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Path Planning for Mobile Robots by Fusing Ant Colony Optimization and Dynamic Window Approach

PLOS One

Dear Dr. Guozhu,

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PLOS One

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“This work was supported by the Key Research and Development Project of the Shanxi Provincial Department of Science and Technology (202102140601015), the 2023 Scientific and Technological Innovation Project of Jinzhong National Agricultural High-tech Zone (Taigu National Science and Technology Innovation Center) (JZNGQBSGZZ004), and the Shanxi Provincial Basic Research Program (202403021222112).”

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Additional Editor Comments:

Dear Authors,

Please work on the comments by the reviewers to improve the paper for publication.

Regards

Academic Editor

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Reviewers' comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.-->

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Partly

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-->2. Has the statistical analysis been performed appropriately and rigorously?-->

Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: No

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: No

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-->5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #1: The authors propose a hybrid path planning method that integrates an enhanced ant colony optimization algorithm with a modified dynamic window approach for mobile robots operating in dynamic environments.This manuscript needs minor revision.

(1)The abstract claims the algorithm reduces the longest path length by 41.26%~48.28% compared to traditional ACO, but Table 2 shows AACO actually produces much longer paths than ACO in some cases, which undermines the validity of this comparison baseline.

(2)Equation (8) defines attractive force, which contradicts standard potential field theory where attraction typically increases as distance decreases; Pls check all the equations and definitions.

(3)The paper states that redundant turning points are removed via connectivity checks, but it doesn't clarify whether this post-processing step is applied after every ACO iteration or only once at the end, affecting computational cost claims.

(4)The evaluation function in Equation (25) adds D_dynamic as a positive term, yet higher collision risk should penalize trajectories—this suggests a possible sign error or misinterpretation of the risk coefficient's role.

(5)The claim that the fusion algorithm detects unknown obstacles in real time isn't substantiated by any sensor model or perception module description, making the “real-time detection” assertion appear unsupported.

(6)For path planning applications, the author could consider more articles: 3D vision technologies for a self-developed structural external crack damage recognition robot; Automation in Construction.

Reviewer #2: General Assessment

This manuscript proposes a hybrid path-planning framework that integrates Ant Colony Optimization (ACO) for global path planning with the Dynamic Window Approach (DWA) for local obstacle avoidance and motion control. The motivation to combine the global optimality and exploration strengths of ACO with the real-time feasibility and safety guarantees of DWA is well established and relevant to autonomous mobile robotics.

The paper is technically coherent, addresses a well-defined problem, and demonstrates the feasibility of the proposed approach through simulation-based experiments. The manuscript fits within the scope of PLOS ONE, which prioritizes technical soundness and reproducibility over claims of radical novelty.

However, while the work is competently executed, it currently falls short of the rigor and clarity needed to fully justify publication without revision. The main concerns relate to novelty positioning, experimental validation depth, and statistical robustness of performance claims.

1. Technical Soundness and Validity of Conclusions

The manuscript describes a technically sound approach:

The separation of global and local planning roles between ACO and DWA is conceptually correct.

The algorithmic flow is logically structured.

The mathematical formulations of both ACO pheromone updating and DWA velocity-space evaluation are consistent with established literature.

The simulation results generally support the claim that the fused approach improves path smoothness and collision avoidance relative to single-method planners.

That said, the conclusions occasionally extend beyond what the presented data can strictly support. Performance improvements are reported largely through illustrative comparisons rather than through rigorous quantitative analysis across multiple scenarios and randomized trials.

Assessment:

Technically sound, but conclusions should be more cautiously framed and better supported by systematic evidence.

2. Novelty and Contribution to State-of-the-Art

The idea of combining a global metaheuristic planner (ACO) with a local reactive planner (DWA) is not fundamentally new; similar hybrid global–local planning architectures have been explored extensively in the robotics literature using A*, GA, PSO, RRT variants, and other heuristics.

