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摘要:
小尺寸零件的表面积小、结构复杂，传统标志点拼接方法需要在零件表面人工粘贴标志点，导致表面的测量数据缺失出现孔洞。基于特征的点云拼接方法要求零件表面具有易区分的几何或距离特征，不适用于包含重复性特征的回转体零件。本文提出一种基于机械拼接的无标志点扫描测量方法，不需要粘贴标志点，不依赖于零件表面特征。首先，采用基于摄影测量的相机标定方法得到相机的高精度内外参数，重建标定板上靶点的高精度三维坐标，接着通过跟踪编码靶点的位置建立转台不同转角对应的旋转矩阵，进而解算出转轴方向向量和轴上定点坐标，实现转轴和相机的同步标定。在完成两个转轴位姿精确标定的基础上，利用转台转角构建旋转拼接矩阵，实现多视角点云粗配准。最后，基于法向迭代最近点算法(Normal Iterative Closest Point, NICP)完成点云的精配准。实验结果表明：使用靶点跟踪法标定后的两转轴夹角误差较传统的标准球拟合法低0.023°，标定后测量标准球的整体平均尺寸误差小于0.012 mm；在小尺寸零件自动化测量时，机械拼接方法在精配准后的点云拼接效果与标志点拼接方法相近，且拼接稳定性更高。机械拼接方法适用于无法粘贴标记点的小尺寸零件三维形貌测量场景。
Abstract:Small-size parts have a small surface area and complex structure. The traditional mark splicing method needs to manually paste marks on the surface of parts, resulting in missing the measurement data of the surface and becoming holes. The feature splicing method requires the surface of parts to have easily distinguishable geometric or distance features, which are not suitable for rotating parts containing repetitive features. We propose a scanning measurement method without marks based on mechanical splicing, which does not need to paste marks or depend on the surface features of parts. Firstly, the camera calibration method based on photogrammetry is used to reconstruct the high-precision three-dimensional coordinates of the target on the calibration board. By tracking the position of the coded target, the rotation matrix corresponding to different angles of the turntable is established, and the direction vector of the rotation axis and the fixed point coordinates on the axis are solved. Then the synchronous calibration of the rotation axis and the camera is completed. Secondly, based on the accurate calibration of poses of two rotation axes, the rotation mosaic matrix is constructed by using the turntable angle to realize the rough registration of multi-view point clouds. Finally, based on the Normal Iterative Closest Point (NICP) algorithm, the fine registration of the point clouds is completed. Experimental results show that the angle error between the two rotation axes calibrated by the target tracking method is 0.023° lower than that of the traditional standard ball fitting method. After calibration, the average size error of the standard ball is less than 0.012 mm. In the automatic measurement of small-size parts, the point cloud splicing effect of the mechanical splicing method after fine registration is similar to that of the mark splicing method, and the splicing stability is higher. The mechanical splicing method is suitable for the 3D topography measurement of small-size parts where the marks cannot be pasted.
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Key words:
- structured light /
- mechanical splicing /
- small-size parts /
- axis calibration /
- NICP algorithm
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图 1 无标志点扫描测量方法的流程图
Figure 1. Flowchart of the scanning measurement method without marks
图 5 标准球拟合法单个转轴位姿标定
Figure 5. Position and pose calibration of single rotation axis using standard ball fitting method
图 6 多视角点云旋转拼接原理图
Figure 6. Schematic diagram of multi-view point cloud rotation splicing
图 7 绕空间任意转轴的旋转变换关系
Figure 7. The rotation transformation relation around any rotation axis in space
图 9 桌面式数控转台光学测量系统(a)实物图及(b)示意图
Figure 9. (a) Physical setup and (b) its schematic diagram of tabletop CNC turntable optical measurement system
图 11 标准球机械拼接绝对值误差统计结果
Figure 11. Statistical results of absolute value error of standard ball mechanical splicing
图 12 小尺寸零件的点云拼接效果图
Figure 12. Point cloud splicing effect diagrams of small-size parts
表 1 相机标定内参数
Table 1. Camera calibration internal parameters
内参数 左相机 右相机 f/pixel 4666.2300 4666.5600 $ {x}_{0}/{\mathrm{pixel }}$ 47.6090 −14.4401 $ {y}_{0}/{\mathrm{pixel}} $ 10.2786 −14.5546 $ {K}_{1} $ −3.4003×10−9 −4.1734×10−9 $ {K}_{2} $ 1.1598×10−15 1.8279×10−15 $ {K}_{3} $ 1.8523×10−22 −2.2075×10−23 $ {P}_{1} $ −7.4732×10−8 1.5797×10−8 $ {P}_{2} $ 1.0306×10−8 −2.0569×10−9 $ {b}_{1} $ 1.2749×10−4 2.4643×10−6 $ {b}_{2} $ −2.2662×10−5 3.9066×10−5 
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表 2 相机标定外参数
Table 2. Camera calibration external parameters
相机编号 ${{\boldsymbol{R}}_C}$ ${{\boldsymbol{T}}_C}$ 左相机 1 0 0 0 0 1 0 0 0 0 1 0 右相机 0.8992 −0.0098 0.4374 176.2110 0.0063 0.9999 0.0094 −0.1690 −0.4374 −0.0057 0.8992 −40.5125
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表 3 标准球拟合法与本文方法的性能对比
Table 3. Comparison between standard ball fitting method and the proposed method
实验
编号标准球拟合法[22] 本文方法 夹角/
(°)点积 夹角误差/
(°)夹角/
(°)点积 夹角误差/
(°)1 89.938 0.001078 0.062 89.962 0.000666 0.038 2 89.923 0.001341 0.077 89.949 0.000883 0.051 3 89.934 0.001145 0.066 89.962 0.000658 0.038 4 89.939 0.001072 0.061 89.955 0.000786 0.045 5 89.940 0.001048 0.060 89.961 0.000686 0.039 6 89.929 0.001245 0.071 89.965 0.000604 0.035 7 89.938 0.001079 0.062 89.952 0.000838 0.048 8 89.938 0.001085 0.062 89.947 0.000922 0.053 9 89.939 0.001058 0.061 89.965 0.000606 0.035 10 89.940 0.001048 0.060 89.967 0.000583 0.033 平均 89.936 0.001120 0.064 89.959 0.000723 0.041
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