Trot Gait Stability Control of Small Quadruped Robot Based on MPC and ZMP Methods
Round 1
Reviewer 1 Report
This paper presents the stability control of a small quadruped robot using MPC and ZMP methods. Some simulation and experimental results are carried out to verify the suggested control method. I have some comments for the authors as follows.
1. The introduction can be improved with a more typical literature review. It's better to logically reorganize and emphasize the recent studies on MPC and ZMP control of quadruped robots, which can be referred to improve the literature review.
2. The paper's contributions should be listed one by one for more clarity.
3. MPC and ZMP are not new methods, so I don't know what the author's innovation is. The author should provide comparisons to other methods, such as PID, LQR, etc. The table to summarize the control performance of all comparative controllers is also offered.
4. Please use the unique unit for the angle (rad or degree) in Figure 13. (Maybe change the Yaw angle to degree)
5. Please provide the experimental verification of subsection 3.6
6. All the controller parameters of all simulations and experiments must be listed.
Author Response
Reviewer#1
Thank you very much for your affirmation of our paper, and thank you for your valuable and thoughtful advice. Next, we will sincerely response your comments one by one.
Comment 1: The introduction can be improved with a more typical literature review. It's better to logically reorganize and emphasize the recent studies on MPC and ZMP control of quadruped robots, which can be referred to improve the literature review.
Response: The introduction has been revised with some typical literature reviews.
Comment 2: The paper's contributions should be listed one by one for more clarity.
Response: The conclusion has been modified, and the contribution has been explained in the conclusion.
Comment 3: MPC and ZMP are not new methods, so I don't know what the author's innovation is. The author should provide comparisons to other methods, such as PID, LQR, etc. The table to summarize the control performance of all comparative controllers is also offered.
Response: Thank you for your valuable and thoughtful advice. In the following research on quadruped robot, we will compare the method in this paper with PID, LQR and other methods.
Comment 4: Please use the unique unit for the angle (rad or degree) in Figure 13. (Maybe change the Yaw angle to degree)
Response: The Figure 13 (b) has been modified according to your comment.
Comment 5: Please provide the experimental verification of subsection 3.6.
Response: We will further add relevant contents of test verification in the subsequent research.
Comment 6: All the controller parameters of all simulations and experiments must be listed.
Response: All the controller parameters of all simulations and experiments have been added in the paper.
Once again, thank you very much for your constructive comments and suggestions which would help us in depth to improve the quality of the paper.
Kind regards,
Wenfei Liu
E-mail: [email protected]
Author Response File: 
Author Response.doc
Reviewer 2 Report
The paper looks theoretically correct. However, the issues discussed in this paper need further improvements in the following several aspects:
The theoretical contributions should be stressed in detail in Introduction.
More comparisons between different algorithms (2021-2022) with the proposed method will increase the impact of the paper.
The most recent references such as: Desired tracking of delayed quadrotor UAV under model uncertainty; Event-triggered fractional-order sliding mode control for quadrotor, should be cited in this paper.
Future research goals should be expanded more in the last of conclusions.
Some of the parameters and variables have not been defined in the paper. Please check all symbols and parameters.
It is also required to study more recently-published 2022 references in the literature.
Author Response
Reviewer#2
Thank you very much for your affirmation of our paper, and thank you for your valuable and thoughtful advice. Next, we will sincerely response your comments one by one.
Comment 1: The theoretical contributions should be stressed in detail in Introduction.
Response: The introduction has been modified according to your comment.
Comment 2: More comparisons between different algorithms (2021-2022) with the proposed method will increase the impact of the paper.
Response: In the following research on quadruped robot, we will compare the method in this paper with different algorithms.
Comment 3: The most recent references such as: Desired tracking of delayed quadrotor UAV under model uncertainty; Event-triggered fractional-order sliding mode control for quadrotor, should be cited in this paper
Response: The literatures have been cited.
Comment 4: Future research goals should be expanded more in the last of conclusions.
Response: The conclusion has been modified.
Comment 5: Some of the parameters and variables have not been defined in the paper. Please check all symbols and parameters.