The contribution of this paper therefore lies not in conceptual novelty, but in:

a specific integration strategy between ACO and DWA,

parameter coordination between the two layers, and

empirical demonstration of feasibility.

However, the manuscript does not sufficiently distinguish its approach from prior hybrid planners nor clearly articulate what is substantively new beyond implementation-level integration.

Recommendation:

The authors should strengthen the literature review and explicitly position their contribution relative to existing ACO-based and DWA-based hybrid methods, clarifying whether the novelty lies in algorithmic coupling, parameter design, or performance characteristics.

3. Statistical Rigor and Experimental Design

The experimental validation is one of the weaker aspects of the manuscript.

Simulations appear to be conducted on a limited set of environments.

Results are presented primarily as single-run or deterministic comparisons.

There is no reporting of variance, confidence intervals, or statistical significance.

Parameter sensitivity and robustness are not systematically examined.

Given the stochastic nature of ACO, multiple independent runs with aggregated statistics are essential to support performance claims.

Assessment:

The experimental design demonstrates feasibility but not robustness.

Required improvements include:

Multiple-run evaluations with mean ± variance.

Statistical comparison against baseline planners.

Clear justification of parameter choices.

Inclusion of more complex or dynamic environments, if feasible.

4. Reproducibility and Transparency

The manuscript provides algorithm descriptions and pseudo-code-level explanations, which is positive. However:

Parameter values are not always fully specified.

Simulation settings (map resolution, robot dynamics, sensor assumptions) are not described in sufficient detail.

There is no indication of code or data availability.

For PLOS ONE, reproducibility is essential.

Recommendation:

The authors should provide a full parameter table and, ideally, a public repository containing simulation code or configuration files.

5. Presentation Quality and Language

The manuscript is generally well written in standard academic English. The structure is logical, and figures are relevant and clear.

Minor issues include:

Occasional grammatical inconsistencies.

Overly assertive language in the discussion that should be moderated.

Figure captions that could be more self-contained and descriptive.

6. Ethical and Publication Considerations

There are no ethical concerns related to the research content. The work does not raise issues of dual publication, misuse of data, or ethical non-compliance.

Overall Recommendation

Decision: Major Revision

This manuscript presents a competent and relevant study in mobile robot path planning and aligns with PLOS ONE’s scope. However, it currently does not meet the journal’s standards for analytical rigor and evidentiary support.

To merit publication, the authors should:

Clearly articulate the novelty of their approach relative to prior hybrid planners.

Strengthen experimental validation with statistically robust comparisons.

Improve reproducibility through detailed parameter reporting and, ideally, code sharing.

Moderate conclusions to reflect the exploratory nature of the results.

With these revisions, the manuscript could become a solid, publishable contribution to the applied robotics literature.

Reviewer #3: The authors' purpose is to present a path planning method fusing the ant colony optimization (ACO) and dynamic window approach (DWA), namely the ACO-DWA-DPP algorithm. The authors argue that the simulation results show that, compared with the traditional ant colony optimization, the improved algorithm reduces the longest path length by 41.26%-48.28%, shortens the shortest path by 10.68%-12.64%, decreases the number of iterations by 83.37%-89.51%, and reduces the number of turning points by 66.94%-81.37%.

In my opinion, the article presents some weak points. The authors need to show significant improvement over other approaches on several test scenarios to claim the advancement and novelty of their proposal.

Some points must be taken to improve the quality of the article:

* The paper contains some grammatical mistakes and typos. The whole paper must be carefully reviewed.

* The main contributions should be reviewed and stated in a clear form in the first section using bullets.

* Should have text between section title and section subtitle (e.g., between 2 and 2.1, and so on).

* Transitions from section to section should be smoother, please work on this issue to enhance readability.

* It is not clear what are the advantages, disadvantages, issues, etc. related to the implementation of the ant colony optimization in the proposal. The text should guide the reader to understand why the authors selected and implemented this approach over other methods.

