FE simulation for model training. The overall error was small with a mean of 0.6995 mm, achieving a high goodness-of-fit with a correlation coefficient >0.999. The results support the feasibility of using a data-driven method to model the strain-morphology mapping prior to its real sensor fabrication, and the clear variation in fiber strains indicates that surface morphology could be well-differentiated and thus reconstructed from the strain data.
The shape sensor flexibility was tested with various high-order deformation such that the surface nodes would undergo large displacements (Figure. 1 and Video 1). To evaluate shape sensing accuracy, 300 deformation instances were randomly selected to compare with the EM-tracked ground truth nodes. Note that such distinct deformation instances were not used in the previous model training. A histogram of 2,700 nodal displacement errors (300×9 nodes) is shown in Figure. 4a, which indicates that nearly 90% of the samples were well below 5 mm with a mean of 2.28 mm. The root-mean-square error (RMSe) of each tracked node and the fixed point (A7), with respect to their position on the sensor, is illustrated in Figure. 4b and Figure. 4c. The warmer color of dots indicates a larger displacement sensing error. It can be observed that the prediction error of each node has a strong relationship with its distance to the fixed point and the mean displacement it underwent (Figure. 4c). The nodes A1, K1 and K7 have the largest error, likely because they have a higher degree of freedom, and hence underwent larger displacement.
In this test, rather than only fixing a corner, a shorter edge of the shape sensor was clamped (Figure. 4d), enabling a larger degree of deformation along the long edge. The sensor was bent upward, downward, then back to the neutral position, counting as one bending cycle. The bending motion was generated by a linear actuator driving the distal edge (nodes K1 to K7) vertically, in order to carry out the sensing hysteresis test  (Figure. S2).