Double-Loop Sliding Mode Controller with An Ocean Current Observer for the Trajectory Tracking of ROV

Round 1

Reviewer 1 Report

The paper entitled “Double-loop sliding mode controller with an ocean current observer for the trajectory tracking of ROV” proposes a new control scheme that compensates for large unknown currents. The research is of relevance to the journal. The methodology used is scientifically sound and the results presented are potentially of interest to the readers. The paper is well structured and referenced. There are only minor problems with the English language. There are a number of minor remarks to the authors, which I have included in the attached pdf. I do disagree with the authors when they claim that fuzzy control comes with large computational effort – the opposite is the case. That was – according to Ludfi Zadeh - the reason why Fuzzy control became popular in the 1990’s, when computer power in embedded computers was very limited! Also, the conclusions are on the shorter side of things. For example, it would be good to see some discussion of the impact of localisation error on the performance of the new control scheme.

Comments for author File: Comments.pdf

Author Response

On behalf of my co-authors,  we appreciate t'he reviewers very much for your positive and constructive comments and suggestions on our manuscript entitled “Double-loop sliding mode controller with an ocean current observer for the trajectory tracking of ROV.” (ID: jmse-1363008). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied reviewer’s comments carefully and have tried our best to revise our manuscript according to the comments. The responds to the reviewer’s comments are as flowing:

1. Response to comment: There are minor problems with the English language. There are a number of minor remarks to the authors, which I have included in the attached pdf.

Response: We are grateful to the reviewers for their careful revision and constructive suggestions on the language presented in the PDF file. We also apologize for the language errors in the first draft. We have made detailed changes to each of the issues and suggestions marked by the reviewers in the manuscript, and have used the "track changes" function to mark them.

2. Response to comment: I do disagree with the authors when they claim that fuzzy control comes with large computational effort.

Response: We apologize for any confusion caused to reviewers by the lack of clarity in the manuscript. We strongly agree that fuzzy control has great advantages in arithmetic-constrained conditions. The high complexity control scheme expressed in the manuscript specifically refers to a composite control scheme such as neural network-based PID control or fuzzy sliding mode control. We have uniformly corrected this expression in the manuscript.

3. Response to comment: The conclusions are on the shorter side of things. For example, it would be good to see some discussion of the impact of localization error on the performance of the new control scheme.

Response: It is really true as reviewer suggested that the conclusion of the manuscript is the biggest failure. The overall generalization is not enough and fails to highlight the contribution points of the article. We have re-written the conclusions according to the reviewer’s suggestion. Furthermore, the discussion of the impact of localization error was added.

Reviewer 2 Report

The paper presents a trajectory tracking controller for ROVs that employs a sliding mode control method for the inner and outer loop controllers for velocity and position, respectively. The proposed method also takes into account unmodelled dynamics and constant ocean currents. Numerical simulations show that the proposed methods yield satisfactory performance.

The paper is well-written and clear. There are, however, a few issues that could be improved before an eventual publication:

• Since the method relies heavily upon sliding mode control theory, a brief theoretical introduction to the subject would make the paper clearer for readers that are not familiar with that subject.
• In sections 3.1 and 3.2, the authors should state what the final dynamics of the sliding surface variables S_{v} and S_{\eta} are after the introduction of the control laws.
• The authors should introduce and explain the meaning of parameters sigma and theta.
• The authors should discuss the stability of the overall system after the introduction of the inner and outer loop controllers. In particular, it is not clear if for certain cases a current can be misidentified as an unmodelled dynamics or vice-versa.
• The authors should also discuss which sensors the ROVs should have, to apply the proposed controller.
• The authors should define more clearly what is the classical SMC used for comparison in section 4.

Author Response

On behalf of my co-authors,  we appreciate t'he reviewers very much for your positive and constructive comments and suggestions on our manuscript entitled “Double-loop sliding mode controller with an ocean current observer for the trajectory tracking of ROV.” (ID: jmse-1363008). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied reviewer’s comments carefully and have tried our best to revise our manuscript according to the comments. The responds to the reviewer’s comments are as flowing:

1. Response to comment: Since the method relies heavily upon sliding mode control theory, a brief theoretical introduction to the subject would make the paper clearer for readers that are not familiar with that subject.

