# Design of Hybrid Phase Sliding Mode Control Scheme for Lower Extremity Exoskeleton
## 2 Methods
### Design of SMC Based on ESO
#### 2.2.2 Design of Sliding Mode Controller
The reason may be that the toes play a small role when the person walks. The data of HEELL and HEELR was averaged and considered to be the sampling of the heel. Therefore, High Dynamic Force Sensing Resistor-Insole was regarded as collecting six channels data at once time. The gait recognition method based on plantar pressure is the important content of switching. First, the gait characteristics are selected as the force characteristic and the force trend characteristic of the hallux (M), the forefoot (N), the arch (P) and the heel (Q). According to the gait characteristics of the people, the phase labels of the gait data is obtained through the collected pressure signal. Figure 4 shows a snapshot of the signal acquisition process, and ABCDE represents five gaits during the subject motion. The selected gait characteristics are shown in Table 1, and the gait phase is classified, as shown in Figure 5:  
Figure 4: The subject motion snapshot  
Figure 3: The left shows the division of seven gait phases, which represent the statistical results of the plantar pressure signal; the plantar pressure data is collected by the right High Dynamic Force Sensing Resistor-Insole. (**a**) Gait division; (**b**)High Dynamic Force Sensing Resistor-Insole. The real-time phase is identified, so the gait can be predicted in advance: this work benefits from smooth switching of the controller. First of all, the gait should be classified. The classification result of gait phase is shown in Figure 5.  
As a neural network, the Extreme Learning Machine can be applied to the train the phase detector and complete the gait recognition, which is designed by the following specific steps:  
1. The number of neurons in the hidden layer is 200;
2. The activation function of the hidden layer neurons is \(sigmoid(x)=(\frac{1}{1+e^{-x}})\), and computes the hidden layer output matrix \(H\);
3. Compute output layer weight \(\hat{\beta}\): \(\hat{\beta}=H+T^{\prime}\). The extreme learning machine model based on the plantar pressure signal has good prediction accuracy. Figure 6 shows the classification result of data from 1000 gaits (actual test sets). Experiments show that the extreme learning machine can guarantee the accuracy to more than 95%, so it has practical meaning to use this identification model in the switching motion of the exoskeleton. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Pressure Feature**} & \multicolumn{4}{c}{**Plantar Pressure**} & \multicolumn{4}{c}{**Plantar Pressure Trend**} \\ \cline{2-9}  & \(S_{Q}\) & \(S_{P}\) & \(S_{N}\) & \(R_{M}\) & \(R_{Q}\) & \(R_{P}\) & \(R_{N}\) & \(S_{M}\) \\ \hline (A) init-st & 1 & 0 & 0 & 0 & 1 & 1 and \(-1\) & 1 and \(-1\) & 1 and \(-1\) \\ (B) mid-st & 1 & 1 & 1 & 1 & 1 and \(-1\) & 1 and \(-1\) & 1 & 1 \\ (C) term-st & 0 & 1 & 1 & 1 & 1 and \(-1\) & \(-1\) & 1 and \(-1\) & 1 \\ (D) pre-st & 0 & 0 & 1 & 1 & 1 and \(-1\) & 1 and \(-1\) & \(-1\) & 1 and \(-1\) \\ (E) swing phase & 0 & 0 & 0 & 0 & 1 and \(-1\) & 1 and \(-1\) & 1 and \(-1\) & 1 and \(-1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Gait characteristics correspondence table in each state. (1 means the force is gradually increasing, and \(-1\) means the force is gradually decreasing. 0 means the position is not under pressure.) Figure 5: Gait phase classified by plantar pressure data. This picture shows how the pressure data of one cycle can be divided into five gaits. The starting point of the black line represents the touch of the ground by the heel; the starting point of the purple line represents the full touch of the right foot (left toe off the ground); the end of the black line represents the right heel off the ground (the left and right feet are exchanged); the end of the purple line represents the right arch of the foot is off the ground (the left heel touches the ground); the end of the red line represents the right toe off the ground.