## 3 Methods
### Variable Admittance Controller Design  
In humans, the brain is the controller, and the muscle is the actuator. In normal walking, the main problem of patients with lower muscle strength is that their muscles cannot provide the required torque to make them walk normally. In other words, when the human leg is in a swing phase, the torque provided by the muscles is not enough to make the human leg swing to the desired angle. Therefore, an admittance controller is proposed, which can judge human motion intention according to the interaction force between the human and the exoskeleton, and control the human exoskeleton system to make  
Figure 5: Expression of impedance and admittance of coupling model of the human lower limb and the exoskeleton. the human leg swing to the desired angle. The admittance control structure of the human-exoskeleton coupling system is shown in Figure 6. It is worth noting that the movement is still determined by the wearer, and the admittance controller adjusts the reference rehabilitation training trajectory to provide appropriate assistance according to the wearer's motion intention. Admittance controller is the reciprocal variant of the impedance controller, whose performance depends on the accuracy of the force sensor and the position sensor. Compared with impedance control, admittance control is usually easier to implement in hardware. According to the definition of impedance, the desired impedance model of interaction between the human lower limbs and the exoskeleton can be designed as:  
\[\left\{ \begin{array}{l}\widetilde{\mathbf{T}}_{\mathbf{h}}(t)=\mathbf{J}_{ \mathbf{d}}\Delta\dot{\mathbf{q}}(t)+\mathbf{B}_{\mathbf{d}}\Delta\dot{\mathbf{q }}(t)+\mathbf{K}_{\mathbf{d}}\Delta\mathbf{q}(t)\\ \Delta\mathbf{q}(t)=\mathbf{q}_{\mathbf{a}}(t)-\mathbf{q}_{\mathbf{d}}(t) \end{array} \right., \tag{12}\]  
where \(\mathbf{J}_{\mathbf{d}}\), \(\mathbf{B}_{\mathbf{d}}\), and \(\mathbf{K}_{\mathbf{d}}\) are desired rotary inertia matrix, desired rotary damping matrix and desired rotary stiffness matrix respectively; \(\mathbf{q}_{\mathbf{d}}\) and \(\mathbf{q}_{\mathbf{a}}\) are desired move trajectory vector and desired control trajectory vector of the exoskeleton for rehabilitation of human lower limb in joint space, so \(\Delta\mathbf{q}\) is the correction of the desired trajectory; \(\widetilde{\mathbf{T}}_{\mathbf{h}}\) is the estimated voluntary torque generated by the human joint, which can be obtained by the above method. Because the patient's own muscle strength is small, the patient's movement is relatively slow in the rehabilitation training. Thus, the acceleration term in the impedance model could be ignored; by only considering the rotation damping coefficient and rotation stiffness coefficient, the following impedance model could be obtained:  
\[\left\{ \begin{array}{l}\widetilde{\mathbf{T}}_{\mathbf{h}}(t)=\mathbf{B}_{ \mathbf{d}}\Delta\dot{\mathbf{q}}(t)+\mathbf{K}_{\mathbf{d}}\Delta\mathbf{q}( t)\\ \Delta\mathbf{q}(t)=\mathbf{q}_{\mathbf{a}}(t)-\mathbf{q}_{\mathbf{d}}(t) \end{array} \right., \tag{13}\]  
In the frequency domain space of the control system of exoskeleton, Equation (13) can be rephrased as:  
\[Y(s)=\frac{\Delta\mathbf{Q}(s)}{\widetilde{\mathbf{T}}_{\mathbf{h}}(s)}=\frac {1}{\mathbf{B}_{\mathbf{d}}s+\mathbf{K}_{\mathbf{d}}}, \tag{14}\]  
In the process of rehabilitation training, the rotational stiffness and damping of the human lower limb joint will change according to the voluntary torque of the human; therefore, the parameters of the admittance controller also need to be changed according to changes in human voluntary  
Figure 6: Admittance control structure of the human exoskeleton coupling system. torque. Based on the voluntary torque of the wearer's lower limb joint, the admittance parameters are changed. When the voluntary torque of the human joint is large, the parameters of the admittance controller should be appropriately increased to increase the training intensity and active participation of the wearer.