Development of Topologically Optimized Mobile Robotic System with Machine Learning-Based Energy-Efficient Path Planning Structure

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This article presents the design and development of a structurally optimized mobile robotic system with a machine learning-based energy-efficient path planning framework.

1. Insufficient Detail on the Machine Learning Architecture
   Although machine learning is mentioned as a central component of the energy-aware path planning framework, the manuscript lacks a thorough explanation of the model's internal structure. Critical details—such as the type of input features used, model architecture (e.g., decision tree, neural network, XGBoost parameters), training procedure, dataset size, preprocessing techniques, hyperparameter tuning, and validation methods—are not provided. This omission hinders reproducibility and undermines the credibility of the ML-based claims.
2. The manuscript references the use of XGBoost, but does not justify its selection over alternative models (e.g., Random Forest, SVM, neural networks). There is also no benchmarking against baseline or traditional models for energy prediction, which limits insight into its relative performance or robustness.
3. The study does not include any interpretability analysis, such as feature importance rankings, SHAP values, or partial dependence plots. These tools are essential to understand what physical or sensory parameters influence energy consumption and would significantly enhance the practical relevance of the model.
4. While the manuscript mentions data collection across different terrains, it lacks quantitative detail on the dataset (e.g., number of samples, sampling frequency, time span, sensor calibration methods). Moreover, there is no discussion on dataset partitioning (training/test/validation splits) or overfitting prevention, which are standard practices in ML-based research.
5. Real-time applicability is mentioned, but the paper does not provide any timing benchmarks for model training or inference. This is critical in embedded robotic applications where computational constraints are significant.
6. The manuscript dedicates significant space to mechanical design, topology optimization, and manufacturing—well-structured and valuable—but this results in the machine learning section appearing underdeveloped by comparison. Given that ML is central to the path planning claim, this imbalance weakens the manuscript’s contribution to intelligent robotics literature.
7. The manuscript is currently not well suited for a scholarly or research-oriented audience. Its structure and tone more closely resemble an experimental progress report rather than a fully developed scientific paper. The writing lacks the analytical depth and critical discussion expected in peer-reviewed literature, particularly in framing hypotheses, interpreting results, and engaging with existing research.

8. Inadequate Detail on Testing and Validation
   The manuscript lacks a rigorous description of the testing methodology, including:

   How the terrain was prepared and validated

   The number of test runs, trial durations, and environmental controls

   Statistical treatment of the collected data (e.g., confidence intervals, variance)

Author Response

Manuscript ID: machines-3702373

Title: Development of a Topology-Optimized Mobile Robotic System with Energy-Aware Path Planning Based on Machine Learning

We sincerely thank Reviewer for the thoughtful and constructive feedback, which greatly helped us enhance the scientific quality and clarity of our manuscript. We have carefully revised the paper in response to all comments and provided a detailed summary below outlining how each concern was addressed:

Sincerely,
Dr. Hilmi Saygin Sucuoglu

 

1. Insufficient Detail on the Machine Learning Architecture Although machine learning is mentioned as a central component of the energy-aware path planning framework, the manuscript lacks a thorough explanation of the model's internal structure. Critical details—such as the type of input features used, model architecture (e.g., decision tree, neural network, XGBoost parameters), training procedure, dataset size, preprocessing techniques, hyperparameter tuning, and validation methods—are not provided. This omission hinders reproducibility and undermines the credibility of the ML-based claims.

We fully agree that clarity and transparency in the machine learning (ML) methodology are crucial for reproducibility. In response, we have revised Sections 2.5 and 2.6 (Data Collection and Training Strategy) to emphasize critical aspects of the ML-based path planning framework. Specifically, we now explicitly detail:

Input features used (e.g., kinematic parameters, terrain descriptors, energy context, pose history)

Dataset size and structure (4,500 labeled samples across five terrain types)

Data preprocessing pipeline (Butterworth filtering, interpolation, outlier clipping, normalization)

Feature engineering and learning targets

Model architecture evaluated (XGBoost, Random Forest, Multi-layer Perceptron)

Hyperparameter tuning (Bayesian optimization with stratified 5×5 cross-validation)

Evaluation metrics (MAE, RMSE, composite loss J)

These additions improve the clarity of the proposed ML methodology and support future reproducibility. Relevant details can be found in the revised Section 2.6.

1. The manuscript references the use of XGBoost, but does not justify its selection over alternative models (e.g., Random Forest, SVM, neural networks). There is also no benchmarking against baseline or traditional models for energy prediction, which limits insight into its relative performance or robustness.

To address this, we revised Section 2.6.5 (Evaluation Metrics) to include an explicit benchmarking study. Specifically, we compared XGBoost against two alternative models—Random Forest and a two-layer Multi-Layer Perceptron (MLP)—using the same dataset, feature structure, training pipeline, and evaluation metrics. The results, now presented in Table 2, show that XGBoost achieved the lowest prediction errors and the best composite loss score, outperforming the other models by 17–22%. Its ability to handle heterogeneous input features, robustness to overfitting, and fast convergence under limited data conditions justify its selection as the final energy-aware cost estimator integrated into the path planner.

1. The study does not include any interpretability analysis, such as feature importance rankings, SHAP values, or partial dependence plots. These tools are essential to understand what physical or sensory parameters influence energy consumption and would significantly enhance the practical relevance of the model.

