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REVIEW 4 major objections 5 minor 86 references

SpineWave: Harnessing Fish Rigid-Flexible Spinal Kinematics for Enhancing Biomimetic Robotic Locomotion

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A robotic fish with a passive magnetic spine and evolutionary gait tuning swims 38 percent faster and completes a 360-degree turn in 10 seconds.

desk verdict A genuinely new modular biomimetic fish platform, but the headline performance gains rest on single unreplicated measurements; treat them as suggestive until replicates and error bars appear. read the letter →

arxiv 2505.16453 v1 pith:VSNO5XL3 submitted 2025-05-22 cs.RO cs.SYeess.SY

Qu He , Weikun Li , Guangmin Dai , Hao Chen , Qimeng Liu , Xiaoqing Tian , Jie You , Weicheng Cui
show 2 more authors
Michael S. Triantafyllou Dixia Fan
This is my paper · ORCID
classification cs.ROcs.SYeess.SY
keywords biomimeticroboticfishrigid-flexiblespinemagneticexoskeletoncentralpatterngeneratorefficientglobaloptimizationunderwaterroboticsbio-inspiredlocomotionfieldvalidation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

SpineWave is a modular robotic fish whose rigid servo-driven spine is wrapped in a passive magnetic exoskeleton, with ribcage magnets arranged to repel one another and act like muscle springs. The paper's central claim is that this rigid-flexible combination maintains a stable undulatory body wave, and that tuning the CPG gait parameters with a surrogate-based evolutionary optimizer (EGO) produces large, measurable gains: speed rises from 0.32 to 0.44 body lengths per second (38%), a 360-degree turn drops from 23 to 10 seconds, and the turning radius falls by 35%. If correct, this shows that a hybrid rigid-flexible magnetic spine plus data-efficient black-box optimization can give biomimetic robots the maneuverability and endurance needed for field tasks such as environmental monitoring. The same platform was reconfigured into three fish body plans and validated in open water, including an 800-meter swim and dives to 4.2 meters in a marine environment.

What carries the argument

The load-bearing mechanism is the magnetic ribcage exoskeleton: each ribcage holds eight neodymium magnets arranged so opposing poles repel, creating a passive magnetic spring around each servo-driven joint, mimicking the stretch-and-recoil of fish muscle. The second half is the EGO optimizer: a Kriging surrogate model of the hydrodynamic objective is built from a handful of real six-axis force-sensor trials, and the next CPG parameter set is chosen by maximizing expected improvement, so the gait is tuned with minimal additional experiments. The CPG model itself, with coupled nonlinear oscillators, supplies the rhythmic joint commands that the optimizer shapes.

What would settle it

Run the same optimized gait on the robot in free swimming with the magnetic exoskeleton and with equal-mass steel balls; if speed and body-wave amplitude stability do not favor the magnetic version under identical CPG parameters, the exoskeleton's claimed contribution is not supported. Separately, measure joint angles in water with a camera or inertial sensors and compare them with the quasi-static simulation; disagreement at working frequencies would falsify the model that the stability claim rests on.

Watch

Extended reading notes

Core claim

The central discovery is that a fish-like rigid-flexible transition—a rigid internal skeleton of actively actuated segments coupled to a passive exoskeleton of repelling magnets—keeps the body wave smooth and symmetric under cyclic loading, while an equal-weight non-magnetic module moves chaotically with larger, offset amplitude. On this base, Efficient Global Optimization with a Kriging surrogate maps a seven-parameter CPG control space to hydrodynamic objectives (mean thrust, torque, and turning moment) using a small number of physical experiments. After optimization the robot's straight-line speed increased from 0.32 to 0.44 BL/s, its 360-degree turn time fell from 23 to 10 seconds, and its turning radius was cut by 35%; the authors read these results as evidence that the magnetic spine provides stability and that the optimized gait transfers from stationary force measurements to free swimming.

Load-bearing premise

The claimed benefit of the magnetic exoskeleton assumes that replacing the magnets with equal-weight steel balls is a fair control and that the quasi-static magnetic-force simulation represents what happens when the robot moves through water, since the authors state that predicting passive joint angles in water remains future work.

