Nonlinear Disturbance Observer-Based Bearing-Only Unmanned Aerial Vehicle Formation Control

Round 1

Reviewer 1 Report

This paper investigates a nonlinear formation tracking only bearing control for UAV systems with uncertainty and perturbations, based on a perturbation observer. The distributed control strategy used in this study uses only relative information about the bearing of neighboring UAVs. To solve the problems of unknown perturbations and system uncertainty, a new nonlinear perturbation observer is proposed that effectively mitigates their effects. In addition, the problem of unknown controller orientation arising from controller singularities is solved by introducing a low-pass Butterworth filter that converts the unknown controller gain function to a constant value of 1. Subsequently, a directional-only shaping tracking controller is developed using a reverse-pitch control approach. The stability of closed-loop control systems is rigorously proved using Lyapunov theory. Finally, numerical simulations are performed to confirm the effectiveness of the proposed scheme in achieving the formation control objectives.

Comments:

1) Line 164: What is "u"?

2) Assumption 2: If we are talking about a safe distance, but it is guaranteed that the coordinates of the objects do not match, which means zero distance. How is this consistent?

3) Line 284: At the end of the proof, the arrow shows that the bearing errors tend to zero, but all that is really proved is that the trajectories tend to a closed bounded set.

4) In the simulation it is not clear what models of UAVs are used. Also the graphics are of very poor quality. For example, Figures 5c show practically nothing changing, after a short transient, but shows a zero plot over a very long time interval.

 

 

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

I have the following comments and recommendations to the paper:

—Title and Abstract: Although the abbreviation UAV is well-known, it could be defined in Abstract. (It is defined further in Introduction.)

—Maybe the reason why the Butterworth filter (and no other type) has been used can be mentioned in Abstract.

—Line 56: What does it mean "almost global convergence". (I am a bit sceptical to such formulations...)

—Line 67: You could recommend some general reference to the multiagent systems.

—Lines 84 through 102: The novel approaches are well defined. Again, the presence of Butterworth filter should be explained. (Why not another type of filter?)

—A note to notations (after line 112): There is a small difference between the scalar and vector symbols (scalar R and vector R). Maybe you can emphasize vectors a bit. (LaTeX has a better possibilities with the symbols...)

—Line 115: The symbols V and epsilon are located below the line. (Really, for future papers, you should use LaTeX instead of Word...)

—Line 122: The symbol m is well above the line. Really, typing the equations is not good...

—Line 126: Terrible location of the equation with the sum. More and more typing problems, it will be a LOT of work to repair it.

—System model of SAV (after line 113): It is quite difficult to read, lots of symbols and formulae. I recommend appropriate structuring the first long paragraph, etc.

—Line 135: The symbol of transposing (T) should be written in Roman letters (it is not a variable).

—Lemma 1, Remark 1, etc.: Maybe some of this could be located in an appendix.

—Line 161: Wrong transposition symbol, again.

—Line 176: Butterworth: Again, why especially this type of filter. (Why not a Tchebyschev filter?)

—Line 211: Probably wrong word "theirs". (their?)

—Line 225: Lyapunov... it is necessary to include a citation what it is generally.

—Line 243: Again, the transposition symbol...

—Line 259: The MDPI standard is Figure 1 (not "fig 1")

—Line 270: "diag" is a function, so it should be written by Roman letters.

—Line 345: "figures 5": Please use a better formulation like "graphs in Figure 5", e.g.

—Figures 4 and 5: The letters in graphs are very small. Please use full page width to enhance the size of the figures. (The MDPI template enables to use wide figures.)

—Figures 6, 7, and 7: The same cases, why you don't use the full page width for the graph?

—Conclusion: OK

—References: The number of references (32) is appropriate, and there are many new ones, e.g., from the year 2022. (And even two ones from the year 2023.)

Generally, the paper is very well structured as described in the lines 103 through 109. From the theoretical (mathematical point of view), the paper is well founded, and the novelty is clear, and needs only minor revision from this point of view. However, the equations and figures were not prepared well, and the paper needs major revision to improve typing the equations and graphs.

I have found only a very small number of errors. (English seems OK to me.)

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Authors have revised the manusript according to comments