Robust Continuous Sliding-Mode-Based Assistive Torque Control for Series Elastic Actuator-Driven Hip Exoskeleton

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors The work deals with a real-time torque assist control system for a hip exoskeleton driven by a series elastic actuator.

Comments: • The mechanical design of the SEA is interesting as it allows a relatively simple change in stiffness. The focus is on avoiding the excessive stiffness of traditional exoskeletons and providing passive safety (due to elasticity). • The use of medium torque BLDC actuators with 1 kHz control is suitable for walk assistance applications. • The CSMC + ESO control is excellent in terms of fast convergence, low drift and disturbance rejection capability. The sgn(s) integrator eliminates vibration and allows a smooth transition in control force. • Tests with different gear profiles, higher speeds or terrains have not yet been performed. • It would be good to work with the nonlinear dynamic model to avoid certain uncertainties. • A comparison between different sgn(s) activation functions, such as the saturator function or the hyperbolic tangent, would be good. • Improve the quality of some graphs. Comments on the Quality of English Language

The English language could be improved.

Author Response

Comment : The mechanical design of the SEA is interesting as it allows a relatively simple change in stiffness. The focus is on avoiding the excessive stiffness of traditional exoskeletons and providing passive safety (due to elasticity). The use of medium torque BLDC actuators with 1 kHz control is suitable for walk assistance applications. The CSMC + ESO control is excellent in terms of fast convergence, low drift and disturbance rejection capability. The sgn(s) integrator eliminates vibration and allows a smooth transition in control force.

Response : We are deeply grateful for your positive evaluation of our research methodology and outcomes, along with your professional recommendations. We have tried our best to revise the manuscript based on your comments.

Question 1: Tests with different gear profiles, higher speeds or terrains have not yet been performed.

Response : Thanks for your professional comment.This study developed a novel series elastic actuator (SEA) for the hip joint lower-limb exoskeleton. By dynamically adjusting the stiffness of the elastic element, the proposed design effectively addresses the issues of insufficient shock absorption and uneven torque output in traditional exoskeletons, thereby improving interaction safety and user comfort. Currently, the research is still in the testing phase. To ensure controlled experimental variables and rigorous algorithm comparison, initial validation was conducted using a fixed-speed flat treadmill. However, due to current equipment limitations, we have not yet established the experimental conditions required for variable-speed or complex terrain testing.

To address potential concerns regarding the control methods effectiveness under different conditions, we have supplemented the experimental section with data from 5 additional test subjects (Page 16), further validating the adaptability of the SEA and the CSMC+ESO control scheme across individuals. Furthermore, we plan to procure an adjustable treadmill with controllable incline angles and variable speeds to conduct tests under dynamic conditions (e.g., acceleration/deceleration and slope walking), enabling a comprehensive evaluation of the exoskeletons performance in more complex scenarios. The current study has successfully validated the effectiveness of the core innovations, while more extensive verification under broader testing conditions will be the primary focus of subsequent research.

The detailed modifications are presented as follows.

(Page 16) To evaluate the performance of the hip exoskeleton controller, treadmill-based experiments were conducted with five healthy male participants (age: 26 ± 2 y.o.; height: 175.3 ± 5.2 cm; weight: 68 ± 9.2 kg). All participants provided written informed consent prior to testing. The experimental setup is illustrated in Figure 10. Participants performed walking trials while wearing the exoskeleton under three distinct control approaches including the novel control strategy proposed in this study along with conventional PID control and ADRC. Twenty trials were conducted for each control strategy (5 participants ×4 trials per participant), with each 5-minute trial followed by a 30-minute rest period to control for fatigue. For analysis, a representative 15-second interval comprising 8 complete gait cycles was selected from each trial. The treadmill maintained a constant speed of 1 m/s throughout all experiments.

(Page 18)

Question 2: It would be good to work with the nonlinear dynamic model to avoid certain uncertainties.

