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

TL;DR

The paper tackles simultaneous shape and contact force estimation along highly deformable flexible surgical manipulators using sparse measurements from a single-core helically wrapped FBG fiber embedded in a soft sensing tube. It introduces a unified learning framework with a shared spatial FBG encoder and three encoder variants (FC, LSTM, Conv1D) feeding shape (curvature and twist) and force (magnitude and location) decoders, including a Gaussian-like force distribution model. Experimental results on a robotic ureteroscope platform show that Conv1D-based encoding consistently provides the best static and dynamic accuracy, achieving near sub-millimeter tip precision and robust force localization while reducing reliance on precise FBG placement. The work demonstrates a practical, low-cost approach to real-time, location-aware shape/force sensing in unknown environments, with potential impact on safety-critical minimally invasive procedures.

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.

Figures (5)

• Figure 1: Design of FBG-based soft sensing tube. (a) Conceptual representation of flexible endoscope with FBG sensing in kidney; (b) Soft tube with a helically wrapped single-core FBG fiber; (c) FBG strain decomposition; (d) Cross-section diagram of the tube.
• Figure 2: Overall diagram of the proposed learning models for simultaneous shape and force estimation of flexible surgical robots..
• Figure 3: Data collection platform including a helical single-core FBG fiber, a multi-core FBG fiber, and a force-optical tracking system.
• Figure 4: Task setups with initial bending (left) of (a) 30$^\circ$, (b) 85$^\circ$, (c) 120$^\circ$, and (d) 185$^\circ$, and their strain input from helical single-core FBGs (top-right) with shape sensing results (bottom-right).
• Figure 5: The results versus time iteration including tip position error (top), contact location (middle), and force magnitude (bottom) of four experiments (a) - (d) corresponding to the tasks in Fig. \ref{['fig:setup']} (a) - (d), respectively. Note that the middle and bottom rows show the ground truth (GT) in blue dash-dotted curves instead of the results using the model-based method (Model) in the top row.