Task-Space Cooperative Tracking Control for Networked Uncalibrated Multiple Euler–Lagrange Systems
Round 1
Reviewer 1 Report
The authors revised a lot since the last version and answered most of the questions from the last round of review. However, some critical issues are still not adequately addressed.
Major issues:
- The most critical issue is that the authors claimed several contributions of this work in the introduction, but the analysis didn't reflect the contributions. For example, the authors mentioned time-varying delays. Where is it modeled in this manuscript?
- Some assumptions don't make sense. If an assumption is given, the authors need to explain why it makes sense if it is not intuitive. For example, in Lines 169-170, the authors assumed the changing rate of delays is not larger than 1. Why this assumption makes sense?
- The writing still needs improvements. The derivations are not well organized, which makes the derivations hard to follow.
- What are the control gains and plots of controls used for each agent? Was saturation considered?
- What are the results of parameter error? It would be great if the critical results were included.
Minor issues:
- There are still a lot of English or formatting mistakes, such as typos, capitalization, space, and numbering.
Author Response
Reply to the Review Report (Reviewer 1)
1.The most critical issue is that the authors claimed several contributions of this work in the introduction, but the analysis didn't reflect the contributions. For example, the authors mentioned time-varying delays. Where is it modeled in this manuscript?
Response: In this paper, when we design the task space cooperative controller, in order to achieve such a goal that all the Euler-Lagrange subsystems asymptotically track a collectively desired task-space trajectory, the gain coefficients of network mutual coupling term() related to the time-delay rate() are included in equation (14), This is one of the key points to ensure the good performance of the system in the presence of time-varying delay.
2.Some assumptions don't make sense. If an assumption is given, the authors need to explain why it makes sense if it is not intuitive. For example, in Lines 169-170, the authors assumed the changing rate of delays is not larger than 1. Why this assumption makes sense?
Response: Although there are inevitably time-varying delays in communication between agents, with the development of modern communication technology, these delays generally change slowly over time, which is why we assume that the rate of change of delay is not greater than one. Of course, when the network communication performance is very poor, the rate of change of delay will also be greater than 1. In this case, we will discuss the control problem in future studies.
3.The writing still needs improvements. The derivations are not well organized, which makes the derivations hard to follow.
Response: We have reorganized the derivation process and optimized the representation. For example, we derive equation (21) again, and give the detailed derivation process.
4.What are the control gains and plots of controls used for each agent? Was saturation considered?
Response: The block diagram of the cooperative controller for the ith Euler-Lagrange subsystem is shown in figure 1, 、 are control gain matrices of the ith Euler-Lagrange subsystem. The output amplitude of the cooperative controller (i.e. the input of the ith Euler-Lagrange subsystem) is limited according to the maximum allowable input of the ith Euler-Lagrange subsystem.
5.What are the results of parameter error? It would be great if the critical results were included.
Response: Figure 6 is supplemented in this paper, which shows the convergence of the estimates of the kinematic parameters when the initial estimates of the kinematic parameters take three different values.
6.Minor issues: There are still a lot of English or formatting mistakes, such as typos, capitalization, space, and numbering.
Response: The deficiencies in English and format in the paper have been carefully revised.
Reviewer 2 Report
This manuscript deals with the issue of tracking control in a networked systems, for which each node/agent is governed by an Euler-Lagrange dynamics. Specifically, the problem of dealing with imperfect communications (including time delays and uncertainties) is addressed by the authors, who introduce a means to overcome the issue by a proper task-space cooperative control strategy.
Overall, the research question is clearly framed and the problem certainly worth investigating from the theoretical and numerical perspectives. The mathematical derivations are sound and the results interesting. I am not sure why part of the text is highlighted in red. Is this manuscript a resubmission?
Beyond the scientific merit of this work, I feel that the authors are ``cutting corners'' in their literature review and analysis of related works (see more details below). Another major issue is the numerical example studied at the very end of the manuscript (again more details about this below). I believe it is imperative that the authors address these two major concerns before this manuscript possibly considered for publication.
Main comments:
* The authors do not do a good job at motivating their research question and work. They should provide more practical and/or concrete examples.
* As briefly alluded to above, the Introduction is too short. Specifically the literature review and report on related works is completely inadequate. There are numerous recent work dealing with this problem. For instance in Komareji et al. "Consensus in topologically interacting swarms under communication constraints and time-delays." Nonlinear Dynamics 93.3 (2018): 1287-1300, the authors present a thorough analysis of the influence of time delays and unreliable communications on control of a networked system.
Similarly, the authors emphasize that little attention has been paid to problems with networked Euler-Lagrange systems. Unfortunately, the authors omit the fact that Tripathy et al. "Robust stabilization of a class of nonlinear systems via aperiodic sensing and actuation." IEEE Access 8 (2020): 157403-157417, have looked at event-triggering data management, which can be considered as more challenging from the control perspective (owing to the fact that an admissible event-triggering law has to be identified). In summary, the authors should provide a more faithful report on the literature related to their problem.
* As stated above, the theoretical results are interesting and sound. Unfortunately, that is far from being the case of the numerical example studied. The authors effectively use a very basic/simple 6-DOF manipulator system. Too few nodes are considered. What is the network topology considered? In my opinion, this numerical example does a disservice to the rest of the paper. The authors should consider a larger system, with a more complex network topology.
Minor comments:
* There are numerous issues with English, including syntax and grammar. I am sure that the authors can address those in their revision.
Author Response
Reply to the Review Report (Reviewer 2)
1. I am not sure why part of the text is highlighted in red. Is this manuscript a resubmission?
Response: Yes, this manuscript is a resubmission.
2.As briefly alluded to above, the Introduction is too short. Specifically the literature review and report on related works is completely inadequate. There are numerous recent work dealing with this problem. For instance in Komareji et al. "Consensus in topologically interacting swarms under communication constraints and time-delays." Nonlinear Dynamics 93.3 (2018): 1287-1300, the authors present a thorough analysis of the influence of time delays and unreliable communications on control of a networked system.
Similarly, the authors emphasize that little attention has been paid to problems with networked Euler-Lagrange systems. Unfortunately, the authors omit the fact that Tripathy et al. "Robust stabilization of a class of nonlinear systems via aperiodic sensing and actuation." IEEE Access 8 (2020): 157403-157417, have looked at event-triggering data management, which can be considered as more challenging from the control perspective (owing to the fact that an admissible event-triggering law has to be identified). In summary, the authors should provide a more faithful report on the literature related to their problem.
Response: The introduction section has been carefully revised, several valuable references have been added, including the two you suggested, and the relevant literature has been reviewed.
3.As stated above, the theoretical results are interesting and sound. Unfortunately, that is far from being the case of the numerical example studied. The authors effectively use a very basic/simple 6-DOF manipulator system. Too few nodes are considered. What is the network topology considered? In my opinion, this numerical example does a disservice to the rest of the paper. The authors should consider a larger system, with a more complex network topology.
Response: Your question is very professional and inspires me a lot. What this paper reports is only the research results of the first stage of this research, which will be verified in the future including more complex networked agent system.
4.The authors do not do a good job at motivating their research question and work. They should provide more practical and/or concrete examples.
Minor comments: here are numerous issues with English, including syntax and grammar. I am sure that the authors can address those in their revision.
Response: Deficiencies in English, grammar and format have been carefully revised.
Round 2
Reviewer 1 Report
The authors have addressed all the concerns properly. I have no further questions.
Reviewer 2 Report
The authors have addressed all my comments and their revised manuscript is now suitable for publication.
