Pectoral Fin-Assisted Braking and Agile Turning: A Biomimetic Approach to Improve Underwater Robot Maneuverability
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
Very interesting paper and novel use of pectoral fins to aid maneuvering. Well written and presented.
Author Response
We appreciate the reviewer's kind feedback for our paper. We have made further enhancements to improve our representation.
Reviewer 2 Report
Comments and Suggestions for Authors
The manuscript studies the integration of a pectoral fin mechanism based on a 4-bar linkage, into a robotic fish. Before publishing the article, I believe that authors should take into account the following:
1) Figure 1 should be positioned immediately after Line 79. Likewise, in the case of figure 2, which should be placed after Line 93
2)I think paragraphs 2.2 and 2.2.1 can be merged. At the beginning of paragraph 2.2 Experimental setup, the authors can provide a brief description in a few lines of the entire experimental setup and then start directly with the summary description of the components used, as it is in 2.2.1 Hardware Setup. Same suggestion for paragraphs 2.3 and 2.3.1
3) The authors refer to a force/torque sensor connected to the fin mechanism via a custom adapter. Where exactly did they connect the sensor? In the extension of the servomotor shaft or in the joint of the effector arm?
4) There is no reference to Figures 4, 5 and 6 in the text of the manuscript. I also believe that these figures should be grouped together and the authors should provide a detailed description of them. What is the purpose of figure 6 and how does it help a better understanding of the system proposed by the authors
5) In paragraph 2.4 the authors mention the use of particle image velocimetry (PIV). Besides the brief description of the whole system, perhaps the authors could also present an image of the experimental setup. Especially since most of the experimental results are based on the use of this system.
6) My opinion is that images (a) through (f) in Figure 7, which represent vortex dynamics, are equally important as the figure that represents the average drag force over time. Which, by the way, is not labeled. I suggest the authors try increasing the size of snapshots (a) to (f). The same suggestion for Figures 8 and 9
Author Response
Comments 1:
The manuscript studies the integration of a pectoral fin mechanism based on a 4-bar linkage, into a robotic fish. Before publishing the article, I believe that authors should take into account the following:
1) Figure 1 should be positioned immediately after Line 79. Likewise, in the case of figure 2, which should be placed after Line 93
Response 1:
We thank the reviewer for this suggestion. In the revised manuscript, the environment for Figure 1 has been moved to immediately follow the sentence ending “…the output angle (θ₂) corresponds to the servo shaft angle (θ₁).” (formerly Line 79). Likewise, Figure 2 now appears immediately after the description of the PIV system in the sentence ending “…a continuous laser sheet and a high-speed camera for selected experiments.” (formerly Line 93). All figure numbering and cross-references have been updated accordingly.
Comments 2:
I think paragraphs 2.2 and 2.2.1 can be merged. At the beginning of paragraph 2.2 Experimental setup, the authors can provide a brief description in a few lines of the entire experimental setup and then start directly with the summary description of the components used, as it is in 2.2.1 Hardware Setup. Same suggestion for paragraphs 2.3 and 2.3.1
Response 2:
We concur and have reorganized the manuscript to improve flow. Paragraphs 2.2 (“Experimental Setup”) and 2.2.1 (“Hardware Setup”) have been merged into a single subsection (now titled “2.2 Experimental Setup”) that begins with a concise overview of the full apparatus, followed seamlessly by the detailed hardware description. Similarly, Sections 2.3 and 2.3.1 have been combined into “2.3 Static Behavior under Constant Flow Conditions,” which opens with a brief description of the static‐flow experiments and then proceeds directly into the discussion of force measurements.
Comments 3:The authors refer to a force/torque sensor connected to the fin mechanism via a custom adapter. Where exactly did they connect the sensor? In the extension of the servomotor shaft or in the joint of the effector arm?
Response 3:
We apologize for the lack of clarity. The six-axis force/torque sensor is mounted directly on the servo motor’s output shaft via our custom 3D printed adapter; the fin attaches to the opposite face of this adapter. This configuration preserves the full rotational freedom of the servo shaft. A photograph of the assembled adapter-sensor-fin interface has been added to supplementary material.
