# Design and Research of a Flexible Foot for a Multi-Foot Bionic Robot
## 4 Flexible Foot Mechanism Calibration
### Omnidirectional Force Calibration  
HC9000 was selected as a flexible material for the foot by calibrating the force of different materials. In order to analyze the sense of the force of the foot-end structure in different directions, an omnidirectional force calibration experiment was designed. The end of the foot was fixed to the digital display. Based on observations while the robot walks, the variation range of the angle between  
Figure 6: Comparisons of foot-tip flexible materials. the foot end and the \(z\)-axis direction was determined to be 0-45 degrees. During the experiment, the \(x\)-\(y\) direction was changed by 15 degrees. As shown in Figure 7b, r1 indicates that the foot tip was 15\({}^{\circ}\) from the \(z\)-axis, r2 indicates that the foot tip was 30 degrees from the \(z\)-axis, and r3 indicates that the foot tip was 45 degrees from the \(z\)-axis. In the \(x\)-axis direction, since the foot tips were symmetric, take three points r1, r2, and r3 on the \(x\)-axis as xr1, xr2, and xr3, and take three points r1, r2, and r3 on the \(y\)-axis as yr1, yr2, and yr3. During the experiment, voltage values of three points and their symmetrical points were measured, and the average values were assigned to points xr1, xr2, xr3 and yr1, yr2, yr3, respectively. The mass of weights was increased in different directions in turn, while the other parameters remained unchanged, and only the force direction of the foot was changed; the change of the voltage value of the FSS pressure sensor was recorded. The results obtained from the experiment are shown in Figure 8, where r1, r2, and r3 represent the different angular positions of the foot tip. It can be seen from the figure that on r1, r2, and r3, the stresses on the calibration stress points on x and y were basically the same. At different points of the r1 position, xr1 and yr1 exhibited the same voltage change trend as the weight quality increased, and the error was small, as shown by the red and blue curves in the figure. It can be said that the force of the foot tip was almost the same at any position of the r1 circle. At the r2 and r3 positions, the same change could also be seen. The foot mechanism designed in this paper had uniformity in the perception of the foot-end force. At the same time, it can be seen that under the same external force, the voltage variations of r1, r2, and r3 were also different. The amount of change in voltage was related to the position of the force. The closer to the r1 position at the center of the tip of the foot, the greater the amount of change in the output voltage, and the further away from the center of the foot, the smaller the amount of voltage change. This was because when the weight was applied, the force generated was applied to different positions, and the force angle of the foot tip was also different. In order to discuss the relationship between the amount of change in the FSS voltage of the foot tip force sensor and the force angle, the same force was applied to the foot tip, the weight was selected to be 500 g, and only the force angle was changed. The force point was selected on the \(x\)-axis, and angle values that changed in the negative direction of x were recorded as negative, and angle values that changed in the positive direction of x were recorded as positive; when the foot was perpendicular to the plate, it was recorded as 0\({}^{\circ}\). The amount of voltage change was measured, the average value of three measurements was calculated, and the recorded results are shown in Table 2. The force angle-voltage curve is shown in Figure 9.  
Figure 7: Experiments of full-direction force acting on the foot tip: (**a**) change of foot direction; (**b**) calibration of stress point position.