A Distance Function Based Approach for Localization and Profile Error Evaluation of Complex Surface
A Distance Function Based Approach for Localization and Profile Error Evaluation of Complex Surface
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DOI：
10.1115/1.1763186
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发表时间：
2004-08
影响因子：
4
通讯作者：
Limin Zhu;Z. Xiong;H. Ding;Y. Xiong
中科院分区：
文献类型：
--
作者：
Limin Zhu;Z. Xiong;H. Ding;Y. Xiong
本文提出了一个统一的框架，通过调整其位置（位置/方向）来将复杂刚性表面与测量的 3D 坐标数据进行最佳拟合。对于机器参考系中表示的点和其自身模型系中表示的名义表面，定义了带符号的点到表面距离函数，并研究了其性质，特别是推导了其相对于表面微分运动的增量，直至二阶。在此基础上，将复杂曲面的定位和轮廓误差评估分别表述为非线性最小二乘问题和非线性约束优化问题，并开发了序贯逼近算法来求解它们。两种算法均具有实现简单、计算效率高、鲁棒性好的优点。还提出了估计初始解和补偿探针半径的策略。示例证实了所提出方法的有效性。
This paper presents a unified framework for best-fitting of complex rigid surface to measured 3-D coordinate data by adjusting its location (position/orientation). For a point expressed in the machine reference frame and a nominal surface represented in its own model frame, a signed point-to-surface distance function is defined, and its properties are investigated, especially, its increment with respect to the differential motion of the surface, up to the second order, is derived. On this basis, localization and profile error evaluation of complex surface are formulated as a nonlinear least-squares problem and nonlinear constrained optimization problem respectively, and sequential approximation algorithms are developed to solve them. The two algorithms have the advantages of implementational simplicity, computational efficiency and robustness. Also strategies for estimating initial solution and compensating probe radius are presented. Examples confirm the validity of the proposed approach.