Research on Mobile Robot Path Planning Based on an Improved Bidirectional Jump Point Search Algorithm

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The author proposes an improved B-JPS path planning algorithm by focusing on two key aspects: adaptive weight coefficients and dynamic constraint circles. The article is well-written and logically structured. However, it seems overly polished, for instance, all referenced literature is cited in the format "Literature 1..n has done what work," which deviates slightly from typical human writing conventions. Additionally, the description of personal innovations within the paper is not detailed enough. Assuming no AI assistance was involved in the writing process, I believe the article could be acceptable after undergoing the following revisions.

(1) Please rewrite your abstract. It is recommended to clearly emphasize the novelty (adaptive weight coefficients and dynamic constraint circles) of this work.

(2) The weight coefficient mentioned in Section 3.1 should be clearly or fully expressed. Is it referring to the coefficient of h(x) in Equation (3)? If so, the parameter for the weight coefficient has not been presented in the text.

(3) The pseudocode could be further elaborated with specific parameter expressions or assignments, rather than merely narrative descriptions in the text.

(4) The discussion and analysis in the test section require further enhancement. The Result section was not clearly written. More explanations about the details of the results are necessary.

(5) The conclusion section should not only summarize the main content of the article but also provide a forward-looking perspective for the future. Please include this aspect in your revision.

Author Response

Comments 1：Please rewrite your abstract. It is recommended to clearly emphasize the novelty (adaptive weight coefficients and dynamic constraint circles) of this work.

Response 1：Thank you very much for your valuable suggestion. We fully agree with your comment. Accordingly, we have carefully rewritten the abstract to explicitly highlight the key novelties of this study, especially the introduction of the adaptive weight coefficient in the heuristic function and the use of the dynamic constraint circle during the bidirectional search process. These core improvements are now clearly emphasized in the revised abstract (Lines 7–22 in the revised manuscript).

 

Comments 2：The weight coefficient mentioned in Section 3.1 should be clearly or fully expressed. Is it referring to the coefficient of h(x) in Equation (3)? If so, the parameter for the weight coefficient has not been presented in the text.

Response 2：Thank you for your careful review. We agree with your comment. The weight coefficient indeed refers to the scaling factor of the heuristic function h(x) in Equation (3). To address this issue, we have revised the text to clearly define and explain this parameter. The improved explanation has been added in Lines 185–189 of the revised manuscript.

 

Comments 3：The pseudocode could be further elaborated with specific parameter expressions or assignments, rather than merely narrative descriptions in the text.

Response 3：We sincerely thank you for this valuable suggestion. We fully agree that the original pseudocode lacked clarity and detail. In response, we have thoroughly rewritten the pseudocode to include explicit parameter expressions, variable assignments, and decision-making logic, thereby enhancing its technical accuracy and readability. Additionally, we have included a corresponding flowchart to visually illustrate the overall algorithm structure. These revisions can be found in Lines 342–344 of the revised manuscript.

 

Comments 4：The discussion and analysis in the test section require further enhancement. The Result section was not clearly written. More explanations about the details of the results are necessary.

Response 4：Thank you very much for your constructive feedback. We fully agree with your comment. The test and result sections indeed required improvement in both clarity and depth of analysis. Accordingly, we have revised the manuscript to enhance the structure, expand the result interpretations. These improvements have been made in Lines 384–389, 398–402, 429–432, 440–471, and 496–511 of the revised manuscript.

 

Comments 5：The conclusion section should not only summarize the main content of the article but also provide a forward-looking perspective for the future. Please include this aspect in your revision.

Response 5：Thank you very much for your insightful suggestion. We completely agree. In the revised version, we have added a dedicated forward-looking perspective to the conclusion section, outlining potential future directions for extending the algorithm, such as its integration with local obstacle avoidance methods and its application in dynamic or partially unknown environments. Additionally, to maintain consistency with the improvements made in the abstract (as suggested in your earlier comment), we have revised the summary portion of the conclusion accordingly. These modifications can be found in Lines 516–525 and 541–546 of the revised manuscript.

 

We have used professional language editing service and attached the certificate as supplementary material for the editor's reference.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Comments to Authors:

 

The recommendation of this reviewer is “Accept after minor revisions”, the following suggestions are for the authors’ reference.

 

(1) The paper provides a description of the improved algorithm but lacks a rigorous theoretical analysis of its performance guarantees. For example, the adaptive heuristic function is introduced, but its mathematical properties (e.g., admissibility and consistency) are not formally proven.

The dynamic constraint circle is a novel concept, but the paper does not provide a theoretical justification for why this approach reduces search time or improves path quality.

