Abstract When the terminal position and shape detection properties of a fiber Bragg grating (FBG) curve sensor are used in medicine, the positioning accuracy of the FBG curve sensor is critical in the prediagnosis and treatment of diseases. To improve the shape reconstruction accuracy, two updated reconstruction algorithms are proposed based on the error accumulation of a single-point recursive reconstruction algorithm according to the Frenet coordinate system. First, the motion coordinate system depends on the curve and tangent vector. Next, the curvature vector is synthesized in the motion coordinate system on the close plane, the motion coordinate transformation matrix of the discrete point is calculated in the close plane, and the relevant formula is deduced subsequently. Finally, the improved algorithms are verified out. Experimental results indicate that the proposed algorithms improved the terminal position accuracy. Compared with the single point recursive algorithm, in a single bending experiment, the maximum shape errors of the terminal position are 2.65% and 2.53% using the fitting method of multipoint curvature and nonfixed point fitting method based on the Frenet frame, respectively. In double bending experiment, the maximum shape errors of the applied improved algorithms are 2.74% and 2.60%, respectively, which exhibit good planar shape reconstruction accuracy. In an out-of-plane three-dimensional shape reconstruction experiment, the maximum shape errors of these two improved methods are 3.40% and 3.32%, respectively. The improved algorithms provide an algorithm basis for the improvement of space curve reconstruction accuracy, and they can be applied in the detection of wing deformation structure and real-time detection of soil deformation in shield engineering.

中文翻译：

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使用 FBG 传感器更新空间曲线的形状传感算法

摘要 光纤布拉格光栅（FBG）曲线传感器的终端位置和形状检测特性在医学上应用时，FBG曲线传感器的定位精度对疾病的预诊和治疗至关重要。为了提高形状重建精度，基于Frenet坐标系单点递归重建算法的误差累积，提出了两种更新的重建算法。首先，运动坐标系取决于曲线和切线矢量。接下来，在近平面上的运动坐标系中合成曲率矢量，在近平面上计算离散点的运动坐标变换矩阵，然后推导出相关公式。最后对改进后的算法进行了验证。实验结果表明，所提出的算法提高了终端定位精度。与单点递归算法相比，在单次弯曲实验中，采用多点曲率拟合方法和基于Frenet框架的非定点拟合方法，终端位置的最大形状误差分别为2.65%和2.53%。在双弯曲实验中，应用改进算法的最大形状误差分别为2.74%和2.60%，表现出良好的平面形状重建精度。在平面外三维形状重建实验中，这两种改进方法的最大形状误差分别为3.40%和3.32%。改进后的算法为空间曲线重建精度的提高提供了算法基础，