Formation Tracking Control for Multi-Agent Systems with Collision Avoidance and Connectivity Maintenance

Round 1

Reviewer 1 Report (Previous Reviewer 1)

1)   The authors incorporate all my comments except comment number 7. All the terms in Equation (18) should have the same units, although mathematically correct with the understanding that there is a constant k with unity and correct units. In the first reference the authors mentioned and followed, the mistake appeared. So I suggest to the authors to add ki with value of 1 and correct units. Then later they delete it for simplicity.

2)   In remark 14, the confidentiality of providing the Simulink figure should be mentioned in a footnote such that the reader will not spend time of thinking how it comes.

Author Response

Please see attached response. Thank you!

Author Response File: Author Response.docx

Reviewer 2 Report (Previous Reviewer 2)

The authors have taken into account all my suggestions.

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report (Previous Reviewer 3)

Thank you for taking into account my suggestions, only to precise:

Response (3)

In the first draft paper I received, line 346 starts with (a>0). One provides the any position of p_1^*.... This statment must be revised.

Response (5)

Please discuss this claim in the paper in order to support the selection of a double integrator model for this work

aditionally,

There are some odd characters on eqs (1) and (2) on revised draft, I don´t know if its due the platform but check if it prints like \dot{x} in the final version 

Author Response

Please see attached response. Thank you!

Author Response File: Author Response.docx

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

See the attached file.

Comments for author File: Comments.pdf

Author Response

Please see attached response, thank you!

Author Response File: Author Response.docx

Reviewer 2 Report

The article addresses the formation tracking problem, collision avoidance, and connectivity for a multi-agent system composed of second-order agents. The topic considered in this paper has already been widely studied, and therefore the contribution of this paper is insufficient. Even though the article is well documented and the theoretical results seem to be right, there are some issues that the authors should be clarified.

1.  The agents' dynamics appear very simple, with just a second-order model. The current literature addresses a more challenging framework, with high-order dynamics.

2. I do not understand equation (17), why e_i=e_j? If that is so, therefore in (18) e_i-e_j=0 and the first term will disappear.

3. The authors need to check for grammar and some writing errors and do not use contractions (e.g. didn´t, closest, more simple)

4. For Theorem 3 part 1, you have stated that "agents' velocities approach the velocity of the virtual leader asymptotically", therefore, v1=v2=...v3 only will be true if time tends to infinity. Please verify.

5. It is well-known that when using potential functions for collision avoidance, undesired equilibrium points appeared. Please give an analysis of the undesired equilibrium points and how can you avoid them.

6. For the first simulation, the initial conditions of the agents do not effectively display the collision avoidance part. Please propose initial conditions where agents have to cross paths.

7. Simulation 2 adds nothing to the article. Instead, I encouraged the authors to give a comparison with another collision avoidance approach and justify the use of your approach.

8. Please cite the following reference where the collision avoidance and formation control are achieved for a group of quadrotors using an innovative approach based on repulsive vector fields

Jaime González-Sierra, Alejandro Dzul & Héctor Ríos (2019) Robust sliding-mode formation control and collision avoidance via repulsive vector fields for a group of Quad-Rotors, International Journal of Systems Science, 50:7, 1483-1500, DOI: 10.1080/00207721.2019.1616128

Author Response

Please see attached response, thank you!

Author Response File: Author Response.docx

Reviewer 3 Report

Your solution to the problem is sound, combining trajectory tracking, collision avoidance and connectivity maintenance, the group can behave as stated in Reynolds rules for flocking. However, doble integrator dynamics are widely studied and there are plenty solutions that can cope this problem.

Center Figure 2, also the agents’ labels are unaligned, see label of Agent 1 in Figure 2b, is not complete.

Connectivity maintenance relies on that R is big enough that always there is at least one sensed robot, do you have a potential solution to navigate an isolated robot? I mean something like the observer strategy that are you proposing for the virtual leader tracking.

Review grammar of sentence in line 346

Proof of theorem 3: there is a missing space between the word part and the number in each part of the proof.

I suggest that you include another simulation with a nonlinear agent, such a rigid body spacecraft, a UAV or a Wheeled Mobile robot. There are some control strategies in the literature that can transform these agents to a doble integrator behavior, please see: 

 Oriolo, G., de Luca, A., & Vendittelli, M. (2002). Wmr control via dynamic feedback linearization: Wrm control via dynamic feedback linearization: design implementation and experiments. IEEE Transactions on Control Systems Technology, 10(6), 835-852.

 Pliego-Jiménez, J., Martínez-Clark, R., Cruz-Hernández, C., & Arellano-Delgado, A. (2021). Trajectory tracking of wheeled mobile robots using only Cartesian position measurements. Automatica, 133, 109756.

Round 2

Reviewer 2 Report

I still have doubts about experiment 4.2. Of course, if no potential term is added for collision avoidance, therefore, the agents will collide. Please give a comparison between your approach and another methodology to determine the advantages of your approach. Moreover, cite [31] is mispelled.

Author Response

Please see attached response letter.

Author Response File: Author Response.docx

Round 3

Reviewer 2 Report

What I am only asking you is to compare your approach (only the collision avoidance approach) with other existing techniques to avoid collisions.