 

(2) While the paper includes simulation experiments and physical robot tests, the experimental validation is not comprehensive enough. For example, the simulations are limited to grid maps of fixed sizes (20×20, 50×50, and 200×200), and there is no discussion of how the algorithm performs in more complex or dynamic environments.

 

(3) Figure 9 and Table 3 should be presented at appropriate location within the text to avoid spanning across multiple pages.

 

(4) While the concept of the dynamic constraint circle is introduced, the exact mechanism for updating the circle's position and radius is unclear. For example, how often is the circle updated during the search process, and how is the obstacle coverage rate calculated in real-time?

Author Response

Comments 1：The paper provides a description of the improved algorithm but lacks a rigorous theoretical analysis of its performance guarantees. For example, the adaptive heuristic function is introduced, but its mathematical properties (e.g., admissibility and consistency) are not formally proven.

The dynamic constraint circle is a novel concept, but the paper does not provide a theoretical justification for why this approach reduces search time or improves path quality.

Response 1：Thank you very much for your thoughtful and valuable comments. We fully acknowledge the importance of theoretical analysis in algorithm design and appreciate your feedback.

Regarding the adaptive heuristic function, we designed it to dynamically adjust the weight of the heuristic component based on the relative distance between the current node and the goal. Specifically, the function introduces a factor of  in Equation (3), where α is the current distance to the goal and β is the total distance from the start to the goal. This coefficient gradually approaches 1 as the search progresses, thereby maintaining near-admissibility in the early stages and improving accuracy near the target. While we have not provided a formal mathematical proof of admissibility or consistency, the heuristic follows principles similar to those in weighted A* algorithms and has demonstrated empirical effectiveness across all test scenarios.

For the dynamic constraint circle, the constraint circle is dynamically constructed based on the midpoint between the lowest-cost forward and backward nodes, and its radius is controlled by the obstacle coverage rate and a tuning parameter λ. This mechanism helps limit the node expansion area, prioritize important directions, and reduce redundant exploration. We have conducted extensive simulations and physical robot experiments showing consistent reductions in search time and better path quality (see Table 5 and Table 6).

Moreover, based on your suggestion, we have added a detailed algorithmic flowchart (Figure 9) (Lines 342 in the revised manuscript) to clearly present the interaction between adaptive components—including the constraint circle, bidirectional targets, and jump point selection strategy. This structured visualization provides more intuitive support for the algorithm’s efficiency gains and practical applicability.

We sincerely appreciate your comments.

 

Comments 2：While the paper includes simulation experiments and physical robot tests, the experimental validation is not comprehensive enough. For example, the simulations are limited to grid maps of fixed sizes (20×20, 50×50, and 200×200), and there is no discussion of how the algorithm performs in more complex or dynamic environments.

Response 2：Thank you very much for your valuable suggestion. We fully acknowledge this limitation. The improved algorithm proposed in this paper is primarily designed for global path planning in static environments. However, we also recognize the importance of dynamic and partially unknown environments in real-world applications.

To address this, we have added a future research perspective in the conclusion section (Lines 541–546), where we propose integrating our improved global algorithm with local real-time obstacle avoidance methods such as DWA (Dynamic Window Approach). This would allow the extended system to operate effectively in dynamic or partially known environments, which we consider a promising direction for further exploration.

 

Comments 3：Figure 9 and Table 3 should be presented at appropriate location within the text to avoid spanning across multiple pages.

Response 3：Thank you very much for your careful observation regarding the formatting issue. We have revised the manuscript layout accordingly, and Figure 9 and Table 3 are now placed appropriately to avoid being split across multiple pages. These corrections can be found in Lines 373 and 377 of the revised manuscript.

 

Comments 4：While the concept of the dynamic constraint circle is introduced, the exact mechanism for updating the circle's position and radius is unclear. For example, how often is the circle updated during the search process, and how is the obstacle coverage rate calculated in real-time?

Response 4：Thank you very much for your insightful question. We are pleased to provide further clarification regarding the update mechanism of the dynamic constraint circle and the calculation of the obstacle coverage rate.

The position of the constraint circle is updated each time a new minimum-cost node is selected in both the forward and backward open lists during the bidirectional search. The center of the circle is defined as the midpoint between these two minimum-cost nodes. This ensures that the search is dynamically focused around the most promising region for path connection.

