Optimization of Energy Efficiency with a Predictive Dynamic Window Approach for Mobile Robot Navigation

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

The authors have significantly improved the manuscript, though certain aspects still require further refinement.

1. The author has enumerated numerous studies on mobile robots and related algorithms (e.g., MPC, DWA) in the introduction section, yet fails to provide adequate critical analysis or identify the limitations of existing techniques. I recommend the author supplement this discussion to better emphasize the significance and contributions of this research.

2. Please enclose formula references in parentheses, as in '(Equation 2)' in line 27.

3. It is recommended to supplement the comparative analysis of computational time consumption between the two algorithms across all four test maps, with quantitative results presented in tabular or graphical form.

Author Response

We sincerely thank you for the constructive comments and valuable suggestions, which have significantly helped us improve the clarity, rigor, and overall quality of the manuscript. Below we provide detailed responses to each point raised.

Comment 1:
"The author has enumerated numerous studies on mobile robots and related algorithms (e.g., MPC, DWA) in the introduction section, yet fails to provide adequate critical analysis or identify the limitations of existing techniques. I recommend the author supplement this discussion to better emphasize the significance and contributions of this research."

Response:
We have revised the Introduction section to include a more critical analysis of the cited approaches (e.g., MPC, genetic algorithms, Q-learning, and classic DWA). We now emphasize the specific limitations of these methods in terms of adaptability, computational load, and energy-awareness. This clarification highlights the unique contribution of our work: proposing a trajectory planner that integrates energy evaluation into the decision-making layer, with a moderate computational cost and improved energy behavior.

Comment 2:
"Please enclose formula references in parentheses, as in '(Equation 2)' in line 27."

Response:
We have carefully reviewed and corrected all inline references to equations throughout the manuscript to follow the journal’s style. All equations are now referenced using parentheses, e.g., (Equation 2).

Comment 3:
"It is recommended to supplement the comparative analysis of computational time consumption between the two algorithms across all four test maps, with quantitative results presented in tabular or graphical form."

Response:
We have included a new table (Table 2) that compares the average computation time per iteration and the total simulation time for both the traditional and proposed P-DWA across all test scenarios. This addition quantifies the computational cost and complements the energy-efficiency analysis.

We are grateful for your thorough evaluation and thoughtful feedback, which have contributed greatly to improving the manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

To achieve optimized energy efficiency in mobile robot navigation, this paper puts forward an improved P-DWA. The authors suggest a technique that predicts possible routes and then judges how much energy they use, in order to pick the most efficient ones. They report a 9% cut in energy use compared to the standard DWA in multiple tests, which they say shows the algorithm's promise for situations where saving energy is key.

However, several issues mean the paper needs major changes. First, the newness of the P-DWA algorithm and its energy use model is not properly shown. The paper does not compare the algorithm well enough with other energy-saving navigation methods and does not clearly state what this work adds beyond small improvements to the DWA setup. Second, the energy use model itself needs a much more detailed explanation and proof. The paper gives a basic view of the model but misses specifics about its accuracy, strength, and how it reacts to different surroundings and operating conditions. More solid proof using real-world data or detailed simulations is needed. Third, the algorithm's performance is mainly tested through simulations on four maps. While these maps show how the algorithm acts in various situations, they don't give enough proof that it would work in real life. The paper should add tests on a real robot to see how the algorithm does in actual, changing environments. Fourth, the paper doesn't talk enough about the algorithm's limits and possible problems. It skips over how the algorithm might react to sensor errors, uncertain surroundings, or the processing load of predicting energy use in real time. A more complete look at these limits is vital to know how strong and reliable the algorithm is. Finally, the paper doesn't properly discuss the extra processing needed for the algorithm. Since real-time performance is key for robot navigation, the P-DWA algorithm's processing efficiency must be fully tested and discussed.

Comments on the Quality of English Language

The English could be improved to more clearly express the research.

Author Response

We greatly appreciate your detailed feedback and insightful comments, which have helped us refine the manuscript substantially. Below we address each point raised.

Comment 1:
"The newness of the P-DWA algorithm and its energy use model is not properly shown. The paper does not compare the algorithm well enough with other energy-saving navigation methods and does not clearly state what this work adds beyond small improvements to the DWA setup."

Response:
We have added a dedicated paragraph in the Introduction and Discussion to clarify our contributions compared to other energy-aware methods. Unlike model predictive control (MPC), our approach does not require extensive optimization over prediction horizons, reducing computational complexity. Compared to heuristics (e.g., genetic algorithms), our method provides deterministic behavior. We also stress that our contribution lies not only in reducing energy consumption (around 9% overall) but also in integrating a prediction-evaluation-selection pipeline into DWA while retaining simplicity and adaptability.

Comment 2:
"The energy use model itself needs a much more detailed explanation and proof. The paper gives a basic view of the model but misses specifics about its accuracy, strength, and how it reacts to different surroundings and operating conditions. More solid proof using real-world data or detailed simulations is needed."