Comments 4:
There is no reference to Figures 4, 5 and 6 in the text of the manuscript. I also believe that these figures should be grouped together and the authors should provide a detailed description of them. What is the purpose of figure 6 and how does it help a better understanding of the system proposed by the authors
Response 4:
Thank you for pointing this out. We have now cited Figures 4–6 in the new Section 2.4 and 2.5, grouping them for coherence. The added text reads:
“Figure 4 presents these measurements as two-dimensional heat maps over the parameter space... Figure 5 presents the raw drag (X) and lift (Y) time-series measured during pectoral fin deployment to 80° in a steady 0.3 m/s flow... Figure 6 shows contour maps of these four quantities plotted versus final fin angle (60–110°) and ramp duration (0.2–2.0 s)...”
Each figure is now described in detail in the main text to aid reader comprehension.
Comments 5:
In paragraph 2.4 the authors mention the use of particle image velocimetry (PIV). Besides the brief description of the whole system, perhaps the authors could also present an image of the experimental setup. Especially since most of the experimental results are based on the use of this system.
Response 5:
We sincerely thank the reviewer for the valuable suggestion to include an image of the Particle Image Velocimetry (PIV) experimental setup. We agree that visual documentation of the system enhances methodological transparency, especially given its pivotal role in generating the core flow field data presented in this study.
In the original manuscript, Figure 2A already provides a schematic diagram illustrating the working plane and simplified operational principles of the PIV system. To further address the reviewer's request, we are submitting two supplemental photographs with this revision to visually document the system implementation:
Response 5 Figure 1: A photograph of the fully assembled PIV system within the experimental facility under normal lighting conditions.
Figure 1
Response 5 Figure 2: An operational photograph captured in low-light conditions, demonstrating the laser sheet illuminating the measurement plane and tracer particles ( hollow glass spheres).
Figure 2
Additionally, we include two supplementary videos:
Extra supplementary video A(FinPIV1.mp4): A video showcasing the integration of the PIV system with the fish fin dynamic platform.
Extra supplementary video B(FinPIV2.mp4): A recording of the PIV system during active data acquisition.
These additions collectively provide a comprehensive visual reference for the experimental methodology, reinforcing the robustness and reproducibility of our PIV-based flow measurements.
6) My opinion is that images (a) through (f) in Figure 7, which represent vortex dynamics, are equally important as the figure that represents the average drag force over time. Which, by the way, is not labeled. I suggest the authors try increasing the size of snapshots (a) to (f). The same suggestion for Figures 8 and 9
We sincerely appreciate the reviewer’s insightful suggestions regarding the visual presentation of vortex dynamics in Figures 7–9. We agree that the instantaneous flow snapshots (subfigures a–f) are equally critical to the time-averaged drag force plot for interpreting transient fluid-structure interactions.
In response:
Enlarged vortex snapshots: The dimensions of subfigures (a)–(f) in Figures 7, 8, and 9 have been uniformly increased to enhance the visibility of vortex shedding patterns.
Added label for drag force plot: The previously unlabeled time-averaged drag plot in Figure 7 is now explicitly designated as " the average drag force over time with corresponding minimum and maximum ranges " (revised Figure 7(g)).
Reviewer 3 Report
Comments and Suggestions for Authors
Please note the following observations:
- Clarify the choice of a single degree of freedom (1-DOF) design for the pectoral fin, including the technological and biological reasoning that justifies this simplification.
- Describe in detail the four-parallelogram bar actuator mechanism and how it allows the fins to be repositioned without affecting the robot's center of gravity.
- Explain how the optimal values for the fin angle were determined in order to maximize braking force and maneuverability.
- Provide a justification for the choice of the three deceleration times (0.2 s, 1.0 s, and 2.0 s) and their impact on vortex dynamics and hydrodynamic forces.
- Detail the methodology for using the particle image velocimetry (PIV) system, including the characteristics of the camera, laser, and image processing procedure.
- To present the selection criteria of the control parameters (angle, frequency, amplitude, duration) and how they influence the robot performance in static and dynamic regimes.
- To comparatively analyze the influence of fast, moderate and slow deceleration on the traction force and the stability of the vortices in the flow field.
- To explain the correlation between the waveforms generated by PIV and the variations of the braking force over time, in all three deceleration scenarios.
- To demonstrate how the use of pectoral fins in asynchronous regime leads to a reduction in the turning radius and to improved robot maneuverability.