The radius of the circle is computed as (λ⋅d)/2, where d is the Euclidean distance between the two nodes and λ is a scaling factor determined by the obstacle coverage rate L. Specifically, we define a rectangular evaluation region with its diagonal spanning the two expanding nodes, and calculate L=m/M×100%, where mmm is the number of obstacle cells (black blocks) and M is the total number of grid cells in the rectangle. This rate is updated dynamically after every bidirectional expansion iteration.

To make this mechanism more intuitive and easier to follow, we have further refined the pseudocode and added a flowchart (Figure 9) (Lines 342-344) to clearly demonstrate the interaction between the dynamic constraint circle, jump point filtering, and bidirectional expansion logic.

We hope this explanation addresses your concerns, and we sincerely appreciate your suggestion to improve the clarity of this key component.

Reviewer 3 Report

Comments and Suggestions for Authors

This paper proposed an improved bidirectional dynamic jump point search (JPS) algorithm for the purpose of addressing the challenges in mobile robot path planning. Authors discussed an interesting research area, however, I recommend to address the following issues to enhance the overall quality of this paper:

1. The A* algorithm was discussed in two sections: in the introduction section (Line 40) and in the Basic Algorithms and Their Limitations section (Line 87). I recommend to avoid repetition. 
2. Authors need to revise Line 94: ".... from the starting node through node xxx". What does xxx refer to ? 
3. Section 3 presents the Improved Bidirectional Algorithm. It is recommended to include a flowchart to visually represent the developed algorithm, along with its pseudocode, to enhance the reader’s understanding.
4. I recommend to include more details about the simulation experiment test-bed. 
5. The developed system has been validated using real robot platform. Authors need to add more details about ROS development environment, the robot platform, and the ROS architecture. 
6. The authors should provide a more in-depth critical analysis and discussion of the obtained real-world results to better support their findings. 
7. Authors may consider the following relevant research works:

               a. Mobile robot path planning based on improved A* algorithm.

               b. An autonomous maze-solving robotic system based on an enhanced wall-follower approach

      

Author Response

Comments 1：The A* algorithm was discussed in two sections: in the introduction section (Line 40) and in the Basic Algorithms and Their Limitations section (Line 87). I recommend to avoid repetition.

Response 1：Thank you very much for your valuable suggestion. We fully agree that this repetition was unnecessary. In the revised manuscript, we have removed the redundant description and streamlined the discussion of the A* algorithm to avoid duplication. The changes have been made in Lines 55–57 of the revised manuscript.

 

Comments 2：Authors need to revise Line 94: ".... from the starting node through node xxx". What does xxx refer to ? 

Response 2：Thank you very much for your careful review. The term "xxx" was mistakenly left in the manuscript during editing. It was intended to refer to node x. We have corrected this error in the revised version of the manuscript (see Line 111).

 

Comments 3：Section 3 presents the Improved Bidirectional Algorithm. It is recommended to include a flowchart to visually represent the developed algorithm, along with its pseudocode, to enhance the reader’s understanding.

Response 3：Thank you very much for your helpful suggestion. We fully agree that a visual representation improves clarity and understanding. In response, we have added a flowchart to accompany the pseudocode of the improved bidirectional algorithm. The flowchart has been inserted in the revised manuscript at Line 342.

 

Comments 4：I recommend to include more details about the simulation experiment test-bed. 

Response 4：Thank you very much for your constructive suggestion. We agree that the description of the simulation test-bed was insufficient. In the revised manuscript, we have added more detailed information about the simulation environment and experimental setup. These additions can be found in Lines 347–357 of the revised manuscript.

 

Comments 5：The developed system has been validated using real robot platform. Authors need to add more details about ROS development environment, the robot platform, and the ROS architecture. 

Response 5：Thank you very much for your insightful comment. We fully agree that a more detailed description of the real robot platform and its ROS-based system is necessary. In the revised manuscript, we have added comprehensive information regarding the ROS development environment, the hardware setup of the wheeled robot, and the ROS architecture, including the use of the SLAM-Gmapping module. These details can be found in Lines 440–471 of the revised manuscript.

 

Comments 6：The authors should provide a more in-depth critical analysis and discussion of the obtained real-world results to better support their findings. 

Response 6：Thank you very much for your valuable suggestion. We fully agree that the real-world experimental results required deeper analysis to better support the conclusions. In the revised manuscript, we have expanded the discussion and provided a more detailed, critical analysis of the experimental data, highlighting the comparative performance of the proposed algorithm. These improvements can be found in Lines 496–511 of the revised manuscript.

 

Comments 7：Authors may consider the following relevant research works:

1. Mobile robot path planning based on improved A* algorithm.
2. An autonomous maze-solving robotic system based on an enhanced wall-follower approach

Response 7：Thank you very much for your recommendation of relevant literature. We appreciate your suggestions and will take them into consideration to further improve the depth and completeness of our future research.

