Updated shape sensing algorithm for space curves with FBG sensors

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.