Editorial extensions

If this is right

  • Passive magnetic joints can provide the stabilizing body flexibility that purely rigid or purely soft fish robots achieve only with more complex active or material-based solutions.
  • EGO-style surrogate optimization is sufficient to improve swimming speed and turning performance with tens of experiments rather than thousands, making real-robot gait tuning practical.
  • A single modular spine can be reconfigured to mimic thunniform, subcarangiform, and anguilliform swimming, so performance gains should transfer across body plans.
  • Field-tested endurance (800 m in 50 minutes, dives to 4.2 m) makes the platform usable for environmental monitoring and close-range observation of wildlife without disturbance.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the magnetic-exoskeleton stability effect generalizes to other speeds and body sizes, replacing fixed magnets with tunable electromagnets should let one robot adjust its body stiffness in the field, trading speed for maneuverability as a mission requires.
  • A stronger test of the exoskeleton's contribution than the current bench comparison would be a free-swimming A/B test with the optimized gait run once with magnets and once with equal-mass steel balls; the magnetic version should be faster or more stable under identical CPG parameters.
  • The claim that quasi-static magnetic-force simulation predicts wet behavior is the softest link, since joint angles in water remain unmeasured; a direct underwater joint-angle measurement at typical tail-beat frequencies would settle whether the stability advantage is real under load.
  • The same EGO-plus-Kriging pipeline could be applied to other expensive black-box problems in robotics, including aerial or legged platforms where physical trials are costly.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper describes SpineWave, a modular biomimetic robotic fish whose body combines a servo-driven rigid endoskeleton with a passive magnetic exoskeleton intended to emulate the rigid-flexible spine of fish. A seven-parameter central pattern generator (CPG) is tuned by an efficient global optimization (EGO) procedure using stationary force-sensor experiments, and the optimized parameters are then applied to free swimming. The reported outcomes are an increase in straight-line speed from 0.32 to 0.44 BL/s (38%), a reduction in 360-degree turn time from 23 s to 10 s, and a 35% reduction in turning radius. The paper also demonstrates three modular body configurations (thunniform, subcarangiform, anguilliform) and reports open-water endurance and diving trials.

Significance. If the performance gains survive replication, SpineWave would be a valuable testbed: the modular spine hardware, the use of passive magnetic constraints, and the closed-loop EGO workflow are all potentially useful for the biomimetic underwater robotics community. The paper makes its controller and optimizer equations explicit, and the open-water demonstrations (800 m endurance swim, 2 km cumulative diving, unperturbed wildlife interaction) give qualitative evidence of robustness and acceptability. However, the central quantitative claims currently rest on single unreplicated measurements with no statistical analysis, so the significance of the headline improvements cannot be assessed from the manuscript as written.

major comments (4)
  1. [Results, Close water swimming performance] The 38% speed gain, the reduction in 360-degree turn time from 23 s to 10 s, and the 35% turning-radius reduction are reported as single values with no number of trials, standard deviations, confidence intervals, or statistical tests. The baseline is one parameter set selected as the best of 50 random samples, and the optimized value is likewise a single outcome of a noisy physical process that includes battery state, water currents, teleoperation, and starting conditions. Because these three numbers are the entire evidence for the paper's headline claim of significant improvements, repeated trials and an appropriate statistical comparison are required before that claim can be accepted; please also report the raw trajectories or per-trial measurements.
  2. [Evolutionary optimization for hydrodynamics] The optimization is performed on a stationary force-sensor rig (Fig. 5B) and then transferred to free swimming, but the free-swim validation is the same unreplicated comparison discussed above. Because EGO is an optimizer, any improvement over a baseline on the training objective is expected by construction; the paper should therefore present the closed-water results as a demonstration of the optimization workflow, not as an independent prediction of SpineWave's performance. To support the transfer claim, the authors should report force-sensor measurement uncertainty, the number of EGO trials evaluated, and repeated free-swim measurements with the optimized parameters.
  3. [Results, Magnetically constrained bionic exoskeleton] The magnetic-exoskeleton stability advantage is supported only by qualitative deformation snapshots and amplitude traces (Figs. 3C.1 and 3C.2) without quantitative uncertainty or replicate counts, and the authors explicitly state that predicting passive joint angles in water is a future goal. Consequently, the claim that magnetic constraints provide stability under actual swimming loads is not yet demonstrated; the equal-mass steel-ball control addresses mass distribution, but the comparison needs quantitative metrics such as amplitude variance over multiple cycles and multiple trials, and ideally measurements in water.
  4. [Materials and Methods, Efficient global optimization] The EGO presentation contains inconsistencies that prevent reproducibility: Algorithm 1 initializes the database with 'LHS with 10Dim' but enters the while loop with '5Dim' although the CPG has seven parameters; Eq. (5) has a bracket mismatch; and Eq. (13) defines EI for minimization while the thrust objective is maximized. These should be corrected, and the seven optimized CPG parameters should be explicitly listed with their bounds.
minor comments (5)
  1. [Fig. 4 and general text] The label 'Thuniform' should read 'Thunniform'; elsewhere 'ultilizes', 'Notedly', and 'donates' are typographical errors, and 'IEEEASME' in the references should be 'IEEE/ASME'.
  2. [Materials and Methods, Central pattern generators control method] In Eq. (1), the coupling coefficients h and j are introduced but their values or tuning procedure are not given; please specify them or state explicitly that they are constants with particular values.
  3. [Algorithm 1] The pseudocode mentions crossover and mutation probabilities for a genetic algorithm used in the infill criterion, but that GA is not described; please add a brief description or a citation so that the procedure is reproducible.
  4. [Results, Open water human-robot interaction] The open-water endurance (800 m in 50 min) and the dive statistics over eight dives are also single-session reports; a table with the number of runs, durations, and environmental conditions would make the robustness claims checkable.
  5. [Data and materials availability] The data availability statement says all data are in the paper or the Supplementary Materials, but the closed-water performance data are not shown as raw values; please deposit trajectories, force-sensor log files, and trial counts in a repository.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: EGO is an openly fitted optimizer, and the reported speed/turn gains come from separate free-swim trials rather than from the optimized objective.