Response: We are grateful for the suggestion. The manuscript truly neglected the introduction of relevant fundamental theories at the beginning of editing, resulting in a slightly abrupt and illogical structure of the article. Considering the reviewer's suggestion, we added the introduction of traditional sliding mode control theory at the beginning of Chapter 3 to make the article structured more rationally.

2. Response to comment: In sections 3.1 and 3.2, the authors should state what the final dynamics of the sliding surface variables S_{v} and S_{\eta} are after the introduction of the control laws.

Response: In the inner-loop and outer-loop controllers, the equivalent control term is calculated when the derivative of the sliding mode surface is zero (i.e., s'=0), and it can be obtained that the state quantities will eventually converge to zero. The switching control term is designed to satisfy s=0, then the state of the system will converge to zero along the sliding mode plane. Therefore, the final dynamics of the sliding surface variables S_{v} and S_{eta} are converging to zero along the sliding surface curve.

3. Response to comment: The authors should introduce and explain the meaning of parameters sigma and theta.

Response: We thank the reviewers for helpful comments. It is true that the authors neglected to explain this problem, and we have added it in the manuscript to improve it. Since the switching term is discontinuous on both sides of the sliding surface, it leads to the chattering problem of sliding mode control. The boundary layer method is the most commonly used jitter elimination method at present. Therefore, we choose sigma and theta to define the boundary layer thickness of the inner and outer loop sliding mode controller to eliminate the jitter phenomenon.

4. Response to comment: The authors should discuss the stability of the overall system after the introduction of the inner and outer loop controllers. In particular, it is not clear if for certain cases a current can be misidentified as an unmodelled dynamics or vice-versa.

Response: We thank the reviewers for their suggestions regarding the stability of the inner and outer loop controllers. We have therefore deliberately added the stability proofs of the system and placed the relevant proofs in the appendix section of the article.

It is a good question that whether the ocean currents could be mistaken for unmodeled disturbances. In the modeling, we consider the unknown dynamics as disturbing forces and the effect of ocean currents as velocity effects, so we consider the two to be decoupled. We certainly appreciate the reviewer's reminder and will continue to study this issue in depth subsequently.

5. Response to comment: The authors should also discuss which sensors the ROVs should have, to apply the proposed controller.

Response: Thanks for the helpful comments. The ROV is equipped with GPS positioning module, bathymetry sensor, acceleration sensor and gyroscope, which can achieve the basic functions of precise navigation, depth perception, attitude perception, etc. We have added the description of the mounted sensors to section 4 of the manuscript.

6. Response to comment: The authors should define more clearly what is the classical SMC used for comparison in section 4.

Response: We have carefully considered the suggestions of the reviewers. We have briefly introduced the traditional classical SMC scheme in section 3, so that it can fit better with the simulation and verification process in section 4.

Reviewer 3 Report

This paper presented the tracking control of the 4DOF ROV system using a double-loop sliding mode controller with an ocean current observer. The topic addressed in the paper is potentially interesting in both theory and practice, however, the submission should be carefully revised based on the following comments:

1/ Despite the motivating topic and the paper seems to have a contribution. However, the novelty of the approach is rather low since it seems all the methods are existing, the SMC is well known. And the experimental contribution does not consider. This paper should have more theoretical contributions.

2/ Benefit of the proposed method is not clear. This should be clarified. The objective/problem statement needs to be explained. What are the novelties of the proposed method? what the research challenges/motivations of the paper are?

