## 3 Methods
### Experimental Design and Implementation
#### 3.5.2 Track Tracking Experiments Under Different Admittance Conditions  
The track tracking experiments under different admittance conditions mainly includes three sub-experiments, which are track tracking experiment with no admittance, track tracking experiment with fixed admittance, and track tracking experiment with variable admittance. Track tracking experiment with no admittance was carried out to verify the position control performance of the proposed ASMVA controller. Through the track tracking experiment with fixed admittance, the influence of different fixed admittance parameters on track tracking was analyzed. Track tracking  
Figure 8: The experimental procedure. (**a**) Vertical state. (**b**) Hip-joint starts to flex. (**c**) Hip-joint rotates to 35 degrees. (**d**) Knee joint starts to extend. (**e**) Knee joint rotates to 60 degrees. (**f**) Exoskeleton restores to vertical state. Figure 7: The LLRE robot prototype worn by a healthy subject. experiment with variable admittance was carried out to verify that the proposed ASMVA controller could adjust admittance parameters according to patients' movement intention in training. According to the overall block diagram of the control strategy shown in Figure 6, the inner loop ASMC (adaptive sliding mode controller) controller is responsible for accurate tracking of the preset trajectory of the knee-joint adjusted by the admittance controller. In fact, if the admittance parameters are all set to infinity, the ASMVA controller can be transformed into a position controller to track the predefined training track. Therefore, this track tracking experiment with no admittance was carried out to prove the control accuracy of the inner loop ASMC controller. The initial state of track tracking experiment was that the hip joint of exoskeleton drove the subject's leg to rotate 35 degrees, and then the hip joint was locked. During this experiment, the knee joint track was preset as a sine wave track with frequency of 0.1 Hz, peak amplitude of 50 degrees and phase of \(\pi/2\). The time required for each experiment was 20 s, that was, the subject's shank swung two cycles along the preset sine wave track driven by the exoskeleton. In order to ensure control accuracy and system stability, the parameters of the GSMC (general sliding mode controller) algorithm were tested many times and modulated optimally. The recommended control parameters for ASMVA controller were set to \(\Lambda=50\), \(K=55\), \(\varepsilon_{N}=0.5\), \(b_{d}=0.6\), \(B_{p0}=B_{n0}=10^{10}\), \(K_{p0}=K_{n0}=10^{10}\), \(\alpha_{p}=\alpha_{n}=0\), \(\beta_{p}=\beta_{n}=0\). The recommended configurations of the RBF neural network were: the number of hidden layer nodes was 7, \(\textbf{c}=[-1.5,\ -1.0,\ -0.5,\ 0\,\ 0.5,\ 1.0,\ 1.5]\), \(\textbf{b}=[12,\ 12,\ 12,\ 12,\ 12,\ 12,\ 12,\ 12]\). The purpose of the passive training mode with no admittance is to ensure the accuracy of repeated track tracking during rehabilitation training, and it is suitable for patients without any active muscle strength. However, if the patient restores part of muscle strength, the introduction of admittance control into passive training mode can improve the flexibility of human-exoskeleton interaction and ensure the comfort of the patient in the training process. In order to verify the influence of the ASMVA controller on track tracking under different fixed admittance parameters, subject H1 (male, 24 years old, weight/60 kg, height/1.70 m) was required to wear the exoskeleton for a track tracking experiment under three different admittance controller configurations of large admittance, medium admittance, and small admittance.