full rationale

The paper's central quantitative claims are experimental before/after comparisons. The EGO routine is explicitly a fitting procedure: CPG parameters are optimized against force-sensor measurements of thrust and torque ('Objectives varied by flow conditions: for straight-line swimming... we aimed to maximize positive mean thrust'), and the headline improvements (0.32 to 0.44 BL/s, 360-degree turn from 23 to 10 s, turning radius reduced by 35%) are reported from separate free-swimming trials in the 'Close water swimming performance' section. Because the free-swim speed and turning metrics are not the optimized objective and are not reconstructed from the Kriging surrogate, the comparison is not circular: the optimized parameters could have failed to transfer to free swimming. The magnetic-exoskeleton validation likewise compares a forward kinematic model built on declared magnet parameters and frame dimensions to experimental bending angles (Fig. 3B), not a fit of the target angles. The authors explicitly acknowledge that predicting passive joint angles in water remains a future goal, which further limits the claim rather than making it circular. Self-citations (refs. 16 and 86) support background context and a standard Kriging formula, but the EGO formulation is also attributed to Jones et al. (ref. 58); no load-bearing premise depends on an unverified self-citation. The absence of error bars and single unreplicated measurements is a legitimate statistical and correctness concern, but it is not a circularity: no equation or fitted parameter is renamed as an independent prediction.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central performance claims rest on the EGO-fitted CPG parameters and on the untested assumption that the quasi-static magnetic model captures underwater behavior. The ledger counts the fitted parameters and domain assumptions; no new physical entities are introduced.

free parameters (2)
  • 7 CPG gait parameters = not reported in main text
    EGO tuned these to maximize mean thrust (straight swimming), minimize thrust and torque (side flow), achieve near-zero thrust (vortex), or maximize torque (turning). The reported speed and turning improvements are the result of this fit.
  • Kriging/Gaussian process hyperparameters theta_k = estimated by maximum likelihood (Eq. 11)
    These determine the surrogate predictions and the expected-improvement acquisition points; they are estimated from the same experimental data used to claim convergence, so they are internal to the optimization rather than independent.
assumptions (4)
  • domain assumption The quasi-static magnetic repulsion model accurately predicts exoskeleton joint angles and stability in water.
    Invoked in Magnetically constrained bionic exoskeleton, where simulations are said to match experiments; the authors note that full dynamic simulation was not done and that predicting passive joint angles in water is a future goal.
  • domain assumption The 7-parameter CPG model is sufficiently expressive to capture relevant swimming dynamics for optimization.
    The optimization searches only within this parameterization (Results, Evolutionary optimization); if the family excludes beneficial gaits, the reported optimum is conditional on this choice.
  • domain assumption The robot platform, especially the magnetic exoskeleton, adequately represents fish rigid-flexible musculoskeletal mechanics.
    Stated in the Introduction and Discussion; this is the biomimetic premise of the design and is not validated against fish biomechanics data.
  • standard math Kriging surrogate assumptions (stationary Gaussian process, chosen correlation function) hold for the hydrodynamic objectives.
    Equations (4)-(7) rely on standard Gaussian process regression; the validity of these assumptions for thrust and torque surfaces is assumed, not tested with held-out data.