- To clarify the methodology for measuring forces with the six-axis sensor and the synchronization mode with the robot controls.
- To present the impact of implementing optimal parameters on the robot performance in free swimming regime, with emphasis on the transition between the propulsion and braking phases.
- To evaluate the limit of the current design (rigidity, lack of adaptability) and the potential for integrating adaptive materials or intelligent control.
- To discuss the possibility of integrating a hybrid propulsion strategy (pectoral fins + tail) to increase the stability and speed of the robot.
- To identify the advantages and disadvantages of applying biomimetic principles compared to classic underwater propulsion systems.
- To justify the choice of a controlled hydraulic channel test model over testing in natural environments.
Author Response
Comments 1:
Clarify the choice of a single degree of freedom (1-DOF) design for the pectoral fin, including the technological and biological reasoning that justifies this simplification.
Response 1:
We thank the reviewer for this insightful comment. We deliberately adopted a 1-DOF fin design to minimize both hardware cost and control complexity. Fully waterproof servomotors suitable for underwater use remain comparatively large and heavy, so adding extra rotational axes would substantially increase system weight and power consumption. Biologically, many fish brake by a simple abduction/adduction of the pectoral fins, rotating them forward in a single plane to generate drag, while sharp turns arise from an asymmetric one-axis rotation of the outside fin (Drucker & Lauder 2002). Even in rapid burst-braking, trout fins pivot about their base as the principal axis, with finer deformations playing a secondary role (Lauder & Drucker 2004; Higham et al. 2005). These studies show that a single-hinge motion captures the dominant force component in both braking and turning, justifying our 1-DOF fin approach.
Higham, T.E. et al. (2005). J. Exp. Biol. 208: 4391-4405 – Constraints on starting and stopping: behavior compensates for reduced pectoral fin area during braking of the bluegill sunfish Lepomis macrochirus
Drucker, E.G. & Lauder, G.V. (2002). J. Exp. Biol. 205: 2397-2409 – Wake dynamics and locomotor function in fishes: interpreting evolutionary patterns in pectoral fin design
Lauder, G.V. & Drucker, E.G. (2004). IEEE J. Oceanic Eng. 29(3): 556-571 – Morphology and experimental hydrodynamics of fish fin control surfaces
We also added these to the introduction section of the updated manuscript.
Comments 2:
Describe in detail the four-parallelogram bar actuator mechanism and how it allows the fins to be repositioned without affecting the robot's center of gravity.
Response 2:
We thank the reviewer for requesting deeper mechanical detail. Our actuator uses a four-bar parallelogram linkage constructed from 3D-printed PLA (density ≈ 1.25 g/cm³), which net buoyancy in water is nearly neutral. By mounting the servomotor at the vehicle’s center of mass, and extending the parallelogram linkage forward, we can place the fin up to 20 cm ahead of the motor’s center of gravity without shifting the overall center of mass in the submerged robot. This arrangement preserves dynamic stability regardless of fin deployment angle, since the heavy motor stays fixed at the geometric center of gravity.
We have added this description to updated section “Design and Construction of the Servo Pectoral Fin Mechanism”.
Comments 3:
Explain how the optimal values for the fin angle were determined in order to maximize braking force and maneuverability.
Response 3:
We thank the reviewer for highlighting this key experimental procedure. We conducted a systematic sweep of fin angles from 0° to 180° in 5° increments. Using our six-axis force/torque sensor, we independently extracted drag (X-axis) and lift (Y-axis) components at each angle. The optimum braking angle was then chosen based on the peak drag force, with maneuverability trade-offs evaluated via the lift component.
Detailed explanations have been updated in “Static Behavior of the Pectoral Fin under Constant Flow Conditions”.
Comments 4:
Provide a justification for the choice of the three deceleration times (0.2 s, 1.0 s, and 2.0 s) and their impact on vortex dynamics and hydrodynamic forces.
Response 4:
We thank the reviewer for this request. The 0.2 s ramp represents the fastest safe deceleration: beyond this, the servo stalls or skips steps, corrupting the commanded trajectory. The 2.0 s ramp is the slowest that avoids perceptible jitter (PWM switching noise appears at longer ramps due to low-speed torque ripple). The intermediate 1.0 s case provides a mid‐point for parametric comparison.
