Abstract
A biomimetic robotic fish tailored for environmental monitoring and hydrographic exploration is examined in this study. Traditional fish robots, driven by tail oscillations, often grapple with constrained maneuverability in a single plane. This article focuses on mitigating these limitations through an exploration of the dynamic behavior of a bioinspired soft robotic fish. Unlike prior designs that employed similar actuators for the robot's tail, which either lacked the ability for out-of-plane motion or relied on other propulsion systems, the single propulsion design proposed in our model enables movement along three-dimensional trajectories, leading to improved efficiency and maneuverability due to tail oscillation dynamics. The proposed design integrates strategically positioned nozzles for out-of-plane movements, alongside parallel fluid channels on the tail's neutral plate. Actuation is achieved by manipulating the internal fluid pressure within these channels. To precisely model tail deflection, we introduce a novel method utilizing Euler–Bernoulli beam theory considering nonlinear characteristics arising from internal fluid stress. For instance, following the proposed approximate analytical method, we optimize the fluidic actuator, considering that the soft tail deformation increases by 65% as the channel shape transitions from a semicircular to a square cross-section. The comprehensive comparison with analytical nonlinear method, finite element method, and experimental-driven analytical method extends our approach as an effective tool in terms of accuracy and computation time, demonstrating the effectiveness of validation processes. This study unveils a simplified and robust fish robot design, outperforming traditional mechanisms in efficacy. Despite its simplicity, the proposed design delivers comparable performance, presenting an effective alternative for achieving requisite functionality in fish robots.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
Data Availability
The data presented in this study are available on request from the corresponding author. The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
Abbreviations
- \(l\) :
-
SFA channel- total length
- \({l}_{c}\) :
-
SFA—length of one channel
- \(h\) :
-
Tail thickness
- \({b}_{s}\) :
-
Tail width
- \(f(\text{X},\text{T})\) :
-
External distributed force
- \(w\) :
-
Tail- transverse displacement
- \({U}_{c}\), \({V}_{c}\),\({W}_{c}\) :
-
Fluid velocity—channel’s coordinates
- \(P\) :
-
Fluid pressure
- \(A\) :
-
Tail- cross sectional area
- \({A}_{m}\) :
-
Generalized coordinate for tail transverse displacement
- \({\Psi }_{m}\) :
-
Tail- mode shape
- \({K}_{n}\) :
-
Generalized coordinate for fluid pressure
- \({w}_{Fluid}\) :
-
Tail deflection—internal fluid pressure
- \({t}_{a}\) :
-
Time of water-absorbed
- \(e\) :
-
Fluid total energy per unit mass
- \(\Delta\) :
-
Deflection—single channel
- \({w}_{Ex}\) :
-
Tail deflection—external forces
- \(c\) :
-
Proportional damping
- \(\rho\) :
-
Tail density
- \(L\) :
-
Tail Length
- \(I\) :
-
Tail second moment of area
- \(T\) :
-
Time
- \(n\) :
-
Number of channels
- \(E\) :
-
Tail- Young's modulus
- \(\gamma\) :
-
Tail- normalized deflection for a single channel
- \({\text{h}}_{\text{f}}\) :
-
Channel height
- \(\varphi\) :
-
Channel density function
- \({\phi }^{*}\) :
-
Normalized channel density
- \({P}_{\omega }\) :
-
Pump power
- \(V\) :
-
Fluid velocity in actuator channels
References
Ali, Z.A., Li, X., Tanveer, M.A.: Controlling and stabilizing the position of remotely operated underwater vehicle equipped with a gripper. Wireless Pers. Commun. 116(2), 1107–1122 (2021). https://doi.org/10.1007/s11277-019-06938-2
