TY - JOUR

T1 - Shape Sensing Based on Longitudinal Strain Measurements Considering Elongation, Bending and Twisting

AU - Modes, Vincent

AU - Ortmaier, Tobias

AU - Burgner-Kahrs, Jessica

N1 - Funding information: Manuscript received October 1, 2020; accepted November 25, 2020. Date of publication December 11, 2020; date of current version February 5, 2021. This work was supported in part by the German Research Foundation under Grant BU 2935/1-1. The associate editor coordinating the review of this article and approving it for publication was Dr. Sanket Goel. (Corresponding author: Vincent Modes.) Vincent Modes and Tobias Ortmaier are with the Institute of Mechatronic Systems, Leibniz University Hannover, 30823 Garbsen, Germany (e-mail: vincent.modes@imes.uni-hannover.de).

PY - 2020/12/11

Y1 - 2020/12/11

N2 - The inherent flexibility, the small dimensions as well as the curvilinear shape of continuum robots makes it challenging to precisely measure their shape. Optical fibers with Bragg gratings (FBGs) provide a powerful tool to reconstruct the centerline of continuum robots. We present a theoretical model to determine the shape of such a sensor array based on longitudinal strain measurements and incorporating bending, twisting, and elongation. To validate our approach, we conduct several simulations by calculating arbitrary shapes based on the Cosserat rod theory. Our algorithm showed a maximum mean relative shape deviation of 0.04%, although the sensor array was twisted up to 78°. Because we derive a closed-form solution for the strain curvature twist model, we also give analytical sensitivity values for the model, which can be used in the calculation of error propagation.

AB - The inherent flexibility, the small dimensions as well as the curvilinear shape of continuum robots makes it challenging to precisely measure their shape. Optical fibers with Bragg gratings (FBGs) provide a powerful tool to reconstruct the centerline of continuum robots. We present a theoretical model to determine the shape of such a sensor array based on longitudinal strain measurements and incorporating bending, twisting, and elongation. To validate our approach, we conduct several simulations by calculating arbitrary shapes based on the Cosserat rod theory. Our algorithm showed a maximum mean relative shape deviation of 0.04%, although the sensor array was twisted up to 78°. Because we derive a closed-form solution for the strain curvature twist model, we also give analytical sensitivity values for the model, which can be used in the calculation of error propagation.

KW - continuum robot

KW - fiber Bragg grating sensors

KW - multi-core optical fiber

KW - shape sensing

UR - http://www.scopus.com/inward/record.url?scp=85097938547&partnerID=8YFLogxK

U2 - 10.1109/jsen.2020.3043999

DO - 10.1109/jsen.2020.3043999

M3 - Article

VL - 21

SP - 6712

EP - 6723

JO - IEEE sensors journal

JF - IEEE sensors journal

SN - 1530-437X

IS - 5

M1 - 9291439

ER -