The subsection “Vortex Dynamics of Pectoral Fin Deceleration under Constant Flow: Deceleration Rate Effects” has been updated with a clearer explanation.
Comments 5:
Detail the methodology for using the particle image velocimetry (PIV) system, including the characteristics of the camera, laser, and image processing procedure.
Response 5:
We thank the reviewer for requesting methodological details. The PIV system specifications are summarized as follows:
Camera: Photron CCD (1280×1024 px, 105 fps, 532 nm optical filter).
Laser: Continuous 532 nm laser (10 W), 2 mm-thick light sheet.
Processing: Multi-pass cross-correlation (25×25 px windows), sub-pixel Gaussian fitting, phase-averaging over 13 bins.
The updated detail has been added to the PIV section.
Comments 6:
To present the selection criteria of the control parameters (angle, frequency, amplitude, duration) and how they influence the robot performance in static and dynamic regimes.
Response 6:
We thank the reviewer for this suggestion. All parameter ranges were dictated by actuator mechanical limits (maximum torque and travel). We plotted the average combined force as our primary thrust metric, and the RMS normal force as a consistency/stability metric. The control parameters are picked based on the consideration of both machine limits and the data clarity. We wanted to pick a region where the optimum values are visible and can be transferred to real environments. We also performed the experiment in a controlled hydraulic channel with 0.15m/s and 0.3m/s flow settings. This is to simulate a dynamic stop from those swim speeds. Because the control code runs on the same microcontroller in both benchtop tests and the final robotic fish, the selected settings transfer directly from test bench to our robotic fish. We have updated section “Experimental Setup” to help clarify these.
Comments 7:
To comparatively analyze the influence of fast, moderate and slow deceleration on the traction force and the stability of the vortices in the flow field.
Response 7:
We sincerely appreciate your insightful query on deceleration effects. Our manuscript explicitly addresses traction force and vortex stability across deceleration rates in Section 2.5 (Figures 5–9) . Key findings include:
Fast deceleration (0.2 s) induces intense vortex shedding, causing a high traction force peak (∼12 N) and chaotic wake turbulence due to abrupt vortex detachment, as captured in Figure 7(a)–(f).
Moderate deceleration (1.0 s) yields coherent vortices with controlled detachment, reducing traction force peaks to ∼7 N and stabilizing wake patterns into periodic vortex streets Figure 8(a)–(f).
Slow deceleration (2.0 s) minimizes vortex intensity, enabling smooth traction convergence (∼3 N peak) and symmetric, low-turbulence wakes through quasi- static diffusion Figure 9(a)–(f).
Comments 8:
To explain the correlation between the waveforms generated by PIV and the variations of the braking force over time, in all three deceleration scenarios.
Response 8:
We thank the reviewer for raising this point. In Sections 2.5.1-2.5.4 (Figures 7–9) , we explicitly establish the correlation between PIV-derived vortex dynamics and braking force (drag) variations for all deceleration scenarios:
Rapid deceleration (0.2 s) : High-intensity vortices induce abrupt pressure gradients, aligning with the 12 N drag spike and subsequent oscillations due to chaotic vortex detachment (Fig. 7(a)-(f), Fig. 5).
Moderate deceleration (1.0 s) : Coherent vortex merging yields gradual pressure modulation, reducing the peak drag to 7 N with damped fluctuations as vortices shed periodically (Fig. 8(a)-(f), Fig. 5).
Slow deceleration (2.0 s) : Diffuse vortices decay via quasi-static diffusion, generating minimal pressure changes and a smooth 3 N drag peak with near-stable equilibrium (Fig. 9(a)-(f), Fig. 5).
As summarized in Section 2.5.6, braking force transients are directly governed by vortex intensity (peak force magnitude) and shedding stability (force oscillation damping). This causality is empirically validated through time-synchronized PIV and force measurements.
Comments 9:
To demonstrate how the use of pectoral fins in asynchronous regime leads to a reduction in the turning radius and to improved robot maneuverability.
Response 9:
We thank the reviewer for highlighting the importance of maneuverability in asynchronous fin operation. In the previous version of the manuscript, we focused primarily on the fin’s ability to generate drag and reduce stopping distance. In response to your suggestion, we have conducted additional turning experiments and found that asynchronous deployment of the pectoral fins reduces the minimum turning radius from 0.47 m to 0.23 m, a greater than 50% improvement. These new results, along with representative trajectory plots, have been added to the updated Supplementary Material.
