## 4 Control Design
### Joint Compliance Control  
AAN is one of the most important requirements of the robotic rehabilitation system due to the fact that the disability level of patients not only varies from subject to subject but also changes during training process with each subject. In order to implement the AAN strategy, the disability level of the patient is needed to be estimated first. Then, the compliance of the system is changed accordingly to encourage the patient effort during training. In this study, the relationship between joint compliance and the nominal pressure in the work by [PERSON] et al. (2016) is employed. The compliance \(\gamma_{j}\) of an antagonistic actuator powered by \(n\) couple of PAMs can be described by  
\[\gamma_{j}=\frac{\theta_{j}}{n\left[2R^{2}K_{0j}\theta_{j}+K_{1j}(R^{2}\pi P_ {A0}-P_{AP}y_{A}R)+\Delta P_{j}K_{1j}R^{2}\right]} \tag{17}\]  
in which \(K_{0j}\) and \(K_{1j}\) are the parameters of the spring element of the couple of PAMs which drive actuator \(j\), respectively. These parameters of the developed system are provided in Table 3. The length of anterior PAM corresponding to joint angle \(\theta_{j}\) is \(y_{A}\). Note that \(\theta_{i}\) and \(\Delta P_{j}\) are regulated by the trajectory tracking controller while \(P_{AP}\) is fixed since it decides the initial position of the actuator. Therefore, the nominal pressure \(P_{A0}\) dominates the compliance of the actuators. Figure 4: The block diagram of decoupled channels. \(P_{0}\) is the nominal pressure supplied to the PAM, \(P_{AP}\) is the different pressure of two PAMs. For estimation of the disability level, a new strategy is proposed as follows. Define the human-robot interactive torque (HRIT) as  
\[T_{int}=T_{int}^{passive}-T_{h} \tag{18}\]  
in which \(T_{h}= \begin{bmatrix}T_{h}^{hip}&T_{h}^{bnee}\end{bmatrix} \) are active torques represent the contributions of subjects to the movement of the robotic orthosis. The HRIT is measured by using bar-shaped load cells attached on thigh and shank as shown in Figure 5a. If the effort of subjects is trivial, i.e., \(T_{h}\approx \begin{bmatrix}0&0\end{bmatrix} \), the signals provided by the load cells represent the HRIT of the passive mode in which the disability level of the patient is highest and the robotic orthosis provides full support to dominate the movement of the lower limb. In this case, \(T_{int}=T_{int}^{passive}\) is saved as the torque profile of the subject as illustrated by the black line in Figure 5b. If the subject generates active force which positively contributes to the movement (\(T_{h}>0\)), the signal \(T_{int}^{active}\) from load cells tends to be smaller in comparison with \(T_{int}^{passive}\) (Zone A in Figure 5b). In contrast, \(T_{int}^{active}\) increases when the active force against the movement of the robotic lower limb (\(T_{h}<0\)) which is illustrated by Zone B in Figure 5b. This difference can be treated as human active torque \(T_{h}\) and is utilized to adjust the compliance of the robotic orthosis. Since \(T_{int}^{passive}\) not only varies from subjects to subjects, but also changes with the same subject during the training process, the following procedure is proposed to online estimate \(T_{h}\). _Step 1:_ At the beginning of the training process, the subject is asked to walk on the treadmill in passive mode with full support from the robotic orthosis. Then, the data from the load cells attached to the thigh and shank positions in 30 gait cycles (GCs) are saved as \(T_{int}^{passive}\). This data is the basic profile of each subject and used during the training process. _Step 2:_ In this step, the subject is encouraged to move actively. The signals from the load cells in this step represent \(T_{int}^{active}\). The active torque \(T_{h}\) generated by human effort can be estimated by  
Figure 5: The compliance control method of the AIRGAIT robot orthosis: (**a**) The position of the load cell on robot orthosis and (**b**) the dependence of the robot compliance base on the human effort.