Disturbance-Resilient Flatness-Based Control for End-Effector Rehabilitation Robotics

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Human rehabilitation is a very demanding and complicated process, and in recent years, the use of electromechanical systems for rehabilitation assistance has been expanding. Experience shows that this is a progressive method of rehabilitation with excellent results. This study introduces a new iTbot device for upper limb rehabilitation with the possibility of human interaction with this device. The authors refer to this device as the Robot. The authors' goal is to achieve accurate and adaptive trajectory tracking in the presence of unmeasured dynamics and forces of human-robot interaction.

The introduction of the article contains an overview of the current state of the art in this area and justifies the need for this research solution.
Control design is an important part of this work and is extensively described in the next part of this article.
Stability study is also an important part.
Simulation results show that the proposed controller meets the requirements.
Experiments also confirm the correctness of the proposed solution.
The article brings new benefits to this area and brings new principles for solving the identified problems.

Comments:
1. Figure 1 is nice, but it is necessary to supplement this figure with a kinematic diagram defining the coordinate system and individual quantities.
2. Figure 2 is distorted and of poor quality. It needs to be reworked.
3. Figure 3 is also in poor resolution and of poor quality.
4. Some equations in the article are not numbered. For example, the last equation on page 9 and page 10 is not numbered. Also on pages 12, 13, 16, 17 the authors stopped numbering the equations.
5. On some pages where there are figures, blank spaces are unnecessarily left.

Author Response

Comments:
1. Figure 1 is nice, but it is necessary to supplement this figure with a kinematic diagram defining the coordinate system and individual quantities.

Thank you for your valuable suggestion. The purpose of Figure 1 is to present the mechanical architecture and highlight the components relevant to the mechanical design of the iTbot platform. The kinematic configuration, including the definition of coordinate systems and associated quantities, is indeed important but is intentionally addressed in the later section titled “Kinematics and Mathematical Model of iTbot”, where Figure 3 provides a detailed kinematic diagram. To clarify this distinction for the reader, we have added a sentence in the caption of Figure 1 and updated the main text to reference the relevant figure and section discussing the kinematics.

2. 
   Figure 2 is distorted and of poor quality. It needs to be reworked.

Thank you for pointing this out. We agree with your observation. In the revised manuscript, we have reworked Figure 2 by improving its resolution and adjusting its dimensions to ensure better clarity and visual quality. We believe the updated version enhances the readability and presentation of the figure.

3. 
   Figure 3 is also in poor resolution and of poor quality.

Thank you for your feedback. We acknowledge the quality issue with Figure 3. In the revised version of the manuscript, we have updated this figure by enhancing its resolution and graphical clarity to ensure all elements—particularly coordinate frames, joint variables, and linkages—are clearly visible and legible. We trust the improved version now meets the expected publication standards.

4. 
   Some equations in the article are not numbered. For example, the last equation on page 9 and page 10 is not numbered. Also on pages 12, 13, 16, 17 the authors stopped numbering the equations.

Thank you for your careful review. We appreciate your attention to detail. In the revised manuscript, we have thoroughly reviewed all equations and ensured consistent and sequential numbering throughout the entire article, including the previously unnumbered equations on pages 9, 10, 12, 13, 16, and 17.

5. 
   On some pages where there are figures, blank spaces are unnecessarily left.

Thank you for bringing this to our attention. The blank spaces around some figures are a result of the journal's template and its layout constraints during manuscript preparation. If the paper is accepted, we trust that the journal's editorial and production team will assist in resolving these layout issues during the final typesetting stage to ensure optimal formatting.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript presents an interesting study with good results. The paper is well written and organized, with actual references.

The author should correct some issues:

In equation 28, J(k) should be identified.

Page 17, line 422, the author mentioned "Standard Deviation of the Control (SDC)", but it is never defined or used. I believe this is an important performance parameter.

In the conclusion, the author mentioned "Both simulation and experimental results consistently illustrate improved tracking accuracy, compliance, and robustness compared to traditional approaches", but the author never presented comparison with other approaches!! Therefore, the author should include results from other approaches and compare.

 

Author Response

In equation 28, J(k) should be identified.

The matrix J is  the control  input matrix, and it defined in Eq. 29 (updated version).

Page 17, line 422, the author mentioned "Standard Deviation of the Control (SDC)", but it is never defined or used. I believe this is an important performance parameter.

Thank you for noticing this inconsistency. The term “SDC” was introduced inadvertently; the study actually evaluates performance using Mean Absolute Error (MAE) and Standard Deviation of the Error (SDE), as reported in Table 3. In the revised manuscript we have

• Deleted the stray reference to SDC on p. 17, l. 422;
• Added an explicit definition of SDE immediately before Table 3; and
• Checked the entire text to ensure only MAE and SDE are used consistently.

These two metrics capture both accuracy (MAE) and dispersion/robustness (SDE) of the tracking performance. Investigating additional indices such as SDC is an interesting direction, but it is beyond the scope of the present paper. We believe the correction now eliminates any ambiguity.

 

3. In the conclusion, the author mentioned "Both simulation and experimental results consistently illustrate improved tracking accuracy, compliance, and robustness compared to traditional approaches", but the author never presented comparison with other approaches!! Therefore, the author should include results from other approaches and compare.

Thank you for your comment. We would like to clarify that a comparative evaluation is already provided in the manuscript. Specifically, in Section 5.3, the proposed disturbance-resilient flatness-based control is compared against the conventional flatness-based control in two distinct scenarios: Without external disturbances, and With external disturbances applied.

Performance metrics (MAE and SDE) are reported in Table 3 to highlight differences in tracking accuracy and robustness. These results demonstrate the improved performance of our approach in both simulation and experimental settings. To improve clarity, we have revised the conclusion to explicitly reference the comparative nature of the study and the corresponding results.

 

 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript has been sufficiently improved to warrant publication in Actuators.