FBG-based 3D shape reconstruction of flexible rods using multi-source error compensation and sparrow search optimization

Three-dimensional (3D) shape reconstruction of flexible rods using fiber Bragg grating (FBG) sensors is susceptible to temperature drift, strain transfer loss, and fiber installation angle deviations, which introduce curvature errors that accumulate along the rod length and ultimately degrade reconstruction fidelity. This paper proposes a 3D shape reconstruction framework that integrates temperature compensation, strain transfer correction, and sparrow search algorithm (SSA)-based angle optimization for a Nitinol flexible rod sensor with three optical fibers symmetrically arranged at 120°. A temperature–strain–curvature decoupled model is established to eliminate curvature errors induced by temperature drift and strain transfer loss. Subsequently, a curvature–bending direction correction model is constructed, in which SSA is employed to globally optimize the circumferential installation angle deviations and calibration direction deviations, yielding more accurate curvature estimates. 3D shape reconstruction is then achieved through Frenet–Serret frame numerical integration of the corrected curvatures. Experiments on C-shaped, S-shaped, and Ω-shaped rods demonstrate that the proposed framework reduces the root mean square relative error from 9.76%, 9.59%, and 10.34% to 1.66%, 1.05%, and 2.99%, respectively. These results confirm that the framework effectively suppresses multi-source error accumulation and substantially improves FBG-based 3D shape reconstruction accuracy for flexible rods.