Spherical Inverted Pendulum on a Quadrotor UAV: A Flatness and Discontinuous Extended State Observer Approach

Round 1

Reviewer 1 Report

The Authors have overall not answered the question of how this is novel enough to be published. This is due to the following reasons

1. The paper claims that the main contribution is the development of the dynamics of the quadcopter with spherical inverted pendulum (pg 3 line 92-94). This is not true. Over the years various researcher have developed this using the Lagrangian modellng method (eg. Hehn & D'Andrea, A flying inverted pendulum 2011)

2. How does this paper differ from reference 20?

3. Other authors have also used differential flatness with active disturbance rejection (eg. Ref 21) what improvement does this paper bring to the body of knowledge?

4. The concept of ADRC-DESO was used in this work. It would be nice to cite the original reference or patent for the method

Overall, In my opinion I think this paper puts together importance concepts such as Langrangian modelling, ADRC-DESO, Quadcopter plus Inverted Spherical Pendulum but all of these  and a combination of a few of these have been done by other researchers. 

Author Response

Thank you very much for your comments

We have written a general document to assert your comments and answer them.

Kind regards

Author Response File: Author Response.pdf

Reviewer 2 Report

The author can make the modification according to the following modification suggestions, and can be accepted after modification:

1. The author can give more detailed sources for many derivation formulas of the paper, and the derivation process is more detailed.

2. The author had better carry out experimental verification.

On the whole, this paper is good, with novel ideas, complete research routes and complete research work.

Author Response

Thank you very much for your comments

We have written a general document to assert your comments and answer them.

Kind regards

Author Response File: Author Response.pdf

Reviewer 3 Report

Very well presented, interesting work. Minimal english mistakes.

Author Response

Thank you very much for your comments

We have written a general document to assert your comments and answer them.

Kind regards

Author Response File: Author Response.pdf

Reviewer 4 Report

Abstract are too long (218 wors). From template "A single paragraph of about 200 words maximum. For research articles, abstracts should give a pertinent overview of the work."

Line 6                  Correct "Euler-Lagrnage" to  "Euler-Lagrange"

Keywords: must be separated with ";"

You can't use expression like "as in []", in [] etc. Please correct all paper from these expressions. For example, is better to say "Marcelino M. de Almeida et all present three-level-cascade nonlinear "

What is LQR, UAV etc. you can't use abbreviation without to say what they mean.

For example, " linear quadratic regulator (LQR) "

Line 139 "The Lagrangian of the system is considered as;" move to next page after figure 1 , correct ; tp :

Also explain the annotation from figure 1

Usually after equation we don't use "." (equation 5 and 6) and "," equation (7) - correct all equation

Line 170 you have "A1" please give more explication or delete it

Line 242 and 243 something are missing here.

Line 311 to 331 Figure 4 to Figure 13 try to give some explication fro each figure. You must re-write this chapter.

Give more explication at conclusions

Missing text line 350 to 356

What is the role of chapter 4?

Author Response

Thank you very much for your comments

We have written a general document to assert your comments and answer them.

Kind regards

Author Response File: Author Response.pdf

Reviewer 5 Report

This study used a full dynamic model obtained through the Euler-Lagrange formalism to solve the problem of balancing an inverted spherical pendulum on a quadrotor. However, the entire article is incomplete. Basically, there is no problem in the calculation process of formula derivation, but authors have to display additional actual cases which are applied to the results of the proposed model and furtherly compare the situations before and after the improvements of importing model calculation. In addition, the following topics must be considered for revision.

 A considerable number of spelling errors must be corrected. For example, “Euler-Lagrnage formalism” should be “Euler-Lagrange formalism”, and please authors check throughout the manuscript. A lot of abbreviations should be spelt in detail at the first appearance in this article, like LQR, UAV, ADRC, SSO3, PVTOL and ROESO. Please authors check throughout the manuscript.

 Citations [6]~[18] in the text should be revised as “author’s last name et al. (xxxx) [x]”. Please authors revise all the statements of such improper citations.

Titles of Figs. 5~9 are too simple (less than 10 words), and please authors exactly provide better titles for increasing the readability of figures.

Figs. 12 and 13, the blue line and red line are partially overlapped. Please authors revise these two figures to be better presented. In addition, the related statements of these two figures must be modified simultaneously.

Author Response

Thank you very much for your comments

We have written a general document to assert your comments and answer them.

Kind regards

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I think the added sections add more clarity to the publication. There are minor spelling and grammar mistakes

Author Response

Dear reviewer

We have responded to one of your thoughtful comments. These are in the following PDF, we thank you in advance for all your time in our review.

Kind regards

Author Response File: Author Response.pdf

Reviewer 4 Report

Your abstract are more than 200 words.

References in your text must be [1], [2], [3]

I don't understand why you have [2] and the next one is [7].

[9] and the next one are [16] after are [10]

You can delete the text from line 124 to 132 - it's not science

Author Response

Dear reviewer

We have responded to one of your thoughtful comments. These are in the following PDF, we thank you in advance for all your time in our review.

Kind regards

Author Response File: Author Response.pdf

Reviewer 5 Report

Referring to the comments at the first run, authors has partially modified the citation formats in the text. However, at Lines 99,104,113 and 118, the citatation info has not been exactally revised.  

Author Response

Dear reviewer

We have responded to one of your thoughtful comments. These are in the following PDF, we thank you in advance for all your time in our review.

Kind regards

Author Response File: Author Response.pdf