* In the results, there is not a comparison concerning the state of the art. The results are insufficient to provide a valid evaluation of the proposed method.

* The test scenario presented is insufficient. The experiments are very limited to provide a valid evaluation of the proposal. The author needs to provide more scenarios to test their proposal.

*In Section 7, there is a lack of parameter setting discussion for the experimental settings. The parameter values have not been described. How would the result of your implementation vary with increasing/decreasing those values?

* The proposal must be tested on a real mobile robot. The author must present evidence of the implementation and results of the test process on the real mobile robot.

* The conclusion section should be improved to provide real useful conclusions. Not to be an overview of the previous paragraphs.

* On the conclusions, the authors need to provide solid and insightful future research directions in a separate paragraph.

* More references to path planning papers should be reviewed and included, like: “Hybrid path planning algorithm based on membrane pseudo-bacterial potential field for autonomous mobile robots,” “Mobile robot path planning using membrane evolutionary artificial potential field,” and "Mobile robot path planning using a QAPF learning algorithm for known and unknown environments".

* The references must be carefully reviewed, updated, and extended. The number of references is low for a journal paper (usually 40-50 references for journal papers), please consider the previous comments on this issue.

* A review of the state of the art is required.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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-->PONE-D-25-67110R1-->-->Path Planning for Mobile Robots by Fusing Ant Colony Optimization and Dynamic Window Approach-->-->PLOS One

Dear Dr. Guozhu,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by May 29 2026 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:-->

• A letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

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If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

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We look forward to receiving your revised manuscript.

Kind regards,

Ravneil Nand

Academic Editor

PLOS One

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2. Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Additional Editor Comments:

Please share code via online repository.

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Reviewer's Responses to Questions

-->Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.-->

Reviewer #1: All comments have been addressed

Reviewer #2: (No Response)

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-->2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. -->

Reviewer #1: (No Response)

Reviewer #2: Partly

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Reviewer #1: (No Response)

Reviewer #2: No

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The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #1: (No Response)

Reviewer #2: No

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PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.-->

Reviewer #1: (No Response)

Reviewer #2: Yes

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-->6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #1: accept~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~accept~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~accept~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~accept~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Reviewer #2: Thank you for the opportunity to review this revised manuscript.

1. Summary of the Manuscript: The manuscript proposes a hybrid path-planning framework (ACO-DWA-DPP) that integrates an improved Ant Colony Optimization (ACO) algorithm for global path planning with an enhanced Dynamic Window Approach (DWA) for local trajectory planning and dynamic obstacle avoidance. The study introduces several modifications including a potential-field-based heuristic function, a pheromone reward–punishment mechanism, an adaptive evaporation strategy, and a dynamic collision-risk coefficient within the DWA evaluation function. Simulation experiments are conducted to evaluate performance across several environments, and comparisons are made against conventional ACO-based algorithms.

The revised manuscript presents a technically sound algorithmic framework for mobile robot path planning. The fusion of global ACO optimisation with local DWA trajectory control is conceptually appropriate and consistent with established practices in robotics path-planning research.

2. Technical Soundness and Validity of the Study: I have read the rebuttal letter and the revised text carefully and I acknowledge that the authors have made a genuine and constructive effort to address the concerns raised in the first round of review. Several important corrections have been made, and the manuscript is more clearly organised and more precisely written than the original submission. These improvements are appreciated.

3. Novelty and Contribution:

The revised manuscript now clearly identifies the principal contributions of the proposed approach in the Introduction (lines 83–99). These include:

A bidirectional closed-loop feedback mechanism between the global ACO planner and the local DWA planner.

A dynamic collision-risk model incorporating relative distance, velocity, and acceleration of obstacles.

A connectivity-based path smoothing strategy applied after algorithm convergence to remove redundant turning points.

The explicit articulation of these contributions significantly improves the clarity of the paper and helps distinguish the proposed approach from existing hybrid path-planning frameworks.

