Maximum Principle in Autonomous Multi-Object Safe Trajectory Optimization

Round 1

Reviewer 1 Report

Dear authors, I read the article "Maximum Principle in Autonomous Multi-Object Safe Trajectory Optimization," which is very interesting. The authors present a work in which the control of an autonomous object in a group of other objects is optimized using Pontryagin's bounded maximum principle. To do this, consider constraints that reflect the movement of passing objects.

I have the following minor observations:


1.- the abstract must contain the quantitative results,
2.- The English of the article must be corrected.
3. The introduction needs to adequately compare the proposed method or mention its numerical results. Perhaps a comparative table with the results of other methods will help highlight this comparison.
4.- The reason for analyzing the proposed method is not defined, nor is the method used in the comparison.
5.- Although the authors mention that it applies to different types of autonomous robots, the equations they describe are not valid for all kinds of robots that they mention.

I conclude that the work should address minor corrections before publication.

Extensive editing of the English language was required, and several errors in English were detected.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Dear Authors:

Thanks for the great work.

This paper presents the task of optimizing the control of an autonomous object in a group of other objects passed by, using Pontryagin's bounded maximum principle. The oganization is poorly structured, and needed further improvement. Here are other comments as follows:

Q1: Please check grammar. There are many words which have wrong spellings too.

Q2: In Figure 1, it is shown as alpha_0, but here is a_0. Please be consistent on the symbols used.

Q3: Where are y_0 and y_j in Figure 1? The notations are different from the context.

Q4: In Eq. (1)(2): What is the psi_0 definition? Should the equations be switched?

Q5: In Eq. (2): Please be consistent in the symbols between equations and context. The equation numbering is not correct also.

Q6: In Eq. (4): Please make it clear on the notations of symbols, e.g. x_30, x_40, x_50, etc.

Q7: In Eq. (6): What is h? Please denote it clearly.

Q8: In Eq. (7): Please re-check this equation. This equation leads to a trivial result.

Q9: In Eq. (8): Please re-check this equation.

Q10: In Figure (3)(4)(5): From this Figure 3, 4, 5, how do we interpret the trajectories of different objects as time goes by? And what are the distances between each objects at the same moment of time?

Q11: In Figure (3)(4)(5): In addition, this is only focusing on the trajectory of Object 0 to avoid collision between the rest. But what about the rest collision avoidance?

Thanks and Best Regards

English is not good enough for publishing this paper. Please review and revise.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

The reviewer has a few minor concerns:

1. Page 2: A proofreading is suggested, and the mistakes, such as '... ooptimacy ...' should be avoided

2. Page 3: The reviewer suggests changing 'Study Objectives' to 'Research Objectives'

N/A

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have addressed my main concerns

Only minor details.

Author Response

I would like to thank the reviewer for his valuable comments, which improved the quality of the presentation of my manuscript.

Reviewer 2 Report

Dear Author:

Thanks for the efforts in revising the paper.

However, there are still issues with this current paper as follows:

Q1: In Eq. (4): Is it a term called alpha_0m? Please be consistent with previous alpha_0 in  Eq. (3).

Q2: In Eq. (5): Please re-check these terms. Be consistent in presentation on mathematical symbols.

Q3: In Eq. (7): What is f_0? Cannot see the relationship between this and Eq. (4).

Q4: As asked in previous review, In Figure (3)(4)(5): This is only focusing on maneuvering the trajectory of Object 0 to avoid collision between the rest. As you put in response, "assuming no maneuvering of the encountered j objects", but the other j objects are able to have potential collisions too according to your figures shown. So this simulation result may not be a solid result to show the performance effectiveness.

Thanks and Best Regards

English has been improved, but there still are some flaws to enhance.

Author Response

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Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

Dear Author(s):

Thank you for the revision.

There are some presentation errors in your equations. 

Please kindly revise those ones listed as follows:

In Eq. (9) >>> Subscript "30" should be subscript "3,0". etc.

In Eq. (13) >>> Subscript "50" should be subscript "5,0". etc.

In Eq. (15) >>> Subscript "20" should be subscript "2,0". etc.

In Eq. (16) >>> Subscript "10" should be subscript "1,0". etc.

In Eq. (17) >>> Subscript "10" should be subscript "1,0". etc.

In Eq. (18-20) >>> Subscript "ij" should be subscript "i, j". etc.

In Algorithm section >>>  Subscript "ij" should be subscript "i, j". etc.

Thanks and Best Regards

Acceptable English Quality with moderate revision.

Author Response

The marking of subscripts has been corrected throughout the text of the manuscript.
I would like to thank the Reviewer for carefully checking my manuscript.

Author Response File: Author Response.docx