Adaptive Model Predictive Control for Underwater Manipulators Using Gaussian Process Regression

Round 1

Reviewer 1 Report

Some corrections are reqired:

1. Please define all abreviations in the text before use: EKF, DOF, etc.

2. Correct N*M -> N*m.

3. The transients showed big difference between the peak torque and its steady state values. What are the real limits of the drives? This point shold be clearly stated in the paper.

4. What is the measurement accuracy? It seems that the control uses precise data from the model without any noises.

5. How the effect of shading (when one link is shading the flow to another) is taken into account? I suggest to use FEM of the flows to check the proposed method.

Author Response

Dear editor and reviewers:

We would like to express our gratitude to the editor and the reviewers for your constructive and insightful comments on our manuscript. We have carefully considered these comments and have improved the manuscript accordingly in the revised version.

To clearly point out the improvements in our revision we will respond to the feedback of the editor and the reviewers step by step. To make a distinction the italic font is used for the comments from the reviewer, while the regular font is applied for the authors’ replies. In the revised manuscript, the revisions we made according to the reviewers are highlighted in the yellow color. Please refer to the attachment for specific replies to the comments.

Author Response File: Author Response.pdf

Reviewer 2 Report

Dear Authors.

I revised the paper very carefully to understand each aspect of the presented research. I think that this is an interesting paper with high scientific potential.

The title is appropriate and accurately reflects the content of the manuscript.

The abstract is concise and informative. Also, the keywords accurately indicate the area of the presented research.

The organization of the research is well done. The research process is described step-by-step in a logical way.

The critical literature review was presented in an appropriate manner. The advantages and disadvantages of several existing methods were discussed briefly. The main contributions of the paper are listed in “Introduction”. The forces exerted on the manipulator are calculated. Next, the controller was developed. It must be pointed out that you presented the diagram of the MPC (Figure 2) that explains the proposed workflow. This is a positive aspect of the study. Next, the trajectory tracking problem of the six degrees of freedom manipulator was used to verify the effectiveness of the developed method. The formulated conclusions are supported by the presented results. The manuscript ends with a summary of the main findings and suggestions for further possible research directions.

This is an original paper. I did not detect plagiarism.

The length of the manuscript is suitable, but I think that it can be a bit longer.

 

General comments

*** The topic of control of underwater manipulators is not new. The modeling and control of manipulators is a rather mature field. The main problem with this paper is probably a lack of novelty. Could you explain and prove that the developed method is better than other existing approaches?

*** The presented results should be reproducible by the other researchers. This is one of the most important issues. I suggest that you should edit extensively the description of the research process.

*** In “Introduction” you should include more citations. There exist a lot of important publications on the topic of underwater manipulators.

*** The authors presented only simulation results. Is it possible to perform some experiments with the real hardware? Such a study will be much more interesting for the readers.

*** Did you try to develop the 3D visualization of the manipulator? I strongly suggest including such visualization in the paper. I think that at least you should present 3D plot with the position of the last link of the manipulator.

*** From “Figure 7” and “Table 1” someone might conclude that the performance of the proposed method is quite similar to the MPC. The presented method is only a bit better than MPC.

*** Did you consider the influence of errors of sensors on the overall system performance? This issue might be crucial in real applications.

*** In “Appendix A” you presented some data. Are they obtained from the real, existing system, or you assumed such values for the purpose of the numerical simulations?

*** Could you include more simulation scenarios to prove that the method is better than SMC and MPC for a wide range of operating conditions?

*** “Appendix B” is very messy and cannot be accepted for publication in the presented form. It is obvious that the presented formulas are very long, but it is possible to present them in a more “organized and elegant” form. Could you include a numeration of these equations? They should be easily distinguishable from each other. Ideally, I think that quite a good idea is to prepare a simple piece of code (for example, MATLAB script) with these equations and include it as supplementary material. In that way, you can significantly increase the reproducibility of the results.

Specific comments

*** Figure 3. 6-DOF manipulator

Figure 3 is a bit unclear. You presented only a simplified, generic diagram of the manipulator. Could you include better visualization of the system (for example, using a simple 3D CAD model)?

The coordinate system connected with link 1 is denoted as x0y0z0. However, the coordinate frames connected with other links are x1y1z1. This convention is a bit confusing.

Is the first element attached to a moving platform of fixed support?

