Trajectory Tracking Nonlinear Controller for Underactuated Underwater Vehicles Based on Velocity Transformation

Round 1

Reviewer 1 Report

This paper addresses the development of a nonlinear tracking control algorithm for underactuated ocean vehicles under the action of disturbances. The algorithm is tested at simulation level using the model of two underwater vehicles with different dynamics. 

The topic is interesting a relevant to the navigation, guidance, and control area. Some suggestions to improve the paper:

1. Some keywords are too general. For instance, "simulation" is not a good keyword to describe the paper content. More precise terms are required.

2. Some grammar adjustments can be done in order to improve the quality of the document.

3. No drawbacks or limitations are addressed. For instance, the proposed algorithm is not compared to other techniques. The controller design relies on the tuning capabilities and no comments are done around this topic. ¿Are there other controllers that when properly tuned offer a similar performance? If this is not covered, the limitations of the proposed technique should at least be stated.

Author Response

I am enclosing my responses to the review.

Author Response File: Author Response.pdf

Reviewer 2 Report

Interesting research about backstepping and sliding mode control of an underactuated underwater vehicles (e.g. SIRENE, CETUS II), and the work is assembled into a decently drafted manuscript that needs some mild revisions.

·        The manuscript is clear, relevant for the field and presented in a well-structured manner. The cited references are current (some few within the last 5 years), while suggested very recently published references are suggested in review to aid revision. The manuscript is scientifically sound, and the experimental design is appropriate to test the hypothesis. The manuscript’s results are reproducible based on the details given in the methods section. The figures/tables/images/schemes appropriate and properly show the data. They are easy to interpret and understand. The data is interpreted appropriately and consistently throughout the manuscript. The conclusions are consistent with the evidence and arguments presented.

The Abstract is okay but is not likely to entice the readership to continue reading the rest of the manuscript.

·        Use of acronyms/abbreviations in an abstract is unlikely to attract readers not already aware of the manuscript’s content.

·        Results are only presented in a weak, qualitative fashion. Highest quality expression of main conclusions or interpretations is quantitative results discussed in the broadest context possible, e.g., percent performance improvement compared to a declared benchmark. “…results were supported by simulation studies…” is very weakly stated results compared to “…xxx percent performance improvement over conventional methods was achieved….”

·        Line 5 mentions an undefined “…e new variables”. Please define or eliminate typo.

The Introduction is decently done with some omitted very recent literature and some mild abuse of multi-citation without elaboration (9 double-citations and 1 quadruple citations).

·        Lyapunov, backstepping, sliding mode, neural networks, fuzzy logic and even-triggered control are all reviewed, but some newly proposed competing alternatives were neglected, particularly deterministic artificial intelligence, in favor of older approaches.

·        Deterministic artificial intelligence was developed for unmanned underwater vehicles in 10.3390/jmse8080578 as a competing alternative.

·        Osler with the U.S. Navy applied the method to remotely operated ocean vehicles in 10.3390/app12062810.

·        Shah presented UUV motor tracking control 10.3390/app11114972 as a sequel to 10.3390/app11052144, and Koo with the U.S. Navy presented follow-on work in 10.3390/jmse10030419.

·        Zhai developed the competing alternative using deep learning in 10.3390/math10030453 and offered a direct comparison to DAI in 10.3390/s22176362.

·        Please elaborate a reason for the reader to investigate each of the quadruple cited references [17,28-30] in the introduction.

Equations are scientifically sound and well presented, enhancing the manuscript quality.

Figures are decently done with some mandatory improvements to ensure the readership has access to the content.

·        Internal font size is occasionally too small.  Please notice the smallest font size permissible in the manuscript template (to ensure legibility by the reader) is the figure caption which provides a conveniently proximal prototype for sizing figures. 

·        Line styles and sizes are identical in figures are marvelously varied rendering the disparate data clearly distinguishable when the manuscript is read in printed hardcopy (particularly in black and white) enhancing the value of the figures.

Tables are decently done to introduce problem formation (aiding repeatability), but quantitative results are poorly presented in only table 2.  

·        Particularly for comparative figures (e.g., 2–7), please add a table of accompanying canonical figures of merit (e.g., means and deviations of difference, or others) to help the reader ascertain quantitative differences between the plotted data.

·        Please add a companion table to Table 2 where the same raw data is presented as percent difference from a declared benchmark, so the readership has more easy access to the comparative conclusions.

·        For such a manuscript, heavy in acronym and variable usage, please add period tables of proximal definitions, so the readership is not required to flip back and forth between pages to remind themselves of acronym and variable definitions.

·        Inclusion of a table defining variables and acronyms in an appendix is welcome and effective. Please add such. 

Author Response

I am enclosing my responses to the review.

Author Response File: Author Response.pdf

Reviewer 3 Report

At first glance, the manuscript is interesting. The manuscript is well written, the content organization is logical, and the results are potentially useful, and the topic could be of interest to the readers of the journal. The work has potential for publication, however, the submission should be carefully revised based on the following comments:

1/ The literature survey is quite good. However, I think that the authors could enrich the reference section by discussing the concept of sliding mode control should be discussed, some new works related to sliding mode control of marine vehicles or second order systems, especially the dynamic sliding mode control methods, robust sliding mode method, multiple sliding mode methods and so on, should be included. For example, station-keeping control of a hovering over-actuated autonomous underwater vehicle under ocean current effects and model uncertainties in horizontal plane, robust position control of an over-actuated underwater vehicle under model uncertainties and ocean current effects using dynamic sliding mode surface and optimal allocation control, design of a non-singular adaptive integral-type finite time tracking control for nonlinear systems with external disturbances. Moreover, what research gap did you find from previous researchers in your field (it is still partially described, but needs to be expanded and made clearer)?  Mention it in the Novelties section. It will improve the strength of the manuscript.

2/ The motivation and background of wide practical use of the theoretic results presented should be clearly emphasized to facilitate the readers. What are the underlying factors that led to better performance of the proposed method?

3/ In section II, a sub-section “Assumptions” should be added to make the problem clearer. All assumptions and physical constraints should be provided. The author can refer to the assumption part of following paper, study on dynamic behavior of unmanned surface vehicle-linked unmanned underwater vehicle system for underwater exploration.

4/ It is recommended to give an intuitive representation (e.g., a flow chart) of the whole technical procedure of the detailed implementation information. The authors can add the steps of implementing the algorithms. The steps will be for the benefit of the readers, maybe they’ll help the readers to implement the proposed algorithm.

5/ In simulations, how to select the control parameters in controller in Eqs. (62)-(67)? How the full-state constraints are chosen? It is better to explain how the values of the control parameters in the proposed method are adjusted?

6/ If the Lyapunov functions are chosen via the viewpoint of practical application, the authors should give some effective suggestions. What new modifications are introduced in the Lyapunov stability method?

7/ In this manuscript, the disturbances fu(t), fv(t) and fr(t) in Eq. (61) what is the principle of choosing these disturbances? Maybe these disturbances are too small compared to control inputs?

8/ In the simulation part, more comparison results to other solutions are welcomed. If possible, the authors are encouraged to include some comparative studies over a recently published work to demonstrate the superiority of the proposed method.

9/ To prove the effectiveness of the proposed control system in actual applications, the system performance is expected in actual experiments with your proposed method. The authors should use practical systems to validate the proposed methods with experiment results.

10/ The conclusion section is superficial and should include quantitative results, advantages and disadvantages, limitations, and recommendations for new implementations and future work. The reviewers recommend that more future work should be added to Conclusion Section.

Author Response

I am enclosing my responses to the review.

Author Response File: Author Response.pdf