• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2017, Vol. 53 ›› Issue (16): 190-198.doi: 10.3901/JME.2017.16.190

• 交叉与前沿 • 上一篇    下一篇

基于方差最小化原理的三维匹配数学建模与误差分析

李文龙, 谢核, 尹周平, 丁汉   

  1. 华中科技大学数字制造装备与技术国家重点实验室 武汉 430074
  • 收稿日期:2016-11-27 修回日期:2017-05-02 发布日期:2017-08-20
  • 通讯作者: 李文龙(通信作者),男,1980年出生,博士,副教授。主要研究方向为复杂曲面精密测量、机器人操作。E-mail:wlli@mail.hust.edu.cn E-mail:wlli@mail.hust.edu.cn
  • 作者简介:谢核,男,1990年出生,博士研究生。主要研究方向为曲面检测。E-mail:xiehe@mail.hust.edu.cn;尹周平,男,1972年出生,教授,博士研究生导师。主要研究方向为电子制造技术与装备、数字化智能化制造技术等。E-mail:yinzhp@mail.hust.edu.cn;丁汉,男,1963年出生,中国科学院院士,博士研究生导师。主要研究方向为数字化制造技术、机器人操作等。E-mail:dinghan@mail.hust.edu.cn
  • 基金资助:
    国家自然科学基金(51535004,91648111,51635007)和国家重点基础研究发展计划(973计划,2015CB057304)资助项目

Mathematical Modeling and Error Analysis of 3D Matching Based on Variance Minimization Principle

LI Wenlong, XIE He, YIN Zhouping, DING Han   

  1. State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074
  • Received:2016-11-27 Revised:2017-05-02 Published:2017-08-20

摘要: 三维匹配是复杂曲面零件加工余量分配与轮廓误差评估的基础,现有方法难以克服固有测量缺陷(测点分布不均、密度不均、局部缺失等)对匹配精度的影响。提出一种基于方差最小化原理的三维匹配数学建模与计算方法,可线性求解运动变量,具有二次收敛性;研究方差最小化匹配与传统TDM (Tangent distance minimization)匹配的等效条件,推导匹配参数误差和测点位置误差的定量表示;以叶片机器人磨抛视觉定位、螺旋桨桨叶加工余量分配、曲轴轮廓检测等为例验证所提方法,试验表明方差最小化方法可解决匹配目标函数倾向于满足高密度测点或噪音点平方距离最小化问题。

关键词: 法/矩通量, 方差最小化, 复杂曲面, 三维匹配

Abstract: 3D matching is the basis for machining allowance distribution and profile error evaluation of complex surface, but existing methods are hard to guarantee stable matching accuracy, due to inherent measurement defects such as uneven point distribution, uneven density and local point missing. This paper proposes a novel 3D matching method of mathematical modeling and parameter calculation based on the variance minimization principle. It can linearly calculate the motion variables during each iteration, and appear quadratic convergence. The equivalent condition between the variance minimization matching and the TDM matching is derived, and the quantitative representations of both matching parameter error and point position error are analyzed. In addition, the effectiveness of the proposed method is demonstrated by the experiments of visual localization in robot grinding, allowance distribution in propeller machining and profile analysis in crankshaft inspection. It shows that the variance minimization has the advantage of overcoming the wrong squared distance minimization with respect to the high-density points or noisy points.

Key words: 3D matching, complex surface, normal/moment flow, variance minimization

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