We expanded the analysis to qualitatively discuss the model’s internal behavior across terrain types based on observed energy usage patterns and mission dynamics (Section 3.3). As detailed in the revised manuscript, the XGBoost-based model consistently identified terrain resistance factors—such as slope and vibration—as key drivers of energy consumption, as evidenced by higher energy usage on inclined and destabilizing surfaces.

Furthermore, terrain-wise performance metrics (e.g., actual energy draw, mission time, and path elongation) presented in Table 5 were used to derive insights into the implicit influence of physical parameters on energy consumption.

This enhancement strengthens the practical relevance of our framework, as now reflected in Section 3.3 of the revised manuscript.

1. While the manuscript mentions data collection across different terrains, it lacks quantitative detail on the dataset (e.g., number of samples, sampling frequency, time span, sensor calibration methods). Moreover, there is no discussion on dataset partitioning (training/test/validation splits) or overfitting prevention, which are standard practices in ML-based research.

In response, we have updated Section 2.5 (Data Collection) to explicitly state the total number of labeled samples (4,500), the sampling frequency (1 Hz), the duration of each trial (180 seconds), and the number of repetitions per terrain type (five). We also clarified that the ACS 712 current sensor was factory-calibrated, and its readings were converted using the manufacturer-specified gain factor (185 mV·A⁻¹). Additionally, we have expanded Section 2.6.4 (Hyperparameter Optimization) to provide a more detailed explanation of the data partitioning strategy and overfitting mitigation techniques. Specifically, we describe the use of a nested 5×5 stratified cross-validation scheme, along with Bayesian hyperparameter optimization, early stopping (patience = 20 epochs), and ℓ₂-regularization to ensure model generalizability and robustness. We believe these clarifications significantly improve the transparency and reproducibility of the study.

1. Real-time applicability is mentioned, but the paper does not provide any timing benchmarks for model training or inference. This is critical in embedded robotic applications where computational constraints are significant.

In response, we have revised Section 3.3 to explicitly report the inference time of the proposed XGBoost-based planner on the embedded Raspberry Pi 4B platform. The planner achieved an average execution latency of 34 ms (±5 ms) per decision cycle, which is well below the 500 ms replanning interval. This confirms that the system meets real-time constraints and is suitable for deployment in resource-constrained embedded environments.

1. The manuscript dedicates significant space to mechanical design, topology optimization, and manufacturing—well-structured and valuable—but this results in the machine learning section appearing underdeveloped by comparison. Given that ML is central to the path planning claim, this imbalance weakens the manuscript’s contribution to intelligent robotics literature.

 In the revised manuscript, we have significantly expanded the coverage of the machine learning methodology in both the Material and Method and Results and Discussion sections. The Material and Method section now includes detailed explanations of the model architecture, input features, preprocessing steps, training strategy, cross-validation scheme, and hyperparameter tuning procedure. In the Results and Discussion section, we further elaborated on the predictive performance of different regression models, provided benchmarking results, and clarified the real-time applicability of the selected XGBoost-based energy estimator. These comprehensive additions ensure that the machine learning component is presented with the same level of rigor as the mechanical and topological parts, better reflecting its central role in the proposed system.

1. The manuscript is currently not well suited for a scholarly or research-oriented audience. Its structure and tone more closely resemble an experimental progress report rather than a fully developed scientific paper. Writing lacks the analytical depth and critical discussion expected in peer-reviewed literature, particularly in framing hypotheses, interpreting results, and engaging with existing research.

We sincerely appreciate the reviewer’s concern regarding the scholarly tone and depth of the manuscript. In the revised version, we undertook a comprehensive restructuring of the text to enhance its scientific clarity, critical reasoning, and academic rigor. Specifically:

The Introduction now more clearly motivates the research hypotheses and contextualizes the dual-objective optimization problem within current literature.

The Material and Method section has been enriched with structured subsections detailing the machine learning pipeline, data handling procedures, and model evaluation methodology.

The Results and Discussion section was significantly revised to provide analytical interpretation, quantitative comparisons with relevant prior work, and critical insights on how the proposed system advances both structural and computational aspects of mobile robotics.

We trust that these improvements address the reviewer’s valid concern and now present the manuscript as a fully developed scientific contribution suited for a scholarly audience.

1. Inadequate Detail on Testing and Validation
   The manuscript lacks a rigorous description of the testing methodology, including:

How the terrain was prepared and validated

The number of test runs, trial durations, and environmental controls

Statistical treatment of the data collected (e.g., confidence intervals, variance)

In the revised manuscript, Section 2.5 (Data Collection) now includes detailed descriptions of each terrain condition—inclined surfaces, gravel paths, obstacles, and directional barriers—along with precise dimensions and layout specifications. Each scenario was repeated five times, with 180 seconds of data collected at 1 Hz per trial, yielding 900 samples per terrain type. We also clarified that all experiments were conducted in a controlled indoor environment to ensure consistency and eliminate ambient disturbances such as lighting or temperature variation. In Section 2.6.5, we added statistical performance measures such as MAE ± SD and RMSE, and comparative benchmarks for all tested regression models. These enhancements aim to provide full transparency and reproducibility of the testing and validation procedures.

 

 

 

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript presents a highly relevant and innovative integration of topology optimization (TO), additive manufacturing (AM), power-aware machine learning (ML)-based path planning, and real-world energy monitoring for mobile robotic systems. The study stands out in its practical execution, combining simulation and real-world experiments on a terrain-diverse testbed.