Katzschmann, R.K., De Maille, A., Dorhout, D.L., Rus, D.: Cyclic hydraulic actuation for soft robotic devices. In: 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 3048–3055. IEEE (2016). https://doi.org/10.1109/IROS.2016.7759472
Low, K.H.: August. Parametric study of modular and reconfigurable robotic fish with oscillating caudal fin mechanisms. In: 2007 International Conference on Mechatronics and Automation, pp. 123–128. IEEE (2007). https://doi.org/10.1109/ICMA.2007.4303527
Rusu, D.M., Mândru, S.D., Biriș, C.M., Petrașcu, O.L., Morariu, F., Ianosi-Andreeva-Dimitrova, A.: Soft robotics: A systematic review and bibliometric analysis. Micromachines 14(2), 359 (2023). https://doi.org/10.3390/mi14020359
Webster-Wood, V.A., Guix, M., Xu, N.W., Behkam, B., Sato, H., Sarkar, D., Sanchez, S., Shimizu, M., Parker, K.K.: Biohybrid robots: Recent progress, challenges, and perspectives. Bioinspir. Biomim. (2022). https://doi.org/10.1088/1748-3190/ac9c3b
Onal, C.D., Rus, D.: A modular approach to soft robots. In: 2012 4th IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob), pp. 1038–1045. IEEE (2012). https://doi.org/10.1109/BioRob.2012.6290290
Raj, A., Thakur, A.: Fish-inspired robots: design, sensing, actuation, and autonomy—a review of research. Bioinspir. Biomim. 11(3), 031001 (2016). https://doi.org/10.1088/1748-3190/11/3/031001
Xavier, M.S., Tawk, C.D., Zolfagharian, A., Pinskier, J., Howard, D., Young, T., Lai, J., Harrison, S.M., Yong, Y.K., Bodaghi, M., Fleming, A.J.: Soft pneumatic actuators: A review of design, fabrication, modeling, sensing, control and applications. IEEE Access 10, 59442–59485 (2022). https://doi.org/10.1109/ACCESS.2022.3179589
Cha, Y., Verotti, M., Walcott, H., Peterson, S.D., Porfiri, M.: Energy harvesting from the tail beating of a carangiform swimmer using ionic polymer–metal composites. Bioinspir. Biomim. 8(3), 036003 (2013). https://doi.org/10.1088/1748-3182/8/3/036003
Marchese, A.D., Katzschmann, R.K., Rus, D.: A recipe for soft fluidic elastomer robots. Soft Rob. 2(1), 7–25 (2015). https://doi.org/10.1089/soro.2014.0022
El Daou, H., Salumäe, T., Chambers, L.D., Megill, W.M., Kruusmaa, M.: Modelling of a biologically inspired robotic fish driven by compliant parts. Bioinspir. Biomim. 9(1), 016010 (2014). https://doi.org/10.1088/1748-3182/9/1/016010
Colgate, J.E., Lynch, K.M.: Mechanics and control of swimming: A review. IEEE J. Oceanic Eng. 29(3), 660–673 (2004). https://doi.org/10.1109/JOE.2004.833208
Li, J., Yang, F.: Task assignment strategy for multi-robot based on improved Grey Wolf Optimizer. J. Ambient. Intell. Humaniz. Comput. 11(12), 6319–6335 (2020). https://doi.org/10.1007/s12652-020-02224-3
Suebsaiprom, P., Lin, C.L.: Maneuverability modeling and trajectory tracking for fish robot. Control Eng. Pract. 45, 22–36 (2015). https://doi.org/10.1016/j.conengprac.2015.08.010
Jiang, H., Liu, Y.: Nonlinear analysis of compliant robotic fish locomotion. J. Vib. Control. 28(13–14), 1673–1685 (2022). https://doi.org/10.1177/1077546321997608
Triantafyllou, M.S., Triantafyllou, G.S., Yue, D.K.P.: Hydrodynamics of fishlike swimming. Annu. Rev. Fluid Mech. 32(1), 33–53 (2000)
Valdivia y Alvarado, P., Youcef-Toumi, K.: Design of machines with compliant bodies for biomimetic locomotion in liquid environments. ASME J. Dyn. Syst., Meas., Control 128(1), 3–13 (2006). https://doi.org/10.1115/1.2168476
Basta, E., Ghommem, M., Romdhane, L., Hajj, M.R.: Hybrid tail excitation for robotic fish: Modeling and performance analysis. Ocean Eng. 234, 109296 (2021). https://doi.org/10.1016/j.oceaneng.2021.109296
Onal, C.D., Rus, D.: Autonomous undulatory serpentine locomotion utilizing body dynamics of a fluidic soft robot. Bioinspir. Biomim. 8(2), 026003 (2013). https://doi.org/10.1088/1748-3182/8/2/026003
Jeong, S., Yoo, H.H.: Flexibility modeling of a beam undergoing large deflection using the assumed mode method. Int. J. Mech. Sci. 133, 611–618 (2017). https://doi.org/10.1016/j.ijmecsci.2017.08.059
