## 4 Simulation and Experimental Analysis
### Simulation Results and Discussion  
To compare the performances of the control algorithms, the patient's interference with the lower limb rehabilitation exoskeleton robot was regarded as step interference. At 1.5 s and 3.5 s, \(\tau_{d1}=50\text{N}\cdot\text{m}\) and \(\tau_{d2}=75\text{N}\cdot\text{m}\) were applied to each joint of the robot for a duration of 0.2 s. These interferences also represent strong environmental interference to the lower limb rehabilitation exoskeleton robot. The trajectory tracking curve and tracking error curve of each joint of the lower limb rehabilitation exoskeleton robot are shown in Figures 5-8. RHq, RKq, LHq, and LKq are the desired trajectories of the right hip, right knee, left hip, and left knee joints. All three control methods can achieve robot trajectory tracking to a certain extent, and the maximum tracking error occurs during the interference period. The following is a detailed analysis of the control accuracy and anti-interference performances. Figure 5: The tracking curve and error of the right hip. (**a**) The tracking curve of the right hip; (**b**) The tracking error of the right hip. Figure 8: The angle tracking curve and error of the left knee. (**a**) The tracking curve of the left knee; (**b**) The tracking error of the left knee. Figure 6: The tracking curve and error of the right knee. (**a**) The tracking curve of the right knee; (**b**) The tracking error of the right knee. Figure 7: The angle tracking curve and error of the left hip. (**a**) The tracking curve of the left hip; (**b**) The tracking error of the left hip. To compare the control accuracy of the three control methods, the maximum absolute tracking error \(e_{a}\), the average absolute tracking error \(e_{m}\), and the root mean square error \(r_{e}\) were used as measurement indicators. When the control system is stable, the tracking error is calculated between 1 s and 5 s. The maximum absolute tracking error, average tracking absolute error, and root mean square error of the three control methods are shown in Table 4. Compared with the errors when using the traditional computed torque, the percentage of tracking error reduction is shown in Table 4.  
In terms of Table 4, it is clear that the maximum absolute error, average absolute error, and root mean square error of the DP-SMC were reduced by 16.54%, 15.54%, and 16.22%, respectively, compared with the PID-CTM under the interference of the patient. In addition, the maximum absolute error of the SACDP-SMC, the mean absolute error, and the root mean square error were reduced by 76.61%, 71.77%, and 73.44%, respectively. Both the DP-SMC and SACDP-SMC effectively reduce the trajectory tracking error and improve control accuracy, but the SACDP-SMC achieves the best control accuracy. Even if the patient simultaneously generates 75 Nm of interference torque on each joint of the robot, the maximum absolute error of the proposed SACDP-SMC was only 0.547\({}^{\circ}\). Based on the maximum absolute error \(e_{a}\); the average absolute error \(e_{m}\); and the root and mean square error \(r_{e}\); the SACDP-SMC proposed in this paper sharply reduced the trajectory tracking error of the lower limb rehabilitation exoskeleton robot and improved the control accuracy. To compare the anti-interference capabilities of the three control methods, the error variation \(\Delta e\) and the interference adjustment time \(\Delta t\) were used as measurement indicators. Under patient interference, the maximum error variations of the three control methods are shown in Table 5.  
In terms of Table 5, compared with PID-CTM, the maximum error variation of DP-SMC was reduced by 34.29% and 17.13%, and the maximum error variation of SACDP-SMC was reduced by 73.03% and 76.77%. Both the DP-SMC and SACDP-SMC effectively reduced the impact of interference, but the SACDP-SMC achieved the best anti-interference effect. When the patient simultaneously generated 75 Nm of interference torque on each joint, the maximum error variation of SACDP-SMC was 0.5425\({}^{\circ}\).