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Cite this review

Pith. "Pith review of SpineWave: Harnessing Fish Rigid-Flexible Spinal Kinematics for Enhancing Biomimetic Robotic Locomotion." pith.science (2026). https://pith.science/paper/VSNO5XL3

@misc{pith2026250516453,
  author       = {Pith},
  title        = {Pith review of: SpineWave: Harnessing Fish Rigid-Flexible Spinal Kinematics for Enhancing Biomimetic Robotic Locomotion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VSNO5XL3}},
  note         = {Machine review of arXiv:2505.16453}
}
read the original abstract

Fish have endured millions of years of evolution, and their distinct rigid-flexible body structures offer inspiration for overcoming challenges in underwater robotics, such as limited mobility, high energy consumption, and adaptability. This paper introduces SpineWave, a biomimetic robotic fish featuring a fish-spine-like rigid-flexible transition structure. The structure integrates expandable fishbone-like ribs and adjustable magnets, mimicking the stretch and recoil of fish muscles to balance rigidity and flexibility. In addition, we employed an evolutionary algorithm to optimize the hydrodynamics of the robot, achieving significant improvements in swimming performance. Real-world tests demonstrated robustness and potential for environmental monitoring, underwater exploration, and industrial inspection. These tests established SpineWave as a transformative platform for aquatic robotics.

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Works this paper leans on

86 extracted references · 80 canonical work pages

  1. [1]

    & Williams, G

    Singh, H., Maksym, T., Wilkinson, J. & Williams, G. Inexpensive, small AUVs for studying ice- covered polar environments. Sci. Robot. 2, eaan4809 (2017)

    2017

  2. [2]

    Masmitja, I. et al. Mobile robotic platforms for the acoustic tracking of deep-sea demersal fishery resources. Sci. Robot. 5, eabc3701 (2020)

    2020

  3. [3]

    Neira, J. et al. Review on unmanned underwater robotics, structure designs, materials, sensors, actuators, and navigation control. J. Robot. 2021, 5542920 (2021)

    2021

  4. [4]

    He, Y., Wang, D. B. & Ali, Z. A. A review of different designs and control models of remotely operated underwater vehicle. Meas. Control 53, 1561–1570 (2020)

    2020

  5. [5]

    Fish, F. E. Advantages of aquatic animals as models for bio-inspired drones over present AUV technology. Bioinspir. Biomim. 15, 25001 (2020)

    2020

  6. [6]

    & Reznick, D

    Langerhans, B. & Reznick, D. Ecology and Evolution of Swimming Performance in Fishes: Predicting Evolution with Biomechanics. Fish Locomot. Etho-Ecol. Perspect. (2009)

    2009

  7. [7]

    Putnam, N. H. et al. The amphioxus genome and the evolution of the chordate karyotype. Nature 453, 1064–1071 (2008)

    work page 2008

  8. [8]

    & Zhang, J

    Alben, S., Shelley, M. & Zhang, J. Drag reduction through self-similar bending of a flexible body. Nature 420, 479–481 (2002)

    work page 2002

Show all 86 references
  1. [9]

    & Li, C.-W

    Chen, J.-Y., Huang, D.-Y. & Li, C.-W. An early Cambrian craniate-like chordate. Nature 402, 518– 522 (1999)

    1999

  2. [10]

    Fetcho, J. R. The Spinal Motor System in Early Vertebrates and Some of Its Evolutionary Changes. Brain. Behav. Evol. 40, 82–97 (2008)

    2008

  3. [11]

    The Macroevolutionary History of Bony Fishes: A Paleontological View

    Friedman, M. The Macroevolutionary History of Bony Fishes: A Paleontological View. Annu. Rev. Ecol. Evol. Syst. 53, 353–377 (2022)

    2022

  4. [12]

    Sfakiotakis, M., Lane, D. M. & Davies, J. B. C. Review of fish swimming modes for aquatic locomotion. IEEE J. Ocean. Eng. 24, 237–252 (1999)

    1999

  5. [13]

    P., Triantafyllou, M

    Maertens, A. P., Triantafyllou, M. S. & Yue, D. K. P. Efficiency of fish propulsion. Bioinspir. Biomim. 10, 046013 (2015)

    2015

  6. [14]