The work is well-written, experimentally rigorous, and provides both quantitative and qualitative advancements. However, a few areas require clarification, deeper comparative positioning, and improvements in presentation.

1. A comparison table with recent TO or ML-based robotic systems would better showcase where your work excels. Add a table comparing this work with 4–5 recent related studies (e.g., in topology optimization, AM robotics, or energy-aware planning) on key aspects like dataset use, real-world testing, and optimization method.
2. The energy-aware planner is described clearly, and the scalarized cost function is well-designed with a tunable trade-off (α). However, more insight is needed on: The sensitivity to α. How retraining or adaptation works if terrain characteristics change significantly. Add a paragraph discussing the effect of varying α on path choice and battery consumption. Also, consider a discussion on online learning or model updating.
3. Add a track layout diagram with terrain zones and annotated energy profiles or error margins.
4. Also, consider discussing potential environmental variability (e.g., lighting, temperature).
5. Expand the Limitations section with a table or bullet points on: What was addressed? What is left for future work (e.g., scaling to swarm systems, UAVs).
6. Language needs to be improved.
7. Enhance the Figure quality.
8. How was the topology optimization performed?
9. From FEA, what is the significance of von Misses stress value? 
10. What is the FoS considered in this design?
11. Limited evaluation of robustness to real-world variability (e.g., sensor noise, battery aging).
12. There is a need for more comparative benchmarking against similar robotic systems.
13. The path planning part was explored in detail in the results and discussion section.

Comments on the Quality of English Language

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

Author Response

Manuscript ID: machines-3702373

Title: Development of a Topology-Optimized Mobile Robotic System with Energy-Aware Path Planning Based on Machine Learning

We sincerely thank Reviewer for the thoughtful and constructive feedback, which greatly helped us enhance the scientific quality and clarity of our manuscript. We have carefully revised the paper in response to all comments and provided a detailed summary below outlining how each concern was addressed:

Sincerely,
Dr. Hilmi Saygin Sucuoglu

 

The manuscript presents a highly relevant and innovative integration of topology optimization (TO), additive manufacturing (AM), power-aware machine learning (ML)-based path planning, and real-world energy monitoring for mobile robotic systems. The study stands out in its practical execution, combining simulation and real-world experiments on a terrain-diverse testbed.

The work is well-written, experimentally rigorous, and provides both quantitative and qualitative advancements. However, a few areas require clarification, deeper comparative positioning, and improvements in presentation.

1. A comparison table with recent TO or ML-based robotic systems would better showcase where your work excels. Add a table comparing this work with 4–5 recent related studies (e.g., in topology optimization, AM robotics, or energy-aware planning) on key aspects like dataset use, real-world testing, and optimization method.

 To better contextualize the contribution of our work, we have added Table 6 in the Results and Discussion section. This table provides a comparative overview of our framework against several recent and relevant studies involving mobile robotics. Key differences are highlighted in terms of dataset usage, real-world testing, optimization targets, and methodological integration.

1. The energy-aware planner is described clearly, and the scalarized cost function is well-designed with a tunable trade-off (α). However, more insight is needed on: The sensitivity to α. How retraining or adaptation works if terrain characteristics change significantly. Add a paragraph discussing the effect of varying α on path choice and battery consumption. Also, consider a discussion on online learning or model updating.

In response, we have added a new paragraph in Section 2.6.5 that discusses the planner’s sensitivity to different α values and their impact on energy consumption and path length. Additionally, we included a forward-looking discussion on incorporating online learning or incremental retraining strategies to adapt to dynamic or previously unseen terrain conditions.

1. Add a track layout diagram with terrain zones and annotated energy profiles or error margins.

To enhance the clarity and visual communication of our experimental setup and energy-aware planner performance, we have now added a new figure (Figure 12) that combines: A top-down diagram of the test track layout with labeled terrain zones (A–E), including inclined surfaces, vibration-inducing obstacles, gravel paths, direction-altering barriers, and a flat control segment. A bar chart comparing actual vs. predicted energy consumption for each segment, with values drawn from Table 4.

This visual clearly demonstrates the model’s prediction accuracy across different terrain conditions and further substantiates the robustness of the proposed energy-aware planning strategy. The figure has been inserted in the Results and Discussion section, following the explanation of segment-wise model performance.

1. Also, consider discussing potential environmental variability (e.g., lighting, temperature).

We fully agree that environmental variability—such as lighting, ambient temperature, and humidity—can significantly affect the performance of embedded robotic systems, particularly in terms of sensor reliability, traction, and battery behavior. To address this, we have expanded the Conclusion section to explicitly discuss these factors and their potential impact on the proposed framework. Although such variables were held stable during our experiments to isolate terrain-related energy dynamics, we now clarify that future work will systematically incorporate these environmental conditions into model training and testing. This will enable more robust energy-aware planning under diverse real-world scenarios.

1. Expand the Limitations section with a table or bullet points on: What was addressed? What is left for future work (e.g., scaling to swarm systems, UAVs).

