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

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.