    & Hale, M

    Domenici, P. & Hale, M. E. Escape responses of fish: a review of the diversity in motor control, kinematics and behaviour. J. Exp. Biol. 222, jeb166009 (2019)

    2019

  7. [15]

    Li, T. et al. Fast-moving soft electronic fish. Sci. Adv. 3, e1602045 (2017)

    2017

  8. [16]

    K., Chen, H., Cui, W

    Li, W. K., Chen, H., Cui, W. C., Song, C. H. & Chen, L. K. Multi-objective evolutionary design of central pattern generator network for biomimetic robotic fish. Complex Intell. Syst. 9, 1707–1727 (2023)

    2023

  9. [17]

    & Wen, L

    Liang, J., Wang, T. & Wen, L. Development of a two‐joint robotic fish for real‐world exploration. J. Field Robot. 28, 70–79 (2011)

    2011

  10. [18]

    Struebig, K. et al. Design and development of the efficient anguilliform swimming robot— MAR. Bioinspir. Biomim. 15, 035001 (2020)

    2020

  11. [19]

    & Ijspeert, A

    Crespi, A., Karakasiliotis, K., Guignard, A. & Ijspeert, A. J. Salamandra Robotica II: An Amphibious Robot to Study Salamander-Like Swimming and Walking Gaits. IEEE Trans. Robot. 29, 308–320 (2013)

    2013

  12. [20]

    Clapham, R. J. & Hu, H. iSplash: Realizing Fast Carangiform Swimming to Outperform a Real Fish. in Robot Fish (eds. Du, R., Li, Z., Youcef-Toumi, K. & Valdivia Y Alvarado, P.) 193–218 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2015). doi:10.1007/978-3-662-46870-8_7

    2015 doi

  13. [21]

    Clapham, R. J. & Hu, H. iSplash-I: High performance swimming motion of a carangiform robotic fish with full-body coordination. in 2014 IEEE International Conference on Robotics and Automation (ICRA) 322–327 (2014). doi:10.1109/ICRA.2014.6906629

    2014

  14. [22]

    & Ijspeert, A

    Bayat, B., Crespi, A. & Ijspeert, A. Envirobot: A bio-inspired environmental monitoring platform. in 2016 IEEE/OES Autonomous Underwater Vehicles (AUV) 381–386 (IEEE, Tokyo, Japan, 2016). doi:10.1109/AUV.2016.7778700

    2016

  15. [23]

    & Romano, D

    Manduca, G., Santaera, G., Dario, P., Stefanini, C. & Romano, D. Underactuated robotic fish control: Maneuverability and adaptability through proprioceptive feedback. in Biomimetic and Biohybrid Systems (eds. Meder, F., Hunt, A., Margheri, L., Mura, A. & Mazzolai, B.) 231–243 ...

    2023 doi

  16. [24]

    & Wang, C

    Zhong, Y., Wang, Q., Yang, J. & Wang, C. Design, modeling, and experiment of underactuated flexible gliding robotic fish. IEEEASME Trans. Mechatron. 29, 2266–2276 (2024)

    2024

  17. [25]

    & Stefanini, C

    Romano, D., Wahi, A., Miraglia, M. & Stefanini, C. Development of a novel underactuated robotic fish with magnetic transmission system. Machines 10, 755 (2022)

    2022

  18. [26]

    Zhong, Y., Li, Z. & Du, R. A novel robot fish with wire-driven active body and compliant tail. IEEEASME Trans. Mechatron. 22, 1633–1643 (2017). Page 15 of 17

    2017

  19. [27]

    Stefanini, C. et al. A novel autonomous, bioinspired swimming robot developed by neuroscientists and bioengineers. Bioinspir. Biomim. 7, 25001 (2012)

    2012

  20. [28]

    & Wang, Y

    Lin, X., Liu, X. & Wang, Y. Learning agile swimming: an end-to-end approach without CPGs. IEEE Robot. Autom. Lett. 10, 1992–1999 (2025)

    2025

  21. [29]

    Hao, Y. et al. Bioinspired closed-loop CPG-based control of a robotic manta for autonomous swimming. J. Bionic Eng. 21, 177–191 (2024)

    2024

  22. [30]

    & Ren, L

    Liu, S., Liu, C., Wei, G., Ren, L. & Ren, L. Design, modeling, and optimization of hydraulically powered double-joint soft robotic fish. IEEE Trans. Robot. 41, 1211–1223 (2025)

    2025

  23. [31]

