# Research on Optimal Landing Trajectory Planning Method between an UAV and a Moving Vessel

*Reviewer 1:*Anonymous

*Reviewer 2:*Anonymous

**Round 1**

*Reviewer 1 Report*

Why do you have a section 0? It seems more appropriate to have it start at 1.

I don't understand your notation. You have the point A0 denoting the initial position but it isn't bold even though it is technically a vector since it has coordinates x,y,z.

You then define VA which is bold implying a vector and signify that it is a function of time. You then define the speed direction in a rather odd way. You say that phi is the direction and denote that it is a function of psi and theta. This makes sense because vectors only have two angles of rotation to imply direction. However your choice direction function would confuse the standard aerospace engineer like myself since phi is typically reserved for the roll angle of a vehicle. It seems more appropriate to denote a unit vector that is tangential to the direction of travel like vhat or nhat and have that unit vector denote the speed direction.

I would also full define notation before you simply jump into the first section. A nomenclature section would help but defining within the text would be sufficient.

Equation 7 I think is supposed to read arctan not argtan.

A3 is not denoted in Figure 2. It is obvious where it is but for completion I think it needs to be depicted.

I think the authors are using the phrase "landing gear" incorrectly. Landing gear is supposed to denote a noun like the struts and wheels on a fixed wing UAV rather than a place like the landing pad on the ship or vessel. I would go through and be sure you are using the correct vocabulary because as of right now this is pretty confusing.

In equation 11 what is the arg function?

In equation 14 what happens if the UAV and Ship are parrallel? What sign do you default to?

Your nomenclature for time is also not consistent. In section 1 you use lower case t to denote time but then begin to use capital T starting on page 5.

In at least two places in the text you refer to the inertia of the UAV control system. Inertia however is a scientific quantity referring to mass distribution and momentum. Control systems do not have inertia. Please change this phrase to adequately describe what you are referring too.

Page 8 has a few inline equations that look like superscripts. Why?

If Trajectory 4 is out of scope of this paper then what reference do we have to learn about trajectory 4. This seems like really bad form to not include at least a summary of trajectory 4 or at least a reference to some other literature.

Equation 29 looks like MATLAB syntax rather than a mathematical equation. Again this is bad form and must be changed.

What does the subscript mp mean? I don't think it is defined in the text.

Section 2.2 completely redefines the time variables T1-T4. This must be fixed as well.

Given the number of blunders and issues that must be fixed I suggest this paper be reconsidered once the issues above have been adequately addressed. As such I have skipped the results section and gone straight to the conclusions for comment.

Is your landing plan truly optimal? Isn't it possible your method could run into local minima? Since the method is numerical can you truly gaurantee optimality? Typically truly optimal solutions are found analytically rather than using a numerical iteration scheme.

Since the velocity of both the UAV and the landing pad are both known as noted in section 1, why do the authors not discuss model predictive control? Surely someone has looked at this.

When you say conventional algorithms what do you mean? Path planning algoritms? PID? What about unconventional techniques? What have other researchers done to tackle this issue and what did they find?

It looks like Figure 3 is a large Simulink Model of the entire system? Does your model work if nonlinearities or more degrees of freedom are added. How does sensor noise and atmospheric disturbances affect the performance of your controller.

*Author Response*

Dear Reviewer:

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “Research on Optimal Landing Trajectory Planning Method between UAV and Moving Vessel” (ID: applsci-568114). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are marked in yellow in the paper. The main corrections in the paper and the responds to the associate reviewer comments are as flowing:

Please see the attachment!

We would like to express our great appreciation to you and reviewers for comments on our paper. Looking forward to hearing from you.

Thank you and best regards.

Yours sincerely,

author

Author Response File: Author Response.docx

*Reviewer 2 Report*

This paper introduces a method that allows an UAV to land on a moving platform, i.e. a vessel. Differently to the methods used in the open literature based on MPC, this paper uses a deterministic method to plan the trajectory and divides guidance and planning phases. The paper is not clearly written, some changes must be addressed for the sake of reader comprehension.

1 - The literature widely talks about UAV landing on vessels. I believe the introduction should include more papers about this topic, highlighting the contribution of the present paper to the literature.

2 - The introduction should introduce better the approach presented in this paper, clarifying the innovation and the motivation for th introduction of this approach.