Response: All of the parameters and variables have been defined.
Comment 6: It is also required to study more recently-published 2022 references in the literature.
Response: The recently-published 2022 references have been added in the paper.
Once again, thank you very much for your constructive comments and suggestions which would help us in depth to improve the quality of the paper.
Kind regards,
Wenfei Liu
E-mail: [email protected]
Author Response File: Author Response.doc
Reviewer 3 Report
This work aims to theoretically and experimentally integrate model predictive control and the zero moment point in order to improve the gait stability of a quadruped robot. In my opinion, the paper in question needs revision before it can be considered for publication in the processes journal. Some things to think about are as follows.
1- The state of the art is somehow weak. It should be improved in light of recent references that emphasize the gait stability of quadruped robots.
2- In the definitions after Figure 3, Vyw is not defined.
3- The authors state that this paper aims at combining MPC and ZMP to control trot gait stability. However, the results presented in Figure 13 show the effect of MPC and the effect of ZMP alone.
4- The paper represented the experimental results. However, the authors neither include any pictures of this model nor its specifications.
5- The references should be updated to include the most recent ones. From 2019 to 2021, there were just five mentions out of 25. In the year 2022, there are no mentions.
Comments for author File: 
Comments.pdf
Author Response
Reviewer#3
Thank you very much for your affirmation of our paper, and thank you for your valuable and thoughtful advice. Next, we will sincerely response your comments one by one.
Comment 1: Line 109 is the incorrect numbering of the equation.
Response: The numbering of the equations have been corrected.
Comment 2: No spacing after equations, for example, line 113 and others. Please check it in all parts of the article.
Response: The spacing after equations have been added in the paper.
Comment 3: Directly after chapter 3 could be a brief description of touched chapters and subchapters.
Response: We don't think it is necessary, because the conclusions has summarized the relevant contents of Chapter 3 .
Comment 4: Fig.11, 12, and 13 do not look like the Matlab software. Also, their quality is not sufficient.
Response: In fact, all the figures in this paper are drawn by origin, and the data comes from MATLAB simulation.
Comment 5: Overall: the results do not look serious.
Response: Thank you for your valuable and thoughtful advice.
Comment 6: Conclusions are poor.
Response: The conclusion has been modified.
Once again, thank you very much for your constructive comments and suggestions which would help us in depth to improve the quality of the paper.
Kind regards,
Wenfei Liu
E-mail: [email protected]
Author Response File: Author Response.doc
Reviewer 4 Report
- Line 109 is the incorrect numbering of the equation.
- No spacing after equations, for example, line 113 and others. Please check it in all parts of the article.
- Directly after chapter 3 could be a brief description of touched chapters and subchapters.
- Fig.11, 12, and 13 do not look like the Matlab software. Also, their quality is not sufficient.
- Overall: the results do not look serious.
Conclusions are poor.
Author Response
Reviewer#4
Thank you very much for your affirmation of our paper, and thank you for your valuable and thoughtful advice. Next, we will sincerely response your comments one by one.
Comment 1: Line 109 is the incorrect numbering of the equation.
Response: The numbering of the equations have been corrected.
Comment 2: No spacing after equations, for example, line 113 and others. Please check it in all parts of the article.
Response: The spacing after equations have been added in the paper.
Comment 3: Directly after chapter 3 could be a brief description of touched chapters and subchapters.
Response: We don't think it is necessary, because the conclusions has summarized the relevant contents of Chapter 3 .
Comment 4: Fig.11, 12, and 13 do not look like the Matlab software. Also, their quality is not sufficient.
Response: In fact, all the figures in this paper are drawn by origin, and the data comes from MATLAB simulation.
Comment 5: Overall: the results do not look serious.
Response: Thank you for your valuable and thoughtful advice.
Comment 6: Conclusions are poor.
Response: The conclusion has been modified.
Once again, thank you very much for your constructive comments and suggestions which would help us in depth to improve the quality of the paper.
