Optimal Time–Jerk Trajectory Planning for Delta Parallel Robot Based on Improved Butterfly Optimization Algorithm
Round 1
Reviewer 1 Report
The authors propose: Optimal Time-Jerk Trajectory Planning for Delta Parallel Robot Based on Improved Butterfly Optimization Algorithm. I have some concerns and my suggestions are listed below:
1- The contribution is not adequately explained in the abstract. There is no driving force behind the essay. The information was not presented in a way that was understandable and straightforward. The main idea of the work should be emphasized in the abstract section.
2- To highlight research gaps and innovations, the writers should include a Literature Review in the form of tables and concentrate on the study's primary problem in the introductory part.
3- It is important to improve experimental results, validation, and comparison to alternative strategies. More debates and analyses are required.
4- The authors did not evaluate the advantages and disadvantages of the related works. Please evaluate that how their study is different from others in the related work section? What do they have where others do not? Why they are better or how? What's new/novel here?
5- It is crucial to describe the Improved Butterfly Optimization Algorithm’ computational complexity.
6- For experiments, nonparametric tests should be used.
7- The authors should clarify the pros and cons of the method. What are the limitation(s) methodology(ies) adopted in this work? Please indicate practical advantages and discuss research limitations.
8- If you have developed any code or software, it is recommended that you provide a link to the code for other readers and to enhance the impact of the paper and its applicability
9- According to all comments, the conclusion section must be improved
Author Response
On behalf of my co-authors, we thank you very much for giving us an opportunity to revise our manuscript, we appreciate you very much for your positive and constructive comments and suggestions on our manuscript entitled "Optimal Time-Jerk Trajectory Planning for Delta Parallel Robot Based on Improved Butterfly Optimization Algorithm". The paper has been revised thoroughly with respect to all comments. Please find below our response and explanations on changes made.
1. The contribution is not adequately explained in the abstract. There is no driving force behind the essay. The information was not presented in a way that was understandable and straightforward. The main idea of the work should be emphasized in the abstract section.
Response:
Delta parallel robot is used to complete high-speed pickup tasks. Because the robot has high speed and high acceleration in the process of motion, it will cause residual vibration of the robot. In order to make the robot have good dynamic positioning accuracy and running stability at high speed, we use the trajectory planning method to improve the dynamic performance of the robot, on the one hand to ensure the smoothness of motion, on the other hand to improve the pickup efficiency. This is the driving force of this study. We updated the summary section of this article.
2. To highlight research gaps and innovations, the writers should include a Literature Review in the form of tables and concentrate on the study's primary problem in the introductory part.
Response:
We thank the reviewer for this good suggestion.
The purpose of this paper is to improve the stability of the robot in the process of high-speed motion by trajectory optimization. Therefore, we propose an improved butterfly optimization algorithm to solve the problem. The innovation is to optimize by using the combination of circle chaotic mapping and fractional differential method. This method effectively expands the global search scope of the algorithm and reduces the risk of falling into local optimization. At the same time, faster convergence speed is obtained. Through the test function and simulation experiments, the results show that the IBOA can converge quickly, and the optimization results are better than other algorithms of the same type.
We give a supplementary description of this part in the introduction of the article, and marked in blue.
3. It is important to improve experimental results, validation, and comparison to alternative strategies. More debates and analyses are required.
Response:
We thank the reviewer for this good suggestion.
In response to this comment, we have added part 6.1. And in this new Section, we evaluate the superiority of the algorithm from the aspects of optimization results and test functions.
4. The authors did not evaluate the advantages and disadvantages of the related works. Please evaluate that how their study is different from others in the related work section? What do they have where others do not? Why they are better or how? What's new/novel here?
Response:
Scholars have made many research achievements in using algorithms to solve optimization problems, and the algorithms also have their own advantages. For this part, the analysis of algorithms is added in the introduction of the manuscript. Compared with other algorithms, boa is a novel algorithm, and its advantage is to solve the combination problem. This paper improves boa to solve the multi-objective optimization problem. By adjusting fewer parameters (that is, boa parameters include c, a and p), we can achieve good optimization results.
In our research, the combination of chaotic mapping and fractional differentiation greatly improves the search ability and convergence speed of the algorithm, making it more competitive compared with other algorithms.
We give a supplementary description of this part in the introduction of the article, and marked in blue.
5. It is crucial to describe the Improved Butterfly Optimization Algorithm’ computational complexity.
Response:
The BOA is a novel optimization method, but similar to GA, WOA and other algorithms, the initial algorithm is easy to fall into local optimization, and the convergence speed is slow. This manuscript proposes a method combining chaos and fractional differentiation to improve the original boa algorithm, aiming to improve the convergence speed of the algorithm and avoid falling into local optimization. The chaotic sequence adopts the method of circle mapping and is distributed between [0,1], which can make the population more evenly distributed in the search space.
Fractional differentiation is an important part of improving boa. Fractional differentiation can more accurately remember and inherit the optimal part of the previous iteration, which can greatly improve the speed and accuracy of algorithm convergence. So how to obtain enough optimal solutions from the last iteration has become a research difficulty. This paper obtains solutions through multiple iterations of the primary population to obtain more accurate solutions from these optimal solutions.
