Complex Modal Characteristic Analysis of a Tensegrity Robotic Fish’s Body Waves

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

Thanks for the update.

Comments on the Quality of English Language

minor revision needed.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

I read the manuscript and I have the following comments, questions, and suggestions.

My major concern is with the experimental results presented in Figures 7-9. I don't think the fit curves (lines) show anything special about the data. The conclusions based on the fitted curves are not supported by the data. I don't know how the authors have determined those fit curves.  For example, in Figure 7, the authors mention that the steepest decline in velocity is for a driving amplitude of 54 degrees. However, the experimental results do not support it. The only conclusions I can make from Figure 7 is that the velocity for 54 and 63 are almost the same, on average, and larger than that of 45. And the velocity for 45 is larger than that of 36, on average. I really cannot conclude anything from the results for 54 deg in Figures 8 and 9.  I think the authors should reconsider their conclusions made from the experimental data and do a more convincing data analysis.

I also have some minor comments as follows.

1. The abstract is too long and seems more like a conclusion. It also contains some issues. For example, the abbreviation BCF is not defined. (In general, I don't think using abbreviations in the abstract is a good idea.) Or, there are terminology which the reader may not be familiar with and are defined much later in the main text or not defined at all, for example, travelling index.

2. In line 63, the abbreviation COT is defined in the opposite way. It should be cost of Transport (COT), not the other way.

3. In lines 88-89, it is not clear if the authors have developed the robotic fish in the current research or in [43]. Please clarify.

4. In equation (1), "h" is a function of "t". However, there is no "t" in the equation. Please correct.

5. Equations (1) and (2) and lines 129-130, it is not clear where x_f is measured from. Please add a new picture or show it in one of the existing pictures.

6. Line 171, it is not clear what has the abbreviation COV to do with "mean square amplitudes"!

7. In equation (10), the condition number (cond) is not defined. Please define it.

8. Line 366, it is clear what the authors mean by "the Reynolds number of the fluid". How is the Reynolds number defined in this research?

9. The conclusions section is very long. Also, there are lots of detailed information which are not general and are only valid for the specific robot used in this manuscript. I suggest only mention the general conclusions made from the research.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

This manuscript addresses an interesting problem. It is well organized and is clearly written. However, I have some concerns that must be addressed:

1) In the Introduction, you must justify why you use the COD method. Are not other methods to assess the motion waves?. Which are the advantages of using this method?. By the way, perhaps the state of the art could be extended including other motion waves analysis methods and their advantages and disadvantages when approaching the proposed problem.  

2) Figs 7, 8 and 9 plot fitted lines, that only weakly show tendencies, i.e., the fitting indexes seem to below. Then, conclusions derived from them are questionable and have to be better justified.

3) Fig. 10 lacks the fitting curves pointed out in the right side legend. 

4) In Fig. 11, the block "Change the drive amplitude and drive frequency of the servo motor" misses some connections: is not any feedback to this block?, when does it start?, when does it stop?, how is starting/stopping indicated to this block from the results of the operations of the other blocks?, which algorithm do you use to decide the changes of amplitudes and frequencies?. 

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report (New Reviewer)

Comments and Suggestions for Authors

Bingxing Chen et al have introduced a bionic robotic fish with a flexible structure that mimics real fish body waves to generate thrust for undulate propulsion. By analyzing its complex modal characteristics using the COD method, the fish's body wave is broken down into distinct components. Experimental results show similarities between the robotic fish's waves and those of certain fish types. The research highlights a relationship between a "travelling index" and swimming performance, indicating potential for enhancing performance through parameter adjustments in the robotic fish design. The following comments/concerns needs to resolved.

1. There should be atleast three sets of experiments at each frequency with standard deviations so the fitting with be more accurate.

2. There are lot of space throughout the manuscript with spelling errors. Example, In figure 4 and 5 travelling wave in x-axis label is named as 'tranveling Wave and figure 6, y axis label also have spelling error.

 

Comments on the Quality of English Language

Spelling errors needs to resolved in the manuscripts and figures

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

Thank you for answering my questions and revising the manuscript. I don't have any other questions. 

Author Response

Thank you for your recognition and support. In subsequent experiments, we will optimize the design method and experimental results. If you have any other suggestions or need further modifications, please feel free to let me know. Thank you very much for your valuable comments and time.

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

My comments have been adequately addressed. This manuscript can be published.

Author Response

Thank you for your recognition and support. If you have any other suggestions or need further modifications, please feel free to let me know. Thank you very much for your valuable comments and time.

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

Comments and Suggestions for Authors

This work investigated the characterization of a tensegrity robotic fish under vibration excitation. The fish body waves of several different types of fish are analyzed, and the motion is quantitatively described and modeled. Then, different driving strategies are examined and compared with several kinds of fish. Overall, the quality is good and should meet the acceptance criteria after the comments below are appropriately addressed.

·      Reference should be updated with more recent works in the field; most cited work was over ten years ago.

·      Please clarify the head and tail notion in Fig. 1b, even if this information can be derived from the displacement magnitude.

·      An experiment video should be summarized as supplemental material to illustrate better the different experiments conducted in this work.

·      Is the robotic fish fixed at one location? If not, how do the authors resolve the location deviation and distortion caused by the free swimming of the robotic fish in the workspace and the corresponding image projection issue? For example, imaging of the fish near the edge of the photo will have a different size compared with that in the middle of the picture and thus brings variations for the extracted motion magnitudes  

Comments on the Quality of English Language

Minor editing of English language required

Reviewer 2 Report

Comments and Suggestions for Authors

1- It appears that there may be some uncertainty regarding the precise definition of tensegrity and its distinction from cable-driven robotics in your work. 

Notably, there is a lack of historical context for tensegrity robots, an absence of formal formulation, and a dearth of a clear-cut definition.

 

2-Following the computation of the correlation matrix, the problem proceeds to formulate an eigenvalue problem, typically represented as Rv = λv. Here, 'v' denotes a complex orthogonal mode (COM), while 'λ' signifies the corresponding complex orthogonal value. It is crucial to emphasize that the reporting of COMs is integral to ensuring the validity of the results.

 

3-To extract complex modal vectors and their associated complex modal coordinates (COCs), the Complex Orthogonal Decomposition (COD) technique NEED TO BE applied to the displacement ensemble. 

The visualization of COC presents both the real and imaginary components of the corresponding COCs. 

LACKING normalization of complex modes and the evaluation of COC modal energy (the COVs) serve to define the amplitude of the COCs.

 

4-The utilization of the term "travelling index," expressed as α = 1/cond([c, d]), within the context of a fish robot warrants further elucidation. 

Particularly, the rationale behind defining this index as the reciprocal of the condition number between the real and imaginary components necessitates more comprehensive clarification. 

This is particularly pertinent since, in your concluding remarks, a strong negative correlation between swimming velocity and the travelling index is mentioned. 

This index plays a pivotal role in your analysis, yet the formulation and underpinning logic require more detailed exposition.

 

5-There is an intrinsic curiosity regarding the optimization strategy for the travelling index with the objective of emulating the body waves of real fish more effectively. 

Furthermore, it remains unclear how the optimization of this index would substantively enhance the swimming performance of the robotic fish. Elaboration on the optimization methodology and its anticipated impact on performance would be valuable.

 

 

Comments on the Quality of English Language

ATTACHED,