In response, we have expanded the limitations section within the Conclusion to include a more structured overview of what has been addressed in this study and what remains as future work. Rather than using a bullet list or table (to maintain narrative cohesion), we integrated these points in a compact sentence form. The paragraph now highlights (i) the contributions already achieved—such as terrain-specific optimization, dual-objective planning, and real-time decision-making—and (ii) future research directions including scaling the framework to swarm systems, UAV platforms, and adaptation through online learning under environmental variability. This addition appears in the penultimate paragraph of the revised Conclusion section

 

 

 

 

1. Language needs to be improved.

The entire manuscript has undergone a comprehensive language revision to enhance clarity, conciseness, and academic tone. Grammatical structures have been refined, technical terminology has been standardized, and sentence flow has been improved throughout. We hope that the revised version meets the linguistic standards expected by the journal.

1. Enhance the Figure quality.

In response, we have carefully revised and enhanced the quality of all figures throughout the manuscript. Improvements include higher resolution exports, clearer labeling, adjusted proportions, and more descriptive captions to improve readability and visual clarity. These changes aim to ensure that each figure effectively communicates its intended content.

1. How was the topology optimization performed?

We agree that a more detailed explanation of the topology optimization (TO) methodology enhances the clarity and reproducibility of our work. Accordingly, we have expanded Section 2.2 by specifying that the TO was performed using the Ansys Topology Optimization tool with the Solid Isotropic Material with Penalization (SIMP) method.

1. From FEA, what is the significance of von Misses stress value? 

In the revised manuscript, we have expanded Section 2.2 to clarify the role of von Mises stress in evaluating the structural safety of the optimized robotic frame. Specifically, von Mises stress is used as the failure criterion to assess the yielding behavior of the ABS material under multiaxial loading. This scalar metric enables comparison between the calculated stress and the material yield strength, thereby ensuring that the topology-optimized frames maintain structural integrity during operation. The updated paragraph explains this clearly in the context of our FEA validation.

1. What is the FoS considered in this design?

In line with the suggestion, the manuscript has been expanded to clearly report the Factor of Safety (FoS) values derived from the finite element analysis (FEA). As described in Section 2.2, the calculated safety factors for the optimized upper and lower frames are approximately 2.7 and 2.3, respectively. These values demonstrate that the optimized structures operate safely within the allowable stress limits, confirming their mechanical reliability under expected loading conditions.

 

 

 

1. Limited evaluation of robustness to real-world variability (e.g., sensor noise, battery aging).

In response, we have expanded the Conclusion section to acknowledge the impact of long-term real-world variability factors such as sensor drift, battery aging, and actuator wear. A dedicated sentence was added to emphasize that these issues will be addressed in future iterations through retraining mechanisms, periodic calibration routines, and hardware-aware diagnostics. This enhancement complemented the existing discussion on environmental variability (e.g., lighting, temperature), ensuring a more comprehensive treatment of system robustness. The revised sentence is:

"Likewise, potential long-term degradation factors—such as sensor drift, battery aging, and actuator wear—will be considered in future robustness evaluations by incorporating retraining mechanisms, periodic calibration routines, and hardware-aware diagnostics."

We hope this addition adequately addresses your concern and improves the completeness of the manuscript.

1. There is a need for more comparative benchmarking against similar robotic systems.

In response, we have substantially expanded Table 6 to include additional recent studies that employ topology optimization, machine learning, or path planning strategies in mobile robotics. The table compares these works across key dimensions such as optimization focus, real-world testing, and dataset type. This broader benchmarking contextualizes our system within the existing literature and emphasizes its distinctive integration of structural optimization with real-time, energy-aware planning. We believe this addition improves the manuscript's comparative analysis and demonstrates the novelty and practical relevance of our approach.

1. The path planning part was explored in detail in the results and discussion section.

We thank the reviewer for acknowledging that the path planning aspects were explored in sufficient detail in the Results and Discussion section. We are glad that the proposed learning-based planner with a scalarized cost function—balancing energy consumption and path length—was found to be well described and appropriately evaluated.

 

 

 

 

 

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

The authors present an integrated framework combining topology optimization (TO), additive manufacturing (AM), and machine learning (ML) to develop a lightweight, energy-efficient mobile robot. It includes structural optimization of robot frames via TO/FEA, fabrication using FDM-ABS, development of a power analysis tool, real-world energy data collection across diverse terrains, and an ML-based path planner that jointly optimizes energy and distance. Experimental validation demonstrates a 4.5% system weight reduction, 5.8% energy savings, and a 20% mission-time extension. The study addresses gaps in prior works by unifying structural efficiency and energy-aware navigation, supported by empirical data. The manuscript is well-organized, technically sound, and offers valuable contributions to the related communities. It can be further improved as below revisions:
1) The optimized frames’ safety factors (1.8–2.1) are near-minimal for structural applications. It should be increased for long-term operation. 
2) While FEA confirms integrity, real-world fatigue (e.g., repeated vibration) is untested. It is recommended to add dynamic loading tests.
3) Experiments cover five terrains but lack extreme conditions (e.g., mud, high stairs), in order to validate the effectiveness of this energy efficient path planner. 
4) Comparisons focus only on traditional methods (e.g., A*). Benchmarking against modern ML planners (e.g., RL-based) would strengthen claims.  
5) In the introduction, the authors should add more citations for path planning, such as:
[1] L. Chen, "Optimized Foothold Planning and Posture Searching for Energy-Efficient Quadruped Locomotion Over Challenging Terrains," IEEE International Conference on Robotics and Automation (ICRA) 2020, pp.399-405, 2020. DOI: https://doi.org/10.1109/ICRA40945.2020.9197135
6) Typos:
Page 9, Fig. 5(b): "Equivalents Stress" → "Equivalent Stress."  
Page 19, Table 2: "von Misses stress" → "von Mises stress".  

