# Design and Research of a Flexible Foot for a Multi-Foot Bionic Robot
## 4 Flexible Foot Mechanism Calibration
### Omnidirectional Force Calibration
As can be seen from the above figure, the amount of voltage change became a symmetrical relationship with the change of the angle value, and the force generated by the weight was F:  
\[\Delta\mathrm{U}=\mathrm{k}\times\mathrm{F_{ss}},\;\mathrm{k}=6\;\mathrm{mV}/ \mathrm{N}. \tag{26}\]  
Combining the obtained data with Equation (24), the following can be obtained:  
\[\mathrm{F_{N}}\approx\mathrm{Fcos}\theta. \tag{27}\]  
\[\mathrm{U}=6\mathrm{F_{ss}}=6\times\frac{1}{3}\mathrm{F_{N}}=2\mathrm{F} \approx 2\mathrm{Fcos}\theta \tag{28}\]  
The experimentally measured result data (27) and the theoretical calculation formula (22) were basically consistent with the theoretical results. It can be seen that the data measured by the foot FSS pressure sensor were relatively accurate. However, due to its flexibility, the stiffness coefficient of the foot \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Parameters** & \multicolumn{8}{c}{**Variation**} \\ \hline Angle (\({}^{\circ}\)) & \(-60\) & \(-45\) & \(-30\) & \(-15\) & \(0\) & \(15\) & \(30\) & \(45\) & \(60\) \\ \hline Voltage change (mV) & 4.8 & 7.0 & 8.5 & 9.7 & 10 & 9.6 & 8.6 & 6.9 & 4.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Spring parameter table. Figure 8: All-directional calibration result curves of foot tip. Figure 9: The relationship between the voltage and angle. flexible material was very small, and it could be deformed by applying a small force. In the process of stress, it can be regarded as amplifying the force point of the push-pull rod. When it was in contact with the pressure plate, the force-receiving area of the push-pull rod was increased, so the flexible deformation also brought a certain error influence. In order to study the error caused by the flexible deformation of the foot on the experimental results, the obtained experimental data were straight-line fitted by MATLAB using the least squares method:  
* When r\({}_{1}\) was deflected by 15 degrees, the fitted straight line was \[\mathrm{U}=1.9533\times\mathrm{F}+0.08\] (29)
* When r\({}_{2}\) was deflected by 30 degrees, the fitted straight line was \[\mathrm{U}=1.7479\times\mathrm{F}+0.10545.\] (30)
* When r\({}_{3}\) was deflected by 45 degrees, the fitted straight line was \[\mathrm{U}=1.4339\times\mathrm{F}+0.052727.\] (31)  
The obtained fitting curve was compared with the force applied by the weight to verify the accuracy of the fitting curve. In combination with the actual situation, the multi-legged robot used in this paper usually did not exceed 5 N when the foot was under no load. When the applied force was 5 N, the accuracy of the measurement of the foot tip could reach 4%, that is, the perception of the voltage at the foot end was of 0.1 mV changes. It can be seen from Equation (22) that the relative force perception was less than 0.1 N. Therefore, the flexible foot designed in this paper can effectively reduce the impact force, cause the force to be even and reliable, accurately reflect the change of the foot-end force, and meet the needs of use in the robot.