3D shape sensing with multicore optical fibers: transformation matrices vs Frenet-Serret equations for real-time application

This paper presents the characterization of an algorithm aimed at performing accurate fiber optic-based shape sensing. The measurement of the shape relies on the evaluation of the strains applied to an optic fiber in order to identify relevant spatial parameters, such as the curvature radii and bending direction, which define its shape. The measurement system is based on a 7-core multicore fiber, containing up to 9 triplets of fiber Bragg grating sensors (FBGs) organized around a central core used as reference. The proposed study aims at comparing the widely used Frenet-Serret equations with an algorithm based on the homogeneous transformation matrices that are normally used in robotics to express the position of a point in different frames, i.e. from local to global coordinates. The numerical results of the performed experiments (with different multicore fibers and setups) extensively prove the superiority of the alternative method over the Frenet-Serret equations in terms of finding a trade-off between accuracy and execution time.