robotic grinding systems. Taking the photographic 3D scanner as the calibration object, the hand-eye calibration mathematical model of the robot was analyzed, and then the calibration scheme was constructed by using the criterion sphere that moved around tool center point in robot end-effector coordinate frame. By virtue of the least square method, the relocalization center coordinate in the scanner coordinate frame was calculated, both translation vector and rotation matrix were calibrated by using the quaternion-based multi-space points coupling, and then the conversion matrix from scanner coordinate frame to robot base coordinate frame was obtained. Both of the hand-eye calibration and blade grinding experiments shows that the sphere fitting radius deviation of the proposed algorithm reduces to 0.068 mm, which is reduced by at least 38% compared with the existing algorithms. Meanwhile, the average blade surface roughness value Ra after grinding is reduced to 0.273 μm from the value of 2.5 μm after milling operation, and the profile errors reach within ±0.08 mm, which meet the technical requirements, thereby the proposed method is verified to be effective and accurate. 

Key words: hand-eye calibration, robotic grinding, complex blade, relocalization, quaternion-based algorithm

摘要： 针对叶片机器人磨抛系统中手眼标定存在人工误差、二次误差等因素导致标定精度差等问题，提出了一种基于“重定位”的手眼标定算法。以拍照式三维扫描仪为标定对象，分析机器人手眼标定数学模型，提出利用标准球在机器人末端坐标系中绕工具中心点做定点变位姿运动的标定方案。通过最小二乘法计算扫描仪坐标系下的“重定位”中心坐标，并根据多空间点四元数耦合方法，同时完成平移和旋转矩阵的标定，进而得到扫描仪坐标系到机器人基坐标系的转换矩阵。手眼标定和叶片磨抛实验结果表明，所提算法的球拟合半径较标准球半径偏差降至0.068 mm，较现有算法标定误差降低至少38%，同时磨抛后的叶片表面粗糙度Ra平均值由磨抛前的2.5 μm降至0.273 μm，型面误差在±0.08 mm以内，满足叶片制造工艺要求，从而验证了所提标定算法的有效性和准确性。

关键词: 手眼标定, 机器人磨抛, 复杂叶片, 重定位, 四元数法