3 - Pag. 3, line 87. Because the vessel is moving on a horizontal plane, θ_{B} is always 0. Hence, the transformation from x,y,z, to x',y',z' occurs only through the rotation around z of the angle θ.

4 - I believe that a plot representing both x,y,z, and x',y',z' frame is required to clarify the reader, and show the trajectory lies on the x',z' plane.

5 - Pag. 4, line 125. Where does β appear in the formula?

6 - Represent on the figure (Figure 3) all the points that you use in the text. Where is A_{3} in that figure?

7 - Pag. 6, equation 16. It is not clear what A_{2II} and A_{2III }are. The author should explain that the termination condition is encountered when the point A_{2} estimated proceeding forward from A_{1} (i.e.A_{2II}) and backward from A_{3} (i.e.A_{2III}) is below a certain threshold.

8 - Pag. 7, line 217. Using the word trajectory for the landing segments I, II and III could be misleading, because the landing trajectory is composed by the landing segments. Use a proper word.

9 - Pag. 8, line 224. The inclination of the trajectory must be constant and equal to the inclination of the x',z' plane, as stated in the hypothesis of the proposed planning algorithm. However, the angle the velocity the UAV has can be different from the inclination of the x',z' plane, as figure 7 shows. You should treat them as separate variables.

10 - Pag. 9, line 256. you already used the symbol T_{3} to identify the landing trajectory time. Please use another symbol to identify the time constant of the UAV.

11 - You should add a figure, like figure 5, to complement figure 9. this figure should show the trajectory obtained using n = 187.

*Author Response*

Dear Reviewer:

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “Research on Optimal Landing Trajectory Planning Method between UAV and Moving Vessel” (ID: applsci-568114). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are marked in yellow in the paper. The main corrections in the paper and the responds to the associate reviewer comments are as flowing:

Please see the attachment！

We would like to express our great appreciation to you and reviewers for comments on our paper. Looking forward to hearing from you.

Thank you and best regards.

Yours sincerely,

author

Author Response File: Author Response.docx

**Round 2**

*Reviewer 1 Report*

All issues have been resolved except for the following 2. The paper can be published after the below comments are addressed.

1.) In equation 14 you have a plus and minus sign. In the text you state that if the UAV and the vessel are facing each other the plus sign is used and

if the UAV and vessel are facing away from each the minus sign is used. But what happens at the boundary? What happens if the UAV and vessel are moving in the same direction where they are not facing each other nor facing away? Does the equation still work? What do you do?

2.) This reference needs to be in the paper "The specific method can refer to the Chinese invention patent (Application number: 2016110212759)."

*Author Response*

Dear Reviewer:

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “Research on Optimal Landing Trajectory Planning Method between UAV and Moving Vessel” (ID: applsci-568114). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are marked in yellow in the paper. The main corrections in the paper and the responds to the associate reviewer comments are as flowing:

1.) In equation 14 you have a plus and minus sign. In the text you state that if the UAV and the vessel are facing each other the plus sign is used and

if the UAV and vessel are facing away from each the minus sign is used. But what happens at the boundary? What happens if the UAV and vessel are moving in the same direction where they are not facing each other nor facing away? Does the equation still work? What do you do?

**Response**: For the UAV landing of this paper, the UAV flight speed vector is the same or opposite to the direction of the ship's navigation speed vector. When the angle between them is less than 90 degrees, it is considered They are in the same direction, and they are considered to be reversed when the angle is between 90 and 180 degrees. 90 degrees is a special case. In this case, the equation is invalid, but the actual situation is a very small probability event, which is beyond the scope of this paper. Agree with the comments of the evaluation experts, and have been revised.

2.) This reference needs to be in the paper "The specific method can refer to the Chinese invention patent (Application number: 2016110212759)."

**Response**: In the line 277 to 282 of the article, "the trajectory IV is out of the scope of this paper." appears, because on the fourth trajectory, the method of guiding the drone to dock with the onboard landing device is based on Autonomous guidance method for machine vision. The specific method can refer to the Chinese invention patent (Application number: 2016110212759).

We would like to express our great appreciation to you and reviewers for comments on our paper. Looking forward to hearing from you.

Thank you and best regards.

Yours sincerely,

author