3/ In the introduction part, the novelty of the proposal is not clearly defined. Moreover, the authors could enrich the reference section by discussing some newly adaptive robust control methods. The concept of sliding mode control should be discussed in terms of a deeper state of the art, some new works related to sliding mode control of second-order systems, especially the dynamic sliding mode control methods, robust sliding mode method, multiple sliding mode methods, and so on, should be included. To help the authors in this direction, I suggest the following references:

DOI: 10.1109/ACCESS.2021.3098327, https://doi.org/10.3390/math9161935, DOI: 10.1109/ACCESS.2020.3048706, https://doi.org/10.3390/math8081371, DOI: 10.1109/ACCESS.2021.3054901

And the introduction should be added to do a better job of explaining the existing methods and why they are or are not valuable.

4/ In section 2, 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 “Assumptions” section of the following paper: https://doi.org/10.3390/s20051329

5/ In section 2, the system in this paper might use 5 or 6 thrusters, the authors need to add one figure of thruster arrangement of the system. The author can refer to the “configuration of thrusters” section of the following paper: https://doi.org/10.3390/s21030747

6/ Figure 2 did not mention in the paper?

7/ For the ROV system, the effect of underwater cable is important to make its locomotion model. See the references, https://doi.org/10.1016/j.oceaneng.2017.02.035, https://doi.org/10.3390/s20051329. The authors should explain why its effect was neglected in the locomotion model of the authors. 

8/ The comment about the stability of the proposed control system (using the Lyapunov function) is missing in the paper. This needs to be incorporated.

9/ In section 4 “Simulation Results and Discussion”, to easily realize the best performance of the proposed strategy more simulation results need to be added in the paper, such as control input (force and moment of thrusters) that vary with the time in both cases. Also, in section 4.2, the authors should add and explain the tracking errors of x, y, z, and yaw angle. And the explanations and analysis of simulation results should be enriched to show the validity of the data.

10/ The analysis in this paper should be supported by experimental results. The authors should use practical systems to validate the proposed methods with experiment results. The validity of these relevant to applications is impossible to judge without experimental testing.

11/ The contribution of the conclusion is not mentioned clearly. The authors need to rewrite the conclusion again to show the objective and contribution of this paper clearly. Also, based on the ideas presented and the results obtained in this paper, the author should indicate the direction of further research in the conclusion section.

12/ The manuscript writing can be further polished with professional English. The manuscript can be thoroughly revised for grammar check. All equations and figures should be in the form “Eq.” and “Figure” respectively, such as Fig. 1 should be Figure 1, equation 1 should be “Eq. 1”. Some typo errors, line 155, “the Equation (5)” should be “Eq. (5)”, line 251 “the Eq. (17)” should be “Eq. (17)”, line 386 “Figures 4 and Figures 5” should be “Figure 4 and Figure 5” or “Figures 4-5”. Please check all!

Author Response

On behalf of my co-authors,  we appreciate t'he reviewers very much for your positive and constructive comments and suggestions on our manuscript entitled “Double-loop sliding mode controller with an ocean current observer for the trajectory tracking of ROV.” (ID: jmse-1363008). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied reviewer’s comments carefully and have tried our best to revise our manuscript according to the comments. The responds to the reviewer’s comments are as flowing:

1. Response to comment: The novelty of the approach is rather low since it seems all the methods are existing, the SMC is well known. And the experimental contribution does not consider. This paper should have more theoretical contributions.

Response: We thank the reviewers for their positive and constructive feedback. Sliding mode control with its unique advantages is a good choice for the control scheme of highly nonlinear systems like ROV. However, the main reason for the chattering phenomenon in SMC is that the sliding mode surface S is often defined as a function of position error. In fact, the speed of change of position error and velocity error are different. Therefore, the combination of dual-loop structure and sliding mode control has good adaptability and application prospects for ROV systems. The role of ocean currents with ROV systems is often complex and difficult to define clearly, so we define ocean currents as environmental velocities. This also causes us to pay extra attention to the velocity error problem in the control scheme. The purpose of introducing the current observer based on this consideration is also to compensate and correct for the ambient velocity. We focus more on the results of the control model and simulation analysis in this paper, and the related experimental validation will be carried out based on the model refinement, which is one of our future goals.

