Title: Simultaneous Estimation of Shape and Force along Highly Deformable Surgical Manipulators Using Sparse FBG Measurement

Abstract: Recently, fiber optic sensors such as fiber Bragg gratings (FBGs) have been widely investigated for shape reconstruction and force estimation of flexible surgical robots. However, most existing approaches need precise model parameters of FBGs inside the fiber and their alignments with the flexible robots for accurate sensing results. Another challenge lies in online acquiring external forces at arbitrary locations along the flexible robots, which is highly required when with large deflections in robotic surgery. In this paper, we propose a novel data-driven paradigm for simultaneous estimation of shape and force along highly deformable flexible robots by using sparse strain measurement from a single-core FBG fiber. A thin-walled soft sensing tube helically embedded with FBG sensors is designed for a robotic-assisted flexible ureteroscope with large deflection up to 270 degrees and a bend radius under 10 mm. We introduce and study three learning models by incorporating spatial strain encoders, and compare their performances in both free space and constrained environments with contact forces at different locations. The experimental results in terms of dynamic shape-force sensing accuracy demonstrate the effectiveness and superiority of the proposed methods.