Path Planning Method for Unmanned Vehicles in Complex Off-Road Environments Based on an Improved A* Algorithm

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. In dealing with dynamic obstacles, the algorithm only mentions the integrated dynamic environment awareness technology, and the actual algorithm has not fully verified the ability to deal with dynamic obstacles.
2. In the process of deducing some key formulas (such as slope calculation and heuristic function related formulas), the explanation is not detailed enough.
3. Please revise the main contributions of the paper. Some of them are not very clear, such as points 2 and 3, which are on pages 3-4.
4. The related works is short and brief, it need to be enriched, with recent articles on path/routing optimization, and related areas, towards enhancing the crowdsourcing door-to-door delivery: an effective model in beijing. The references should focus on both problems and algrithms.
5. Improve quality of tables, such as table 2,3. the bottom lines are missing.
6. The proposed A* algorithm only compared with Depth-First Search and Breadth-First Search. How about the other algorithms, like heuristics and path planning method. More works should be done.
7. Fig 7-10 are not marked in detail enough to clearly explain the meaning of each index and the scale of coordinate axes.

Author Response

Thank you very much for your valuable comments and professional advice. Your suggestions have greatly contributed to enhancing the academic rigor of our article. In accordance with your recommendations, we have carefully revised the manuscript and made the necessary modifications.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper presents an enhanced A* algorithm for obstacle avoidance and path planning in unmanned ground vehicles. The terrain is modeled as a multi-layered grid map incorporating elevation, risk, and surface attributes. The authors design three heuristic functions and corresponding search strategies aimed at minimizing travel time, reducing risk, and improving path smoothness. The algorithm is further refined by leveraging domain-specific characteristics, and demonstrates successful performance in a simulated off-road environment. This paper covers but is not limited to the following issues.

1. Table 1 contains punctuation errors. In the descriptions of Equations (4) and (5), the letter "e" appears redundantly. The variable "Sl" used in Equations (4) and (5) does not effectively convey the indexing of slope difference segments. In Equation (8), two formulas are joined without proper separation, which considerably impairs readability. Moreover, the captions for Figure 7(a) and 7(b) are identical, which may cause confusion.
2. The A* algorithm requires discretizing a continuous environment into a grid, and the choice of sampling resolution is a critical consideration. An overly fine resolution can lead to increased computational complexity, while an overly coarse one may fail to capture essential road surface details. The use of 100 m² grid cells may overlook significant environmental features. It is therefore recommended that the authors justify their selection of both the individual grid cell size and the total area of the test environment. Furthermore, reporting the algorithm’s computation time is advised to evaluate its real-time performance, and to verify that the additional computational cost introduced by the 24-neighborhood search remains within an acceptable range.
3. In the A* algorithm, the heuristic function must not overestimate the actual cost from a given node to the goal. However, the heuristic formulations used for the risk and smoothness cost functions do not guarantee this condition, which means that incorporating these heuristics independently into the A* search may compromise the algorithm's optimality. It is recommended that the algorithm and its description be revised or additional explanations be provided to address this issue.
   Moreover, the heuristics associated with the risk and smoothness cost functions seem not to account for potential risks or terrain irregularities along the path from the current grid cell to the goal. This contradicts the explanations provided in the final three paragraphs of Section 3.2. It is recommended that the algorithm be revised or additional explanations be provided.
   In the experimental scenario that jointly considers time, risk, and smoothness as cost components, it is strongly recommended to explain how these three functions are integrated into a unified cost function. This is a crucial detail, as optimizing each cost independently could result in suboptimal or unrealistic paths in certain situations. To underscore the paper's novelty, the combination strategy should be clearly described in the methodology section.
4. A critical consideration in autonomous driving is the constraint imposed by the vehicle’s minimum turning radius. When the planned path involves turning maneuvers, it is recommended that the authors explicitly address how the path is smoothed to ensure drivability, and how potential collisions with nearby obstacles are avoided during turning maneuvers.

 

Comments on the Quality of English Language

Table 1 contains punctuation errors. In the descriptions of Equations (4) and (5), the letter "e" appears redundantly. The variable "Sl" used in Equations (4) and (5) does not effectively convey the indexing of slope difference segments. In Equation (8), two formulas are joined without proper separation, which considerably impairs readability. Moreover, the captions for Figure 7(a) and 7(b) are identical, which may cause confusion.

Author Response

Thank you very much for your valuable comments and professional advice. Your suggestions have greatly contributed to enhancing the academic rigor of our article. In accordance with your recommendations, we have carefully revised the manuscript and made the necessary modifications.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript is devoted to solving the problem of drone trajectory optimisation in off-road conditions. The authors of the manuscript proposed an improved method that takes into account the peculiarities of the surface on which the drone moves, taking into account a new mechanism for selecting optimal candidate points for drone movement. With the sweeping fashion for unmanned vehicles, the work seems quite logical. But there are a few points that keep me from giving this work a favourable evaluation:
The main problem. The authors provide several single formulas that take into account the different characteristics of the surface on which the drone is travelling. The authors use a 24 neighbourhood search instead of the 8 neighbourhoods in the standard algorithm. I would like to know why the authors managed to cut the time of calculating the optimal path almost in half? I would like to see calculations on time and space complexity of the algorithm. At the moment it is very difficult to trust all the percentage improvements presented by the authors. 
Some comments and additions: It is not clear why the trajectory calculation does not take into account the characteristics of the unmanned vehicle. At least the parameter-risk should be necessarily related to these characteristics. 
How much does stationarity affect the quality of the calculated trajectory?
Please explain figure 6.
Please comment on Figure 11 and make the superscripts clearer. 

