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

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