Shape reconstruction of flexible cable structures based on distributed optical fiber sensors

Timely and accurate acquisition of the dynamic morphological characteristics of flexible cable structures is crucial for mitigating entanglement risks in tethered satellite systems and ensuring operational safety in deep-sea exploration. In this study, a shape-reconstruction method that integrates the Rotation-Minimizing Frame (RMF) theory with Optical Frequency Domain Reflectometry (OFDR)-based distributed fiber-optic sensing is proposed. This method overcomes the limitations of the classical Frenet frame, particularly its inability to define torsion at zero-curvature segments and its inherent instability during spatial curve evolution. By leveraging the optical fibers embedded within the cable as distributed sensors, the proposed approach enables high-resolution measurement of strain distribution along the entire length of flexible cable structures. An experimental platform for shape monitoring based on distributed fiber-optic sensing is constructed, and functional validation is carried out under representative loading conditions. The results demonstrate that the developed method provides essential technical support for health monitoring and digital-twin construction of space tethered-satellite systems and deep-sea flexible umbilical cables.