Estimating and Localizing External Forces Applied on Flexible Instruments by Shape Sensing

Abstract

Force sensing is highly desirable in medical applications showing great potential to reduce tissue damage and enhance manipulation safety. Embedding force sensors in medical devices is however challenging and costly. Provided that the medical device is long, slender and largely compliant, we show in this paper that it is possible to estimate multiple loads along the length of the flexible instrument using a Cosserat-rod model and Fiber Bragg Grating sensors, which allows simultaneous shape and force sensing. We perform experiments that illustrate the feasibility of using this method to locate multiple contact forces along the instrument, and to estimate the magnitudes of the forces that are applied along the length of the instrument. Results show that one-directional force magnitude and location can be estimated with an average error of 6.3% and 5.4 mm (3.0% of rod length), respectively. In the worst case, the error for magnitude and location can go up to 22.6% and 13.9 mm (7.7% of rod length), respectively. For two-directional forces, results show an average error of 9.8% for magnitude and 6.4 mm (3.6% of rod length) for the location. The errors on magnitude and location do not exceed 27.4% and 17.4 mm (9.7% of rod length), respectively.

FBG-Based Estimation of External Forces Along Flexible Instrument Bodies

“…The most common algorithms include: sliding window, top-down, and bottom-up. Qiao et al previously employed a top-down linear segmentation approach to estimate one or two point forces applied on a Nitinol rod Qiao et al (2019). The problem with top-down segmentation approaches, or most conventional linear segmentation approaches for that matter, is that they typically do not consider a penalty on the number of segments constructed.…”

“…Qiao et al made use of curvature measurements using multi-core fibers (MCFs) inscribed with fiber Bragg grating (FBG) sensors, a Cosserat rod model, and linear segmentation of curvature to estimate 2D lateral point forces subjected to an elastic rod body. The feasibility was tested on a Nitinol rod with two point loads (Qiao et al, 2019). In a later work, Qiao et al employed an extended Kalman filter and pose information in combination with a Cosserat rod model to estimate point loads (Qiao et al, 2021).…”

Efficient Force Estimation for Continuum Robot

“…After knowing the distributed forces along the rod. The mechanics model is complete and curvature can then be calculated through the integration of ( 19) - (23).…”

“…Several curvaturebased methods have been investigated for force estimation. Qiao [23] utilized FBGS to measure the curvatures along the manipulator and calculates the force (mean error of 9.8% error) and locations (mean error of 3.6% error) directly using constitutive law. Al-Ahmad [24] utilized unscented Kalman filter to the measured curvatures, which achieved 7.3% error of force magnitude and 4.6% error of location.…”

Shape Sensing Based on Longitudinal Strain Measurements Considering Elongation, Bending, and Twisting

“…Various researchers apply this approach to reconstruct the centerline of continuum robots, e.g. [13], [14] or [15]. In contrast to models based on geometric relations, Sefati et al [16] implement a data-driven linear regression model which requires an extensive pre-operative model training.…”