I am able to confirm that the following issues from the prior review have been satisfactorily resolved. The sign convention in the dynamic collision-risk evaluation function (Equation 25) has been corrected so that trajectories with higher collision risk receive lower evaluation scores. The path smoothing step is now described as a post-convergence operation that is applied once after the ACO algorithm has reached a final path, which resolves the ambiguity regarding its effect on computational cost. The claim of real-time obstacle detection has been appropriately contextualised as referring to the algorithm's capacity to respond to obstacle information within an idealised simulation environment, rather than to the output of a physical sensing system. The three principal contributions of the framework are now stated explicitly in numbered form in the Introduction. Transitional paragraphs have been added between sections, and the analysis of traditional ACO limitations has been strengthened.

Despite these improvements, a number of concerns remain that must be addressed before the manuscript can be accepted. I present these below, ordered by scientific significance, with specific reference to the relevant sections and line numbers in the revised manuscript.

Comment 1: Statistical Reporting (Major). The experimental results in Tables 2 through 5 report mean performance values across 30 independent runs but provide no measures of dispersion and no inferential statistical analysis. For stochastic population-based algorithms such as ACO, mean-only reporting is insufficient to characterise the reliability of the observed performance differences. Without standard deviations or equivalent dispersion measures, it is not possible for the reader to determine whether the reported improvements represent a consistent advantage or fall within the natural run-to-run variability of the algorithm.

This concern is most acute for the comparisons presented in Table 3, where the proposed algorithm's improvements in shortest path length relative to IACO and AACO range from 4.2 to 6.1 percent. Differences of this magnitude in stochastic optimization cannot be interpreted without supporting statistical evidence. I request that the authors add standard deviation values to all entries in Tables 2 through 5 and apply a non-parametric pairwise significance test, such as the Wilcoxon signed-rank test, to each algorithm comparison. The test statistic and the corresponding p-value should be reported for each pairwise comparison. This revision is necessary for the conclusions drawn in Section 7.2 to be scientifically defensible.

Comment 2: Dimensional Error in Equation (22) (Major). Equation (22) defines the relative velocity v_rel between the mobile robot and a dynamic obstacle. In the second term under the square root, the expression 'y_r sin(theta_r)' appears, where y_r is the y-coordinate of the robot's position. In the context of a velocity magnitude computation, this term is dimensionally inconsistent: y_r has units of length (metres) whereas the expression requires a velocity component (metres per second). The physically correct term is 'v_r sin(theta_r)', where v_r is the linear velocity of the robot and theta_r is its heading angle with respect to the obstacle.

This is not a minor typographic error. The relative velocity v_rel is the direct input to the collision time estimate T_collision in Equation (23), which in turn determines the dynamic collision-risk coefficient D_dynamic in Equation (24). D_dynamic is one of the three claimed primary contributions of this work and is central to the improved performance reported in Section 7.3. The authors must correct Equation (22), recompute all affected derived quantities, and confirm that the simulation results presented in the manuscript are based on the corrected formulation.

Comment 3: Geometric Validity of the Segment Intersection Test in Equation (14) (Major). Section 3.4 describes the path secondary optimization procedure, which prunes redundant turning points by testing whether direct connections between non-adjacent path nodes intersect obstacle boundaries. The intersection criterion is expressed in Equation (14), where the sign of the scalar cross product of two directional vectors is used to classify intersection (positive), parallelism or overlap (zero), and non-intersection (negative).

This criterion is mathematically incorrect for the purpose of bounded segment intersection. The sign of the cross product of two directional vectors determines only the angular relationship between the two supporting lines; it does not establish whether the bounded segments share a common point. A rigorous segment intersection test requires computing four cross products and verifying that the endpoints of each segment straddle the supporting line of the other segment. The test as formulated in Equation (14) will classify non-intersecting segments as intersecting whenever the extensions of their supporting lines cross at an angle, and will misclassify the intersection status of segments that meet near their midpoints. Since the correctness of the path pruning operation depends entirely on this test, its invalidity is a substantive concern.

