A Robust Graph-Based Framework for 3-D Shape Reconstruction of Flexible Medical Instruments Using Multi-Core FBGs

This paper proposes a novel graph-based framework for 3-D shape sensing of flexible medical instruments using multi-core fiber Bragg grating (FBG) sensors. Due to noisy signals, deformability of instruments, and environmental disturbances, conventional shape sensing methods using direct FBG measurements are far from accurate and stable, especially for long devices. The localization errors will substantially accumulate with the increase of sensing lengths. To tackle this challenge, we propose a generic 3-D shape graph to optimize the entire shape of flexible instruments globally and account for the accumulative errors in both spatial and temporal domains. By leveraging the geometry configurations of FBG cores as the measurement model, a robust dynamic filtering approach is introduced for iterative curvature and twist estimation, which guarantees edge constraints of the graph-based shape optimization. Dedicated experiments are processed to validate our sensing approach in both structured and unstructured environments, where a robotic-assisted colonoscope system embedded with a multi-core FBG fiber is manipulated for the evaluations of bending as well as paths following in 3-D space. The results demonstrate the superiority of our framework as a promising solution for 3-D shape reconstruction of flexible instruments and continuum robots in terms of accuracy, robustness, and fast response compared to state-of-the-art works.