Comments on the Quality of English Language

The English is good. It can be further improved. 

Author Response

Manuscript ID: machines-3702373

Title: Development of a Topology-Optimized Mobile Robotic System with Energy-Aware Path Planning Based on Machine Learning

We sincerely thank Reviewer for the thoughtful and constructive feedback, which greatly helped us enhance the scientific quality and clarity of our manuscript. We have carefully revised the paper in response to all comments and provided a detailed summary below outlining how each concern was addressed:

Sincerely,
Dr. Hilmi Saygin Sucuoglu

The authors present an integrated framework combining topology optimization (TO), additive manufacturing (AM), and machine learning (ML) to develop a lightweight, energy-efficient mobile robot. It includes structural optimization of robot frames via TO/FEA, fabrication using FDM-ABS, development of a power analysis tool, real-world energy data collection across diverse terrains, and an ML-based path planner that jointly optimizes energy and distance. Experimental validation demonstrates a 4.5% system weight reduction, 5.8% energy savings, and a 20% mission-time extension. The study addresses gaps in prior works by unifying structural efficiency and energy-aware navigation, supported by empirical data. The manuscript is well-organized, technically sound, and offers valuable contributions to the related communities. It can be further improved as below revisions:

1) The optimized frames’ safety factors (1.8–2.1) are near-minimal for structural applications. It should be increased for long-term operation. 

In response, we have revised the optimized frame geometries by incorporating additional ribs and support structures, particularly in the lower sections. As a result, the safety factors have been improved to 2.7 for the upper frame and 2.4 for the lower frame, ensuring more robust structural integrity suitable for long-term deployment. These updated values are now reflected in Table 3 of the revised manuscript.

2) While FEA confirms integrity, real-world fatigue (e.g., repeated vibration) is untested. It is recommended to add dynamic loading tests.

We have now addressed this point in the revised Conclusion section by explicitly noting that dynamic loading and fatigue tests will be incorporated in future studies to evaluate the system's long-term durability under repeated vibrations and operational stresses.

 

 

 

3) Experiments cover five terrains but lack extreme conditions (e.g., mud, high stairs), in order to validate the effectiveness of this energy efficient path planner. 

In response, we have amended the Conclusion to acknowledge the current limitations of terrain diversity and outline our plan to extend testing to more extreme and realistic environments (e.g., muddy paths, stairs, and wet surfaces) to further validate the robustness and generalizability of the proposed energy-efficient path planner.

4) Comparisons focus only on traditional methods (e.g., A*). Benchmarking against modern ML planners (e.g., RL-based) would strengthen claims.  

In response, we have added a detailed comparative analysis between the proposed planner and modern reinforcement learning (RL)-based planners. This comparison, presented in Table 5 of the revised manuscript, highlights distinctions in objectives, computational demand, implementation complexity, and energy-awareness. While RL-based methods offer strong generalization in dynamic environments, they require extensive training data and are less interpretable and harder to deploy on embedded platforms. In contrast, our planner provides real-time performance with deterministic, explainable outputs, making it more suitable for field deployment on low-power systems. We believe this comparison strengthens the justification for our method’s selection and clarifies its practical advantages.

5) In the introduction, the authors should add more citations for path planning, such as:

2020. 
      Chen, "Optimized Foothold Planning and Posture Searching for Energy-Efficient Quadruped Locomotion Over Challenging Terrains," IEEE International Conference on Robotics and Automation (ICRA) 2020, pp.399-405, 2020. DOI:

 https://doi.org/10.1109/ICRA40945.2020.9197135

We agree that the inclusion of additional references will enrich the introduction and better situate our work within the broader path planning literature. Accordingly, we have revised the introduction to incorporate recent and diverse approaches—including heuristic, biologically inspired, and reinforcement learning-based planners. These citations have been meaningfully integrated into the final paragraph of the introduction, where we contrast these emerging learning-based techniques with our own approach that combines deterministic planning and energy-aware modeling.

6) Typos:
Page 9, Fig. 5(b): "Equivalents Stress" → "Equivalent Stress."  
Page 19, Table 2: "von Misses stress" → "von Mises stress". 

All typographical and grammatical errors have been carefully reviewed and corrected throughout the manuscript.

Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

Please find my comments here below that the authors need to address to enhance the manuscript quality :

 Comment 1. (Page 1)
The Abstract lacks a clearly defined statement of novelty. While it summarizes the methodology and results, it does not convincingly articulate what gap in literature the study addresses or how the proposed integration of TO and ML significantly advances the field.

Comment 2. (Page 3-4)
In the Introduction, recent references are lacking. Only a few citations (e.g., [18], [20]) are from the last five years. The authors should integrate more recent studies, particularly from MDPI’s Processes or similar journals, to strengthen the context and relevance.

Comment 3. (Page 5-6)
The FEA methodology would benefit from more detail about mesh quality, element types, convergence criteria, and boundary conditions. These are essential for reproducibility and evaluating simulation reliability.

Comment 4. (Page 14)
In the machine learning training section, there is no mention of data augmentation, model uncertainty, or external validation. The work could be improved by including more robust testing, possibly with out-of-sample terrain types or cross-dataset generalizability.

