# Dynamic Parameter Identification of a Lower Extremity Exoskeleton Using RLS-PSO
## 3 Data Acquisition and Discussion
### The Identification of Parameters
#### 3.2.2 Quantitative Analysis of RLS-PSO Identification Accuracy  
The identification of \(X(6:10)\) was implemented by the data acquired from trajectory 1. The search space of \(X(6:10)\) in Table 3 was defined by RLS. \(X(6:10)\) was identified by LS, PSO, and RLS-PSO, respectively. The identification values are shown in Table 4. In each iteration of PSO and RLS-PSO, the best particle which obtains the minimum error is selected. The best particle convergence of PSO and RLS-PSO is shown in Figure 8. The LS does not have iteration processes, so LS is not shown in Figure 8.  
Trajectory 2 was the reference group, and the identification values of \(X(6:10)\) was quantified by the quantitative evaluation method in Figure 7. Figure 9 is a comparison of the identified torque, the measured torque, and the torque error \(T_{error}\). The absolute values of \(T_{error}\) were averaged. The mean \(\pm\) std of the absolute torque error of LS as shown in Figure 10 is 1.0427 \(\pm\) 0.9047 Nm. The mean \(\pm\) std of the absolute torque error of the PSO is 0.5126 \(\pm\) 0.4386 Nm. The mean \(\pm\) std of the absolute torque error of the RLS-PSO is 0.1887 \(\pm\) 0.2475 Nm. As shown in Figure 10, it is clear that the most accurate \(X(1:5)\) was identified by the RLS-PSO. Under the same conditions, the accuracy of RLS-PSO is improved by 81.9% compared with LS, and the accuracy of RLS-PSO is improved by 63.19% compared with PSO. Similarly, Table 5 is the search space of \(X(1:5)\) defined by RLS. The segmental identification strategy was adopted to identify \(X(1:5)\). Table 6 is the identified values of \(X(1:5)\). The best particle convergence of PSO and RLS-PSO is shown in Figure 11. \begin{table}
\begin{tabular}{c c c c c} \hline \(\mathbf{X}(1)\) & \(\mathbf{X}(2)\) & \(\mathbf{X}(3)\) & \(\mathbf{X}(4)\) & \(\mathbf{X}(5)\) \\ \hline
5.38–11.64 & 2.34–5.20 & 2.01–4.25 & 0.10–7.88 & 0.01–1.70 \\ \hline \end{tabular}
\end{table} 
Table 5: The search space of \(X(1:5)\) defined by RLS. Figure 10: The mean \(\pm\) std. of the absolute errors. Figure 9: Measured torque, identified torque, and \(T_{error}\). Figure 12 shows the identified torque, measured torque, and torque error \(T_{error}\). The mean \(\pm\) std of the absolute torque error of LS as shown in Figure 13 is 4.9922 \(\pm\) 3.7366 Nm. The mean \(\pm\) std \begin{table}
\begin{tabular}{c c c c c c} \hline  & \(X(1)\) & \(X(2)\) & \(X(3)\) & \(X(4)\) & \(X(5)\) \\ \hline LS & 6.5124 & 2.4481 & 2.4996 & 1.7285 & 0.0245 \\ PSO & 7.9970 & 3.4969 & 2.9922 & 1.5914 & 0.0752 \\ RLS-PSO & 7.4433 & 3.1788 & 2.8413 & 1.7285 & 0.0372 \\ \hline \end{tabular}
\end{table} 
Table 6: The identified values of \(X(1:5)\). Figure 11: The convergences of X(1:5) in PSO and RLS-PSO: (**a**) The convergence of best particle in RLS-PSO’s iterations; (**b**) The convergence of best particle in PSO’s iterations. of absolute torque error of PSO is 4.3516 \(\pm\) 3.3602 Nm. The mean \(\pm\) std of absolute torque error of RLS-PSO is 1.2128 \(\pm\) 3.100 Nm. The RLS-PSO obsessed the best accuracy. Compared with the LS, the accuracy of the RLS-PSO is improved by 75.70%. Compared with the PSO, the accuracy of the RLS-PSO is improved by 72.13%. In Figure 11, the number iterations are 120 and 280 for RLS-PSO and PSO, respectively. Obviously, the convergence rate of RLS-PSO is larger than that of PSO. It can be seen from Figures 10 and 13 that the accuracy of RLS-PSO is significantly higher than LS and PSO. This result shows that under the same conditions, pre-defining the search space of PSO through RLS can effectively improve the identification accuracy of PSO. Compared with the LS adopted by BLEEX, RLS-PSO does not require static experiments, which not only reduces the complexity of the experiments but also ensures the accuracy of dynamic parameter identification. The hydraulic drive units caused fluctuations in the dynamic parameters during the movement of the exoskeleton.