Three-Dimensional Curve Reconstruction Based on Material Frame and Twisted Multicore Fiber

Abstract

We propose a curve reconstruction model based on material frame and twisted multicore fiber (MCF), which can reconstruct the position and orientation of MCF simultaneously. The twisted MCF is approximated as a ribbon, whose centerline and surface characteristics are used to characterize the position and orientation of MCF. Material frame corresponding to the ribbon is established, and quantitative analysis is realized by the differential equations between frame basis vectors and fiber deformation parameters. Bending, twisting-strain model is established according to the approximate development of the twisted MCF, and the deformation parameters are obtained. Further, position and orientation of MCF can be reconstructed under the interference of twisting deformation. In simulation, the influence of curvature, torsion of target curves and twist bias, twisting deformation of MCF on curve reconstruction is analyzed. The results indicate that the proposed model is applicable to curves with zero curvature and variable curvature. With 10 rad/m sinusoidal twisting deformation, the deterioration of reconstruction accuracy can be effectively suppressed by introducing twist bias into MCF. For S-shaped curve with curvature and torsion within 1–50 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> and −10-10 rad/m, the tip position error and tip orientation error are less than 5 mm and 5 mrad over the length of 1 m.