As in Figure. 4e, three representative FBGs were selected, of which the Bragg wavelength shifts were read against the variation of distal edge displacement. Each data point was sampled by taking an average of three bending cycles. By fitting a curve along with those sampling points, the hysteresis could be measured as the disparity between the upward and downward bending, with the shadowed region representing the 95% confidence interval. Each hysteretic (or bending) cycle took around 2 s. These disparities could be varied, depending on the FBG locations. In general, they are very small (<0.051 nm), thus implying a low level of sensing hysteresis throughout such large bending cycles. To evaluate the longer-term sensing repeatability, the displacements of three selected lines at the peak of upward motion were calculated and shown in Figure. 4f. Altogether, the results suggest that the sensing was still promising with stable and reliable responses over 1,000 repeated bending cycles. Again, this repeatability could also be varied by the displacement locations. The larger bending displacement detected by our shape sensor, the higher its fluctuation found over such repeated cycles. The fluctuation among those three lines of displacement nodes can be readily comparable on a logarithmic scale. Note that the nodes on the distal side encountered the largest fluctuation (RMS fluctuation ~1.48 mm) as a result of its largest displacement detected.
To further demonstrate the potential of our data-driven approach, we tested our training model in an underwater environment. A manta ray-shaped prototype was fabricated using the same settings of FBG fiber, following a similar procedure with the previous A4-sized design (Figure. 4a). An optical fiber with 29 FBGs was adhered roughly along the edges of the prototype (Figure. 5a), and its FE model is shown in Figure. 5b, where the red nodes represent the location of 8 EM tracking coils for the model training (ground truth). The optical fiber layout for the manta ray prototype is not a dog-bone shape, but a specific one based on its geometry. When we were dealing with this case with irregular shape, we did not just simply copy the fiber layout from the rectangular one (A4-size). The middle fixture of the ray prototype has divided the substrate into two parts such that the resulting possible sensor configuration is fewer than that of the A4 size prototype. When displaced by hydrodynamic force, the deformation magnitude and degree of freedom of the fin edge are larger than that of the inner region. Therefore, we adhered the optical fiber along the edge of the manta ray prototype. Upon vertical actuation (1 Hz), the manta ray was displaced vertically underwater. The sensing performance of the manta ray fins can be referred to in Video 3 as well as Figure. 5, where Figure. 5c shows the ray at three typical deformation instances and Figure. 5d illustrates their corresponding real-time shape reconstruction. The ever-changing water drag did not hinder the sensing performance even with the model training and data-driven analysis initially conducted in the air.