Separation method of bending and torsion in shape sensing based on FBG sensors array

This paper presents a theoretical method for separating bending and torsion of shape sensing sensor to improve sensing accuracy during its deformation. We design a kind of shape sensing sensor by encapsulating three fibers on the surface of a flexible rod and forming a triangular FBG sensors array. According to the configuration of FBG sensors array, we derive the relationship between bending curvature and bending strain, and set up a function about the packaging angle of FBG sensor and strain induced by torsion under different twist angles. Combined with the influence of bending and torsion on strain, we establish a nonlinear matrix equation resolving three unknown parameters including maximum strain, bending direction and wavelength shift induced by torsion and temperature. The three parameters are sufficient to separate bending and torsion, and acquire two scalar functions including curvature and torsion, which could describe 3D shape of rod according to Frenet-Serret formulas. Experimental results show that the relative average error of measurement about maximum strain, bending direction is respectively 2.65% and 0.86% when shape-sensing sensor is bent into an arc with a radius of 260 mm. The separating method also applied to 2D shape and 3D shape of reconstruction, and the absolute spatial position maximum error is respectively 3.79mm and 11.10mm when shape-sensing sensor with length 500mm is bent into arc shape with a radius 260mm and helical curve. The experiment results verify the feasibility of separating method, which would provide effective parameters for precise 3D reconstruction model of shape sensing sensor.