Dynamics Event-Triggered-Based Time-Varying Bearing Formation Control for UAVs

Round 1

Reviewer 1 Report

The work concerns a control method in a group of UAVs where one UAV is the leader, followed by the rest of the UAVs in a defined formation.  The control considers time-varying speed and bearing. The introduced velocity observer allows the leader-follower data exchange to be reduced to a minimum (the idea of event triggers), which is important in the real world where communication can fail from time to time. The control has been tested successfully in simulation and in so-called HITL simulation

My comments on the work:

1) Please consider placing mathematical deductions in the Appendix. Let only the most important steps and results remain in the main text.

2) Please add units to the all physical quantities, e.g. in lines 464 or 601  the starting positions should include a unit (metres or cm or km, etc.)

3) On line 467 it states: "The control parameters of the controller are selected as". Was there any strategy on how to select these settings? 

4) In line 467, 468, 504 : are the parameters a,k,c dimensionless?

5) It is necessary to add units on all axes in all the plots/figures.

6) Is it ok? (line 622): The simulation results are shown in Figures 21 to 6.26. 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The paper presents a novel dynamic event-triggered bearing-based formation control method for UAVs. It addresses the challenge of controlling UAV formations with time-varying velocities and bearings, employing an event-triggered mechanism to minimize continuous communication, thus conserving communication bandwidth and resources. However, the following concerns need to be addressed before it can be considered for publication.

The following term M_{ij}=\dot{B}_{ij}+a_2B_{ij} presented in (3) is a key component of the formation control. Can you provide a more detailed explanation of how this equality contributes to the formation control?

In the derivation of the formation control law u presented in (42), the authors utilize the derivative of the virtual control law \alpha. It is essential to understand the mathematical assumptions and conditions under which this derivative is available for formation control law. Could you please provide a detailed mathematical justification or a reference to these assumptions in this manuscript?"

While the paper lists its primary contribution on event-trigger strategy, it would benefit from a more detailed comparison with existing solutions. Specifically, how does the proposed dynamic event-triggered mechanism improve upon or differ from traditional event-triggering approaches? Including a table to compare these methods quantitatively could significantly enhance the paper's impact. Moreover, how can Zeno behavior be excluded by deploying the event-triggered mechanism in (14)

I noticed many spelling/grammar mistakes that could potentially distract readers from your main points. For example, Line 171 neigbors, an dynamic event-triggered mechanism, Line 337 condistion, Line 372 Lypunov, Line 567 Follwer 5, Line 569 simuulation, Line 642 triggerd, etc.

Moderate editing of English language required.

Author Response

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Reviewer 3 Report

In this paper, the authors present an event based bearing formation control method for UAV swarm. The idea is to use event-triggered method to reduce communication load, while the formation is the use of bearing formation concept. First, the authors present the background. Second, the authors define the problem of the bearing formation control. Third, the designed formation control is presented with the global convergence. Finally, the simulation  studies are given to show the effectiveness of the proposed method. 

Theoretically speaking, the main contribution is that the event-triggered method can reduce the communication load as well as the analysis of the convergence. 

Technically speaking,  the authors discuss the paper, following the route of the background, defining the problem, analyzing the convergence  and giving the formation control. This is reasonable.

The authors may consider the following points when revising the paper.

1) In the introduction, the authors should discuss the swarm control concept and collision avoidance. You may cite the following papers.

[1]Unmanned Aerial Vehicles (UAVs): Collision Avoidance Systems and Approaches," in IEEE Access, vol. 8, pp. 105139-105155, 2020,

[2]Collision avoidance of multi unmanned aerial vehicles: A review,

Annual Reviews in Control 48, 147-16,2019 

2)At Page 4,line 156, the vehicle dynamics is quite simple.  The authors should discuss this point.

3)At page 4, line 158, the assumption 1, the authors claimed that "this assump- 162 tion is not just a practical necessity". In fact, it is important to consider the internal collision avoidance among formation. Please note that even the convergence is ensured and this does not mean that the collision aovidance is guaranteed. 

4) At page 5, line 230, in Assumption 4,  the leaders follow the reference, not control action. The authors should discuss this point. In fact, the leaders may have the offset when executing the commands.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The Authors have addressed my concerns with the original manuscript. The revised manuscript is ready for publication.

Reviewer 3 Report

This paper presents a formation control. The formation is consisted of leader and followers.  The authors propose a leader-follower maneuver method. Since the formation control is challenging, the authors introduce an event-triggered bearing based distributed velocity observer. In addition, this method is also used for the communication.  The authors give a rigid analysis. The proposed method is also demonstrated by simulation studies. 

In the first round, this reviewer suggested several points. I have checked this version.  The authors have revised the paper following my comments. I am satisfactory at the current version.