Force from Shape—Estimating the Location and Magnitude of the External Force on Flexible Instruments

Force sensing is highly desirable in minimally invasive medical applications, since this feature shows great potential for reducing tissue damage and enhancing manipulation safety. However, embedding force sensors in medical devices is challenging and costly. This article explores the possibility to use shape sensing as a measure to extract force information. In this work, a model-based approach that allows simultaneous shape and force sensing is proposed. Shape information is reconstructed employing a multicore fiber with fiber Bragg grating sensors spaced over the fiber length. This fiber is capable of distributed 3D shape sensing. It is shown how by making use of extended Kalman filter and a mechanics model of the flexible instrument, it becomes possible to estimate both the magnitudes and locations of externally applied forces. Experiments were carried out to validate the proposed method for both one and two external forces applied at arbitrary locations in different directions on a flexible instrument. Results show that one-directional force magnitude and location can be estimated with an average error of 23.08 mN (15.39%) and 11.06 mm (6.51%), respectively. For two-directional forces, results of the load near the base show an average error of 52.01 mN (30.59%) for the magnitude and 29.24 mm (17.20%) for the location. For the load applied simultaneously near the tip, the mean magnitude error is 16.79 mN (11.19%) and the average location error is 10.18 mm (5.99%). The force sensing algorithm can run in real time with an approximate frequency of 59 Hz. In these experiments, it can be observed that the force-sensing accuracy, which depends on the sensitivity of the shape of flexible instruments with respect to the external force, can vary drastically in function of the force application point and force direction.