I request that the authors replace Equation (14) with a geometrically correct segment intersection algorithm, such as the standard cross-product straddling test, or provide a clear and rigorous mathematical justification demonstrating that the simplified criterion is sufficient within the specific constraints of their grid-based obstacle representation.

Comment 4: Underspecified Parameters in Equation (12) (Moderate). Equation (12) expresses the adaptive pheromone evaporation coefficient rho as a function of the current iteration k, the maximum iteration count K, an initial value rho_1, a maximum bound rho_max, and a minimum bound rho_min. Table 1 lists rho as a single fixed value of 0.6. Neither rho_max nor rho_min is specified anywhere in the manuscript. The initial value rho_1 = 0.6 is stated in the text at lines 287 to 288, but the relationship between this initial value and the entry in Table 1 is not explained. In the absence of rho_max and rho_min, Equation (12) cannot be independently reproduced. I request that the authors specify these values, together with a description of the effective range of rho across the iterative process, in Table 1 or in the parameter description that follows the equation.

Comment 5: Experimental Comparison with the Most Closely Related Prior Work (Moderate). The manuscript identifies Reference [22] (Xue et al., 2025: A hybrid ant colony optimization and dynamic window method for real-time navigation of unmanned surface vehicles, Sensors) as a prior hybrid ACO-DWA approach. This is the most closely related antecedent to the proposed method in the reference list. The paper is cited in Section 6.1 in the context of the bidirectional feedback architecture but is not included as a comparison algorithm in the experimental evaluation. The absence of this comparison weakens the empirical support for the novelty claims, since it is not possible to determine from the experiments whether the performance advantages reported in Section 7 arise from the proposed contributions specifically or from the general class of ACO-DWA fusion approaches.

I request that the authors either include a quantitative experimental comparison with the method of Xue et al. (2025) or provide a detailed technical analysis in Section 6.1 documenting the specific algorithmic differences that distinguish the proposed framework from that work and explaining why those differences are expected to yield superior performance in the tested environments.

Comment 6: Dynamic Obstacle Validation Scenario (Moderate). The evaluation of dynamic obstacle avoidance performance in Section 7.3 is conducted with one dynamic obstacle alongside multiple static obstacles. The introduction motivates the research with reference to complex dynamic environments, and the primary claimed contribution at the local planning layer is a collision-risk model that incorporates obstacle acceleration. A single dynamic obstacle is insufficient to stress-test this model or to demonstrate the bidirectional feedback mechanism, which is described as being triggered when the local planner detects that the global path is blocked. I recommend that the authors either extend the simulation to include at least two simultaneously moving obstacles with distinct velocity and acceleration profiles, or acknowledge this limitation explicitly in the Conclusion section and identify multi-obstacle dynamic scenarios as a specific and prioritised future work direction.

Comment 7: Kinematic Validity of DWA for the Ackermann Model (Moderate). Section 4.1 specifies that the study examines the Ackermann steering mechanism. The Dynamic Window Approach was originally formulated by Fox, Burgard, and Thrun (1997) for differential-drive robots, for which linear and angular velocity are independently controllable. The Ackermann model imposes different non-holonomic constraints: the turning radius is a function of the wheelbase and steering angle, and the robot cannot rotate in place. The velocity sampling constraints stated in Equations (17) through (19) assume a symmetric, independently controllable velocity space that may not accurately represent the physically reachable set of an Ackermann vehicle. The manuscript provides no justification for applying the standard DWA velocity sampling framework to this platform. The authors should include a brief technical justification or cite prior work that validates this adaptation. If simplifying assumptions have been made, for example treating the Ackermann vehicle as a kinematically equivalent unicycle model for the purposes of velocity sampling, these should be stated explicitly.

