非正交轴系激光经纬仪反向运动学线性模型  

Linear Model of Inverse Kinematics for Non-Orthogonal Shafting Laser Theodolite

作　　者：孙泽峰 康杰虎[1] 梁健 张振[1] 冯橹源 吴斌[1] Sun Zefeng;Kang Jiehu;Liang Jian;Zhang Zhen;Feng Luyuan;Wu Bin(State Key Laboratory of Precision Measurement Technology and Instruments,Tianjin University,Tianjin 300072,China)

机构地区：[1]天津大学精密测试技术及仪器全国重点实验室,天津300072

出　　处：《光学学报》2024年第2期204-212,共9页Acta Optica Sinica

基　　金：国家自然科学基金(62071325);天津市交通运输科技发展项目计划(2022-09);光纤传感与系统北京实验室开放课题(GXKF2022001)。

摘　　要：为满足大尺寸测量仪器性能与制造水平提升的需求,基于非正交轴系架构理念对激光经纬仪进行设计。针对非正交轴系经纬仪在无参考末端情况下计算反向运动旋转角度的难题,提出反向运动线性模型,以实现旋转角度的快速、高精度计算。首先,基于李群李代数基本理论构建非正交轴系经纬仪正向运动学模型。其次,构建空间目标点与视准轴位姿参数间的约束关系,并结合旋转角度误差传递模型,确立用于求解旋转角度误差修正值的线性方程组。最终通过旋转角度初始估计值与误差修正值线性相加,获取高精度的反向旋转角度值。仿真结果表明,该方法所计算的旋转角度误差趋近于0,真实实验的旋转角度误差均小于0.02 mrad,验证了所提反向运动学线性模型的可行性与实用性。Objective The developing modern economy and manufacturing industry have put forward a higher demand for related measuring instruments.However,the requirements for orthogonality of internal structures increase the difficulty of instrument manufacturing,and the production efficiency is reduced.To break through the limitations in the production and manufacturing of large-scale measuring instruments in China,the concept of non-orthogonal shafting measuring instruments is proposed.This kind of instrument does not require the shafting to be perpendicular or intersecting with each other,and the non-orthogonal shafting laser theodolite(N-theodolite)is a typical non-orthogonal shafting instrument.Much research has explored its measurement performance and related theories.However,due to the lack of the reference end on the laser axis for a single N-theodolite,the inverse kinematics model fails to be established accurately.The inverse kinematics model is necessary for precision theory research,which is convenient for data simulation of error spatial distribution.Besides,the guidance technology based on the inverse model can help improve the automatic measurement function of the N-theodolite.Therefore,to address the difficulty of calculating the rotation angle for the N-theodolite in inverse motion without a reference end,the linear model for the inverse motion to achieve fast and high-precision calculation of the rotation angle is proposed in this paper.Method In this paper,the basic theory of Lie groups and Lie algebras is introduced to achieve fast and high-precision calculation of the rotation angle.First,based on the theory of Lie groups and Lie algebras,the kinematics model of the Ntheodolite can be constructed.The coordinate transformation matrix is represented as the product of the exponentials formula(POE)with clear physical meanings.Second,the error model of N-theodolite can be obtained through the corresponding differential calculations,and the parts related to the rotation angle error component are preserved.Then

关 键 词：光学仪器 非正交轴系 反向运动 线性模型 误差传递 

分 类 号：TH721[机械工程—仪器科学与技术]