Procrustes加权整体最小二乘法在激光跟踪仪转站中的应用  

Application of Procrustes weighted overall least squares method in laser tracker transfer station

作　　者：郗唯杰 喻明让[1] 陈云 刘振宇 李保伟 Xi Weijie;Yu Mingrang;Chen Yun;Liu Zhenyu;Li Baowei(College of Aerospace Engineering,North University of China,Shanxi Taiyuan,030051,China;North Institute of Automatic Control Technology,Shanxi Taiyuan,030006,China)

机构地区：[1]中北大学航空宇航学院,山西太原030051 [2]北方自动控制技术研究院,山西太原030006

出　　处：《机械设计与制造工程》2023年第8期67-72,共6页Machine Design and Manufacturing Engineering

基　　金：山西省基础研究计划面上项目(20210302123050)。

摘　　要：在飞机大部件装配过程中,激光跟踪仪转站的关键是坐标转换。由于转站前后存在坐标测量误差,整体最小二乘法的系数矩阵存在随机误差,因此需对激光跟踪仪转站算法进行优化。提出基于Procrustes分析法的EIV-EOPA模型的Procrustes加权整体最小二乘法,建立激光跟踪仪转站模型并进行求解,采用MATLAB进行仿真并使用Leica AT403激光跟踪仪进行实验,验证方法的有效性。结果显示,Procrustes加权整体最小二乘法比加权最小二乘法获得的参数估计值更接近设定值,单位权中误差更小,提高了转站精度,同时还省略了计算中的迭代过程。实验结果进一步证实了Procrustes加权整体最小二乘法的优势。In the assembly process of large aircraft components,the key to the transfer station of the laser tracker is coordinate transformation.Due to the coordinate measurement error before and after the transfer and the random error in the coefficient matrix of the global least squares method,it is necessary to optimize the transfer algorithm of the laser tracker.The Procrustes weighted overall least squares method of the EIV-EOPA model based on the Procrustes analysis method is proposed,and the laser tracker transfer station model is established and solved.The simulation is carried out with MATLAB and the Leica AT403 laser tracker is used for experiments to verify the effectiveness of the method.The results show that the parameter estimates obtained by the Procrustes weighted overall least squares method are closer to the set values than the weighted least squares method,and the error in the unit weight is smaller,which improves the accuracy of the transfer station and omits the iterative process in the calculation.The experimental results further confirm the advantages of the Procrustes weighted overall least squares method.

关 键 词：飞机 装配 激光跟踪仪 Procrustes加权整体最小二乘法 坐标转换 

分 类 号：TH744[机械工程—光学工程]