A Single-Fiber Optical Frequency Domain Reflectometry (OFDR)-Based Shape Sensing of Concentric Tube Steerable Drilling Robots

Continuum manipulators (CMs) are widely used in minimally invasive procedures due to their compliant structure and ability to navigate deep and confined anatomical environments. However, their distributed deformation makes force sensing, contact detection, localization, and force estimation challenging, particularly when interactions occur at unknown arc-length locations along the robot. To address this problem, we propose a cascade learning-based framework (CLF) for CMs instrumented with a single distributed Optical Frequency Domain Reflectometry (OFDR) fiber embedded along one side of the robot. The OFDR sensor provides dense strain measurements along the manipulator backbone, capturing strain perturbations caused by external interactions. The proposed CLF first detects contact using a Gradient Boosting classifier and then estimates contact location and interaction force magnitude using a CNN--FiLM model that predicts a spatial force distribution along the manipulator. Experimental validation on a sensorized tendon-driven CM in an obstructed environment demonstrates that a single distributed OFDR fiber provides sufficient information to jointly infer contact occurrence, location, and force in continuum manipulators.

Continuum robots offer a promising approach for minimally invasive and natural-orifice surgical procedures due to their inherent compliance and dexterity. However, this flexibility also makes estimating the current shape of the robot challenging. Several approaches have been used to reconstruct the shape of these robots, including imaging, optical sensing, magnetic sensing, and resistive sensing. Strain sensors fabricated using direct laser writing (DLW) could provide an alternative sensing method. This technique involves using a laser to induce carbonization of certain polymers to create graphene patterns, such as strain sensors. In this paper, we demonstrate how a flexible continuum joint and a DLW sensor can be machined as one monolithic structure using the same laser and the same setup. The fabricated sensors are characterized using linear and nonlinear models, which are used to predict the joint angle with error as low as 1.76 degrees. Furthermore, we demonstrate how a DLW sensor can be used to implement closed-loop control in a robotic joint, achieving tracking error under 3 degrees.

Shape and force sensing have long been critical bottlenecks in the development of compact capstan-driven continuum surgical robots, primarily due to the difficulty of obtaining cable tension information within the confined capstan assembly. To overcome these challenges, this paper presents an integrated design-modeling-sensing approach based on the concept of actuation-perception co-design. A compliant element is introduced into the motor mounting bracket of the drive system, enabling micro-deformation under the cable reaction force and thereby allowing real-time cable tension measurement without occupying the compact capstan space. To address the modeling complexity arising from unconventional joint configurations introduced by the spatial cable routing strategy, a parallel computation framework based on a multibody short-thick-beam model is proposed, which captures shear effects in short beam segments and synergistic multi-cable interactions while achieving real-time performance. Building on this framework, stable shape and force sensing is achieved by incorporating a proximal multi-axis force/torque sensor as an additional measurement anchor. Following this design-modeling-sensing framework, capstan-driven continuum surgical robots with single- and dual-segment configurations are developed. Experimental results validate the proposed framework in both single- and dual-segment continuum robots, demonstrating real-time tip pose estimation together with contact force and location perception. By enabling cable tension feedback without compromising the compact capstan architecture, the proposed framework makes integrated perception feasible for capstan-driven continuum surgical robots.