Time and Energy Optimal Trajectory Planning of Wheeled Mobile Dual-Arm Robot Based on Tip-Over Stability Constraint
Round 1
Reviewer 1 Report
1. The authors do not adequately highlight the research gap.
2. In the Introduction, the authors need to add one paragraph regarding the aim of the paper and the contribution of the article.
3. The quintic B-spline curve and NSGA-II are not new in the field of trajectory planning of robots. What is the novelty of the paper?
4. How will you consider obstacle avoidance during the planning?
5. Authors need to compare the algorithm with other optimization algorithms.
Author Response
Response to Reviewer 1 Comments
Dear Reviewers,
Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled " Time and energy optimal trajectory Planning of Wheeled Mo-bile Dual-Arm Robot Based on Tip-over Stability Constraint " (manuscript ID: applsci-2117550). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studied the comments carefully and have made a correction which we hope meets with approval.
Point1: The authors do not adequately highlight the research gap.
Response1: Thank you for pointing out the problem. This paper focuses on the stability analysis of the robot, and mainly describes the importance of joint trajectory planning based on the stability constraint for the stable operation of the robot.
Point2: In the Introduction, the authors need to add one paragraph regarding the aim of the paper and the contribution of the article.
Response2: Thank you for pointing out the problem. We revised and adjusted the introduction to make the article more convincing.
Point3: The quintic B-spline curve and NSGA-II are not new in the field of trajectory planning of robots. What is the novelty of the paper?
Response3: Thank you for pointing out the problem. In this paper, there is no innovation in the algorithm. This paper focuses on the simulation of robot stability.
Point4: How will you consider obstacle avoidance during the planning?
Response4: Thank you for pointing out the problem. At the time of writing this paper, the space the robot moves is an ideal space, and the obstacle constraints are not taken into account in the simulation study.
Point5: Authors need to compare the algorithm with other optimization algorithms.
Reseponse5: Thank you for pointing out the problem. This paper focuses on improving the stability of the robot. Due to space limitation, there is no comparison and analysis of the optimization algorithms. In the following paper, PSO optimization algorithm, NSGA-II optimization algorithm and the improved NSGA-II optimization algorithm are planned to be analyzed and compared.
Reviewer 2 Report
The paper is well written. Figures (1 to 8) are not high resolution figures. Please update them. Rest the paper is technically sound.
Author Response
Response to Reviewer 2 Comments
Dear Reviewers,
Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled " Time and energy optimal trajectory Planning of Wheeled Mo-bile Dual-Arm Robot Based on Tip-over Stability Constraint " (manuscript ID: applsci-2117550). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studied the comments carefully and have made a correction which we hope meets with approval.
Point1: The paper is well written. Figures (1 to 8) are not high resolution figures. Please update them. Rest the paper is technically sound.
Response1: Thank you for your affirmation and pointing out the problem. We have updated the image of the paper.
Author Response File: 
Author Response.docx
Reviewer 3 Report
1. The originality of the paper is poor; in fact, the approaches are well known, and many related works can be found in the literature. The motivation for the work is not clear. The authors should clarify their originality (innovation).
2. Please translate the words in Figure 4.
3. We suggest the authors optimize the size and quality of all figures.
4. Equation (10) should be verified.
5. What is the conclusion at the end of Section 1 (Introduction)? We suggest to the authors that they add a paragraph in which they explain the advantages of the proposed contribution (regarding the presented works).
6. The manuscript is not very well organized. The readability needs to be improved.
7. Section 2 (Modeling and Analysis of WMDAR) needs more details on the structure of the robot (dimensions, mass), and the methods employed in the modeling (placement of the reference frames, D-H method, etc.).
8. Resolution approaches: There are several techniques for solving the optimization problem; the authors should justify the choice of using the NSAG II algorithm.
9. There are, on the other hand, many unanswered questions, e.g., the rationale behind the choice of limits for the decision variables, the details of the GA-based optimization process, etc., that are omitted without an exhaustive treatment.
10. We suggest the authors conduct a comparative analysis and explain the advantages of the proposed approach compared with the existing techniques.
11. The authors must make a better effort at referencing the significant papers. There are several papers, published in MDP dealing with WMDAR that are not cited.
12. There are many symbols. A list of symbols (nomenclature) should be given.
13. The relative works in the following references can be mentioned in the introduction:
- Bouzoualegh, Samir, Guechi, El-Hadi and Kelaiaia, Ridha. Model Predictive Control of a Differential-Drive Mobile Robot, Acta Universitatis Sapientiae, Electrical and Mechanical Engineering, vol.10, no.1, 2018, pp.20-41. https://doi.org/10.2478/auseme-2018-0002
- Zhang, X.; Huang, Y.; Rong, Y.; Li, G.; Wang, H.; Liu, C. Optimal Trajectory Planning for Wheeled Mobile Robots under Localization Uncertainty and Energy Efficiency Constraints. Sensors 2021, 21, 335. https://doi.org/10.3390/s21020335
Author Response
Response to Reviewer 3 Comments
Dear Reviewers,
Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled " Time and energy optimal trajectory Planning of Wheeled Mo-bile Dual-Arm Robot Based on Tip-over Stability Constraint " (manuscript ID: applsci-2117550). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studied the comments carefully and have made a correction which we hope meets with approval.
Point1: The originality of the paper is poor; in fact, the approaches are well known, and many related works can be found in the literature. The motivation for the work is not clear. The authors should clarify their originality (innovation).