Comment 8: Computational Complexity and Runtime (Moderate). The manuscript reports iteration count as a proxy for computational efficiency, and Table 4 shows substantial reductions in iteration count for the proposed algorithm relative to the baselines. However, iteration count and wall-clock computation time are not equivalent. The proposed improvements introduce several computationally intensive additions relative to the traditional ACO, including a multi-component heuristic function, a three-tiered pheromone reward-punishment computation, an adaptive evaporation coefficient evaluated at each iteration, and a post-convergence path pruning step. The DWA layer similarly introduces a per-step collision-risk computation involving relative velocity and acceleration estimation. Without reporting actual execution times or providing an analytical complexity discussion, it cannot be determined whether the reduction in iteration count translates to a net reduction in total computation time. I request that the authors report average wall-clock execution times for each algorithm, measured under identical hardware and software conditions, or provide an analytical discussion of the computational complexity trade-offs.

Comment 9: Parameter Sensitivity Results (Recommended Enhancement). Lines 550 through 556 state that a sensitivity analysis was conducted over ranges of alpha, beta, and rho using a controlled variable method, and that the algorithm demonstrated robustness within these ranges. This is a qualitative assertion. The results of the sensitivity analysis are not presented in the manuscript, and no quantitative evidence is provided to support the claim of robustness. I recommend that the authors include a supplementary table or figure reporting the variation in at least one key performance metric across the tested parameter ranges. This would provide empirical support for the robustness claim and would serve as useful practical guidance for readers seeking to apply the method to different problem environments.

Comment 10: Algorithm Scalability (Recommended Enhancement). All simulation experiments are conducted on grid maps of 20 by 20 and 30 by 30 nodes. These scales are modest relative to the operational environments referenced in the motivating applications of intelligent warehouse logistics and autonomous vehicle navigation. The time complexity of ACO grows with the number of nodes and ants, and the addition of a bidirectional feedback mechanism introduces computational coupling between the global and local planning layers. The manuscript does not discuss how the proposed framework is expected to perform at larger scales. I encourage the authors to include a brief scalability discussion in the Conclusion or Future Work sections, acknowledging the computational limitations of the current implementation and proposing how these might be addressed in future research.

In summary, the following revisions are required before the manuscript can be accepted for publication:

1. Supplement Tables 2 through 5 with standard deviation values for all reported metrics. Apply non-parametric pairwise significance testing to each algorithm comparison and report the resulting test statistics and p-values.

2. Correct the dimensional error in Equation (22) by replacing y_r with v_r in the relative velocity expression, and reconfirm that all simulation results are based on the corrected formulation.

3. Correct or provide a rigorous mathematical justification for the segment intersection criterion in Equation (14).

4. Specify rho_max and rho_min in Table 1 or in the parameter description accompanying Equation (12).

5.Conduct a full audit of all in-text equation cross-references and correct those that do not correspond to the rendered equation numbers.

6. Provide either a quantitative experimental comparison with Xue et al. (2025, Reference [22]) or a detailed technical comparison in Section 6.1.

7. Expand the dynamic obstacle validation to include at least two simultaneously moving obstacles, or explicitly acknowledge this limitation in the Conclusion.

8. Replace the unresolved citation placeholder '[citations]' at line 460 with appropriate references.

9. Include a technical justification for applying the standard DWA velocity sampling constraints to the Ackermann kinematic model.

10.Report average wall-clock execution times or provide a computational complexity analysis for the proposed and baseline algorithms.

11. Correct the Figure 8 caption to read 'Comparison of Path Planning in Complex Environments.'

12. Correct the double-period error at line 24 of the abstract.

13. Revise the Acknowledgments section to remove the reference to a listed co-author.

The following enhancements are recommended but not mandatory for acceptance:

14. Include quantitative results from the parameter sensitivity analysis to support the robustness claim at lines 550 through 556.

15. Include a scalability discussion in the Conclusion or Future Work sections.

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Path Planning for Mobile Robots by Fusing Ant Colony Optimization and Dynamic Window Approach

PONE-D-25-67110R2

Dear Dr. Guozhu,

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