# Kinematic Modelling and Experimental Validation of a Foldable Pneumatic Soft Manipulator
## 4 Experiment Design and Validation
### Validation of the Model Prediction Accuracy  
In order to verify the accuracy of the shape deformation predicted by the proposed model, experiments are taken in different working conditions and the numerical results are compared with the experimental results. The coordinates of the observation points are recorded in the experiments in two conditions: one bellows inflated or two bellows inflated simultaneously. The coordinates of the observation points are projected into the Y-Z plane and the X-Y plane to see the difference between the modelling prediction and the experiment measurement clearly. (1) Experiment with one bellows inflated  
Figure 9: Repeatability experiment when two bellows are inflated. First, one bellows is inflated, and the internal pressure is set from 0.02 MPa to 0.1 MPa, with 0.02 MPa as the interval. The coordinates of the observation points are recorded respectively. In this theoretical prediction, the \(k\) value is taken as 23,000 N/m; the length of the straight arm is 0.442 m. Observation points 6 and 9 in Figure 6(b) are taken as calibration points to obtain the errors between the theoretical prediction results and experiment results. The coordinates of these two points are extracted at different internal pressure and compared with the prediction results. The theoretical prediction results and experiment results are compared in Figure 10.  
In Figure 9(a), the shape deformations of the soft module obtained by both experiment and numerical prediction are shown. It can be seen that the distribution of experiment points is almost around the theoretical prediction. When the curves and points are projected into the X-Y plane, the theoretical results merge into a straight line and the experiment points stay around the straight line, as shown in Figure 9(b). This indicates that the pneumatic soft module deforms stably in a single direction under the condition of one bellows inflated, and there is no obvious deviation occurring in the deforming process, which reflects the well stability of the pneumatic soft module. In Figure 9(c), the prediction error of the theoretical model relative to the experiment is shown. It can be seen that the prediction error at both the middle point and the last point reduces with the increasing of the air pressure in the bellow. The maximum at the last point is 33 mm when the internal pressure is 0.02 MPa, and the minimum is 23 mm at the internal pressure of 0.1 MPa. The maximum and minimum at the middle point is respectively 24 mm and 2.5 mm. This is because the bending stiffness of the pneumatic joint is relatively small when the internal pressure is at a low level; thus, the bending amplitude  
Figure 10: Comparison between prediction and experiment results of one bellows. of the pneumatic soft module is greatly influenced by gravity. With the increasing of the internal pressure, the bending stiffness increases; thus, the influence of gravity on the bending amplitude of the pneumatic soft module reduces relatively. (2) Experiment with two bellows inflated  
Inflating two bellows with the same internal pressure after the pneumatic soft module restores it to its original state, and the internal pressure is set from 0.02 MPa to 0.1 MPa, with 0.02 MPa as the interval. The process is the same as the experiment with one bellows inflated. The experiment results and prediction results are shown in Figure 11.  
In Figure 10(a), the shape deformations of the soft module obtained by both experiment and numerical prediction are shown. It can be seen that the distribution of experiment points is almost around the theoretical prediction. When the curves and points are projected into the X-Y plane, the theoretical results merge into a straight line and the experiment points stay around the straight line, as shown in Figure 10(b). Comparing Figure 10(a) with Figure 10(a), it can be seen that the agreement between the theoretical prediction and the experiment improves a great deal. This agreement can also be found in their projection to the X-Y plane.