## 5 Experimental Evaluation
### Experimental Results  
#### 5.2.1 Trajectory Tracking Control  
Firstly, the experiments to compare the performance of the conventional computed torque control and the proposed controller are conducted. These experiments are carried out without the participation of a subject. The results are shown in Figure 7.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Controller Channel** & \(K_{p}\) & \(K_{d}\) & \(\alpha\) \\ \hline Knee mono-arrticular & 0.05 & \(0.8\times 10^{-3}\) & 0.8 \\ Hip mono-arrticular & 0.05 & \(0.5\times 10^{-3}\) & 0.9 \\ Bi-arrticular & 0.04 & \(1.0\times 10^{-3}\) & 0.85 \\ \hline \end{tabular}
\end{table}
Table 5: The parameters of the proposed controller.  
Figure 7: Comparative results between the conventional and proposed computed torque control: (**a**) The hip joint and (**b**) the knee joint.  
It can be seen that by adjusting the additional parameter, i.e. the fractional order \(\alpha\), the tracking performance is significantly improved. With the proposed control method, the system reaches the steady state in 2 GCs and the root mean square tracking error (RMSTE) are \(2.96^{\circ}\) and \(1.89^{\circ}\) for hip and knee joints, respectively. With the conventional computed torque controller, these values are \(3.94^{\circ}\) and \(2.78^{\circ}\), moreover the system can only reach the steady state in 5 GCs. All data are provided in Table 6 in detail. The RMSTE is computed by  
\[RMSTE=\sqrt{\frac{1}{N}\sum_{k=0}^{N}e_{k}^{2}} \tag{22}\]  
in which \(N\) is the total number of sampled data.  
The process starts with the computerised record of the mean of all measured trajectories of participants to evaluate the performance of the system during trajectory tracking mode. Then follows by the maximum tracking error (MTE) and the RMSTE between the average and the desired trajectory are evaluated. Throughout the process, standard deviations (SDs) over the maximum joint angular and compliance errors of subjects are also considered for further study on the intersubject variability. These results are shown in detail in Table 7. The experimental results in passive and active modes are also depicted in Figure 8. As can be observed in Table 7, the MTE and RMSTE are below \(5.85^{\circ}\pm 0.56\) and \(4.25^{\circ}\pm 1.01\) for both hip and knee joints in passive walking mode. In active mode where the participants contribute force to the movement of their lower limb, the tracking performance is slightly degraded, i.e., \(MTE=6.81^{\circ}\pm 2.32\) and \(RMSTE=3.16^{\circ}\pm 1.26\). These results are deemed suitable for rehabilitation system in practice. Also, the small value of SDs means that the control system is robust against the variance of the subjects and is able to guide different types of patients in the rehabilitation process.  
\begin{table}
\begin{tabular}{c c c} \hline \multirow{2}{*}{**Joints**} & \multicolumn{2}{c}{**RMSTE [Degrees]**} \\ \cline{2-3}  & **Conventional Method** & **Proposed Method** \\ \hline Hip & 3.94 & 2.96 \\ Knee & 2.78 & 1.89 \\ \hline \end{tabular}
\end{table}
Table 6: Comparative root mean square tracking error (RMSTE).  
Figure 8: Trajectory tracking control performance of AIRGAIT robotic orthosis in: (**a**) passive mode and (**b**) active mode. The gait data is normalized and plotted as reference trajectories.