Comment 5. (Page 19)
The Results section compares optimized vs. non-optimized structures primarily based on energy and weight. However, it would be stronger with additional metrics such as structural stiffness-to-weight ratio or mechanical durability under repeated load cycles.

Comment 6. (Page 20-21)
The authors use weighted A* but do not compare it against baseline path planners (e.g., A, D, or BIT) using the same metrics. Including comparative plots or statistical significance analysis would improve the robustness of the claim.

Comment 7. (Page 21-22)
The Conclusion overstates the results by asserting "synergistic gains unattainable with single-objective approaches" without presenting a statistically rigorous comparison or sensitivity analysis. It should be toned down or supported by deeper comparative data.

Comment 8. (Page 21)
The novelty claim of integrating topology optimization and machine learning for energy-aware planning is not fully convincing. The manuscript lacks a clear justification of why this integration is novel, how it overcomes prior limitations, or how it outperforms hybrid frameworks (e.g., ML-enhanced RRT or GA-based path planners with structural optimization).

Comment 9. (Page 22-23)
Reference quality should be updated. Many citations are older than five years or not from high-impact robotics or MDPI journals. To align with journal expectations, at least 30% of references should be from 2020–2025 and include more MDPI publications from Processes, Applied Sciences, or Robotics.

Author Response

Manuscript ID: machines-3702373

Title: Development of a Topology-Optimized Mobile Robotic System with Energy-Aware Path Planning Based on Machine Learning

We sincerely thank Reviewer for the thoughtful and constructive feedback, which greatly helped us enhance the scientific quality and clarity of our manuscript. We have carefully revised the paper in response to all comments and provided a detailed summary below outlining how each concern was addressed:

Sincerely,
Dr. Hilmi Saygin Sucuoglu

 

Comment 1. (Page 1)

The Abstract lacks a clearly defined statement of novelty. While it summarizes the methodology and results, it does not convincingly articulate what gap in literature the study addresses or how the proposed integration of TO and ML significantly advances the field.

In response, we have revised the abstract to explicitly highlight the novelty and contribution of our study. Specifically, we now state that this work addresses a critical gap in the literature: the lack of integrated frameworks that simultaneously apply topology optimization (TO) and machine learning (ML)-based energy modeling within a physically deployed mobile robotic system.The revised abstract emphasizes the dual-domain innovation of our approach, where TO enables structural lightweighting and ML supports terrain-aware, energy-optimal path planning. Additionally, the abstract now quantifies key performance improvements—such as a 5.8% reduction in energy use and ≈20% increase in mission duration—which further strengthen the significance of the proposed integration. These changes can be found in the revised abstract section (Page 1), with the newly added novelty components highlighted accordingly.

Comment 2. (Page 3-4)
In the Introduction, recent references are lacking. Only a few citations (e.g., [18], [20]) are from the last five years. The authors should integrate more recent studies, particularly from MDPI’s Processes or similar journals, to strengthen the context and relevance.

Thank you for your valuable observation. We fully agree that the Introduction section required stronger integration of recent literature to better reflect current research directions and relevance. In response, we have revised the Introduction to include several key studies published from 2020 onward. These additions emphasize recent advances in energy-efficient mobile robotics, topology optimization, and machine learning–based path planning, with special attention to research published in MDPI journals such as Processes, Electronics, and Applied Sciences. Specifically, the following recent contributions have been integrated: Chen [35] (2020): optimized foothold and posture strategies for energy-aware quadruped locomotion; Raj and Kos [36] (2023): intelligent particle swarm optimization for minimizing energy and time in mobile navigation; Chen et al. [37] (2024): hybrid Cuckoo–Beetle Swarm Search for heterogeneous mobile robots; Chen et al. [38] (2024): reinforcement learning–based energy-saving planner for UAVs under turbulent wind; Khan et al. [39] (2025): energy-optimized trajectory planning for rehabilitation robotics using RL. These references appear in the revised Introduction (Pages 3–4), and their integration provides a clearer and more current foundation for understanding the novelty and relevance of the proposed research.

Comment 3. (Page 5-6)
The FEA methodology would benefit from more detail about mesh quality, element types, convergence criteria, and boundary conditions. These are essential for reproducibility and evaluating simulation reliability.

In response, we have substantially expanded the content in Section 2.1 to provide greater technical clarity and improve reproducibility. Specifically, we have now included the following methodological details:

Mesh elements: Second-order tetrahedral elements (SOLID187) were used, as they are well-suited for capturing complex geometries and stress concentrations.

Meshing technique: A patch-conforming method was applied, and local mesh controls were introduced around critical regions such as fillets and bolt holes.

Mesh quality: Verified using standard metrics minimum element quality > 0.75, aspect ratio < 3, and skewness < 0.25.

Convergence study: Conducted by refining the mesh iteratively until the variation in maximum von Mises stress between successive runs dropped below 2%.

Convergence criterion: The force convergence tolerance was set to 1×10⁻³ for stable and accurate simulations.

Loads and boundary conditions: A vertical load of 20 N and a torque of 0.2 Nm were applied to the upper and lower frames, respectively, simulating hardware and motor effects.

Comment 4. (Page 14)

In the machine learning training section, there is no mention of data augmentation, model uncertainty, or external validation. The work could be improved by including more robust testing, possibly with out-of-sample terrain types or cross-dataset generalizability.