Reviewer 4 Report

Comments and Suggestions for Authors

We wish researchers for their contribution to the Bidirectional Jump Point Search Algorithm, which has been implemented for Mobile Robot Path Planning.

1. The ideas in Section 2.2, the JPS algorithm and Bidirectional JPS algorithm in Section 2.2, and the improved Bidirectional JPS algorithm presented in Section 3 are presented.

2. The simulated results and hardware implementation are described in Section 4.

Queries & suggestions.

1. Table 2 is not informative, and we try to rearrange the pseudo-code in Table 2 early in Figure 5.

2. The details in Figure 5 are not imparted effectively in figure 6,7 and 8. Make sure the improvised version should provide effective changes comparatively A* and JPS in figure 6,7, and 8.

3. figure 9d considered as improved algorithm based illustration. background/principal did not effectively mention the robot traversing the optimized route in Figure 9d.

4. According to the authors, ROS have been used for mobile robot implementation. The authors can share the Gazebo details through the github with other media to observe your validation, as illustrated in Figure 12.

5. Path planning algorithms are already in real-time implementation and provide qualitative and quantitative comparison results that the authors have achieved through their improved algorithm. Table 6 shows that the A* algorithm should refer to where it has been used from the ROS platform or any authors in the literature.

6. Validation and experimental results can be furnished in the manuscript, and experimental videos can be shared through in authors own channel(server/git hub) to validate the execution.

 

Author Response

Comments 1：Table 2 is not informative, and we try to rearrange the pseudo-code in Table 2 early in Figure 5.

Response 1：Thank you very much for your helpful suggestion. We completely agree with your comment. In response, we have reorganized and rewritten the pseudo-code to improve its structure, clarity, and informativeness. Additionally, we have included a flowchart to visually illustrate the logic and process of the proposed algorithm, making it more intuitive and reader-friendly. These revisions are reflected in the updated Table 2 and Figure 9 of the revised manuscript (Lines 342-344).

 

Comments 2：The details in Figure 5 are not imparted effectively in figure 6,7 and 8. Make sure the improvised version should provide effective changes comparatively A* and JPS in figure 6,7, and 8.

Response 2：Thank you very much for your detailed feedback. We would like to clarify that Figures 6, 7, and 8 are intended as illustrative diagrams, designed to demonstrate the application of the jump point filtering rules introduced in Figure 5. Each figure highlights how the improved algorithm avoids unsafe or unnecessary nodes by applying the enhanced jump point selection mechanism.

Although Figures 6–8 do not provide a direct performance comparison with A* and traditional JPS in terms of numerical metrics, they visually reinforce the filtering strategy and risk avoidance capabilities of the proposed method. These figures strictly follow the logical conditions outlined in Figure 5, showing the valid and forced neighbors, and how our algorithm chooses safer and more efficient paths.

We appreciate your suggestion.

 

Comments 3：figure 9d considered as improved algorithm based illustration. background/principal did not effectively mention the robot traversing the optimized route in Figure 9d.

Response 3：Thank you very much for your careful observation. Due to our oversight during the formatting process, Figure 9c and Figure 9d were mistakenly swapped, which may have caused confusion regarding the illustration of the improved algorithm. We sincerely apologize for this mistake and have corrected and adjusted the figure placement in the revised manuscript.

At the same time, we have also carefully reviewed and adjusted other related figures to ensure that all illustrations are accurately aligned with the corresponding textual descriptions. We greatly appreciate your attention to these details and thank you again for your helpful feedback.

 

Comments 4：According to the authors, ROS have been used for mobile robot implementation. The authors can share the Gazebo details through the github with other media to observe your validation, as illustrated in Figure 12.

Response 4：Thank you very much for your helpful suggestion. We appreciate your interest in reproducibility. In future work, we plan to organize and publish the ROS–Gazebo simulation files and associated source code on GitHub or a similar open-source platform. This will allow other researchers to observe and validate the implementation demonstrated in Figure 12, and further support the transparency and reusability of our method.

 

Comments 5：Path planning algorithms are already in real-time implementation and provide qualitative and quantitative comparison results that the authors have achieved through their improved algorithm. Table 6 shows that the A* algorithm should refer to where it has been used from the ROS platform or any authors in the literature.

Response 5：Thank you very much for your helpful comment. In response, we have supplemented Section 4.2 (Experimental Validation) with more detailed descriptions of the ROS development environment, the robot platform, and the overall ROS architecture used in our real-world implementation (see Lines 440–471 of the revised manuscript). These additions clarify the experimental context in which our improved algorithm—along with A*, JPS, and B-JPS—is applied and compared.

