# Kinematic Modelling and Experimental Validation of a Foldable Pneumatic Soft Manipulator
## 4 Experiment Design and Validation
### Repeatability Test of the Pneumatic Module  
In order to verify the repeated positioning accuracy of the soft manipulator, repeated experiments are taken in different working conditions. Experiments under the same working condition are taken three times, and the coordinates of the observation points are recorded. By comparing the difference of the coordinates of the same observation point in three experiments, the repeated positioning accuracy of the pneumatic soft module is tested. Experiments are taken in two conditions: one bellows inflated or two bellows inflated simultaneously.  
(1) Repetition experiment with one bellows 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 each test, the air in the bellows is vented and then inflated. The experimental results are shown in Figure 8.  
In Figure 7(a), the curves agree well with each other at the same internal pressure in the three experiments. As the internal pressure increases, the curves are almost completely coincided. It can be seen in Figure 7(a) that there is a slight difference between the three curves at a pressure of 0.02 MPa, as the internal pressure increases and the difference becomes smaller. The curves are almost completely coincident at the internal pressure of 0.1 MPa. This indicates that the stability of the soft module improves when the pressure increases. As shown in Figure 8(b), the observation point number 6 is  
Figure 8: Repetition experiment with one bellows inflated.  
Figure 7: Experiment system of one pneumatic module.  
the end point of the pneumatic actuator, and the observation point number 9 is the end point of the straight arm. These two points are taken as calibration points to obtain the maximum position errors in the three measurements. As can be seen in Figure 8b, the maximum error of the repeated positioning accuracy of the two calibration points is no more than 8 mm, and the repeated positioning accuracy improves with the increasing of the internal pressure. When the internal pressure increases to 0.1 MPa, the position error can be limited within 2 mm.  
(2) Repeatability experiment when two bellows are inflated  
We then inflated two bellows with the same internal pressure after the pneumatic soft module restores 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 observation process is the same as the experiment with one bellows inflated. The experiment results are shown in Figure 9.  
In Figure 9a, the curves almost totally agree with each other at the same internal pressure in the three experiments. The difference between the curves in the same internal pressure condition is very small, no matter the internal pressure is low or high. Similarly, observation points 6 and 9 are taken as calibration points. It can be seen in Figure 9b, the maximum position error of the number 9 observation point is about 6 mm; the maximum position error of the number 6 observation point is about 2 mm. It can be seen from the comparison between Figures 8b and 9b that the repeated positioning accuracy improves with the increasing of the internal pressure in the scenario where one bellows is inflated, while the repeated positioning accuracy is stable in the scenario where two bellows are inflated. This is because, when two bellows are inflated at the same time, the bending force generated by pneumatic actuator is greater than that of one bellows, the stability of the pneumatic soft module is also better. This can be seen in Figures 8 and 9, where the maximum error of the repeatability experiment is 8 mm, which is less than 1.5% relative to the total length of the pneumatic soft module (762 mm).