Response1: Thank you for pointing out the problem. This paper focuses on the stability analysis of the robot, and mainly describes the importance of joint trajectory planning based on the stability constraint for the stable operation of the robot.
Point2: Please translate the words in Figure 4.
Response2: Thank you for pointing out the problem. We have translated the words in Figuer4.
Point3: We suggest the authors optimize the size and quality of all figures.
Response3: Thank you for pointing out the problem. We modified the article for readability.
Point4: Equation (10) should be verified.
Response4: Equation(10) in the original text was written in error during editing and has now been corrected.
Point5: What is the conclusion at the end of Section 1 (Introduction)? We suggest to the authors that they add a paragraph in which they explain the advantages of the proposed contribution (regarding the presented works).
Response5: Thank you for pointing out the problem. We revised and adjusted the introduction to make the article more convincing.
Point6: The manuscript is not very well organized. The readability needs to be improved.
Response6: Thank you for pointing out the problem. We reorganized the paper.
Point7: Section 2 (Modeling and Analysis of WMDAR) needs more details on the structure of the robot (dimensions, mass), and the methods employed in the modeling (placement of the reference frames, D-H method, etc.).
Response7: Thank you for pointing out the problem. The mass parameters of each connecting rod of the robot arm have been added in the paper.
Point8: Resolution approaches: There are several techniques for solving the optimization problem; the authors should justify the choice of using the NSAG II algorithm.
Response8: Thank you for pointing out the problem. This paper focuses on improving the stability of the robot. Due to space limitation, there is no comparison and analysis of the optimization algorithms. In the following paper, PSO optimization algorithm, NSGA-II optimization algorithm and the improved NSGA-II optimization algorithm are planned to be analyzed and compared.
Point9: There are, on the other hand, many unanswered questions, e.g., the rationale behind the choice of limits for the decision variables, the details of the GA-based optimization process, etc., that are omitted without an exhaustive treatment.
Response9: Thank you for pointing out the problem. The selection of the limit position is based on experience after reading other people's literature. Due to the limitation of the length of the paper, the optimization process is not elaborated.
Point10: We suggest the authors conduct a comparative analysis and explain the advantages of the proposed approach compared with the existing techniques.
Response10: Thank you for pointing out the problem. This paper focuses on the importance of robot stability constraints, and will conduct in-depth comparative analysis in subsequent studies.
Point11: The authors must make a better effort at referencing the significant papers. There are several papers, published in MDP dealing with WMDAR that are not cited.
Response11: Thank you for pointing out the problem. We have revised the paper to address this problem.
Point12: There are many symbols. A list of symbols (nomenclature) should be given.
Response12: Thank you for pointing out the problem. We added nomenclature to the paper.
Point13: The relative works in the following references can be mentioned in the introduction:
- Bouzoualegh, Samir, Guechi, El-Hadi and Kelaiaia, Ridha. Model Predictive Control of a Differential-Drive Mobile Robot, Acta Universitatis Sapientiae, Electrical and Mechanical Engineering, vol.10, no.1, 2018, pp.20-41. https://doi.org/10.2478/auseme-2018-0002
- Zhang, X.; Huang, Y.; Rong, Y.; Li, G.; Wang, H.; Liu, C. Optimal Trajectory Planning for Wheeled Mobile Robots under Localization Uncertainty and Energy Efficiency Constraints. Sensors 2021, 21, 335. https://doi.org/10.3390/s21020335
Response13: Thank you for the recommended articles, I have gained a lot after reading them and they have given me new inspiration and direction to learn.
Author Response File: Author Response.docx
Round 2
Reviewer 3 Report
Thanks for the point-by-point responses. Here are further suggestions to the manuscript:
1) The manuscript is not very well organized, even after the new round of revision. The readability needs to be improved (especially Section 5).
2) Please verify equations (9) and (11). What basis did you use to write these equations? A term that represents the rotation matrix is missing.
3) The authors say in response10: “This paper focuses on the importance of robot stability constraints, and will conduct in-depth comparative analysis in subsequent studies”. We don't agree with this. It is necessary to validate the results.
Author Response
Dear Reviewers,
Point1: The manuscript is not very well organized, even after the new round of revision. The readability needs to be improved (especially Section 5).
Response1: Thank you for pointing out the problem. We have revised the paper.
Point2: Please verify equations (9) and (11). What basis did you use to write these equations? A term that represents the rotation matrix is missing.
Response2: Thank you for pointing out the problem. Please see the attachment for the derivation process
Point3: The authors say in response10: “This paper focuses on the importance of robot stability constraints, and will conduct in-depth comparative analysis in subsequent studies”. We don't agree with this. It is necessary to validate the results.
Response3: Thank you for pointing out the problem. In this paper, the improved NSGAII algorithm is used, and stability constraints are added to the improved NSGAII algorithm, and the two schemes with and without stability constraints are compared respectively. As shown in Figure 8, the improved NSGAII algorithm without added stability constraints is shown on the left, and the improved NSGAII algorithm with added stability constraints is shown on the right. The NSGAII algorithm with stability constraints not only reduces the energy consumption but also improves the stability.
Author Response File: 
Author Response.pdf
Round 3
Reviewer 3 Report
Thanks for the point-by-point responses. All comments have been responded to. I don't have any further comments. The paper can be accepted for publication.