Response: Many thanks for the valuable comment. In the current study, the Extended State Observer (ESO) has demonstrated effective compensation for unknown disturbances and parametric uncertainties (Section 4.3). While our SEA-CSMC-ESO framework has achieved satisfactory tracking performance (ATE = 0.0501Nm, SDE = 0.0553Nm, MAE = 0.4735Nm), we fully acknowledge that incorporating nonlinear stiffness variations could further enhance robustness. This constitutes our future research focus, with planned investigations into variable impedance modeling under dynamic loading conditions, nonlinear parameter identification during gait transitions, and adaptive control co-design with the enhanced model.

Question 3: A comparison between different sgn(s) activation functions, such as the saturator function or the hyperbolic tangent, would be good.

Response: Thanks for your professional advice. After thorough theoretical analysis, we maintain that the integral sgn(s) function remains optimal for our sliding surface design due to three key considerations: (1) While both saturation and tanh functions can reduce chattering, the saturation function’s non-differentiable nature makes it unsuitable for derivative-based controller design (Page 12 (34)); (2) The tanh function inevitably introduces tuning complexity and phase lag; (3) Our primary innovation lies in the SEA-CSMC-ESO co-design framework, where function selection shows negligible impact on the main conclusions. We sincerely appreciate your understanding regarding the focused scope of the current study, and we will conduct in-depth investigations into activation function optimization in our subsequent research.

Question 4: Improve the quality of some graphs.

Response: Thanks for your carefully reviewing. We have thoroughly examined all figures in the manuscript and made necessary revisions to both the figures and grammatical content.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1.The preliminary human subject experiment section would be stronger if the more details were provided about the trial setup, such as the number of gait cycles captured, measurement methods, and sensor accuracy. Currently, the experiment seems a bit limited in scope with only one subject and may not fully validate the robustness claims.

2.While the comparison between CSMC+ESO and PID control is well laid out, it would be beneficial to include the results from the ADRC method as well, given its earlier mention. This would provide a more complete picture of the relative performance across all discussed strategies.

3.The statistical metrics (ATE, SDE, MAE) are reported and compared effectively. However, no the statistical significance testing (e.g., p-values or confidence intervals) is provided to support the claim that one method is definitively better. This should be addressed to strengthen the experimental validation.

4.The manuscript states that the control strategy is "favorable for practical applications," but no discussion is provided regarding potential challenges in real-world deployment, such as variability across users, fatigue, or long-term wear. Adding a brief discussion on these aspects would make the paper more comprehensive.

Author Response

Question 1: The preliminary human subject experiment section would be stronger if the more details were provided about the trial setup, such as the number of gait cycles captured, measurement methods, and sensor accuracy. Currently, the experiment seems a bit limited in scope with only one subject and may not fully validate the robustness claims.

Our response: Thank you very much for your professional comment and detailed suggestions for revising the paper. We added 10 subjects and supplemented detailed experimental testing methods along with results to make the experimental demonstration more convincing.

The detailed modifications are presented as follows.

(Page 6) The electrical system is depicted in Figure 4, receiving data from the IMU (±0.2° static attitude error, ±20˜40mg accelerometer zero-bias, 0.75mg-rms noise, ±0.5° gyro zero-bias), a Bluetooth-to-serial conversion module (MX-02, MIAOSHARE, China) was used as the communication medium in this study. The control board processes the data received and sends control signals to the motors. As the power source of the exoskeleton, each SEA is powered by a DC brushless servomotor (CRA-RI60-70-PRO, TI5 ROBOT, China) to provide an average maximum driving torque of 32 Nm with a CAN communication period of 1 ms. To achieve closed-loop control, the position and velocity of the SEA outputs need to be measured. An absolute magnetic encoder (eCoder35, 17-bit resolution, ZEROERR, China) is used for this purpose. The encoder communicates via RS485 and sends the measured data to the control board.

(Page 16) To evaluate the performance of the hip exoskeleton controller, treadmill-based experiments were conducted with five healthy male participants (age: 26 ± 2 y.o.; height: 175.3 ± 5.2cm; weight: 68 ± 9.2 kg). All participants provided written informed consent prior to testing. The experimental setup is illustrated in Figure 10. Participants performed walking trials while wearing the exoskeleton under three distinct control approaches including the novel control strategy proposed in this study along with conventional PID control and ADRC. Twenty trials were conducted for each control strategy (5 participants ×4 trials per participant), with each 5-minute trial followed by a 30-minute rest period to control for fatigue. For analysis, a representative 15-second interval comprising 8 complete gait cycles was selected from each trial. The treadmill maintained a constant speed of 1 m/s throughout all experiments.