6. For experiments, nonparametric tests should be used.
Response:
In the new Section 6.1, we analyzed the optimized butterfly population distribution map and tested IBOA with different test functions.
7. The authors should clarify the pros and cons of the method. What are the limitation(s) methodology(ies) adopted in this work? Please indicate practical advantages and discuss research limitations.
Response:
With the help of IBOA, the trajectory optimization is carried out by setting control points, taking the maximum speed, acceleration and jerk as constraints, and taking the shortest time and the smallest jerk as the goal, which effectively improves the operation efficiency and reduces the residual vibration of the robot in the process of high-speed movement. However, because the optimization process will change the position of NURBS curve control points, resulting in a certain degree of deformation of the planned curve, the trajectory needs to be further modified. It has good adaptability when the robot takes and places the trajectory with a small span, and the trajectory needs to be further modified if the span is too large.
This part is supplemented in the updated conclusion.
8. If you have developed any code or software, it is recommended that you provide a link to the code for other readers and to enhance the impact of the paper and its applicability。
Response:
If readers are interested in our research results, we will feel very honored. Readers contact us through the corresponding author, and we will be happy to share our code.
9. According to all comments, the conclusion section must be improved
Response:
In Section 7 of the article, we updated the conclusion.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This paper presents a multi-objective integrated optimal trajectory planning method. Its aim is to improve work efficiency and reduce the jerk of high-speed parallel robots. The application to Delta robot to evaluate the performance of the algorithm is interesting and results are very well detailed.
I think this paper has merit, it's interesting and well-written.
I suggest to explain how you have chosen the other algorithms to compare IBOA with.
Author Response
On behalf of my co-authors, we thank you very much for giving us an opportunity to revise our manuscript, we appreciate you very much for your positive and constructive comments and suggestions on our manuscript entitled "Optimal Time-Jerk Trajectory Planning for Delta Parallel Robot Based on Improved Butterfly Optimization Algorithm". The paper has been revised thoroughly with respect to all comments. Please find below our response and explanations on changes made.
This paper presents a multi-objective integrated optimal trajectory planning method. Its aim is to improve work efficiency and reduce the jerk of high-speed parallel robots. The application to Delta robot to evaluate the performance of the algorithm is interesting and results are very well detailed.
I think this paper has merit, it's interesting and well-written.
Response:
The authors thank the reviewer for this positive comment.
1. I suggest to explain how you have chosen the other algorithms to compare IBOA with.
Response:
Optimization algorithm plays an important role in solving optimization problems. Some meta heuristic algorithms are used to solve the trajectory optimization problems of robots, such as WOA [1], GA [2], PSO [3], etc. in order to verify the superiority of IBOA proposed in this paper, IBOA and unmodified boa are compared and analyzed, and the same type of unmodified WOA and GA algorithms are compared and studied. In order to further verify the superiority of IBOA, we choose other improved boa algorithms. In this paper, we choose HPSOBOA [4]. Comparative experiments show that IBOA has stronger competitiveness.
References：
[1] Zhang X, Ming Z. Trajectory Planning and Optimization for a Par4 Parallel Robot Based on Energy Consumption[J]. Applied Sciences, 2019, 9(13):2770.
[2] Qie Xiaohan et al. Trajectory Planning and Simulation Study of Redundant Robotic Arm for Upper Limb Rehabilitation Based on Back Propagation Neural Network and Genetic Algorithm[J]. Sensors, 2022, 22(11) : 4071-4071.
[3] Liu C, Cao G H, Yong-Yin Q U, et al. An improved PSO algorithm for time-optimal trajectory planning of Delta robot in intelligent packaging[J]. International Journal of Advanced Manufacturing Technology, 2020, 107(1).
[4] Zhang M , Long D , Qin T , et al. A Chaotic Hybrid Butterfly Optimization Algorithm with Particle Swarm Optimization for High-Dimensional Optimization Problems[J]. Symmetry, 2020, 12(11):1800.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The revised version of the manuscript is in a much better form. They have added a section 6.1 to improve experimental results, validation, and comparison to alternative strategies.
However, for this comment "For experiments, nonparametric tests should be used", I mean methods of statistical analysis such as Friedman and Wilcoxon's tests.
I advise the authors to thoroughly review the entire paper again. I recommend accepting the paper with minor revisions.
Author Response
On behalf of all the authors, we thank you for your review of this manuscript. We have further supplemented it according to your valuable comments.
For easy of reading, comments from the technical editor and the reviewers are displayed in “Normal, black”, while our reply is typed in “Blue”.
The revised version of the manuscript is in a much better form. They have added a section 6.1 to improve experimental results, validation, and comparison to alternative strategies.
However, for this comment "For experiments, nonparametric tests should be used", I mean methods of statistical analysis such as Friedman and Wilcoxon's tests.
I advise the authors to thoroughly review the entire paper again. I recommend accepting the paper with minor revisions
Response:
The authors thank the reviewer for this positive comment.
Friedman test is used to obtain the ranking of multiple algorithms, and Wilcoxon signed rank test is used to obtain whether there is a significant difference between the two algorithms. In Article 6.1, we supplement and analyze the nonparametric detection of IBOA, which is marked in blue font in the article.
Author Response File: 
Author Response.docx
