# Design and Experimental Development of
## 4 Experiments
### Experiment on a Biped Robot  
This experiment aims to test the performance of the new foot system on a physical biped robot when the biped robot walks on the ground with small bumps. A lightweight biped robot developed by our research team is utilized in the experiment [38]. The biped robot has two three-segmented legs composed of the thigh, shank, and foot. Each leg has three planar revolute joints, namely, the hip, knee, and ankle joints. The lengths of each link from the thigh to the foot are 0.37 m, 0.36 m and 0.2 m, respectively. Their corresponding masses are 1.8 kg, 1.5 kg and 0.2 kg. The right and left legs are connected by the torso whose mass is 3 kg. The movement of the biped robot in the coronal plane is constrained by a frame presented in Figure 13, without affecting the motion in the sagittal plane [39]. For the sake of comparison, the experiment is performed with two conditions, i.e., (1) the biped robot walks with traditional flat feet; and (2) the biped robot walks with the new feet. The two kinds of feet have the same size, weight, as well as configuration of FSRs. On the ground are some small bumps promiscuously placed, of which the maximum height is 8 mm. The preplanned step length is 0.25 m, and the gait cycle is 1 s. The walking patterns are generated based on the ZMP theory. Under each condition, the biped robot is controlled to walk for ten trials and 5 m each trial. The performances of the two kinds of feet, including the behavior of the foot when contacting with the bumps and the overall walking stability, are compared. In the case of walking with the flat feet, the contact area significantly decreased because the foot could not adapt to the bumps. Here we analyze a typical process of the foot contacting with the bumps, which was presented in Figure 14. In this figure, the images in the red panes are partially-enlarged images. During the whole phase from the foot touching the ground to the foot lifting off the ground, three contact states between the foot, ground, and bumps were shown. Firstly, after the foot stepped on the bump, only the trailing edge of the foot, rather than the whole sole, was in contact with the ground (see the upper images in Figure 14). The support polygon was a triangle encircled by the foot's trailing edge and the contact point between the foot and bump. Secondly, as the robot walked forward, the body weight was shifted to this foot which became the new support foot. The forward movement of the CoM of the robot body caused the trailing edge of the foot off the ground. Thus, the whole robot was only supported by the bump (shown in the middle images in Figure 14). Thirdly, the robot continued swinging forward, and the leading edge of the foot touched the ground. The support polygon turned into a triangle encircled by the leading edge of the foot and the contact point between the foot and bump (see the lower images in Figure 14). These three contact states could not provide sufficient and stable support to the biped robot. Consequently, the slippage of the foot on the ground occurred frequently, and the predetermined posture of the robot was easily affected, sometimes causing the robot to fall. Figure 13: Experimental apparatus of the biped robot. (**a**) Prototype of the biped robot; (**b**) schematic diagram of the biped robot; and (**c**) the coordinate system of the biped robot for ZMP computation. On the other hand, the performance was much better in the case of walking with the new feet. The behavior of the new feet contacting with the bumps on the ground is presented in Figure 15. When the pneumatic bladders under the foot sole touched the bumps, the corresponding reversing valves were triggered successfully, and the pneumatic bladders became soft and were compressed to follow the shape of the bumps. For the pneumatic bladders which had no contact with the bumps, there were no wrong triggers occurred, and they kept high stiffness and maintained stable contact with the ground.