Timescale-Separation-Based Source Seeking for USV
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsGeneral comment This manuscript proposes a timescale-separation-based source-seeking control strategy for USVs. The authors decompose the overall system into a slow subsystem, which generates reference heading and velocity commands, and a fast subsystem, which quickly tracks the desired control inputs. Using singular perturbation theory and Lyapunov-based stability analysis, the paper provides a rigorous theoretical derivation and proves system stability. Numerical simulations are conducted to verify the convergence performance of the proposed algorithm in a two-dimensional scalar field under multiple initial conditions. Overall, the study presents a clear research motivation (e.g., autonomous source localization for marine oil-spill emergency monitoring), a well-structured control framework, and mathematically sound derivations. The idea of introducing a timescale-separation mechanism into the USV source-seeking problem shows a certain degree of originality and practical significance. However, the paper still has some limitations: it lacks quantitative comparison with existing methods, does not sufficiently evaluate robustness under environmental disturbances and noise, and presents minor inconsistencies in notation and clarity. In addition, the readability of the stability proof and the reproducibility of the simulation could be further improved. Major comments 1. The paper introduces the concept of multi-timescale (singular perturbation) separation into USV source-seeking control. However, this idea has already been widely applied in control and optimization fields. It is suggested that the Introduction and Related Work sections should more clearly highlight the specific innovations and novel contributions of this paper. In addition, the current description of innovation points contains overly long sentences, which makes it somewhat difficult for readers to follow. 2. The simulation results could be enhanced by adding comparative experiments with other existing methods to better demonstrate the originality and advantages of the proposed approach. 3. Figure 7 presents simulation results under multiple initial conditions. It would be valuable to design quantitative performance metrics (e.g., convergence rate, steady-state error, control effort) and perform Monte Carlo simulations to statistically illustrate the superiority and robustness of the proposed method. Minor comments 1. In the main text, the content labeled as Proposition, Remark, and Assumption should not be italicized. It is recommended to use a consistent upright font style to improve readability and formatting consistency. 2. In Figures 4–7, the font size is too small, making the labels difficult to read. Please enlarge the axis labels, legends, and titles for better clarity. 3. In Algorithm 1, the abbreviation “USV” has already been defined earlier in the paper, so there is no need to write the full term “Unmanned Surface Vehicle” again. 4. Please double-check the title of Figure 6, as it appears to be incorrect or inconsistent with the figure content. 5. I think this paper contains many long sentences, which are difficult to follow. I recommend rephrasing them.
Comments on the Quality of English LanguageI think this paper contains many long sentences, which are difficult to follow. I recommend rephrasing them.
Author Response
Thank you very much for your comments. Our point-by-point responses are provided in the attached PDF.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe manuscript presents a hierarchical timescale-separation-based control algorithm for unmanned surface vehicles (USVs) performing autonomous source seeking in scalar fields. The topic is relevant to marine robotics and environmental monitoring, and the work integrates theoretical control analysis with simulation validation. However, the paper requires several clarifications and improvements before it can be considered for publication.
- What specific aspects of this implementation are fundamentally different from previous work? How does "hierarchical integration" extend beyond established single disturbance control methods?
- How robust is the algorithm when these assumptions are violated (e.g., crosswind, surface currents)? Would small disturbances destabilize the slow subsystem?
- Why only one simulation scenario was used? Could they add results for different field configurations or noise conditions to demonstrate robustness?
- The authors should revise the text to correct English grammar, typographical errors, and ensure uniform notation.
- Do the authors have plans for real-world testing, or could they at least include a discussion on practical issues like sensor noise, GPS errors, and actuator limits?
- The authors should refer to all figures in the text and briefly explain what each one shows.
Author Response
Thank you very much for your comments. Our point-by-point responses are provided in the attached PDF.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsTitle: Review of Manuscript on Source/Extremum Seeking for USVs via Time-Scale Separation
Scope and Objective
The manuscript presents a control algorithm for “source seeking” with an unmanned surface vehicle (USV). The stated objective is to autonomously locate the extremum of an unknown scalar field using real-time measurements, within a hierarchical architecture that separates “slow” pose evolution (which generates heading and speed references) from a “fast” tracking subsystem.
Overall Evaluation
Although the topic is relevant, the paper is confusing, hard to follow, and in parts likely incorrect. Several elements in the presentation and in the technical development undermine clarity and credibility. In its current form, I recommend rejection.
