Two-Time-Scale Cooperative UAV Transportation of a Cable-Suspended Load: A Minimal Swing Approach

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper provides substantial derivations and proofs for cooperative transportation problems. The abstract is concise and summarizes the entire text well; the introduction offers detailed background information with extensive references; and the conclusion is comprehensive. However, there are several points worth noting:

1. The dynamic model and controller design do not explicitly incorporate aerodynamic models (such as wind disturbances, gusts, or air resistance directly affecting the UAVs and the load). This simplification aids theoretical derivation but may reduce robustness in real-world environments.
2. The model assumes the cable remains taut at all times (no slack state), which may not hold in practical transportation scenarios. For example, when the load suddenly moves or the UAV accelerates, the cable could become slack, leading to model failure.
3. The load is treated as a point mass, ignoring its actual rotational inertia (such as additional swinging effects from asymmetric loads), which can affect the authenticity of control performance.
4. In the simulation validation, only idealized swing suppression is tested, without considering fault scenarios such as cable slackening or breakage.
5. Some letters in figures are too large. It is suggested to adjust them to be similar in size to the figure titles, such as the letters in Figure 2 and Figure A1.
6. The font sizes of sub-figure labels (e.g., "a)" and "b)" in Figure 1) differ from the main figure title size. These should be unified.
7. The table titles have inconsistent formatting. For instance, Table 2's title ends without a period, while Table 3's title ends with a period. The format should be standardized.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The article presents a modern method of controlling a two-agent system for transporting suspended cargo by drones (UAVs), taking into account swing damping and control of trajectory and formation geometry. The work is characterised by a high level of originality and a strong foundation in existing scientific literature. The research methodology is based on the analysis of elastic disturbances and the concept of two-time-scale dynamics, which allows the vibration damping process to be separated from the trajectory tracking task. 

The manuscript is coherent and logically organised. 
The introductory section (pages 1–3) effectively presents the problem and the context of the research. The methodological section (pages 4–10) is detailed and appropriately illustrated with graphs and diagrams (e.g. Figures 1 and 2 on pages 4–5). The simulations (pages 12–17) are well chosen and adequately compare the proposed method with the classical approach.

The literature used mainly covers works from the last five years, including relevant references to current solutions for model predictive control (MPC) and distributed control (e.g. 
[19]–[22]). There is no excess of references to the authors' own works. The article refers to a wide range of sources from various areas, both theoretical and practical, in the field of UAV applications. 

The control method has been developed on a solid theoretical basis – disturbance analysis, time separation, nonlinear control, singular perturbation theory (Appendix B). 
The physical model takes into account aerodynamic forces and internal cable parameters (pages 6–10), and validation is performed in high-fidelity simulations (MATLAB/Simulink). The presented experimental design appears to be appropriate and comprehensive.

The description of methods and parameters is very detailed. Table 1 on page 10 contains all relevant values. However, the lack of a public code repository may make it difficult to fully replicate the study. The authors stated that the data can be made available upon request (page 21, line 506), which is in line with good practice, although not optimal. 
The figures (Figs. 
4–8, pages 13–16) are clear, well described, and illustrate the reduced angle of deviation and energy consumption. The performance indicators (Tables 2 and 4) clearly show the advantage of the proposed solution. The statistical analysis is mainly based on integral analysis and average values, which is appropriate, although it is worth considering the inclusion of confidence intervals. 
The conclusions (pages 17–18) are consistent with the results presented. 
They highlight the advantages of the method, such as stability, scalability, and low computational cost. They do not contain excessive generalisation.
The authors' declarations are transparent and appropriate.
There are no ethical controversies. The statement on data availability (line 506) meets the basic requirements.

Comments for improvement (with line numbers)
1. No information about the availability of the simulation code – it is recommended to add a link to the repository (e.g. additional material) with the code (line 506).
2.    A clearer description of the limitations of the method is required – especially when assuming ideal position measurements (lines 188–190).
3. The section on the influence of control parameters could include a sensitivity analysis – e.g. with respect to Kx, Kz (pp. 13–14).
4.    The physical limitations of the UAV, e.g. thrust saturation, are not indicated – this should be taken into account when discussing the simulation results (p. 14).
5. Editorial note: typo in equation (1) – the description of rotation should be more explicit about the direction of axis rotation (p. 3, line 122).
6. Clearer separation of test cases – e.g. Test Case 1 and Test Case 2 could be organised into separate subsections (pp. 13–17).
7.    Consider extending the analysis to three-agent cases – currently, the limitation to two UAVs is indicated in the text, but without justification for the limitations of the method (p. 3, line 83).
The article is an important contribution to the field of UAV formation control and payload oscillation suppression. The method based on a two-scale control approach offers a practical and efficient solution for suspended payload transport. Publication is recommended after incorporating the minor corrections and additions indicated.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper addresses an interesting area of study. Below are the review comments for the manuscript.

1. In the introduction section of the paper its is good state briefly how inter-vehicle communication or sensing uncertainties are handled as cooperative control highly depends on information transferring.

 

2. In the remark 2 section. It would be better to clearly indicate the approximate bandwidth ratios (or frequency ranges) assigned with each layer to support the validity of the time-scale separation.

 

3. Paper mentioned the method is “readily extendable to different UAV configurations or to larger formations” in line 410. It is better if authors state whether such scalability depends on symmetrical agent dynamics, communication topology assumptions, or centralized versus decentralized implementations. This will increase the clarity of the paper

 

4. In line 408-409 paper states “The control law depends on only a handful of easily measured parameters and admit a clear physical interpretation”, It is better to discuss briefly how physical parameters such as cable stiffness, vehicle mass influence the gain selection or how singular perturbation theory guides stability analysis. This will enhance the quality of the paper.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have thoroughly addressed all my concerns in their revision. The manuscript now meets the journal's standards, and I endorse its publication.