*** Figure 7

The font size used in the axis labels is a bit too small. Ideally, it should be the same as in the main text. Could you increase the font size to make the graph more readable?

*** Section “4. Simulation results”

Could you include more details about the implementation? What software was used (MATLAB, C, or something else)? What solver was used to solve the equations of motion? Such details are very important because, without them, it will be rather difficult to reproduce the presented results.

*** I have found a lot of minor typographical mistakes. I highlighted them using yellow color in the attached PDF file. Could you correct them in the next version of the paper?

*** In ”Table A2.” you presented the center of gravity of the manipulator. In which coordinate system you expressed these values? This issue is not clear.

I think that the paper might be published in the future.

Kind regards,

 

Reviewer

Comments for author File: Comments.pdf

I have found several language mistakes. I suggest revising the whole text carefully to eliminate problematic issues. I highlighted most of the errors in the attached pdf file.

Author Response

Dear editor and reviewers:

We would like to express our gratitude to the editor and the reviewers for your constructive and insightful comments on our manuscript. We have carefully considered these comments and have improved the manuscript accordingly in the revised version.

To clearly point out the improvements in our revision we will respond to the feedback of the editor and the reviewers step by step. To make a distinction the italic font is used for the comments from the reviewer, while the regular font is applied for the authors’ replies. In the revised manuscript, the revisions we made according to the reviewers are highlighted in the yellow color. Please refer to the attachment for specific replies to the comments.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Authors addressed all my remarks and comments.

Author Response

Dear reviewer:

We again thank the reviewer for your valuable comments and suggestions.

Reviewer 2 Report

Dear Authors.

Thank you kindly for the revised version of the manuscript. I studied the paper again carefully. Especially thanks for the point-by-point responses to all my questions. In the attached PDF file with the manuscript, you clearly highlighted the changes.

The proposed paper is much more interesting and valuable when compared to the initial version. The influence of noise on the simulation results was taken into consideration. In that way, the presented simulation scenario is more realistic. The “Appendix B” was also improved significantly. Now the equations are easier to understand.

However, I detected another set of minor issues that should be explained. In the presented form, the paper is rather not publishable. Below please find the list of my suggestions how to improve the quality of the paper.

*** Line 60 ***

“separately. [17].” should be replaced by “separately [17].” (dot symbol is unnecessary).

*** Line 143 ***

You mentioned that “…represents eht matched lumped disturbance”. Could you explain what “eht” means? This is a bit unclear.

*** Lines 198 – 199, Equation 11 ***

Did you derive this formula by yourself or find it in the literature? Could you include an appropriate citation before Equation 11? This issue is not clear. The same issue with other equations. If they are copied from the other publications, please add the references.

*** Lines 164 – 165, Figure 1 ***

The parameters “dx” and “x” are written in the bold font. I suggest unifying the font style.

*** Lines 378 – 379 ***

The sentence “When Gaussian white noises with mean 0 and variance 0.001 are introduced into the feedback values of joint position and joint velocity, the experimental results are as follows:” is unclear and a bit confusing. After this sentence, you included “Figure 12”. Could you try to rephrase this sentence? It should be something like this: “The Gaussian white noises with mean 0 and variance 0.001 are introduced into the feedback values of joint position and joint velocity, and the obtained results are presented in Figure 12”.

*** Lines 421 – 422 ***

Could you replace “MPC Model predictiove control” with “MPC Model predictive control”. This is probably a typographical mistake.

*** Appendix B ***

How did you derive these equations? Did you try to check them using Computer Algebra System and ensure that they are correct?

*** Line 487 ***

“Where.” should be replaced by “where:”

 

I highlighted these problems using blue color in the attached PDF file. I think that the manuscript will be ready for publication when you explain the abovementioned issues.

Kind regards,

 

Reviewer

Comments for author File: Comments.pdf

English language is rather fine. I detected a set of minor typographical mistakes.

Author Response

Dear reviewers:

We would like to express our gratitude to the editor and the reviewers for your constructive and insightful comments on our manuscript. We have carefully considered these comments and have improved the manuscript accordingly in the revised version.

To clearly point out the improvements in our revision we will respond to the feedback of the editor and the reviewers step by step. To make a distinction the italic font is used for the comments from the reviewer, while the regular font is applied for the authors’ replies. In the revised manuscript, the revisions we made according to the reviewers are highlighted in the yellow color. Please check the attachment for detailed responses to comments

Author Response File: Author Response.docx