    & Deng, X

    Kodati, P., Hinkle, J., Winn, A. & Deng, X. Microautonomous Robotic Ostraciiform (MARCO): Hydrodynamics, Design, and Fabrication. IEEE Trans. Robot. 24, 105–117 (2008)

    2008

  24. [32]

    & Yang, J

    Zhang, S., Qian, Y., Liao, P., Qin, F. & Yang, J. Design and Control of an Agile Robotic Fish With Integrative Biomimetic Mechanisms. IEEEASME Trans. Mechatron. 21, 1846–1857 (2016)

    2016

  25. [33]

    D., Onal, C

    Marchese, A. D., Onal, C. D. & Rus, D. Autonomous Soft Robotic Fish Capable of Escape Maneuvers Using Fluidic Elastomer Actuators. Soft Robot. 1, 75–87 (2014)

    2014

  26. [34]

    Nguyen, D. Q. & Ho, V. A. Anguilliform Swimming Performance of an Eel-Inspired Soft Robot. Soft Robot. 9, 425–439 (2022)

    2022

  27. [35]

    Li, G. et al. Self-powered soft robot in the Mariana Trench. Nature 591, 66–71 (2021)

    2021

  28. [36]

    K., DelPreto, J., MacCurdy, R

    Katzschmann, R. K., DelPreto, J., MacCurdy, R. & Rus, D. Exploration of underwater life with an acoustically controlled soft robotic fish. Sci. Robot. 3, eaar3449 (2018)

    2018

  29. [37]

    Breier, J. A. et al. Revealing ocean-scale biochemical structure with a deep-diving vertical profiling autonomous vehicle. Sci. Robot. 5, eabc7104 (2020)

    2020

  30. [38]

    Yoerger, D. R. et al. A hybrid underwater robot for multidisciplinary investigation of the ocean twilight zone. Sci. Robot. 6, eabe1901 (2021)

    2021

  31. [39]

    Tolkoff, S. W. Robotics and power measurements of the RoboTuna. (Massachusetts Institute of Technology, 1999)

    1999

  32. [40]

    & Abdelkefi, A

    Salazar, R., Fuentes, V. & Abdelkefi, A. Classification of biological and bioinspired aquatic systems: A review. Ocean Eng. 148, 75–114 (2018)

    2018

  33. [41]

    & Zhang, J

    Yu, J., Wang, M., Su, Z., Tan, M. & Zhang, J. Dynamic modeling of a CPG-governed multijoint robotic fish. Adv. Robot. 27, 275–285 (2013)

    2013

  34. [42]

    Liao, X., Zhou, C., Zou, Q., Wang, J. & Lu, B. Dynamic modeling and performance analysis for a wire-driven elastic robotic fish. IEEE Robot. Autom. Lett. 7, 11174–11181 (2022)

    2022

  35. [43]

    & Tan, M

    Lu, B., Zhou, C., Wang, J., Zhang, Z. & Tan, M. Toward swimming speed optimization of a multi- flexible robotic fish with low cost of transport. IEEE Trans. Autom. Sci. Eng. 21, 2804–2815 (2024)

    2024

  36. [44]

    Svendsen, M. B. S. et al. Maximum swimming speeds of sailfish and three other large marine predatory fish species based on muscle contraction time and stride length: a myth revisited. Biol. Open 5, 1415–1419 (2016)

    2016

  37. [45]

    Webb, P. W. The effect of size on the fast-start performance of rainbow trout salmo gairdneri, and a consideration of piscivorous predator-prey interactions. J. Exp. Biol. 65, 157–178 (1976)

    1976

  38. [46]

    Green, A. et al. Evidence of long-distance coastal sea migration of atlantic salmon, salmo salar, smolts from northwest England (river derwent). Anim. Biotelemetry 10, 3 (2022)

    2022

  39. [47]

    K., Lawelle, S

    Pangerang, U. K., Lawelle, S. A., Fekri, L., Idris, M. & Marthen, J. L. Diversity of eel (glass eel) based on morphometric measurements in the konaweha river, southeast sulawesi. in 495–501 (Atlantis Press, 2022). doi:10.2991/absr.k.220309.095

    2022 doi

  40. [48]

    How and why do flying fish fly? Rev

    Davenport, J. How and why do flying fish fly? Rev. Fish Biol. Fish. 4, 184–214 (1994)

    1994

  41. [49]

    & Tolley, M

    Rus, D. & Tolley, M. T. Design, fabrication and control of soft robots. Nature 521, 467–475 (2015)