In addition, we have expanded the analysis of the experimental results in Lines 496–511, highlighting both quantitative and qualitative improvements achieved by the proposed method. We confirm that the A* algorithm referenced in Table 6 was implemented and executed within the same ROS framework and tested under the same conditions as the improved algorithm, to ensure fairness and consistency in the comparison.

 

Comments 6：Validation and experimental results can be furnished in the manuscript, and experimental videos can be shared through in authors own channel(server/git hub) to validate the execution.

Response 6：Thank you very much for your valuable suggestion. We fully agree with your comment. In the revised manuscript, we have supplemented the validation and experimental result analysis in several locations to improve clarity and support our conclusions. These additions can be found in Lines 384–389, 398–410, 429–432, and 496–511.

As for the experimental videos, we plan to share them in a follow-up through an open platform, such as GitHub, to provide visual support for the real-world execution of the proposed algorithm.

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Authors have addressed most of the raised issues, however, other issues are required to be addressed by the authors,

1. In Figure 9, authors presented openlist1 and openlist 2, with no prior descriptions about those two open-lists.
2. In the Experimental validation section, authors presented a description on ROS packages. However, there is no presentation about the ROS nodes architecture. Therefore, I recommend to include the ROS nodes architecture that can be obtained directly from ROS environment. 
3. I recommend to add a Table showing the robot architecture, including sensor name and type. 
4. I recommend to include more discussion and analysis on the obtained results. 
5. I strongly recommend to include the following recent relevant research works: 

              a. Mobile robot path planning based on improved A* algorithm.

              b. An autonomous maze-solving robotic system based on an enhanced wall-follower approach

Author Response

Comments 1：In Figure 9, authors presented openlist1 and openlist2, with no prior descriptions about those two open-lists.

Response 1：Thank you for your valuable comment. We have made the requested revision in the revised manuscript (Lines 318–320). We have added a brief explanation of openlist1 and openlist2 before the introduction of Figure 9 to clarify their roles in the bidirectional search process.

Comments 2：In the Experimental validation section, authors presented a description on ROS packages. However, there is no presentation about the ROS nodes architecture. Therefore, I recommend to include the ROS nodes architecture that can be obtained directly from ROS environment.

Response 2：Thank you very much for your valuable suggestion. As recommended, we have now included a detailed presentation of the ROS nodes architecture obtained directly from the ROS environment. The revised description can be found in the updated manuscript (Lines 429–448).

Comments 3：I recommend to add a Table showing the robot architecture, including sensor name and type. 

Response 3：Thank you very much for your helpful suggestion. As recommended, we have added a table titled "Hardware Architecture of the Wheeled Mobile Robot" at Line 403 in the revised manuscript.

Comments 4：I recommend to include more discussion and analysis on the obtained results. 

Response 4：Thank you very much for your continued attention to the discussion and analysis of the experimental results. We would like to respectfully note that this comment was also raised during the first round of review, and in response, we made substantial and thorough revisions to the relevant sections of the manuscript. The discussion has been significantly expanded to include detailed performance evaluations, comparative analysis, and reflections on real-world applicability.

As the previous revisions already addressed this point comprehensively, no additional changes have been made in this round. Nonetheless, we sincerely appreciate your suggestion once again, as it has greatly contributed to enhancing the depth and clarity of the manuscript.

Comments 5：I strongly recommend to include the following recent relevant research works: 

1. Mobile robot path planning based on improved A* algorithm.
2. An autonomous maze-solving robotic system based on an enhanced wall-follower approach

Response 5：Thank you very much for your valuable recommendation and for kindly reiterating it in your review. We fully acknowledge the significance of the suggested works and appreciate your effort in highlighting them. However, the primary focus of our current study lies in enhancing the bidirectional JPS algorithm through adaptive heuristic weighting and dynamic constraint mechanisms. These improvements specifically target global path planning efficiency and safety in known environments, which differ in scope and methodology from the improved A* algorithm and wall-following strategies that primarily focus on local search or maze-like scenarios.

Therefore, while we did not incorporate these works directly into this manuscript, we recognize their relevance to the broader field of mobile robot navigation. We will certainly consider referencing and discussing them in future extensions of our research where local path planning strategies or hybrid methods are explored.

Reviewer 4 Report

Comments and Suggestions for Authors

We appreciate the authors, nicely responded for each query in detail. 

Author Response

Thank you very much for your kind acknowledgment and positive feedback.