# Design and Experimental Development of
## 4 Experiments
### Experiment on the Foot System  
The most important function of the proposed foot system is to adapt to small-sized bumps on the ground with the help of the PVSUs and, thus, to reduce the change in the posture of the sole and maintain stable foot-ground contact. Several requirements must be met to guarantee the performance of the foot system, specifically, (1) the reversing valves of the PVSUs in contact with the bumps should be triggered reliably; (2) wrong trigger of the reversing valves of the PVSUs in contact with the flat ground should be avoided; and (3) the foot should be able to adapt to bumps of various sizes within a certain range. Therefore, the following experiment is designed to test the function of the foot from the above aspects. First of all, the foot system is placed on a flat surface with all PVSUs inflated with compressed air of 50 KPa, and a 6 kg mass block which is used to imitate the body weight of biped robots is mounted on the top of the foot through a 230 mm long link, as shown in Figure 11a. Then, some small bumps of various sizes are placed under the pneumatic bladder to see if the foot can adapt to them. The adaptability can be evaluated from the posture changes under different experimental conditions. However, the foot posture cannot be directly measured by the FSRs, the only sensors that the foot has. Instead, the projective position of the center of mass (CoM) on the ground is used because they are related with the foot posture and can be calculated from the measurements of FSRs. Figure 10: Measured force-compression curves of the PVSU. According to the trigger displacement of the reversing valve and the maximum compression of the pneumatic bladder, the heights of the bumps used in the experiment were selected as 3 mm, 5 mm, and 8 mm. Considering that the foot is symmetric about its center, the bumps were only placed under the two pneumatic bladders on one corner, as illustrated in Figure 11b-d. The experiment showed that under each experimental condition, the reversing valve of the PVSU on the bump was successfully triggered to expel out the air, and the pneumatic bladder became soft and generated more compression under the gravity of the mass block. At the same time, the other pneumatic bladders remained in contact with the flat surface with high stiffness. The foot posture was only slightly changed, enabling the mass block to remain stable without falling down. This result was quite consistent with the theoretical working mechanism of the foot system presented in Section 2. Assuming that the origin of the coordinate system is located at the center of the foot sole, the \(X\) axis points to the front, and the \(Y\) axis points to the right. Then the stable values of CoM projections under all conditions can be plotted in the same coordinate system, as shown in Figure 12a. From this figure, it can be easily seen that higher bump resulted in larger changes of CoM projections and foot posture. The changes of the CoM projections were within 11.5 mm, and the maximum angle of inclination of the foot sole was measured to be as small as 2.9\({}^{\circ}\). Figure 12b presents the changing curves of the CoM positions in the \(X\) and \(Y\) axis versus time when the posture change is maximum. In this figure, the CoM position rapidly approached the stable point within 0.1 s, and finally stabilized at the point (11.0, \(-\)8.0) after a small-amplitude vibration. Thus, the response time of the pneumatic bladder when it was compressed can be obtained, i.e., less than 0.1 s. The quite short response time indicates that the foot is able to adapt to the bumps on the ground rapidly, and suggests that if the foot is applied to a biped robot, the foot-ground contact time is negligible compared with the gait cycle. All the above results verified the function of the foot system. Figure 11: The experiment on the foot system. (**a**) The overall experimental apparatus; (**b**) the foot on a 3-mm high bump; (**c**) the foot on a 5-mm high bump; and (**d**) the foot on an 8-mm high bump.