A Vision-Based Underwater Formation Control System Design and Implementation on Small Underwater Spherical Robots

Round 1

Reviewer 1 Report

This paper proposes a vision based formation controller for underwater vehicles by the leader-follower approach. After the presentation of the theoretical developments, experimental results are shown to confirm the theoretical findings. The paper has been written well. However, some serious flaws should be improved by the authors. The following comments are given to the authors to improve the paper presentation:

1. The literature review is not sufficient at all. This field is very attractive to the readers. Many research works on the subject are missing in this paper. For the example, investigate the following useful articles: [10.1016/j.ins.2019.02.050], [10.1016/j.apor.2021.102594], [10.1016/j.oceaneng.2021.109071] and [10.1109/TSMC.2019.2895499].

2. The authors could not express their contributions clearly in the introduction section. The authors should clarify the originality and main novelties in the introduction section in a comparative way.

3. The paper suffers from the lack of a mathematical presentation of the leader-follower scheme. The authors are suggested to present their ideas based on clear mathematical presentation. This will help the readers to get the main ideas.

4. The control law that is applied to the vehicles' actuators is not clear to this reviewer as a feedback control system.

5. If the authors are using a closed-loop control system, a reasonable stability analysis is necessary to ensure its safe operation. 

6. A block diagram of the proposed algorithm is recommended to the authors.

7. The numbering of the paper sections needs to be improved. The zero is not a suitable number for the first section.

8. A xyz plot of the vehicles trajectories is of interest to this reviewer. 

9. The role of kinematic and dynamic models on the formation controller design is not clear to this reviewer. 

10. The English language of the paper must be improved. For the example, "have" should be "has" in the 4th line of the abstract. 

Author Response

Dear Reviewer,

We would like to thank you for your careful reading, helpful comments, and constructive suggestions, which have significantly improved the presentation of our manuscript.

 

We have carefully considered all comments from the reviewers and revised our manuscript accordingly. The manuscript has also been double-checked, and the typos and grammar errors we found have been corrected. In the following section, we summarize our responses to each comment from the reviewers. We believe that our responses have well addressed all concerns from the reviewers. We hope our revised manuscript can be accepted for publication.

 

Best wishes,

Pengxiao Bao

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper sounds good but need to be a little bit clearer e underline some limits.

Some considerations follows. 

It should be emphasized that in water the visual range is limited. We are working on the size of centimeters, in real environment it will be different. The experiment is done over a very small distance. How does the error extend? Please insert some considerations on real application. Increase discussion of results and final considerations. Also, the time scale of the experiment (20 seconds) should be expanded to understand how it works over the long distance. Need a better estimate on the error of the predicted and realized trajectory. The whole discussion should be increased and deepened.

Western literature is totally omitted. Increase citations (i.e. line 42 you can take in consideration "determination position using minimum data", line 53 (Swarm robotics and complex behavior of continuum material) and line 191 (Distance estimations in unknown sea underwater conditions by power LEDs for robotics swarms and "The distances measurement problem for an underwater robotic swarm: a semi-experimental trial, using power LEDs, in unknown sea water conditions") .

Do a spelling check (i.e. line 75,114, etc...). MENS and not MEMS is often used.

Some more info about the robot and photos of the leg. (line 124). How many jets? Without having to read the previous paper I would like to better understand the how robots are made. How many sprays and how are they coordinated? Just two lines without going to the reference. Use better photos and a few more.  They are small and unclear.

Table II does not exist. Line 332 this is table 1

Row 336 already you can see that the error is 10% in only 20 seconds. Enlarge discussion about this and use consistent units of measurement not cm and mm together.

Fig. 11 what are those circles on the bottom of the pool?

Line 352 Fig. 13 not 12. Many figure numberings are wrong: revise them.

The meaning of the 13th figure is not very clear. Do you want to show the follower's reaction to the angle measurement? There is binocular vision and course change measured by mems. Explain further. 

Line 360 fig 14 and not 13. Specify that it is not the distance x but the difference with the desired; otherwise it would not be zero.  Show that the distance is constant.  The z on the other hand is absolute.

Line 365 deepen because you need a frame rate of 15, very high which makes the math heavy.  A few more words on the whole paragraph.

Organize figures better with text you skip too much during reading.

Line 384 the statement about magnetic interference is unclear.

Fig. 20 I do not understand about the coordinate z depth pool. Why does it go down? The x and y coordinates tend to zero (maintaining the trajectory) the z does not. It is unclear. Also, wasn't the depth 100cm? Please specify better

The revised version should be accompanied by highlighting the changes made.

 

Author Response

Dear Reviewer,

We would like to thank you for your careful reading, helpful comments, and constructive suggestions, which have significantly improved the presentation of our manuscript.

 

We have carefully considered all comments from the reviewers and revised our manuscript accordingly. The manuscript has also been double-checked, and the typos and grammar errors we found have been corrected. In the following section, we summarize our responses to each comment from the reviewers. We believe that our responses have well addressed all concerns from the reviewers. We hope our revised manuscript can be accepted for publication.

 

Best wishes,

Pengxiao Bao

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

This version of the paper has been improved. There still exist some minor comments as follows:

1. It was better to combine Figs. 3 and 9 as a single figure that describes a detailed closed-loop control system.

2. What are the differences of this work with respect to the previous works of the authors such as Reference [37]? It seems that some materials are repetitive with [37]. 

3. Is the system underactuated? If yes, how could the authors deal with this difficulty?

4. The control law is still not clear to this reviewer. Maybe some notation improvement is needed. For the example, the control laws are input velocities for the kinematic model. What are the left hand-sides of (15)-(17)? They should be velocities! Please clarify. Meanwhile, use suitable brackets for the representation of vectors in (15)-(20).

Author Response

Dear Editor and Reviewer:

We would like to thank you for your careful reading, helpful comments, and constructive suggestions, which significantly improved the quality of our manuscript.

In the attachment, we summarize our responses to each comment from the reviewer. We believe that our responses have well addressed all concerns from the reviewers. We hope our revised manuscript can be accepted for publication. Thank you again for your generous advice.

Best Regards,

Pengxiao Bao

Author Response File: Author Response.pdf