2. Response to comment: Benefit of the proposed method is not clear. This should be clarified. The objective/problem statement needs to be explained. What are the novelties of the proposed method? what the research challenges/motivations of the paper are?

Response: We thank the reviewers for their suggestions on the article. In our previous study, we have conducted ROV control studies under large ocean current conditions by PID control and pool experiments. However, the nonlinearity of the model poses a great challenge to the control method. Many researchers in the field of ROV motion control have conducted in-depth research on sliding mode control and verified the advantages of sliding mode control through experiments. This is the reason why we choose sliding mode control as the basis. The nature of trajectory tracking should achieve perfect control of both position and velocity, but traditional sliding mode control tends to consider only velocity matching, so the dual-loop control structure becomes our second target solution. The current observer is our solution given to the disturbance of large ocean currents. The focus of this paper is to prove its feasibility through theoretical study and simulation, and more experimental verification analysis will be our goal in the future. The explanation and clarification of this problem are also updated simultaneously to the introduction and conclusion sections of our manuscript to help us better refine our research.

3. Response to comment: In the introduction part, the novelty of the proposal is not clearly defined. Moreover, the authors could enrich the reference section by discussing some newly adaptive robust control methods. And the introduction should be added to do a better job of explaining the existing methods and why they are or are not valuable.

Response: The references suggested by the reviewers have really helped our research tremendously. Some new works related to SMC of second order systems have expanded our scientific horizon. The control method designed in this paper aims to achieve effective motion control under high ocean current conditions. Due to our unclear presentation, we really did not analyze the advantages and disadvantages of the existing control schemes clearly. For this reason, we have reorganized the introductory section of the manuscript and added some of the latest research and our reflections to it.

4. Response to comment: In section 2, a sub-section “Assumptions” should be added to make the problem clearer. All assumptions and physical constraints should be provided.

Response: We sincerely accept the reviewers' suggestions. And the assumptions section is added and improved to section 2.1 of the manuscript

5. Response to comment: In section 2, the system in this paper might use 5 or 6 thrusters, the authors need to add one figure of thruster arrangement of the system.

Response: Since we have not yet considered the control of the monopropellant, we did neglect to describe the way the ROV thrusters are arranged. We have added this section to Chapter 4 of the manuscript.

6. Response to comment: Figure 2 did not mention in the paper?

Response: Figure 2 shows the logic block diagram of the control method constructed in the paper. We are very ashamed of the lack of elaboration in the article due to the author's oversight. And the error was corrected in time in the manuscript.

7. Response to comment: For the ROV system, the effect of underwater cable is important to make its locomotion model. The authors should explain why its effect was neglected in the locomotion model of the authors.

Response: We agree with the reviewer's reference to the umbilical cable issue. The effect of umbilical cables is very important for modeling ROV motion. However, the main objective of this paper is to achieve effective control of ROV motion under large ocean current conditions. In this paper, ocean currents are defined as velocity in the motion model, not disturbance force. The effect of all disturbances on the control is substantially equivalent and essentially affects the final state error. Therefore, we unify the disturbance force of the umbilical cable into the unknown dynamics model for correction. Of course, this assumption is deficient, and we will try to correct it in the subsequent study. We have also revised the explanation of this problem into the manuscript in parallel.

8. Response to comment: The comment about the stability of the proposed control system (using the Lyapunov function) is missing in the paper. This needs to be incorporated.

Response: Thanks to the reviewer's suggestion, we also realize that the elaboration of the stability of the control system is missing in the manuscript. Therefore, we have deliberately added a proof of the stability of the system and placed the relevant proof in the appendix section of the article.

9. Response to comment: In section 4 “Simulation Results and Discussion”, to easily realize the best performance of the proposed strategy more simulation results need to be added in the paper, such as control input (force and moment of thrusters) that vary with the time in both cases. Also, in section 4.2, the authors should add and explain the tracking errors of x, y, z, and yaw angle. And the explanations and analysis of simulation results should be enriched to show the validity of the data.

