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° 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 without interactions as well as 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.

Multi-segment continuum robots, that offer inherent compliance and distal dexterity, are suitable for deployment in minimally invasive surgical procedures. Cable-driven mechanism is commonly used in continuum surgical robots but could lead to inter-segment motion coupling in a multi-segment robot. In this paper, we present a coupled mechanics model for a two-segment notched continuum robot to analyze the coupled deflection in the proximal segment due to the distal cable force. The model has been developed for two different conditions in which the proximal segment is initially bent (general condition) and initially straight (special condition). It allows us to introduce a decoupled design methodology that systematically determines a stiffness parameter in each of the segments, based on the desired coupled bending angle and other design requirements. Using the method, we fabricated a decoupled notched continuum robot and evaluated the model accuracy compared with experimental data with mean errors of 0.57° and 0.61°, respectively for general and special conditions throughout the 90° distal segment bending angle. It was also shown in a demonstration in a maxillary sinus phantom that the distal segment was capable of independently perform omnidirectional steering without the proximal segment getting in contact with its surrounding nasal wall.