# Dynamic Parameter Identification of a Lower Extremity Exoskeleton Using RLS-PSO
## 3 Data Acquisition and Discussion
### Data Acquisition  
The acceleration signal is affected by the vibration of the pedestal [42], resulting in an increase in the identification error. The vibration caused by the simultaneous swing of the hip and knee joint is larger than the vibration of the single knee joint. Therefore, in order to reduce the influence of the vibration of the pedestal, a segmental identification strategy was adopted. First, the hip joint was fixed. The knee joint swung. At this time, the vibration of the pedestal was relatively small. The identification of \(X(6:10)\) was completed first. By then, the hip and knee joints swung together to complete the identification of \(X(1:5)\). The flowchart of segment identification is shown in Figure 5. There are three steps of the segmental identification strategy:  
1. The hip joint is fixed. The knee joint follows the target trajectory. \(T_{2}\) and \(H_{k}\) are acquired. Substitute \(T_{2}\) and \(H_{k}(6:10)\) into Equation (6) to define the range of \(X(6:10)\) as the search space of the PSO. The identification of \(X(6:10)\) is completed by Equation (7) and (8);
2. Both the hip and knee joints follow the target trajectory. After that, \(H_{h}\) is acquired. Substitute \(H_{h}(6:10)\) and \(X(6:10)\) into equation (9) to calculate \(T_{1}^{2}\). \(T_{1}^{2}\) is the torque generated by the hip joint to resist the interference of the swing on the knee joint. \(T_{1}\) is calculated by equation (4). \(T_{1}^{\prime}\) is the difference between \(T_{1}\) and \(T_{1}^{2}\); \[T_{1}^{2}=H_{h}(6:10)X(6:10)\] (9)
3. Substituting \(H_{h}\) and \(T_{1}^{\prime}\) into Equation (6) defines the range of \(X(1:5)\) as the search space of the PSO. \(X(1:5)\) is identified by Equations (7) and (8).  
Figure 4: Flowchart of the recursive least square–particle swarm optimization (RLS-PSO) method.  
The trajectories of the hip and knee joints of APAL are shown in Table 1. No.1 and No.2 are the trajectories of knee joint swing experiments. No.3 and No.4 are the trajectories of the hip and knee joints swing experiments.  
As shown in Figure 6, the APAL's trunk and left lower extremity were fixed to the pedestal and the right lower extremity was suspended. The PID control law was adopted to make the hip and knee joint track the given trajectories in Table 1. The sampling frequency was 1000 Hz. When people walk and run, the frequency of motion is 0.85-5 Hz [43; 44]. According to the sampling theorem, the measured and calculated data were zero-phase filtered with a 10 Hz low-pass filter. Compared to differential filters, zero-phase filters do not cause signal phase shifts and waveform distortion. Therefore, a zero-phase filter was adopted to reduce the effect of waveform distortion on the accuracy of the identification.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Hip Trajectory** & **Knee Trajectory** \\ \hline
1 & \(-10\) & \(45-30\)sin(2\(\pi\)t) \\
2 & \(-10\) & \(60-30\)sin(2\(\pi\)t) \\
3 & \(-30-30\)sin(2\(\pi\)t) & \(75-30\)sin(2\(\pi\)t) \\
4 & \(-45-30\)sin(2\(\pi\)t) & \(60+30\)sin(2\(\pi\)t) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Trajectories of hip and knee joints.  
Figure 5: Flowchart of segmental identification strategy.  
Figure 6: Data acquisition of APAL: **(a)** Hip joint was fixed and knee joint swung; **(b)** Hip and knee joints swung.  
The tracking accuracy and response time of the hip and knee joints in the experiment are shown in Table 2.  
Table 2 shows that APAL has good accuracy and response performance. The hip and knee joints accurately tracked the given trajectories in Table 1. The measured data can be adopted for parameter identification.