    2015

  42. [50]

    & Barrientos, A

    Rossi, C., Colorado, J., Coral, W. & Barrientos, A. Bending continuous structures with SMAs: a novel robotic fish design. Bioinspir. Biomim. 6, 045005 (2011)

    2011

  43. [51]

    & Choi, S

    Li, Y., Chen, Y., Ren, T., Li, Y. & Choi, S. hong. Precharged Pneumatic Soft Actuators and Their Applications to Untethered Soft Robots. Soft Robot. 5, 567–575 (2018)

    2018

  44. [52]

    Lauder, G. V. & Drucker, E. G. Morphology and experimental hydrodynamics of fish fin control surfaces. IEEE J. Ocean. Eng. 29, 556–571 (2004)

    2004

  45. [53]

    Low, K. H. & Chong, C. W. Parametric study of the swimming performance of a fish robot propelled by a flexible caudal fin. Bioinspir. Biomim. 5, 046002 (2010)

    2010

  46. [54]

    Park, Y.-J. et al. Kinematic Condition for Maximizing the Thrust of a Robotic Fish Using a Compliant Caudal Fin. IEEE Trans. Robot. 28, 1216–1227 (2012)

    2012

  47. [55]

    M., Sepulveda, C

    Donley, J. M., Sepulveda, C. A., Konstantinidis, P., Gemballa, S. & Shadwick, R. E. Convergent evolution in mechanical design of lamnid sharks and tunas. Nature 429, 61–65 (2004)

    2004

  48. [56]

    Spierts, I. L. Y. & Leeuwen, J. L. V. Kinematics and muscle dynamics of C- and S-starts of carp (Cyprinus carpio L.). J. Exp. Biol. 202, 393–406 (1999). Page 16 of 17

    1999

  49. [57]

    J., Crespi, A., Ryczko, D

    Ijspeert, A. J., Crespi, A., Ryczko, D. & Cabelguen, J.-M. From Swimming to Walking with a Salamander Robot Driven by a Spinal Cord Model. Science 315, 1416–1420 (2007)

    2007

  50. [58]

    R., Schonlau, M

    Jones, D. R., Schonlau, M. & Welch, W. J. Efficient Global Optimization of Expensive Black-Box Functions. J. Glob. Optim. 13, 455–492 (1998)

    1998

  51. [59]

    Liao, J. C. A review of fish swimming mechanics and behaviour in altered flows. Philos. Trans. R. Soc. B Biol. Sci. 362, 1973–1993 (2007)

    2007

  52. [60]

    Hinch, S. G. et al. Dead fish swimming: a review of research on the early migration and high premature mortality in adult Fraser River sockeye salmon Oncorhynchus nerka. J. Fish Biol. 81, 576–599 (2012)

    2012

  53. [61]

    & Trianni, V

    Dorigo, M., Theraulaz, G. & Trianni, V. Reflections on the future of swarm robotics. Sci. Robot. 5, eabe4385 (2020)

    2020

  54. [62]

    & Sitti, M

    Wang, T., Ren, Z., Hu, W., Li, M. & Sitti, M. Effect of body stiffness distribution on larval fish–like efficient undulatory swimming. Sci. Adv. 7, eabf7364 (2021)

    2021

  55. [63]

    Fluid Structure Interaction II: Modelling, Simulation, Optimization. vol. 73 (Springer, Berlin, Heidelberg, 2010)

    2010

  56. [64]

    Pu, H. et al. Multi-layer electromagnetic spring with tunable negative stiffness for semi-active vibration isolation. Mech. Syst. Signal Process. 121, 942–960 (2019)

    2019

  57. [65]

    Kurumaya, S. et al. A Modular Soft Robotic Wrist for Underwater Manipulation. Soft Robot. 5, 399– 409 (2018)

    2018

  58. [66]

    Zhang, Q. M. et al. An all-organic composite actuator material with a high dielectric constant. Nature 419, 284–287 (2002)

    2002

  59. [67]

    Zhong, Q. et al. Tunable stiffness enables fast and efficient swimming in fish-like robots. Sci. Robot. 6, eabe4088 (2021)

    2021

  60. [68]

    Underwater robots: a review of technologies and applications

    Bogue, R. Underwater robots: a review of technologies and applications. Ind. Robot Int. J. 42, 186– 191 (2015)

    2015

  61. [69]