In response, we have clarified and elaborated on these aspects in the revised manuscript as follows:

Data Augmentation and Terrain Diversity:

To address the need for robustness across terrain types, the manuscript now clearly highlights that the training dataset spans five physically distinct terrain types (inclined, gravel, vibration-inducing, direction-altering, and flat). This natural variability in the empirical data provides an inherent form of augmentation. The revised text (Section 2.5 and Conclusion) now emphasizes how this contributes to improved generalization in the model.

Model Uncertainty and Robust Training:

We have expanded the description of our training pipeline in Section 2.6.4 to note the use of dropout, Bayesian hyperparameter optimization, and early stopping, all of which are standard techniques to reduce overfitting and indirectly handle predictive uncertainty. Additionally, the Conclusions section now includes remarks on future integration of online learning strategies and potential use of quantile regression or ensemble-based adaptation to support uncertainty-aware planning.

Validation and Generalization:

In response to the reviewer’s comment, we have clarified the cross-validation approach used. Specifically, we applied a nested 5×5 stratified cross-validation scheme with trajectory-level grouping to ensure generalization across varying terrain conditions. This approach, detailed in Section 2.6.5, simulates real-world deployment variability and strengthens the reliability of the reported model performance.

These clarifications have been added to the revised manuscript to better reflect the robustness features of the proposed system and to directly address the reviewer’s valuable recommendations.

Comment 5. (Page 19)

The Results section compares optimized vs. non-optimized structures primarily based on energy and weight. However, it would be stronger with additional metrics such as structural stiffness-to-weight ratio or mechanical durability under repeated load cycles.

In response, we have now incorporated a stiffness-to-weight ratio evaluation in the revised Results Section 3.2 and Table 3, based on an applied force of 20 N and the deformation results obtained from finite element analysis. Specifically, the top frame exhibited an improvement from 0.444 to 0.457 N/mm·gram, corresponding to a 2.9% increase, while the bottom frame improved from 0.262 to 0.277 N/mm·gram, reflecting a 5.7% gain in mechanical efficiency per unit mass. These additions provide a more comprehensive performance assessment and confirm that the proposed optimization not only reduces structural mass and energy consumption but also maintains or enhances mechanical robustness.

Comment 6. (Page 20-21)
The authors use weighted A* but do not compare it against baseline path planners (e.g., A, D, or BIT) using the same metrics. Including comparative plots or statistical significance analysis would improve the robustness of the claim.

In response, we have extended Section 3.3 to include a comparative analysis using the same 12 m test track and experimental setup described in the manuscript. Weighted A* was evaluated against Dijkstra, A*, and BIT* algorithms, and consistently outperformed them in terms of path length, energy consumption, and computational efficiency. The corresponding results are now summarized in the extended Results section. We believe this addition significantly strengthens the technical robustness of our path planning approach.

 

Comment 7. (Page 21-22)

The Conclusion overstates the results by asserting "synergistic gains unattainable with single-objective approaches" without presenting a statistically rigorous comparison or sensitivity analysis. It should be toned down or supported by deeper comparative data.

In response, we have revised the sentence to adopt a more balanced and cautious tone. Specifically, the phrase "synergistic gains unattainable with single-objective approaches" has been replaced with: “These results demonstrate promising combined benefits from integrating structural optimization and energy-aware planning, although further statistical benchmarking is needed to conclusively distinguish the advantages over traditional single-objective approaches. ”This revised formulation preserves the key insight of our integrated methodology while avoiding overstatement. We appreciate the reviewer’s input, which has helped us improve the clarity and scientific rigor of our conclusion.

 

Comment 8. (Page 21)

The novelty claim of integrating topology optimization and machine learning for energy-aware planning is not fully convincing. The manuscript lacks a clear justification of why this integration is novel, how it overcomes prior limitations, or how it outperforms hybrid frameworks (e.g., ML-enhanced RRT or GA-based path planners with structural optimization).

In response, we have revised the Introduction section to more explicitly highlight what differentiates our approach from prior hybrid frameworks. While earlier studies have explored combinations of machine learning with RRT* or genetic algorithm-based path planners, these typically focus solely on trajectory optimization and often overlook structural design constraints. In contrast, our method integrates topology optimization (TO) and machine learning-based energy-aware path planning in a tightly coupled framework. As now explained in the revised text, our approach enables terrain-specific energy consumption predictions—learned from empirical current data—to directly inform the Weighted A* planner. Simultaneously, the TO step ensures that the mechanical structure remains lightweight and robust under realistic operating conditions. This dual feedback structure is absent in previous ML-enhanced RRT* or GA-based studies, which often rely on either theoretical energy models or offline computations.

Furthermore, our use of an XGBoost-powered planner supports real-time deployment on embedded systems, improving practical applicability compared to GA-based solutions.

 

 

 

 

 

Comment 9. (Page 22-23)

Reference quality should be updated. Many citations are older than five years or not from high-impact robotics or MDPI journals. To align with journal expectations, at least 30% of references should be from 2020–2025 and include more MDPI publications from Processes, Applied Sciences, or Robotics.

In response, the reference list has been carefully updated to meet the expectations regarding both recency and source quality:

27 out of 49 references (55%) now fall within the 2020–2025 range, thus exceeding the 30% recency threshold recommended by the reviewer.