Question 2: While the comparison between CSMC+ESO and PID control is well laid out, it would be beneficial to include the results from the ADRC method as well, given its earlier mention. This would provide a more complete picture of the relative performance across all discussed strategies.

Our response: Many thanks for the valuable comment. We supplemented the experimental section (Section 5) with ADRC method tests, comparing the proposed control method with PID and ADRC.

The detailed modifications are presented as follows.

(Page 17)

(Page 19) Figures 12 and 13 present the experimental data of the exoskeleton under ADRC and PID strategies, respectively. Table 2 lists three statistical indicators for the these control methods, where ATE, SDE and MAE are calculated using tracking errors during 0s ≤ t ≤ 15s. Figure 14 compares the average tracking accuracy of the three control methods, with each method evaluated on 20 independent datasets. Specifically, Figures 12(a) and 13(a) demonstrate the output torque tracking performance relative to reference torque under ADRC and PID control, respectively. Figures 12(b) and 13(b) illustrate the adaptive phase oscillator’s response to subject gait during ADRC and PID experiments. Figures 12(c) and 13(c) compare the controller’s estimated angular velocity with the true values, showing the estimated values generally meet the requirements and closely fit the true values in both experiments. Figures 12(d) and 13(d) display the deflection angle of the SEA during the ADRC and PID experiment, revealing jitter phenomena compared to the curve in Figure 11, which indicates that the CSMC+ESO control strategy designed in this study outperforms the ADRC and PID algorithms in terms of robustness. The overall tracking accuracy of PID is lower, confirming its limited robustness against uncertainties and external disturbances. In contrast, the high robustness of the proposed control strategy is verified by the MAE metric, consistent with the results shown in Figures 11, 12 and 13. Figures 12(e) and 13(e) depict the tracking error of the ADRC and PID algorithms, showing that it is inferior to the proposed algorithm in terms of tracking accuracy, maximum error, and average error. Notice that the ATE metrics also indicate that the proposed control strategy in the experiment converges faster, proving that the CSMC+ESO control strategy indeed has higher accuracy. Table 2 can illustrates this more precisely. Figures 12(f) and 13(f) show the motor input current during the ADRC and PID experiments, with larger extreme values, higher instantaneous rates of change and more jitter compared to Figure 11, the conclusion is also shown in the SDE metric, which verifies that the proposed improvement reduces jitter vibration in the control process, making it less demanding on the controller and motor, and more favorable for practical applications.

Question 3: The statistical metrics (ATE, SDE, MAE) are reported and compared effectively. However, no the statistical significance testing (e.g., p-values or confidence intervals) is provided to support the claim that one method is definitively better. This should be addressed to strengthen the experimental validation.

Our response: Thanks for your professional advice. We have supplemented statistical significance tests (p-values) to verify that the differences between the proposed control method and the comparative methods in ATE/SDE/MAE metrics are statistically significant (p < 0.05), thereby providing quantitative evidence for the superiority of the control performance.

The detailed modifications are presented as follows.

(Page 18)

Figure 14. Comparison of average tracking errors across the three control algorithms. Error bars represent ±1 SEM, and ∗∗ indicate statistically significant difference (p < 0.05).

Question 4: The manuscript states that the control strategy is ”favorable for practical applications,” but no discussion is provided regarding potential challenges in real-world deployment, such as variability across users, fatigue, or long-term wear. Adding a brief discussion on these aspects would make the paper more comprehensive.

Our response: Thanks for your carefully reviewing. In this revision, we have supplemented experimental data from 5 additional subjects to better reflect inter-user variability in the test results. Since both the proposed SEA for hip exoskeletons and the CSMC+ESO control method are still in the testing phase, our next research focus will address real-world challenges such as fatigue effects and long-term wearability impacts following experimental validation.

Author Response File: Author Response.pdf