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, this study conducts 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. The plate experienced a minimum relative error of 0.549% in end displacement, with a maximum relative error of 8.300%. the center of the surface’s end yielded a 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, a minimum relative error of 2.546%, and a maximum relative error of 14.289% arise in plate reconstruction end displacement. 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.
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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实验平台受力弯曲受力分布图
Figure 6.Distribution diagram of bending force on experimental platform
图 10末端左角450 g（上），右角800 g（下）
Figure 10.450 g at the left corner of the end (upper), 800 g at the right corner (lower)
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 13曲面三维重构算法流程
Figure 13.Schematic diagram of the surface 3D reconstruction algorithm flow
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 stresses
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 stresses
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 stresses
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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