Author Response

Thank you very much for your valuable comments and professional advice. Your suggestions have greatly contributed to enhancing the academic rigor of our article. In accordance with your recommendations, we have carefully revised the manuscript and made the necessary modifications.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The article is devoted to improving the A* algorithm for planning the trajectories of unmanned ground vehicles in complex off-road environments. The authors proposed a new model of grid representation of the environment with multidimensional information and modified the heuristics and search strategy to improve route efficiency and safety. The work is relevant and contains several important technical solutions, but some aspects of the methodology, the rationale for choosing the parameters, and the presentation of the results need to be clarified. Below are specific comments on the content of the paper.

• In the introduction, the authors should more clearly highlight the scientific novelty of the proposed approach in comparison with other improved versions of the A* algorithm and add a description of the general organization of the article at the end.
• The use of an exclusively simulated environment limits the assessment of the impact of external factors inherent in real off-road conditions; it would be advisable to outline the relevant limitations of the experimental approach and discuss how they may affect the generalisability of the results.
• The literature review should include an analysis of modern hybrid or learning methods that show promise in planning in complex unstructured environments.
• The choice of the 24-neighborhood search as the optimal one is not sufficiently justified - there is no analysis of its computational complexity.
• The formulation of the heuristic functions looks technically correct but lacks justification of the parameters in the context of different types of terrain.
• The table of experimental results (Tables 3 and 4) provides valuable metrics but does not indicate the number of runs and statistical variation.
• The conclusions summarise the achievements well but do not cover the limitations associated with extending the approach to 3D or real-time.
• It is recommended to supplement the discussion with the potential for integration with reinforcement learning methods for dynamic scenarios.

 

Author Response

Thank you very much for your valuable comments and professional advice. Your suggestions have greatly contributed to enhancing the academic rigor of our article. In accordance with your recommendations, we have carefully revised the manuscript and made the necessary modifications.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

1. The related works is short and illogical, please summarized the references in a systematical way to compare the existed works and this paper. That is the way to show the contribution of the paper.
2. Secttion 2.2 and 2.3 has the same title “Surface Information Modeling”, why?
3. What is the objective of the path planning model, the paper didn’t show is clearly.
4. Dijkstra algorithm was employed in the new version, however the solution of Dijkstra was not given.
5. What is the value of Table 4? The repeated content has caused confusion.
6. Please point out which version of the A* algorithm will be highlight in the paper? What is the function of designing various deformations?

Author Response

Thank you very much for your valuable comments and professional advice. Your suggestions have greatly contributed to enhancing the academic rigor of our article. In accordance with your recommendations, we have carefully revised the manuscript and made the necessary modifications.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Dear authors of the article, unfortunately, your answer to my main question did not convince me. I still do not trust your results. Please provide calculations of time and space complexity of the algorithm. 
As for your suggestion to provide the source code.
I believe that it is not necessary. But it would be very good to schematically compare your method with methods which are used now for solving similar problems and show on the scheme, due to what improvements are obtained.

Author Response

Thank you very much for your valuable comments and professional advice. Your suggestions have greatly contributed to enhancing the academic rigor of our article. In accordance with your recommendations, we have carefully revised the manuscript and made the necessary modifications.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The authors have taken into account all the comments and made appropriate corrections, and the paper can be published.

Author Response

Dear reviewer,

Thank you sincerely for your valuable feedback and constructive suggestions on our manuscript. We are deeply grateful for the time and expertise you dedicated to improving the quality of this work.

Your insights have not only strengthened this paper but also provided important guidance for our future research directions. We are honored by your decision to accept the manuscript for publication and remain committed to any further refinements if needed.

Once again, thank you for your rigorous review and for contributing to the advancement of our research.

Respectfully yours,

Jinyin Bai

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

Dijkstra algorithm was employed in the new version, however the solution of Dijkstra was not
given,which should be added in the table.

Author Response

Dear Reviewer,

We have added the solution obtained by Dijkstra's algorithm to Table 3.

Once again, I sincerely appreciate the valuable time and effort you have dedicated to the review process. Your insights are of great significance for enhancing this paper. If there are any further content that needs supplementation or adjustment, please feel free to inform me, and I will cooperate fully.

Best regards,

Jinyin Bai

Reviewer 3 Report

Comments and Suggestions for Authors

I have reread the manuscript and the authors' answers to my questions. I am convinced by the authors' last response. I have no objection to you printing the last version of the manuscript.

Author Response

Dear Reviewer,

Once again, I sincerely appreciate the valuable time and effort you have dedicated to the review process. Your insights are of great significance for enhancing this paper. If there are any further content that needs supplementation or adjustment, please feel free to inform me, and I will cooperate fully.

Best regards,

Jinyin Bai