基于拉格朗日乘子法的空间圆弧拟合优化方法  

Spatial arc fitting optimization method based on Lagrangian multiplier method

作　　者：化春键 熊雪梅 陈莹[3] HUA Chun-jian;XIONG Xue-mei;CHEN Ying(School of Mechanical Engineering,Jiangnan University,Wuxi 214122,China;Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment&&.Technology,Wuxi 214122,China;School of Internet of Things Engineering,Jiangnan University,Wuxi 214122,China)

机构地区：[1]江南大学机械工程学院,江苏无锡214122 [2]江苏省食品先进制造装备技术重点实验室,江苏无锡214122 [3]江南大学物联网工程学院,江苏无锡214122

出　　处：《工程设计学报》2018年第6期661-667,共7页Chinese Journal of Engineering Design

基　　金：国家自然科学基金资助项目(61573168)

摘　　要：针对传统的空间圆弧拟合方法鲁棒性低、拟合精度不高等问题,提出了一种鲁棒性较强的空间圆弧拟合优化方法。首先,以拉格朗日乘子法为基础,基于平面条件约束建立目标函数,从而得出空间圆弧拟合方程;其次,采用RANSAC(random sample consensus,随机抽样一致)算法剔除错误跟踪点,将RANSAC算法的高稳定性应用到空间圆弧拟合的点云优化中,进而提高拟合精度。最后,通过实验分析验证了所提空间圆弧拟合优化方法的可行性,并与传统拟合方法进行比较,分析所提方法的拟合精度。实验结果表明:普通圆弧点云拟合的相对精度在0.003左右,复杂圆弧点云拟合的相对精度在0.01左右;相较于传统拟合方法,所提方法有效解决了拟合精度低及鲁棒性差等问题。研究结果表明提出的空间圆弧拟合优化方法一方面可运用拉格朗日乘子法增强鲁棒性,另一方面可通过采用RANSAC方法剔除错误点以提高拟合精度,具有广泛的工程实际应用价值。Aiming at the problems that the traditional spatial arc fitting method has poor robustness and low fitting accuracy,a robust spatial arc fitting optimization method is proposed.Firstly,on the basis of Lagrangian multiplier method,the objective function was established based on the constraint of the plane condition,and then the spatial arc fitting equation was derived.Secondly,the error tracking point was eliminated by using the RANSAC(random sample consensus)algorithm,which applied the high stability of RANSAC to the point cloud optimization of spatial arc fitting to improve the fitting accuracy.Finally,the feasibility of the proposedspatial arc fitting optimization method was verified by experimental analysis,and the fitting accuracy of the proposed method was analyzed through comparing with the traditional fitting method.The experimental results showed that the relative accuracy of ordinary arc point cloud fitting was about 0.003,and the relative accuracy of complex arc point cloud fitting was about 0.01.Compared with the traditional fitting method,the proposed method effectively solved the problems oflow fitting accuracy and poor robustness.The research results indicate that the proposed spatial arc fitting optimization method can enhance robustness by using Lagrange multiplier method and improve fitting accuracy by using RANSAC algorithm to eliminate the error points,which has a wide range of practical engineering application.

关 键 词：三维测量 空间圆弧拟合 拉格朗日乘子法 RANSAN算法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]