Estimating the Expected Time to Enter and Leave a Common Target Area in Robotic Swarms

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript “Estimating the Expected Time to Enter and Leave a Common Target Area in Robotic Swarms” addresses a fundamental challenge in swarm robotics by providing estimation formulas for task completion times under different coordination algorithms, including mixed teams. The study is original, timely, and has practical value for both theoretical analysis and real-world applications. The experimental validation with Stage simulations is extensive, and the comparisons with analytical approximations are convincing.

However, some revisions would strengthen the manuscript further:

• The introduction is comprehensive, but please highlight more clearly how the proposed estimations differ from regression-based approaches and mean-field theory methods (e.g., Chen et al. [56], Lasry and Lions [57]). This will better clarify the novelty.
• The estimation formulas (e.g., Eq. (3) for NC, Eq. (4)–(7) for SQF, Eq. (11)–(14) for TRVF) are primarily presented as empirical fits inspired by simulation. Please provide intermediate steps or a clearer rationale for constants (e.g., CNC1, CNC2, CSQF1, CTRVF). Even brief worked examples would improve reproducibility.
• Section 4 states that constants are obtained by least squares fitting. Please detail the fitting procedure (e.g., error metrics, confidence intervals). This transparency will strengthen scientific rigor.
• Ensure all figures are high resolution (≥300 dpi) and annotated with subfigure explanations.
• Use consistent scientific notation (e.g., 8×1038 \times 10^38×103) instead of “8E3” as noted in Figures 26–31.
• Some figures (e.g., Figs. 1–4, 7–10) could benefit from arrows or labels clarifying states (GT, LT, GC, etc.).
• Section 5 is valuable but could expand on:
• When estimations diverge significantly from simulations (e.g., low N, large s).
• Applicability to heterogeneous swarms and dynamic environments.
• Potential extensions with formal local-to-global mathematical frameworks.
• Adding a few very recent references (2023–2025) in local-to-global analysis or mean-field theory applications to swarm robotics, to reinforce novelty positioning.
• Please ensure in the final typeset version that the separation between the main references and the appendix references is clearer, so that figures are not visually interleaved with the reference list.

 

 

Comments on the Quality of English Language

The English is generally good, but several sentences in Sections 1.1 and 3 are lengthy. Please simplify for clarity.

Author Response

The replies are in the attached file. Thank you for the commendations and suggestions.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Dear authors, in the next paragraphs, my comments about your manuscript.

 

 

The work serves to address the core problem in Swarm Robotics, which is to estimate completion time in congestion. The focus on common target sites would be relevant to several other areas such as rescue, logistics, environmental detection.

The introduction sets up well the importance of performance estimation to lessen the dependence of extensive simulations and represents a relevant practical contribution.

Attempting to relate global behaviors (completion time) to local controllers is conceptually interesting and, therefore, opens up a new line of research.

The use of large-scale simulations in Stage (20 to 300 robots) is suitable for validation of the expressions under a variety of conditions.

The measure of error, NRMSE, alludes rigor to the comparison between estimate and simulation, with low values suggesting a good fit.

No explicit formulation had previously been presented to estimate completion time in common target problems with potential fields.

 

Points to Improve

1. The paper would benefit from a more concise introduction, mainly since it is rather long.
2. In some instances, the mathematical derivations are lengthy and detailed, possibly discouraging the average reader in mathematical physics. It would certainly be better to give a brief overview of them before stating those main equations.
3. Further to the review of studies in physics and swarm robotics, the Related Work section could include more articles from 2022–2024, mainly from journals like IEEE Transactions on Robotics and MDPI Sensors—that will give the impression of utmost relevance.
4. A comparative table should be added in the Related Works to summarize main algorithms and approaches.
5. Figures are illustrated reasonably well for simulated scenarios, but comparative graphs are missing between the estimated and simulated values to include error bars or some other forms of statistical analysis (e.g., ANOVA).
6. The study is based on circular and holonomic scenarios; the discussion could be expanded to other geometries (corridors, non-convex areas) or robots with energy constraints.
7. The discussion is still somewhat descriptive; it would be valuable to see the analysis of the estimate bounds in limiting cases (very high density, heterogeneous speeds).
8. The entire study is proved by simulations. Doing the proof of concept on actual robots, even on a minor scale would add great sturdiness to the work.
9. Only classical algorithms were involved in the evaluation (NC, SQF, and TRVF). What's missing is the evaluation of more recent algorithms that may utilize reinforcement learning or communicate-based planning.
10. Energy consumption is mentioned as a side note, but an analysis based on more time-oriented energy metrics would have been indeed valuable, especially when taking much larger applications into consideration.
11. The mention of algorithms running in parallel is somewhat brief and could definitely be elaborated more on.
12. Any formal discussion on the complexity of the proposed equations as N → ∞, which becomes relevant in swarm robotic studies, is missing.

Author Response

The replies are in the attached file. Thank you for the commendations and suggestions.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors do a good improve based on my comments