Kind regards,
Wenfei Liu
E-mail: [email protected]
Author Response File: Author Response.doc
Round 2
Reviewer 1 Report
I still have some concerns about the manuscript as follows (Based on previous comments)
1. The authors provide some additional references. However, there are only two of them reported in 2021. It seems to be out of date. Please consider some updated papers. It is better if the paper has more than 30 references.
2. I can see the one-by-one contributions of the paper in conclusion. However, it is better if you do that in the Introduction section. It depends on your style. It is OK.
3. I disagree with the explanation of the authors. PID is a very simple method and easy to carry out with simulation. You did not consider the LQR can be accepted. However, the comparison to PID should be included.
4. In Figure 13b, the unit of the upper one is still "o" (degree), and the lower one is "rad."
5. I agree with the explanation of the authors.
6. I can not find the controller parameters in the revised manuscript. At least you must provide the value of sampling time T, and m (equation 14)
7. Some typos exist in the revised manuscript. For example:
- Line 116: where loadb, upb are the upper and lower limits set by the quadratic planning, ... =>where loadb, upb are the lower and upper limits set by the quadratic planning, ...
- difference fonts in line 103
- Check all the redundant "space" (lines 252 to 254)
- Check all the "commas" inside the equation and math type: lines 121, 147, 198, etc
- Consider why using the "multiplication" symbol, * or remove. It should be unique throughout the manuscript.
Author Response
Reviewer#1
Thank you very much for your affirmation of our paper, and thank you for your valuable and thoughtful advice. Next, we will sincerely response your comments one by one.
Comment 1: The authors provide some additional references. However, there are only two of them reported in 2021. It seems to be out of date. Please consider some updated papers. It is better if the paper has more than 30 references.
Response: According to your suggestion, references in recent years have been added.
Comment 2: I can see the one-by-one contributions of the paper in conclusion. However, it is better if you do that in the Introduction section. It depends on your style. It is OK.
Response: Thank you for your valuable advice.
Comment 3: I disagree with the explanation of the authors. PID is a very simple method and easy to carry out with simulation. You did not consider the LQR can be accepted. However, the comparison to PID should be included.
Response: Thank you for your valuable and thoughtful advice. We agree with you that the PID method is indeed simple and widely used. We will compare the PID method with the method in this paper in the subsequent research.
Comment 4: In Figure 13b, the unit of the upper one is still "o" (degree), and the lower one is "rad."
Response: The Figure 13 (b) has been modified according to your comment.
Comment 5: I agree with the explanation of the authors.
Response: Thank you!
Comment 6: I can not find the controller parameters in the revised manuscript. At least you must provide the value of sampling time T, and m (equation 14)
Response: All the controller parameters of all simulations and experiments have been added in the Table 1.
Comment 7: Some typos exist in the revised manuscript. For example:
- Line 116: where loadb, upb are the upper and lower limits set by the quadratic planning, ...
=>where loadb, upb are the lower and upper limits set by the quadratic planning, ...
- difference fonts in line 103
- Check all the redundant "space" (lines 252 to 254)
- Check all the "commas" inside the equation and math type: lines 121, 147, 198, etc
- Consider why using the "multiplication" symbol, * or remove. It should be unique throughout the manuscript.
Response: All the above typos have been corrected.
Author Response File: Author Response.doc
Reviewer 2 Report
I have no more comments.
Author Response
Thank you very much for your affirmation!
Round 3
Reviewer 1 Report
The quality of the paper is improved after the revision. The authors should consider the sampling time T = 0.1s.
I think its value is too big. With 10 points every second, we can not have "smooth" trajectories, as shown in your Figures.
Author Response
Reviewer#1
Comment 1: The quality of the paper is improved after the revision. The authors should consider the sampling time T = 0.1s.
I think its value is too big. With 10 points every second, we can not have "smooth" trajectories, as shown in your Figures.
Response: The sampling time T = 0.1s. For example: the following data are part of the data in Figure 13(b), and the sampling time(Column 1) is really 0.1s.
Once again, thank you very much for your detailed comments on the paper.
Kind regards,
Wenfei Liu
E-mail: [email protected]
Author Response File: Author Response.doc