Response: We thank the reviewers for their feedback and suggestions. We have added a graph of the variability of the control inputs and the associated explanation in Section 4 .1. The system has weak output jitter when encountering large ocean current disturbances and can recover stability quickly. This also confirms the effectiveness of the scheme in this paper.

In addition, in Section 4.2, we add the analysis and explanation of the tracking errors in four degrees of freedom to show the effectiveness of the control scheme. The chattering problem of the conventional sliding film is more obvious, mainly because the speed of change of position error and velocity error is different. Therefore, it is difficult to ensure that the sliding surface S rapidly approaches zero. The double-loop structure is for both position and velocity control, which naturally has great advantages.

10. Response to comment: The analysis in this paper should be supported by experimental results. The authors should use practical systems to validate the proposed methods with experiment results. The validity of these relevant to applications is impossible to judge without experimental testing.

Response: We strongly agree with the reviewer's suggestion that the control scheme should be supported by experimental results. In the early stages of ROV construction, the control logic was built based on PID control and pool experiments were conducted. It is in the pool experiments that we found the limitations of PID control under large ocean current disturbance conditions. This also facilitated our research on the control scheme proposed by this paper. In this paper, we try to investigate the feasibility of the control method in terms of both theoretical modeling and numerical simulation. And the pool experiments of the solid model are not available for us to obtain real experimental results to support the control scheme because the engineering application of the control scheme is not completed at present. Of course, we hope to improve and show it in the subsequent research. For this part regret we have also added to the future research content.

11. Response to comment: The contribution of the conclusion is not mentioned clearly. The authors need to rewrite the conclusion again to show the objective and contribution of this paper clearly. Also, based on the ideas presented and the results obtained in this paper, the author should indicate the direction of further research in the conclusion section.

Response: As the reviewer indeed suggested, the conclusion of the manuscript is the biggest failure. We have rewritten the conclusion based on the reviewers' suggestions. The objectives and contributions of the paper are further clearly shown. In addition, directions about future research have been considered and added into the conclusion section.

12. Response to comment: The manuscript writing can be further polished with professional English. The manuscript can be thoroughly revised for grammar check.

Response: We apologize for the errors in language and details in the manuscript. English expression has been carefully revised to improve readability throughout the manuscript.

Round 2

Reviewer 3 Report

I appreciate your efforts to revise the manuscript in light of the comments addressed in the previous review. Most of the recommendations I made were addressed by the authors, therefore I believe that the paper is now ready for publication.

Other comments:

In ref [40], the author´s name is a little wrong. Please re-arrange as below:

Vu, M.T.; Choi, H.S.; Kang, J.; Ji, D.H.; Jeong, S.K. A study on hovering motion of the underwater vehicle with umbilical cable. Ocean Eng. 2017, 135, 137-157, doi:10.1016/j.oceaneng.2017.02.035

In addition, the format of references needs to be unified with the aim to satisfy the requirement of the journal, and the DOI number of some new references needs to be added in this paper. Please check carefully.

Author Response

On behalf of my co-authors, we appreciate t'he reviewers very much for your positive and constructive comments and suggestions on our manuscript entitled “Double-loop sliding mode controller with an ocean current observer for the trajectory tracking of ROV.” (ID: jmse-1363008). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied reviewer’s comments carefully and have tried our best to revise our manuscript according to the comments. The responds to the reviewer’s comments are as flowing:

1. Response to comment: In ref [40], the author´s name is a little wrong. Please re-arrange.

Response: We are very sorry for our writing errors. Such an error by the author of ref [40] is obviously unacceptable. Therefore, based on the revision of this reference, we checked the formatting of all references again to avoid such errors.

2. Response to comment: The format of references needs to be unified with the aim to satisfy the requirement of the journal, and the DOI number of some new references needs to be added in this paper.

Response:  We thank the reviewers for their effective suggestions on reference formatting, which helped us to improve the manuscript details to the best of our ability. When checking all references, we add new references with DOI numbers according to the formatting requirements of the journal.

Special thanks to you for your good comments.