Path Planning for Autonomous Vehicle Control in Analogy to Supersonic Compressible Fluid Flow—An Obstacle Avoidance Scenario in Vehicular Traffic Flow

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

• What is the rational benefit of this fluid-flow analogy compared to standard path-planning algorithms (e.g., MPC, A*, RRT*)?  Why is this approach superior or more efficient computationally?
• What is the physics behind calling vehicle flow “supersonic” and “compressible”? Clarify whether this is a symbolic analogy or an actual physical equivalence.
• What evidence supports the assertion of “minimum disturbance to traffic flow”? Please clarify and include some numerical values or simulation results to support your claims.
• What are the validation criteria? The results section provides no measurable error or performance indicators. Clarify how success is evaluated.
• What is the computational cost or time of the proposed algorithm? Explain its feasibility for a real-time application.
• What is the scope of applicability? State if this method can handle multiple obstacles, multi-lane conditions, or urban intersections.
• What is the role of the “Traffic Mach Number” in practical control implementation? Clarify how it would be computed in a real vehicle.
• The figures are very dense and difficult to interpret with poor visual clarity.

• Many references are outdated; recent studies on autonomous driving and path planning should be incorporated to provide a more comprehensive understanding.

Author Response

Please see our attached comprehensive response letter. 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript studies and defines the non-dimensional group of Traffic Mach number (M_T).However, some key points are not cleared. The details are listed as follow:

1. Fig 12 and 13 only label “flow field configuration” without explaining the physical meaning of the coordinate axes (such as whether the X-axis is the longitudinal distance and the Y-axis is the lateral distance) and the legend.
2. The existing simulations only target the “single obstacle + two vehicles” scenario and do not involve real traffic scenarios such as multiple obstacles and dynamic obstacles. It is recommended to supplement simulation experiments in complex scenarios.
3. The format of the reference part is confusing. Please unify the format. When formula (37) equates a stationary vehicle to a double-wedge model, the calculation of the “wedge half-angle” only considers the vehicle width and safety distance, without involving the influence of vehicle length and obstacle shape. It is recommended to supplement the sensitivity analysis of the wedge angle model on the path generation results under different obstacle geometries.
4. The conclusion part only mentions “not considering dynamic obstacles” and does not analyze the core limitations of the model. It is recommended to supplement the analysis of the limitations of model assumptions (such as constant reaction time and ideal road conditions) and refine the future research directions.
5. Section 3.2 does not explain the parameter optimization process or the performance comparison with other control parameter combinations. It is recommended to supplement parameter optimization experiments.
6. Section 4 only analyzes the path tracking error and speed tracking effect, without evaluating key performance indicators (such as vehicle lateral acceleration, tire sideslip angle, and energy consumption). It is recommended to supplement the simulation data and analysis of relevant indicators.

Author Response

Please see our attached comprehensive response letter. 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The article "Path Planning for Autonomous Vehicle Control in Analogy to Principles of Supersonic Compressible Fluid Flow for Obstacle Avoidance" was reviewed. I have the following observations:

- In the abstract, please include the main numerical results. Please highlight the novelty of the research. Remove any supplementary information and try to write an abstract with a maximum of 200 words, which is appropriate.

- Keywords should be carefully selected, avoiding long phrases; a maximum of 5 or 6.

- The citation style should be reviewed; read the recommendations for authors and adjust to the journal's format.

- In the initial section of the methodology, it is appropriate to include a diagram that identifies the methodological process adopted in this research. You may include a block diagram or flowchart; this will make it easier for the reader to identify the equations.

- Equations should be numbered; they should be cited before each paragraph where each equation is presented. Each parameter must have its meaning and must be explained in detail in all sections containing equations related to the research.

- Figures 4 and 5 should be better explained, especially those with capital letters. Then, explain based on the programming used.

- In the conclusion, it is necessary to expand its context; a significant effort in the research is evident, but it is concluding with limited conclusions. In addition, mention the future work that emerges from this study, and explain the limitations that have been identified and that are worth acknowledging.

The manuscript is interesting and can be of great contribution to the field of study. Authors are encouraged to make the previously requested changes after a new review of the manuscript.

Author Response

Please see our attached comprehensive response letter. 

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

This paper presents an SMC+PID-based control technique for path planning of an autonomous vehicle, exploiting the analogy with fluidic flow. While the work is original and interesting, the authors need to address the following comments before it can be considered for publication at a reputed venue like 'Future Transportation':   - Work is limited to the simulation environment. Include experimental results acquired using a physical prototype/hardware system to prove the efficacy of the proposed vehicle control technique. - Quantify the results achieved in 1-2 sentences at the end of the Abstract. Words like 'reasonably', are subjective and are thus vague. How much reasonable is reasonable?  - Comment on the scalability of the proposed hybrid control approach in real-world scenarios. - SMC and many of its variants suffer from an inherent chattering phenomenon. Elaborate further on this phenomenon with reference to a literary work such as 'Adaptive Chattering-Free PID Sliding Mode Control for Tracking Problem of Uncertain Dynamical Systems'. Also, include experimental results on chattering mitigation. - Please combine small paragraphs, such as 2-3 line paragraphs given on Page 2. That makes the structure scattered. - Include the paper outlines at the end of Section 1. - It would be nice to include a Table presenting 'similarities' and 'differences' of fluidic motion and vehicle motion. - How does the present work consider and mitigate the model uncertainties that are inherent to systems like an autonomous vehicle? - The pivotal role of obstacle avoidance in path planning, mentioned on page 2, could benefit from work from the literature such as 'IBA: Intelligent bug algorithm – a novel strategy to navigate mobile robots  autonomously'. - What is the source of vehicle model parameters given in Table 1? - The paper considers simple trajectories/scenarios. Include more complex and sophisticated scenarios resembling real-world applications. - How have the controller parameters been selected in the present study? (Table 2) - Update the literature review with notable works such as 'An improved algorithm for collision avoidance in environments having U and H shaped obstacles' - Define all the abbreviations at their first occurrence and later on, simply use the abbreviation. - The paper needs thorough proofreading for typos and other linguistic improvements. - Also, include high-resolution images, particularly in the results section.

Author Response

Please see our attached comprehensive response letter. 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have made the necessary corrections. No further changes are required.

Reviewer 3 Report

Comments and Suggestions for Authors

A new review of the article "Path Planning for Autonomous Vehicle Control in Analogy to Supersonic Compressible Fluid Flow—an Obstacle Avoidance Scenario in Vehicular Traffic Flow" was carried out, the requested changes were mostly addressed, so I suggest the publication of the manuscript.

Reviewer 4 Report

Comments and Suggestions for Authors

The authors have incorporated all suggested comments, leading to significant improvements in the revised version of the paper. It is recommended for acceptance.