Response:
We have expanded the explanation of the energy model in Section 2, including its derivation, parameter dependencies, and expected performance under different motion conditions. We acknowledge that the model does not yet account for dynamic load changes, temperature, or battery degradation, and we explicitly mention these as limitations. This model is suitable for simulation-based evaluations of energy trends, and we are currently working on incorporating more realistic factors and experimental validation in future work.

Comment 3:
"The algorithm's performance is mainly tested through simulations on four maps. While these maps show how the algorithm acts in various situations, they don't give enough proof that it would work in real life. The paper should add tests on a real robot to see how the algorithm does in actual, changing environments."

Response:
As stated in the updated manuscript, our current study focuses on simulation-based trajectory generation for energy-efficient planning. While the proposed algorithm is not implemented on a physical robot, it has been validated on simulated maps with realistic motor models and energy estimations. Based on our experience, the use of simulations is common and widely accepted for evaluating trajectory planners, especially in control-oriented research. We further clarify that experimental deployment is part of our future work.

Comment 4:
"The paper doesn't talk enough about the algorithm's limits and possible problems. It skips over how the algorithm might react to sensor errors, uncertain surroundings, or the processing load of predicting energy use in real time."

Response:
We have added a discussion of limitations at the end of Section 4, where we state the assumptions (e.g., perfect localization, static environments) and acknowledge that P-DWA currently assumes full knowledge of the local environment and sensor reliability. Real-time performance is discussed using the per-iteration computation time (Table 2), and we note that this remains acceptable under typical control frequencies. Future work will include testing under noisy conditions and dynamic settings.

Comment 5:
"The paper doesn't properly discuss the extra processing needed for the algorithm. Since real-time performance is key for robot navigation, the P-DWA algorithm's processing efficiency must be fully tested and discussed."

Response:
We have added quantitative results comparing the average iteration time of both algorithms (Table 2). The proposed P-DWA shows a moderate increase in iteration time (~1 ms on average) due to energy evaluation, which we consider a reasonable trade-off given the achieved energy gains. We emphasize that the algorithm remains compatible with real-time operation at control frequencies of 50 Hz or higher.

Thank you again for your valuable feedback, which has been instrumental in improving the manuscript’s scientific rigor and clarity.

 

Author Response File: Author Response.pdf

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

The paper "Optimization of Energy Efficiency with a Predictive Dynamic Window Approach for a Mobile Robot Navigation" is devoted to the important problem of energy efficiency in mobile robot navigation, which is especially important for agriculture and other energy-dependent applications.

In the paper, the authors propose a modification of the classic DWA algorithm by integrating energy consumption prediction, which demonstrates the potential for reducing energy costs. An improved Predictive Dynamic Window Approach (P-DWA) algorithm is proposed, which, according to the authors, reduces energy consumption by 9% compared to the traditional DWA.

Mathematical models of motors and energy consumption are presented, which ensures the transparency of the method.

In the "Introduction" section, the authors justify the relevance of the topic by the use of mobile robots in agriculture and the need to solve the energy efficiency problem. However, the question arises: how detailed are the existing approaches to energy saving in robot navigation? The literature section mentions various methods, including genetic algorithms and MPC, but it is not entirely clear how their work complements or surpasses these approaches. The Materials and Methods section describes a modification of DWA with the addition of nine trajectories prediction and energy consumption estimation.

The results provide comparisons of energy consumption on different maps. It is noticeable that in Test Map 4, the P-DWA algorithm with energy control showed worse results, which the authors explain by the lengthening of the trajectory. This is an important point indicating possible limitations of the method.

In the conclusions section, the authors acknowledge the trade-off between trajectory length and energy efficiency, but do not offer specific solutions. There is also no discussion of the computational complexity of the P-DWA algorithm compared to traditional DWA. For real systems, this may be critical.

Comments

1. The presented algorithm analyzes 9 trajectories, but the authors do not explain why this number was chosen. It is unclear whether the optimal number of trajectories was studied to balance accuracy and computational complexity. 2. The coefficients in the DWA formula - αD, βD, γD, αD, βD, γD are taken from previous works without experimental justification of their applicability in the context of energy efficiency.
2. The DC motor model does not take into account dynamic load changes, friction, temperature effects or battery degradation, which may distort the results.
3. In the Test Map 4 scenario, P-DWA showed higher energy consumption than traditional DWA due to the lengthening of the trajectory. The authors do not propose mechanisms to minimize such situations, which questions the universality of the method.
4. Although the authors acknowledge the trade-off between path length and energy efficiency, they do not propose adaptive strategies to optimize it (e.g. dynamic adjustment of weight coefficients).
5. The P-DWA algorithm requires multiple executions of DWA for 9 trajectories, which increases the computational load. For real systems with limited resources, this may be a problem, but the authors do not analyze this aspect.
6. The literature review mentions MPC, genetic algorithms, and Q-learning, but does not provide a detailed comparison of P-DWA with these methods in terms of key metrics (energy consumption, time, and robustness to interference).
7. The algorithm's performance in rapidly changing environments (e.g., moving obstacles) or with partial sensor failures is not studied.

The proposed P-DWA algorithm represents an interesting step towards energy-efficient navigation, but requires significant improvement for practical application. Critical shortcomings such as the lack of real-world testing, simplified models, and unaccounted trade-offs reduce confidence in the results.

