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

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.

Design and Fabrication of a Fiber Bragg Grating Shape Sensor for Shape Reconstruction of a Continuum Manipulator

Continuum dexterous manipulators (CDMs) are suitable for performing tasks in a constrained environment due to their high dexterity and maneuverability. Despite the inherent advantages of CDMs in minimally invasive surgery, real-time control of CDMs' shape during non-constant curvature bending is still challenging. This study presents a novel approach for the design and fabrication of a large deflection fiber Bragg grating (FBG) shape sensor embedded within the lumens inside the walls of a CDM with a large instrument channel. The shape sensor consisted of two fibers, each with three FBG nodes. A shape-sensing model was introduced to reconstruct the centerline of the CDM based on FBG wavelengths. Different experiments, including shape sensor tests and CDM shape reconstruction tests, were conducted to assess the overall accuracy of the shape sensing. The FBG sensor evaluation results revealed the linear curvature-wavelength relationship with the large curvature detection of 0.045 mm at a 90 degrees bending angle and a sensitivity of up to 5.50 nm/mm in each bending direction. The CDM's shape reconstruction experiments in a free environment demonstrated the shape tracking accuracy of 0.216+-0.126 mm for positive/negative deflections. Also, the CDM shape reconstruction error for three cases of bending with obstacles were observed to be 0.436+-0.370 mm for the proximal case, 0.485+-0.418 mm for the middle case, and 0.312+-0.261 mm for the distal case. This study indicates the adequate performance of the FBG sensor and the effectiveness of the model for tracking the shape of the large-deflection CDM with nonconstant-curvature bending for minimally-invasive orthopaedic applications.