Comments 10:
To clarify the methodology for measuring forces with the six-axis sensor and the synchronization mode with the robot controls.
Response 10:
We thank the reviewer for asking for synchronization details. The ATI Gamma US-15-50 six-axis sensor was affixed to the fin’s servo assembly via a custom PLA 3D-printed mount. The sensor’s Z-axis aligns with fin pitch (up–down), X with the flow/drag direction, and Y with lift (normal to flow). Data are synchronized by a Python script that simultaneously issues serial triggers to the NI DAQ and to the microcontroller’s servo commands; all timestamps are recorded in the resulting CSV log.
We have updated figure 2 and its description to better explain our experimental setup.
Comments 11:
To present the impact of implementing optimal parameters on the robot performance in free swimming regime, with emphasis on the transition between the propulsion and braking phases.
Response 11:
We thank the reviewer for this interest in system-level performance. Our control architecture treats pectoral fins and the tail fin as separate subsystems, allowing independent mode transitions (e.g. retracted → braking → propulsion). For braking, the controller transitions the pectoral fins from “glide” (0°) to “brake” (80°) over the selected deceleration ramp, while pausing tail undulation. These subsystems run with each of their own time intervals to avoid interference. As shown in Fig. 10, deploying the pectoral fins as speed brakes reduced stopping time and distance by ~50 % compared to unpowered gliding. Deceleration-profile plots (top-right of Fig. 10) show markedly steeper slopes for fin brakes versus glide; the bottom panels illustrate our “fin-assisted turn,” achieving the minimal turning radius via combined propulsion/braking.
The subsection “Free Swimming Performance” has been updated with a more detailed description.
Comments 12:
To evaluate the limit of the current design (rigidity, lack of adaptability) and the potential for integrating adaptive materials or intelligent control.
Response 12:
We thank the reviewer for encouraging discussion of future directions. We acknowledge that PLA printed components limit rigidity and fatigue life under repeated loading. In future iterations we plan to integrate carbon fiber reinforced composites for improved stiffness-to-weight ratios, and to embed flex-sensor elements for closed-loop feedback. We will also explore machine learning based control such as Gaussian process regression to adaptively tune stroke amplitude in response to real-time force measurements.
We updated the discussion section to reflect these changes.
Comments 13:
To discuss the possibility of integrating a hybrid propulsion strategy (pectoral fins + tail) to increase the stability and speed of the robot.
Response 13:
We thank the reviewer for this valuable suggestion. Combining pectoral braking/lift with caudal thrust can yield both high-speed cruising and agile maneuvering. Implementing this hybrid scheme will require a multi-axis force platform and synchronized actuation of both fin sets. We have added this discussion in the manuscript’s Discussion section, but have limited the current study to pectoral fins for clarity and scope control.
Comments 14:
To identify the advantages and disadvantages of applying biomimetic principles compared to classic underwater propulsion systems.
Response 14:
We thank the reviewer for prompting this comparison. Biomimetic fin actuation delivers multifunctional control: thrust, braking, and lateral forces from a single DOF motor, enabling smooth transitions between modes with minimal hardware. It also generates lower acoustic signatures compared to miniature propellers. However, propellers maintain higher propulsive efficiencies for steady cruising and are less sensitive to manufacturing tolerances. We have expanded the Discussion to weigh these tradeoffs quantitatively.
Comments 15:
To justify the choice of a controlled hydraulic channel test model over testing in natural environments.
Response 15:
We thank the reviewer for raising this point. A laboratory-scale hydraulic channel provides precise flow speed and turbulence control, allowing us to isolate individual variables and collect reproducible, high-resolution force and PIV data. Field tests introduce many uncontrollable factors (currents, waves, debris) that would obscure fundamental hydrodynamic mechanisms. We therefore performed all experiments in the channel first and will validate in open-water trials in follow-on studies. We have edited and clarified this in the updated section 2.2 Experimental Setup near the end.
Round 2
Reviewer 2 Report
Comments and Suggestions for Authors
The authors have modified the content of the manuscript according to the recommendations made previously. Therefore, I have no further comments.
Reviewer 3 Report
Comments and Suggestions for Authors
I agree with the new form.