Major Comments (following the manuscript’s flow and claims)
1) “Time-scale separation” is merely renaming established planning and control
The paper advertises a “time separation–based source-seeking” framework with a slow and a fast subsystem. However, this is the well-known planning/guidance (kinematics) versus control/tracking (dynamics) decomposition long used in robotics and marine control. As presented, there is no substantive novelty beyond relabeling; it reads as a change of terminology for a standard split.
2) Introduction claims vs. subsequent simplifying assumptions
The introduction argues that gradient-based algorithms fail for highly nonlinear, complex systems. Yet, the method is then developed under strong simplifications: a 3-DOF model (not the full 6-DOF), very low speeds (≈4 kn), and additional assumptions. Other non-gradient approaches are not discussed, as if they did not exist. These choices contradict the introductory narrative suggesting broad, global applicability; with such limitations, the algorithm is not “global.”
3) Known controllability limitations are ignored
The paper tackles USV positioning under disturbances but does not acknowledge that this problem has been studied and that, without time-varying or scheduled laws, it may be uncontrollable (Brockett-type limitations). The manuscript proceeds as if these prior results did not exist, which is a serious omission given the mathematical background already available.
4) Undefined variables and arbitrary model simplifications
Notation is inconsistent. For example, in Eq. (4) a quantity “e1” appears with no prior definition, making the development hard to follow. The text explicitly “neglects sway,” another simplification introduced without argument, which further reduces realism and is not justified.
5) Assumption 1 lacks concrete values; functions appear before being defined
“Assumption 1” establishes bounds but does not state actual numbers or ranges. Moreover, a cost/field function (φ) appears in Eq. (9) and is only described much later. This ordering prevents the reader from understanding what the equation is doing at the point where it is introduced.
6) Unjustified existence assumptions
On page 6, the manuscript assumes that “an algorithm can always be defined” to handle certain cases. Such a statement must be justified or referenced. As written, it is an unsupported assertion and weakens the argument.
7) Very poor figure quality (e.g., Fig. 2)
Figure 2 is of low quality, with weak visual design and hard-to-read labels. In its current form it should not be included; the figure does not allow meaningful interpretation of the results.
8) “Remark 4” is unclear and unmotivated
Remark 4 is difficult to understand and provides no rationale for why it is true or why it matters for the method. The text needs to explain the point of the remark or remove it.
9) Core design issue in Eq. (13) for the desired heading
The desired angle is chosen as the solution that would be optimal for uniform fields in a continuous setting. This choice is only valid for continuous systems in uniform fields. In discretized implementations or non-uniform fields it may not be optimal, and in many cases it can even fail to achieve the objective. This aligns with prior observations in algorithms like PSO, where such search rules create loops; the paper’s own results show looped trajectories, indicating poor behavior.
10) Notation around Eq. (16) is inconsistent and confusing
Equation (16) introduces an error term (e⋯) and later a heading variable ψ_p is discussed. It is unclear whether ψ_p is the same as other previously defined headings or a different quantity. The notation is informal and inconsistent, making the algorithm hard to follow.
11) Writing issues and conceptual mixing (page 8)
There are multiple typographical problems (words run together), unclear phrases (e.g., “body sin volumen”), and an odd “Remark 7.” The expression “for slow variables” is also inappropriate: a variable is not “slow” by itself; if dynamics are slow, that must be stated precisely. Here, what is actually happening is the usual separation between kinematics (planning) and dynamics (control), which the text conflates.
12) Numerical results do not support the method
The numerical figures (e.g., Fig. 7; also Fig. 4) are low quality and difficult to read. The trajectories are filled with return loops, which is not acceptable in practice and indicates that the algorithm, as implemented, is far from usable. The presentation of results does not improve the paper’s image; rather, it confirms the concerns above.
13)Furthermore, presenting results without comparing them against the very algorithms previously described as inefficient is not good practice.
Recommendation
Reject. The manuscript should not be accepted in its current form. The authors should consult prior work that already addresses these topics and avoid introducing new labels for established concepts. A thorough rewrite is necessary to (i) align claims with the actual simplified setting, (ii) define all variables before use and justify each simplification, (iii) address known controllability constraints, (iv) improve notation and figures, and (v) reassess the heading/reference design to eliminate the looping behavior seen in the results.
Author Response
Thank you very much for your comments. Our point-by-point responses are provided in the attached PDF.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsAccept
Comments on the Quality of English LanguageI think this paper contains many long sentences, which are difficult to follow. I recommend rephrasing them.
Author Response
Please see the attachment about the point-by-point response to the reviewer’s comments.
Author Response File: Author Response.pdf
