  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.