    Cygan, D. F. & McNallan, M. J. Corrosion of NdFeB permanent magnets in humid environments at temperatures up to 150°C. J. Magn. Magn. Mater. 139, 131–138 (1995)

    1995

  62. [70]

    H., JR, Hale, M

    Long, J. H., JR, Hale, M. E., Mchenry, M. J. & Westneat, M. W. Functions of Fish Skin: Flexural Stiffness and Steady Swimming of Longnose Gar Lepisosteus Osseus. J. Exp. Biol. 199, 2139–2151 (1996)

    1996

  63. [71]

    Zhang, Y. et al. Modulus adaptive lubricating prototype inspired by instant muscle hardening mechanism of catfish skin. Nat. Commun. 13, 377 (2022)

    2022

  64. [72]

    & Lauder, G

    Oeffner, J. & Lauder, G. V. The hydrodynamic function of shark skin and two biomimetic applications. J. Exp. Biol. 215, 785–795 (2012)

    2012

  65. [73]

    & Bleckmann, H

    Engelmann, J., Hanke, W., Mogdans, J. & Bleckmann, H. Hydrodynamic stimuli and the fish lateral line. Nature 408, 51–52 (2000)

    2000

  66. [74]

    & Shi, G

    Liu, Q., Chen, J., Li, Y. & Shi, G. High-Performance Strain Sensors with Fish-Scale-Like Graphene- Sensing Layers for Full-Range Detection of Human Motions. ACS Nano 10, 7901–7906 (2016)

    2016

  67. [75]

    Wang, W. et al. Neuromorphic sensorimotor loop embodied by monolithically integrated, low-voltage, soft e-skin. Science 380, 735–742 (2023)

    2023

  68. [76]

    & Breithaupt, T

    Pohlmann, K., Atema, J. & Breithaupt, T. The importance of the lateral line in nocturnal predation of piscivorous catfish. J. Exp. Biol. 207, 2971–2978 (2004)

    2004

  69. [77]

    Smart Skins: Information Processing by Lateral Line Flow Sensors

    Coombs, S. Smart Skins: Information Processing by Lateral Line Flow Sensors. Auton. Robots 11, 255–261 (2001)

    2001

  70. [78]

    N., Hover, F

    Beal, D. N., Hover, F. S., Triantafyllou, M. S., Liao, J. C. & Lauder, G. V. Passive propulsion in vortex wakes. J. Fluid Mech. 549, 385–402 (2006)

    2006

  71. [79]

    Wen, L., Weaver, J. C. & Lauder, G. V. Biomimetic shark skin: design, fabrication and hydrodynamic function. J. Exp. Biol. 217, 1656–1666 (2014)

    2014

  72. [80]

    Lei, B. et al. Bayesian optimization with adaptive surrogate models for automated experimental design. Npj Comput. Mater. 7, 1–12 (2021)

    2021

  73. [81]

    & Cai, J

    Liu, H., Ong, Y.-S., Shen, X. & Cai, J. When Gaussian Process Meets Big Data: A Review of Scalable GPs. IEEE Trans. Neural Netw. Learn. Syst. 31, 4405–4423 (2020)

    2020

  74. [82]

    & Ding, F

    Liu, J., Zhao, Y., Lei, F. & Ding, F. Net-HDMR Metamodeling Method for High-Dimensional Problems. J. Mech. Des. 145, (2023)

    2023

  75. [83]

    & Ganguli, S

    Poole, B., Lahiri, S., Raghu, M., Sohl-Dickstein, J. & Ganguli, S. Exponential expressivity in deep neural networks through transient chaos. in Advances in Neural Information Processing Systems vol. 29 (Curran Associates, Inc., 2016)

    2016

  76. [84]

    Ibarz, J. et al. How to train your robot with deep reinforcement learning: lessons we have learned. Int. J. Robot. Res. 40, 698–721 (2021). Page 17 of 17

    2021

  77. [85]

    Kiran, B. R. et al. Deep Reinforcement Learning for Autonomous Driving: A Survey. IEEE Trans. Intell. Transp. Syst. 23, 4909–4926 (2022)

    2022

  78. [86]

    & Liu, Q

    Chen, H., Li, W., Cui, W. & Liu, Q. A pointwise ensemble of surrogates with adaptive function and heuristic formulation. Struct. Multidiscip. Optim. 65, 113 (2022). Acknowledgments We thank Boai Sun, Fei Han, Xinyu Zeng, Zhen Yang, and Anqi Zhang for their contributions. Fundi...

    2022

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.