17 of the references are from MDPI journals, including Processes, Applied Sciences, Machines, Sustainability, Electronics, Mathematics, and Sensors.

These additions strengthen the manuscript’s relevance to current literature and ensure alignment with the scope of Machines and its readership.

The updated references have been integrated primarily in the Introduction, Related Work, and Discussion sections to better contextualize the contributions of this study.

Author Response File: Author Response.docx

Reviewer 5 Report

Comments and Suggestions for Authors

This paper presents the design, development, and evaluation of a mobile robotic system that integrates topology optimization (TO), additive manufacturing (AM), finite element modeling, and machine learning (ML) for energy-efficient design and optimization. The robot’s structure was optimized to reduce weight without compromising mechanical integrity. An energy-aware path planning framework was developed using XGBoost based on real-world energy consumption data. The optimized design showed improved energy efficiency, reduced material use, and enhanced navigation performance. The topic is compelling, and the work is well-integrated, comprehensive, and methodologically robust, yielding meaningful and practical outcomes. It can be suggested for publication after following questions or concerns been addressed.

1, this paper provides a reasonable overview of the current state of the art in this field, however, the comparison to prior work is mainly descriptive and lacking direct quantitative benchmarks or in-depth analysis of how the approach adopted in this work could outperform existing methods.

2, in the FEM modeling section, only static loading conditions are applied to evaluate stress distribution and safety factors. However, it is doubtful that this setup could reflect the real-world operational conditions considering the complexity differences. It is recommended to add dynamic loading conditions into the regime.

3, some figures may need to be improved, for example: legends are missing in Fig. 4; the words and numbers in Fig. 5b are stretched too hard; Fig. 8 and 11 need to be organized; In Figs. 2-5, snapshots or images from different viewing perspectives (front, side, top, or back for example) could improve the clarity and show more details for understanding. Moreover, the figure captions are generally too short and simple. More descriptive captions that summarize what the figure shows would improve the paper’s readability.

Author Response

Manuscript ID: machines-3702373

Title: Development of a Topology-Optimized Mobile Robotic System with Energy-Aware Path Planning Based on Machine Learning

We sincerely thank Reviewer for the thoughtful and constructive feedback, which greatly helped us enhance the scientific quality and clarity of our manuscript. We have carefully revised the paper in response to all comments and provided a detailed summary below outlining how each concern was addressed:

Sincerely,
Dr. Hilmi Saygin Sucuoglu

 

This paper presents the design, development, and evaluation of a mobile robotic system that integrates topology optimization (TO), additive manufacturing (AM), finite element modeling, and machine learning (ML) for energy-efficient design and optimization. The robot’s structure was optimized to reduce weight without compromising mechanical integrity. An energy-aware path planning framework was developed using XGBoost based on real-world energy consumption data. The optimized design showed improved energy efficiency, reduced material use, and enhanced navigation performance. The topic is compelling, and the work is well-integrated, comprehensive, and methodologically robust, yielding meaningful and practical outcomes. It can be suggested for publication after following questions or concerns been addressed.

1 this paper provides a reasonable overview of the current state of the art in this field, however, the comparison to prior work is mainly descriptive and lacking direct quantitative benchmarks or in-depth analysis of how the approach adopted in this work could outperform existing methods.

To address this point, we have added a new paragraph at the end of Section 3.3 highlighting the quantitative operational improvements achieved by the proposed TO–AM–ML framework. These include reduced energy use, lower current peaks, and extended endurance compared to conventional approaches. This revision clarifies how the co-optimization strategy adopted in this study offers measurable and practical advantages beyond traditional single-objective methods.

2, in the FEM modeling section, only static loading conditions are applied to evaluate stress distribution and safety factors. However, it is doubtful that this setup could reflect the real-world operational conditions considering the complexity differences. It is recommended to add dynamic loading conditions into the regime.

As noted, our current FEA employs static loading to validate design feasibility and guide topology optimization. The limitation of omitting dynamic conditions is explicitly acknowledged in the Conclusions section as part of future work. Furthermore, to strengthen structural evaluation, we have included stiffness-to-weight ratio metrics in Section 3.2 and Table 3, demonstrating performance improvements beyond stress analysis.

3, some figures may need to be improved, for example: legends are missing in Fig. 4; the words and numbers in Fig. 5b are stretched too hard; Fig. 8 and 11 need to be organized; In Figs. 2-5, snapshots or images from different viewing perspectives (front, side, top, or back for example) could improve the clarity and show more details for understanding. Moreover, the figure captions are generally too short and simple. More descriptive captions that summarize what the figure shows would improve the paper’s readability.

We have carefully revised the figures as recommended to improve clarity and readability. Regarding Figure 4, this illustration shows the redesigned frame structures that were developed based on the results of the topology optimization process conducted in ANSYS. Since these visuals represent finalized design proposals rather than parametric plots or simulation outputs, a legend was not included by design. However, we have refined the rendering and updated the caption to more clearly communicate the purpose and context of these models.

Figure 5b has been revised to correct the stretching of labels and numerical indicators for enhanced legibility.

Figures 8 and 11 have been reorganized for better visual flow and consistency.

Additionally, all figure captions have been expanded to provide more descriptive summaries that highlight the key purpose and contents of each illustration.

 

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Congrats to the authors.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have addressed all comments. The manuscript can be accepted now.