FBG shape sensors have become a research hotspot in optic fiber sensing. Compared with other shape reconfiguration technologies, they have a series of advantages such as compact structure, high flexibility, resistance to harsh environments and corrosion, and reusability. With the development of FBG shape sensing technology, the requirements for the reconfiguration accuracy of frequency selective surface are more stringent. The laying angle deviation and calibration error of FBG seriously affect the measurement accuracy of curvature and bending direction, resulting in errors in the shape reconstruction of FBG shape sensors. At present, the calibration coefficient or calibration matrix is the main method to correct the measurement curvature and error bending direction errors. Based on the quantitative analysis of experimental processes, this method reduces the experiment randomness through repeated operations. There are problems such as high experimental complexity, insufficient applicability and experimental repeatability, and lack of strict theoretical model support. Therefore, it is necessary to study the correction methods of measurement curvature error and bending direction errors caused by the FBG laying angle deviation and calibration error and propose a more adaptable, more convenient, and smarter error correction method.

We build a curvature and bending direction error correction model of the FBG shape sensor and a self-correction model of FBG laying angle deviation and calibration error. According to the Frenet-Serret framework, the functional relationship between the curvature and bending direction of the detection point with the FBG laying angle deviation and calibration error is deduced. An improved artificial rabbit optimization (ARO) algorithm is adopted to self-correct the FBG laying angle and calibration coefficient of the shape sensor, which is performed during calibration. Then, the corrected laying angle and calibration coefficient are substituted into the error correction model to correct the curvature and bending direction of the detection point. Meanwhile, ANSYS simulation and self-made shape sensor reconfiguration experiments are employed to verify the error correction model. During the experiment, the FBG shape sensor is fixed into different shapes by the 3D printed model, the sensor shape is reconstructed by the curvature and bending direction after error correction, and the reconstruction results are compared with those without error correction.

The self-calibration model, curvature error correction model, and bending direction error correction model are verified by the simulation model under different FBG laying angle deviations and calibration errors. The results show that the self-calibration model can simply and efficiently optimize the laying angle deviation and calibration coefficient of FBG (Table 1), and substituting the optimized parameters into the correction model improves the measurement accuracy of the curvature and bending direction of the detection point (Fig. 7). The model practicability is verified by the self-made FBG shape sensor reconfiguration experiment. After laying angle deviation and calibration error correction, the measurement error of curvature and bending direction is reduced, with improved reconstruction accuracy of the FBG shape sensor. The tail point reconfiguration errors of the shape sensor in different forms are reduced from 11.66 mm, 14.42 mm, and 22.6 mm to 4.43 mm, 5.67 mm, and 9.57 mm respectively, and the relative errors are from 2.56%, 3.1%, and 4.96% to 0.95%, 1.22%, and 2.06%.

We propose the correction model of measurement curvature error and bending direction error of FBG shape sensors. The functional relationship between the measured curvature and bending direction and FBG laying angle and calibration coefficient is deduced theoretically, and a new calculation method for curvature and bending direction is proposed. Additionally, we build a self-correction model based on the ARO optimization algorithm to solve the difficult correction of FBG laying angle deviation and calibration error. We validate the self-correcting and error-correcting models using simulations and shape reconfiguration experiments. The results show that the proposed method can simply and effectively correct the curvature and bending direction of the detection point, and further improve the reconfiguration accuracy of the shape sensor. We propose a new calculation method of curvature and bending direction, and a new calibration coefficient of FBG and a correction method of laying angle deviation. This method is simpler and more efficient than the existing methods, greatly improving the operability and reproducibility of experiments. Meanwhile, it can obtain the bending direction with less measurement data, which reduces the complexity of experiments and data processing.