## 4 Experiment Testing and Discussions
### Shape Reconstruction of the Soft Actuator  
In order to demonstrate the effectiveness of the shape reconstruction method proposed in this paper, some bending experiments of the soft actuator based on embedded FBGs were carried out. The experimental setup is illustrated in Figure 10. In the experiment, the original center wavelengths of two FBGs (FBG1, FBG2) are 1544 nm and 1546 nm respectively. The peak reflectivity of the FBGs are 70% and the response time of the FBGs is 70 ms. Two FBG sensors are located in the intermediate axis of the soft actuator, and their relative positions as illustrated in Figure 4, Section 2. As the bending curvature of the soft actuator varies with 0 m\({}^{-1}\), 5 m\({}^{-1}\), 10 m\({}^{-1}\), 15 m\({}^{-1}\), 20m\({}^{-1}\) and 25 m\({}^{-1}\), the wavelength and power of the FBG sensors are not the same as the original values. Since the grating characteristics of FBG sensors are varied from the strain loads of polyimide tape as it  
Figure 10: Experimental setup of the soft actuator with embedded FBGs. Figure 9: Motion trajectory of the actuator with different input pressure. bends, the power peaks of the FBGs can be identified accurately. As depicted in Figure 11, the power peaks of the two FBGs were around 1544.498 nm and 1546.611 nm at bending state 1, the curvature of the polyimide skin was increased when the soft actuator bent from state 1 to state 5, and the power peaks of the two FBGs was 1545.956 nm and 1547.541 nm at bending state 5. From Figure 11, it also indicates that the peak wavelength gradually shifts in the direction of a longer wavelength as the bottom surface curvature of the soft actuator increases from 0 m\({}^{-1}\) to 25 m\({}^{-1}\), and the shift value of the two FBG sensors is about 1.458 nm and 0.93 nm, respectively. Consequently, the responses of the two FBGs are sensitive and instantaneous record the variation in power. The dynamic shape deformation of the soft actuator can be measured in real time, and the FBG sensors with different wavelengths can be distributed along a single optical fiber for multi-point shape sensing. When the curvature of the FBGs increases from 0 m\({}^{-1}\) to 25 m\({}^{-1}\), the relationship of the wavelength shift and the curvatures of the soft actuator are illustrated in Figure 12. All measurements have respective average values which were taken from six independent experiments. The bending curvature of the soft actuator at different bending states obtained from the wavelength shift of the FBG sensors, the interpolation algorithm, and the wavelength shift of the FBG sensors were different due to the bending produced strain loads at the different sensing positions. The results showed that the wavelength shift of the FBG sensors increased nonlinearly with the increasing bend in the curvature of the soft actuator. That is because the soft silicone material is extensible and its thickness is variable as  
Figure 11: The wavelength shift of two FBG sensors at different bending states. (**a**) FBG 1. (**b**) FBG 2.  
it sustains different driving loads and contact forces at different bending states. The thickness of the microstructure \(h\) at different sensing points varied and the strain loads induced by the deformation of the soft silicone actuator were different at these sensing points. According to Equation (17), when the bending curvature of the soft actuator increases from 0 m\({}^{-1}\) to 25 m\({}^{-1}\), the wavelength shift and the bending curvature presents a nonlinear variation trend. The wavelength shift of the FBG sensors can be calculated by using the method of polynomial curve fitting, and the calibration equations can also be used to test the bending curvatures of the soft actuator. For the 3D shape reconstruction of the soft actuator at different bending states, the bending curvatures of the two FBG sensors were calculated from the wavelength shift. According to the data obtained from each sensing point, the 3D shape of the soft actuator is reconstructed through the interpolation and curve fitting functions.