Uncertainty-Aware Shape Estimation of a Surgical Continuum Manipulator in Constrained Environments using Fiber Bragg Grating Sensors

TL;DR

This work presents an uncertainty-aware data-driven approach to directly estimate the full shape of a surgical continuum manipulator (CDM) from eight FBG sensor wavelengths, using a two-fiber FBG array embedded in the CDM. A three-layer MLP with dropout supports both direct shape estimation and uncertainty quantification via Monte Carlo sampling, yielding per-marker confidence intervals that reflect model confidence. Ground-truth shapes are obtained from 30 stereo-markers, enabling robust training and evaluation under both freespace and obstacle-constrained bending, including out-of-distribution (OOD) scenarios. The results show that the proposed method reduces shape and tip errors compared with linear and polynomial baselines and demonstrates reliable uncertainty estimates that correlate with prediction accuracy, enhancing safety for surgical robotics. The work also reports practical considerations such as data collection rates, ground-truth extraction, and the impact of distribution shifts on uncertainty, with prospects for future fusion with other modalities (e.g., X-ray) and improved visualization for clinicians.

Abstract

Continuum Dexterous Manipulators (CDMs) are well-suited tools for minimally invasive surgery due to their inherent dexterity and reachability. Nonetheless, their flexible structure and non-linear curvature pose significant challenges for shape-based feedback control. The use of Fiber Bragg Grating (FBG) sensors for shape sensing has shown great potential in estimating the CDM's tip position and subsequently reconstructing the shape using optimization algorithms. This optimization, however, is under-constrained and may be ill-posed for complex shapes, falling into local minima. In this work, we introduce a novel method capable of directly estimating a CDM's shape from FBG sensor wavelengths using a deep neural network. In addition, we propose the integration of uncertainty estimation to address the critical issue of uncertainty in neural network predictions. Neural network predictions are unreliable when the input sample is outside the training distribution or corrupted by noise. Recognizing such deviations is crucial when integrating neural networks within surgical robotics, as inaccurate estimations can pose serious risks to the patient. We present a robust method that not only improves the precision upon existing techniques for FBG-based shape estimation but also incorporates a mechanism to quantify the models' confidence through uncertainty estimation. We validate the uncertainty estimation through extensive experiments, demonstrating its effectiveness and reliability on out-of-distribution (OOD) data, adding an additional layer of safety and precision to minimally invasive surgical robotics.

Figures (8)

• Figure 1: Overview of the proposed method. The wavelength shift $\lambda$ of FBG sensors mounted inside the CDM is measured over time $t$. Mode-corrected wavelength peaks are fed into an uncertainty-aware DNN to predict the shape of the CDM $\mathbf{p}$ and estimate uncertainty $\mathbf{u}$ for each of the predictions.
• Figure 2: Schematic cross-sectional and top-down view of the CDM showing the actuation cable, FBG sensing, and tool channel. The FBG sensing array consists of two optical fibers and a NiTi wire embedded in a polycarbonate tube and is inserted into the CDMs wall (green) below the actuation cable (orange). The CDM bends within the $(x,y)$-plane. Red markers are placed along the centerline for ground truth shape reconstruction.
• Figure 3: Experimental Setup including, the stereo cameras, CDM, actuation unit and FBG sensing unit mounted on the optical table.
• Figure 4: CDM bending experiments with obstacles. Rigid obstacles were placed at the tip position (left), center (middle), and base (right) of the CDM.
• Figure 5: 3D Shape Ground Truth Extraction of the CDM centerline from stereo images using color-based segmentation and triangulation of the detected marker centroids.