Relative Orbital Motion Control of Spacecraft Based on Multi-Objective Optimization

Round 1

Reviewer 1 Report

I have two main concerns about an overall good article.

The first one is technical but very much misleading. As far as I'm concerned, "attitude" means orientation, and "attitude control" depicts the control of the orientation of a satellite with respect to something. Given that, the presented paper is not about an attitude control, it is about a relative orbital motion control or something like that. The title is horrendously misleading.

The second thing that troubles me is the lack of comparison with overall known methods. The epsilon-constraint method is interesting and does (as it seems) work, but it is not clear at all what is the advantage of this method over, say, LQR.

Minor, but nevertheless important things:

-- x(t) depicts two different things in different parts of the paper

-- Lunger Kutta must be Runge-Kutta I suppose

-- f_k maps R^n to R, not to R^p

-- definitions of weakly and strictly efficient solutions must be swapped

Author Response

Thank you so much for your careful check, and we totally understand the reviewer's concern. We have carefully considered your suggestion and make some changes. Response to the review report is attached. 

Author Response File: Author Response.pdf

Reviewer 2 Report

In this paper, the authors developed the relative attitude control problem of a follower spacecraft as a multi-objective optimization problem and, via numerical analysis, validated the effectiveness of the proposed multi-objective optimization approach.

My comments to the authors are as follows:

1.  It was stated that the zero-order hold numerical method was used to convert the state space form of the Hill–Clohessy–Wiltshire (HCW) equation into discrete form. At the first instance of reading your paper by an interested reader, who has never heard about the term zero-order hold, it will be a bit difficult to understand. Please, try to give a short literature review of the term and its applications. This will enable the reader to have a better understanding of the manuscript.

2.  On page 4, the word Runge-Kutta was misspelled as “Lunger Kutta”. Correct this to reflect the exact word.

3. Include the reference to the multi-objective optimization problem (MOP) described in Eq. 8.

4. In demonstrating the effectiveness of the proposed algorithm, a numerical example was given and plots were generated. The software package used to generate the plots was not stated in the manuscript. State the package used so that the interested reader will be able to reproduce your results.

Author Response

Thank you so much for your careful check, and we totally understand the reviewer's concern. We have carefully considered your suggestion and make some changes. Response to the review report is attached. 

Author Response File: Author Response.pdf

Reviewer 3 Report

Dear Authors,

Although your work generally deals with innovative and original issues, I think that considering the issues I have identified will bring your work to a higher level.

- The scientific English language used in the study should be improved,

- You must specify the similarities and differences between the relative position equations and the parameters used in the relative orientation equations (review the parameters used between Equation 1 and Equation 4),

- You should specify in more detail and clearly the transition from the relative orbital position vectors determined using the Hill-Clohessy-Wiltshire equations to the attitute estimation part. You should highlight the differences between the relative position and relative orientation vectors,

- In the introduction, you should highlight new studies in which relative orbit estimations are determined with the help of Kalman filters using up-to-date new references (Fault-tolerant state estimation methods of cluster satellites, Formation Flight for Close Satellites with GPS-Based State Estimation Method),

- In the estimation and optimization methods of the relative states used, it is unclear where you get the measurements from. Which sensor (such as GPS, visual, laser) and which sensor measurements did you obtain simulation results?.

Author Response

Thank you so much for your careful check, and we totally understand the reviewer's concern. We have carefully considered your suggestion and make some changes. Response to the review report is attached. 

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Dear Aurhors

Thank you for re-editing your work with attention to the corrections I suggested. I consider your work as suitable for publication as it is.

Regards