Review Reports

Round 1

Reviewer 1 Report

This paper deals with the flight formation of UAVs. Particularly, the paper presents a reconfiguration strategy for the UAV formation based on a modified artificial bee ant colony algorithm. Specifically, the method employed is based on posing the reconfiguration problem as an optimal problem to minimize the time consumed for the reconfiguration subject to constraints of safety and connection. Then the optimization is discretized, and finally, the modified artificial bee ant colony is used to solve the minimization. Numerical tests are presented to validate the approach. In my opinion, the paper is well-written, and it has a contribution under the scope of the journal. 

 

Some comments to improve the paper: 

* The literature review should be updated. The last year's work report is required to strengthen the justification of the contribution. Some works that might be worth mentioning: Distributed Observer-based Leader-following Consensus Control for LPV Multi-agent Systems: Application to multiple VTOL-UAVs Formation Control, Icuas; Hybrid swarm intelligent algorithm for multi-UAV formation reconfiguration, Complex and Int Syst; Resilient Formation Reconfiguration for Leader–Follower Multi-UAVs, App Sci. 

* Use \mathcal{R} to denote the real numbers.

* Include in Table 1 the units of the parameters. 

* Can you guarantee that the proposed optimization algorithm will have a response in a finite time? In case there is not enough time to solve the optimization problem can be ensured, how can I ensure that a feasible control input is applied?

* Include the stability analysis of the closed-loop system. Under what conditions is the system stable?

* In plots, put the units in parentheses. For example, in Figure 5a: x (km), y (km), z (km). Please revise all the plots. 

* In Figure 6b, the UAV4 and UAV3 have a thurst of 0 N during a time lap. Is it realistic? 

Minor editing of English language required

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

This paper considered a multi-UAV formation reconfiguration problem. They first discretized the system and then utilized the ABC algorithm to solve the problem. Simulation was used to show the effectiveness of the procedure.

Comments to the authors:

1.    The assumption that d_save=5km, is not realistic for UAVs. Usually in Formation Control and to form the shape in Fig. 5(c) few meters are assumed. See for example the same shapes usually form in the maneuvering of air-force (jet fighter) in expiation.

2.    In the simulation, the authors test their mathematical development only in forming one shape. They should test forming different shapes.

3.    Not all the variables in Equation (13) are defined.

4.    Adjust Equation (16).

5.    How the authors find the penalty constraints σ’s in Equation (17). What is their optimal values?

6.    Equation (8) is in continuous form, while Equation (21) should be in discrete form, but still the time variable “t” is used in both equations.

7.    In Equation (23), are the min and max values of S’ known a priory?

8.    In Algorithm 1, the modification suggested by the authors is not clear. Authors should explain clearly their modification to ABC algorithm.

9.    From Table 2, the terminal state of UAV3 is (0,0,0), but the UAV3 did not reach (0,0,0).

10.                       There are other references on formation controls of UAVs to be added such as:

a.     Formation control of quadrotors via potential field and geometric Techniques

b.    Reinforcement Learning-Based Control Strategy for Multi-Agent Systems Subjected to Actuator Cyberattacks During Affine Formation Maneuvers

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

This manuscript proposes a modified ABC algorithm to find a reconfiguration strategy for UAV formation. Experiment results reveal the feasibility of the proposed method. I suggest accepting this paper after a major revision. My comments are below:

 

1. The superiority of the modified ABC should be verified through some classical benchmark functions. A comparison between ABC and modified ABC performance on classical benchmark functions should be presented.

 

2. How the results in Fig. 4 are obtained? Algorithms such as GA, PSO, and ABC are stochastic and usually run at least 30 times. Are the presented convergence curves from the best result? 

 

3. Have the authors implemented and executed the presented algorithms to solve the problem under consideration? What are the values of the algorithm parameters of GA, PSO, HPSOGA and ABC? 

 

4. Is the comparison between the algorithms fair? Are the algorithms executed for the same number of iterations or the same number of objective function calculations?

Fig. 7b is the Objective function versus iteration cycles with different algorithms in the case of 7 UAVs. How many UAVs are considered in the results in Fig. 4?

 

5. Authors say, "The objective function is designed as (22), where the collision avoidance penalty coefficient σ1, communication connection penalty coefficient σ2, and terminal state penalty coefficient σ3 are set to be large enough to ensure that the whole procedure of the reconfiguration satisfies all the constraints." 

The applied values of the penalty coefficient σ can greatly affect the result. How exactly are they selected? What are their specific values?

It is noteworthy that values important for the repetition of the results are not given.

 

6. The reported results "The solution obtained with our method improves the final objective function nearly 10 times than the ABC and nearly 100 times than the HPSOGA [20]." are impressive, to say the least. Still, a 100x improvement sounds implausible. 

Minor editing of English language required.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I suggest that the annotation regarding system stability be more explicit. Directly mentioning that "the proposed method does not guarantee the closed-loop stability of the system."

Fine.

Reviewer 2 Report

The paper is now better than the previous version.

It can be published.

For better formatting, it is better to split Equations (13) and (16) into two lines each.

Also, I do not know how Table 2 be formatted to be lined with the text.

 

Reviewer 3 Report

All my comments have been taken into account. The paper may be published.