Author Response

We sincerely appreciate your thoughtful comments and helpful suggestions, which have allowed us to clarify key aspects of the manuscript and enhance its scientific quality. Below are our detailed responses.

Comment 1:
"It is not entirely clear how the proposed method complements or surpasses the approaches mentioned in the literature review."

Response:
We have revised the introduction to clarify the comparative advantage of our method over genetic algorithms, MPC, and Q-learning-based planners. Our P-DWA retains the reactive, computationally lightweight nature of DWA while introducing trajectory-level energy evaluation, something often missing in learning- or optimization-heavy approaches.

Comment 2:
"The authors do not explain why 9 trajectories were selected."

Response:
We now explain in Section 2 that the choice of 9 trajectories is based on a trade-off between trajectory diversity and computational efficiency. A preliminary study showed that increasing beyond 9 offers minimal improvements in energy savings while linearly increasing the computation time.

Comment 3:
"The DC motor model does not consider load changes, friction, temperature, or battery degradation."

Response:
We acknowledge these limitations and have explicitly stated them in the manuscript. The current model focuses on capturing average energy trends, which are sufficient for evaluating the impact of the planner in simulation. Enhancing the model with dynamic effects is part of our ongoing research.

Comment 4:
"No mechanisms are proposed to minimize energy waste when trajectory length increases."

Response:
We have updated the conclusion to reflect this limitation and now mention that adaptive strategies (e.g., dynamic reweighting of cost terms) are being considered to reduce path elongation effects.

Comment 5:
"The authors should analyze the computational load more thoroughly."

Response:
We have addressed this by including iteration time and total simulation time in Table 2. We clarify that while P-DWA does increase the computational cost, the increase is modest and remains acceptable for real-time execution at practical control frequencies.

Comment 6:
"The literature review mentions other methods but does not compare them using key metrics."

Response:
We have now included a comparative discussion in the revised introduction and Results and Discussion sections, using available benchmarks from literature and focusing on the energy vs. computational load trade-off.

Comment 7:
"Performance in dynamic or partially observable environments is not addressed."

Response:
We mention in the limitations section that this work is constrained to fully observable, static environments, as is standard in simulation-based validation of motion planners. Testing under dynamic and uncertain conditions is planned in our next phase.

Thank you once again for your detailed and thoughtful review, which has significantly enhanced the quality of our manuscript.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

The authors have addressed all of my remarks.

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

Accept in present form.

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

I thank the authors for their detailed answers. I recommend the paper for publication.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. The discussion on agricultural robot applications in the introduction section is overly lengthy and should be streamlined. Additionally, a review of mobile robot navigation algorithms should be included.
2. The paper is highly imprecise in its presentation. For example, Figures 2, 5, 6, and 7 all share the same figure title. Moreover, the structure of the paper is disorganized, with Section 3 notably missing. Additionally, Figures 3 and 4 also share the same figure title.
3. The article repeatedly mentions the improved P-DWA and conducts comparative experiments with the traditional P-DWA. However, it does not provide a detailed explanation of how the P-DWA was improved or where the predictive functionality is specifically implemented. Notably, the entire paper contains only one formula, and the mathematical modeling process is absent. This aspect should be thoroughly discussed and elaborated upon.
4. To enhance the reproducibility of the paper, various simulation parameters should be provided. These include the parameters of the motor energy consumption model, the initial and terminal points of the trajectory, the coordinates of obstacles, and the simulation parameters for the P-DWA, among others.
5. The mathematical modeling of the dynamic window generation and prediction steps is not sufficiently clear. It is necessary to supplement the specific formulas for energy consumption calculations (such as the 3.7 Wh and 4.67 Wh mentioned in line 239) and the rationale behind the parameter selection.
6. In Figure 4, the horizontal axes of Figure 4(c) and Figures 4(a) and (b) are inconsistent.
7. The speed data (Table 2) only provides the mean and median values, but the author does not specifically explain how these data were obtained.
8. The conclusion section is overly lengthy, which does not meet the standards of a qualified academic paper.

Reviewer 2 Report

Comments and Suggestions for Authors

Presented paper considers a novel approach to enhance energy efficiency of mobile robot during navigation. Autonomous mobile robots will became a common in many fields from agriculture to industry. The energy efficiency of robots is significant issue due to its high energy consumption that finally puts on the electrical grid. Thus, search of new approaches to enhance energy efficiency is necessary. Paper well written and presented results looks practically perspective. There are several comments that should be taken into account before paper will be published:

 

1. Please reconsider abstract to highlight results related with energy efficiency for mobile robot navigation;
2. Please give more information concerning how test maps were chosen;
3. Figures 6-8 please highlight how iterations related with time of journey. Total energy consumption is the surface under the graphs in those figures?
4. The main question is next – it looks like presented algorithm does not optimize trajectory and influence only on the speed, thus it looks like simple “go slowly and save power”. Can you add maps that have several possible trajectories and show that presented algorithm can optimize both trajectory and speed?
5. Conclusion section is too big it is more discussion than conclusion. I recommend renaming this section in Discussion and adding small conclusion section with main advantage of research and it results.