# Design of an Active and Passive Control System of Hand Exoskeleton for Rehabilitation
## 5 Experiments
### Experimental Implementation  
* Passive rehabilitation mode:  
The motion ranges of the joints of the volunteer's middle finger are measured by the NDI Optotrak 3-D measurement system, based on which the desired trajectory of the middle finger in joint space is set as:  
\[\mathbf{\theta}_{d}=\left(\begin{array}{l}-0.10t^{3}+0.50t^{2}+18.50t\\ -0.11t^{3}+0.53t^{2}+19.53t\\ -0.83t^{3}+0.42t^{2}+15.38t\end{array}\right). \tag{15}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{3}{c}{**Length of Phalanx (mm)**} & \multicolumn{3}{c}{**Weight of Phalanx (g)**} \\ \hline
**Proximal** & **Middle** & **Distal** & **Proximal** & **Middle** & **Distal** \\ \hline
55 & 34 & 28 & 130 & 65 & 55 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Finger parameters of subject.  
Figure 8: Experimental setup.  
During this experiment, the subject sat before the tablet, wore the glove with exoskeleton on hand, and kept the finger relaxed. The exoskeleton drove the finger to do flexion-extension and track the desired trajectory to make the virtual finger touch the virtual box in the Android tablet. The control block diagram is shown in Figure 6. Control parameters in Equation (9) are \(K_{p}=diag\{0.4,0.4,0.4\}\), \(K_{p}=diag\{0.5,0.5,0.5\}\). The experiment time was 5 s and the data sampling period was 10 ms.  
* Active rehabilitation mode:  
The active rehabilitation mode uses impedance algorithm to drive the exoskeleton by the force on the tip collected by the force sensors.  
During this experiment, the subject sat before the tablet and wore the glove with exoskeleton on hand. The subject was required to exert force on the finger and keep the finger relaxed alternately to stimulate patients with residual motor ability. In the active rehabilitation mode, the exoskeleton follows the hand. The desired trajectory of the active rehabilitation experiment is from the real-time simulation synchronous with the experiment. Control block diagram of the simulation is shown in Figure 7. The contact force in the control law Equation (14) is from the real-time data obtained from the experiment. Other control parameters in Equation (13) during simulation are \(M_{t}=diag\{100,100,100\}\), \(B_{t}=diag\{0.1,0.1,0.1\}\), \(K_{t}=diag\{0.2,0.2,0.2\}\). The parameters in Equation (14) are chosen as \(K_{P}=0.5\), \(K_{I}=0.0625\), \(K_{D}=0.4\). In the simulation, Equation (2) is adopted as the exoskeleton model, and the dynamic parameters are shown in Table 2. During the experiment, the sampling period is 10 ms, and the motion time is 28 s.  
* Active plus passive rehabilitation mode:  
The active plus passive experiment of the hand rehabilitation exoskeleton is the combination of active and passive rehabilitation modes.  
During this experiment, the subject sat before the tablet and wore the glove with exoskeleton on hand. The subject was required to exert force on the finger and occasionally relax the finger to stimulate patients with incomplete motor ability. The sampling period was 10 ms, and the motion time was 5 s. The threshold value of the force on the fingertip was preset to switch the mode between the active and passive rehabilitation automatically. In this experiment, the threshold value was set as 0.6 N from pre-experiments. The desired trajectory of the experiment was also obtained by the real-time simulation. Specifically, if \(\mathbf{F}_{ext}\geq 0.6\) N, then the system considers that the patient is willing to and able to move actively, hence the control system will switch to the active mode. Otherwise, if \(F_{ext}<0.6\) N, then the passive rehabilitation mode is chosen. In order to ensure the stability of the motion, the angular velocities of the joints were calculated by the passive control, and the trajectories were obtained by the integral of velocity.