Three-dimensional surface shape reconstruction of fiber bragg gratings in a ring arrangement
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摘要:
为了提高柔性机器人抓握传感中掌心表面的重构精度，本文基于COMSOL仿真，在436 mm×436 mm×2 mm聚丙烯板上，采用7只经聚二甲基硅氧烷（PDMS）封装的光纤光栅（FBG）柔性传感器，选取环形布设的方式，在板末端中心与两角分别受力的情况下，使用光纤光栅解调仪采集实验中的传感器数据，并通过三次样条插值法进行连续化。设定数个平面
Y 与拟合圆环相交，计算过点函数获得三维曲面点集，实现了空间曲面的拟合可视化显示。在曲面末端中心受力时，板末端位移最小相对误差为0.549%，最大相对误差为8.300%，最小绝对误差为0.051 cm，最大绝对误差为1.255 cm，板末端两角受力时，板面重构末端位移最小相对误差为2.546％，最大相对误差为14.289％，最小绝对误差为0.005 cm，最大绝对误差为0.729 cm。实验结果为柔性机器人掌心抓握传感提供了应用基础。Abstract:To improve the accuracy of palm surface reconstruction in flexible robot grasp sensing, we conduct a COMSOL simulation to select a ring arrangement comprising of 7 fiber Bragg grating (FBG) flexible sensors packaged with polydimethylsiloxane (PDMS) on a 436 mm×436 mm×2 mm polypropylene plate. Assuming that the center and two corner ends of the plate were subjected to stress, respectively, we collected sensor data using a fiber grating demodulation instrument during the experiment. The data was continuously interpolated using cubic spline interpolation. Several planes
Y intersected with the fitting ring which created a three-dimensional surface. We calculated the point function to obtain the point set and achieve a fitting visual display of the spatial surface. When the center of the end of the surface is under stress, the plate experienced a minimum relative error of 0.549% in end displacement, with a maximum relative error of 8.300%, the minimum absolute error of 0.051 cm, and a maximum absolute error of 1.255 cm. When both corners at the end of the plate are under stress, for the end displacement of the plate reconstruction, the minimum relative error is 2.546%, and a maximum relative error is 14.289%, the minimum absolute error is 0.005 cm, and the maximum absolute error is 0.729 cm. These experimental results provide a foundation to implement palm grip sensing in flexible robots.-
Key words:
- curvature interpolation /
- surface fitting /
- FBG /
- ring arrangement /
- curvature calibration
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图 3 传感器1~7在不同曲率下的中心波长偏移量
Figure 3. Center wavelength offsets of sensors 1~7 under different curvatures
图 6 实验平台受力弯曲时的受力分布图
Figure 6. Force distribution diagram of bending experimental platform
图 9 板末端中心加载1200 g负载时的曲率随弧长的变化情况
Figure 9. Curvature change with arc length when 1200 g load is applied to the center of plate end
图 10 末端左角加载450 g负载（虚线），右角加载800 g负载（实线）时曲率随弧长的变化情况
Figure 10. Curvature changes with arc length when the left corner of the end is loaded 450 g (dotted line) and right cornor is loaded 800 g (solid line)
图 11 曲线形状重构原理
Figure 11. Schematic diagram of the principle of curve shape reconstruction
图 12 曲面重构原理
Figure 12. Schematic diagram of the principle of curve surface reconstruction
图 15 不同负载三维曲面重构拟合
Figure 15. Reconstruction and fitting of 3D surfaces under different stresses
图 16 不同重量下板末端位移对比
Figure 16. Comparison of plate end displacement under different stresses
图 17 不同重量下板末端位移相对误差
Figure 17. Relative errors of plate end displacement under different stresses
图 18 不同重量下板末端位移绝对误差
Figure 18. Absolute errors of plate end displacement under different stresses
图 19 两端负载三维曲面重构拟合
Figure 19. Reconstruction and fitting of 3D surface under stress at both ends
图 20 不同重量下板末端位移对比
Figure 20. Comparison of plate end displacement under different load’s weight
图 21 不同重量下板末端位移相对误差
Figure 21. Relative errors of plate end displacement under different load’s weight
图 22 不同重量下板末端位移绝对误差
Figure 22. Absolute errors of plate end displacement under different load’s weight
表 1 实验材料参数
Table 1. Experimental material parameters
材料名称 弹性模量/GPa 泊松比 密度/（kg·m−1） 聚丙烯板 89 0.42 910 裸光纤 72 0.17 2203 硅胶 0.01 0.48 1084 
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