Model-Based Control Allocation During State Transitions of a Variable Recruitment Fluidic Artificial Muscle Bundle

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper contributes to controlling variable recruitment FAM bundles by introducing a model-based approach that mitigates recruitment lag and resistive force effects. The proposed method improves tracking accuracy and actuation efficiency by integrating hydraulic dynamics better than conventional pressure threshold-based control. The following raised comments should be considered to clarify the paper's contributions. 

1. The paper focuses on the control algorithm of FAM and hydraulic system as a MU. So, the authors should rewrite the Introduction section, which provides a literature review of MU's control schemes and control algorithms, with each paragraph related to the typical control scheme, etc. The literature review on the modeling of FAM also needs to be investigated and discussed in this section.

2. System modeling

• I can find the equation (1) in the reference [37]. Please clarify how the authors obtained (1) from the model in [37]. Besides, the model in [37] is the pneumatic muscles, the muscles in the research are hydraulic. The dynamic behavior of pneumatic muscle differs from that of hydraulic. The author must clarify that. In addition, F_ideal and F_mesh must be explained what they mean.
• The relationship between the single FAM model (1) and the Hydraulic system in subsection 2.2.
• An example hydraulic system simulation should be moved to section 2.2 for easy following. How is the Δt_lag modeled? We can not find it from equation (5) to (8). Please clarify.
• The revised manuscript must include experiments to verify the system modeling and obtain the model parameters.

3. Experiment setup and results

• How are the signals collected and processed? For example, sampling time, is any filter used?
• Do the authors do experiments with the pressure compensation only? How about the results in that scenario?

4. Typos and presentation

- Provide a Table of Abbreviations.

- Figures 3 and 6. Include the caption for subfigure (c)

- References

• Reference number [41]: Wrong Doi
• The authors need to update the recent three-year papers about the control and model of artificial muscle, for example.

1. Phan, Phuoc Thien, et al. "Twisting and braiding fluid-driven soft artificial muscle fibers for robotic applications." Soft Robotics 9.4 (2022): 820-836.
2. Hou, Wenhao, Jiao Wang, and Jiu‐an Lv. "Bioinspired liquid crystalline spinning enables scalable fabrication of high‐performing fibrous artificial muscles." Advanced Materials 35.16 (2023): 2211800.
3. Duong, Minh-Duc, et al. "Adaptive fuzzy sliding mode control of an actuator powered by two opposing pneumatic artificial muscles." Scientific Reports 13.1 (2023): 8242.
4. J. Ma, Y. Wang, J. Sun, Z. Yang, Liquid Crystal Elastomer Hollow Fibers as Artificial Muscles with Large and Rapid Actuation Enabled by Thermal-Pneumatic Enhanced Effect. Adv. Funct. Mater. 2024, 34, 2402403.
5. Nguyen, Viet-Thanh, et al. "Sliding mode control of antagonistically coupled pneumatic artificial muscles using radial basis neural network function." SN Applied Sciences 5.9 (2023): 246.
6. Kim, Jeong Yong, and Matthew Bryant. "Electrohydraulic system analysis of variable recruitment fluidic artificial muscle bundles with interaction effects." Journal of Dynamic Systems, Measurement, and Control 146.3 (2024).

Author Response

The response has been added as a Word document.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper presents a theoretically developed controller, confirmed by experiments, which significantly reduces the integrated maximum and absolute control errors of a bundle of fluid artificial muscles (FAM) with variable recruitment. A model of the transitions between the states of the FAM bundles, which are grouped in parallel similar to skeletal muscles, is used. The possibility of operating the FAM in its entire contraction space with improved control and bandwidth at low recruitment states is created. The developed model of the hydraulic system captures the effects of interaction between FAMs and informs the controller when a state transition should be made. The effectiveness of the controller is evaluated by comparing the average and maximum deformation errors of a basic controller.
The paper is written in a good scientific style and contains all the necessary structural units. The cited reference literature is sufficient in number and completely exhaustive.
I have some remarks to the article, which will require minor revisions:

1. In formula (1) for the force F_mesh it is not clear what meaning it has and it would be good to clarify this in terms of meaning, despite the mention of the mesh force on line 115.
2. In formula (2) it is not clear what the quantities V and L represent.
3. In formula (4) it would be better to give a description of the quantities Fc and ε_c .
4. In Figure 2, I think there are also many undescribed variables or parameters.
5. In formula  (14) 𝜀_{𝑚𝑒𝑎𝑠} dot needs clarification on whether the point is differentiation with respect to time.
6. In my opinion, overall, the article lacks some explanations in the formulas and graphs, and for this reason, the authors should pay a little more attention to the description of the symbols in them.

Author Response

The response has been added as a Word document.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Authors have addressed all the issues I raised, and the revised manuscript shows significant improvement. I recommend accepting the paper for publication in Actuators.

However, please note that Figures 11, 12, and 13 should be reformatted for better readability. For example, two images could be presented side by side, or the four images could be arranged in a 2×2 layout to make the figures easier to follow.