Bamdad, M.: Analytical dynamic solution of a flexible cable-suspended manipulator. Front. Mech. Eng. 8(4), 350–359 (2013). https://doi.org/10.1007/s11465-013-0271-9
Bamdad, M., Zarshenas, H.: Robotic rehabilitation with elbow stiffness adjustability. Modares Mech. Eng. 14(11) (2015)
Bamdad, M., Bahri, M.M.: Kinematics and manipulability analysis of a highly articulated soft robotic manipulator. Robotica 37(5), 868–882 (2019). https://doi.org/10.1017/S0263574718001376
Zhou, W., Li, Y.: Modeling and analysis of soft pneumatic actuator with symmetrical chambers used for bionic robotic fish. Soft Rob. 7(2), 168–178 (2020). https://doi.org/10.1089/soro.2018.0087
Saak, J., Siebelts, D., Werner, S.W.: A comparison of second-order model order reduction methods for an artificial fishtail. at-Automatisierungstechnik 67(8), 648–667 (2019). https://doi.org/10.1515/auto-2019-0027
Siebelts, D., Kater, A., Meurer, T.: Modeling and motion planning for an artificial fishtail. IFAC-PapersOnLine 51(2), 319–324 (2018). https://doi.org/10.1016/j.ifacol.2018.03.055
Cheng, X.E., Du, S.S., Li, H.Y., Hu, J.F., Chen, M.L.: Obtaining three-dimensional trajectory of multiple fish in water tank via video tracking. Multimed. Tools Appl. 77, 24499–24519 (2018). https://doi.org/10.1007/s11042-018-5755-5
Verma, S., Xu, J.X.: Analytic modeling for precise speed tracking of multilink robotic fish. IEEE Trans. Industr. Electron. 65(7), 5665–5672 (2017). https://doi.org/10.1109/TIE.2017.2779431
Ozmen Koca, G., Bal, C., Korkmaz, D., Bingol, M.C., Ay, M., Akpolat, Z.H., Yetkin, S.: Three-dimensional modeling of a robotic fish based on real carp locomotion. Appl. Sci. 8(2), 180 (2018). https://doi.org/10.3390/app8020180
Li, X., Ren, Q., Xu, J.X.: Precise speed tracking control of a robotic fish via iterative learning control. IEEE Trans. Industr. Electron. 63(4), 2221–2228 (2015). https://doi.org/10.1109/TIE.2015.2499719
Jung, S., Godoy-Diana, R.: bioinspired fluid-structure interaction. Bioinspir. Biomim. 18(3), 030401 (2023). https://doi.org/10.1088/1748-3190/acc778
Xavier, M.S., Fleming, A.J., Yong, Y.K.: Finite element modeling of soft fluidic actuators: Overview and recent developments. Adv. Intell. Syst. 3(2), 2000187 (2021). https://doi.org/10.1002/aisy.202000187
Wang, W., Cheng, X., Zhang, M., Gong, W., Cui, H.: Effect of the deformation of porous materials on the performance of aerostatic bearings by fluid-solid interaction method. Tribol. Int. 150, 106391 (2020). https://doi.org/10.1016/j.triboint.2020.106391
Zolfagharian, A., Durran, L., Gharaie, S., Rolfe, B., Kaynak, A., Bodaghi, M.: 4D printing soft robots guided by machine learning and finite element models. Sens. Actuators, A 328, 112774 (2021). https://doi.org/10.1016/j.sna.2021.112774
El Hamidi, K., Mjahed, M., El Kari, A., Ayad, H., El Gmili, N.: Design of hybrid neural controller for nonlinear MIMO system based on NARMA-L2 model. IETE J. Res. 69(5), 3038–3051 (2023). https://doi.org/10.1080/03772063.2021.1909507
Tian, Q., Wang, T., Wang, Y., Wang, Z., Liu, C.: A two-level optimization algorithm for path planning of bionic robotic fish in the three-dimensional environment with ocean currents and moving obstacles. Ocean Eng. 266, 112829 (2022). https://doi.org/10.1016/j.oceaneng.2022.112829
Yan, Z., Yang, H., Zhang, W., Gong, Q., Zhang, Y., Zhao, L.: Robust nonlinear model predictive control of a bionic underwater robot with external disturbances. Ocean Eng. 253, 111310 (2022). https://doi.org/10.1016/j.oceaneng.2022.111310
Haji, B.J., Bamdad, M.: Nonlinear Modeling and Analysis of a Novel Robot Fish with Compliant Fluidic Actuator as a Tail. J. Bionic. Eng. 19(3), 629–642 (2022). https://doi.org/10.1007/s42235-022-00166-4
Breitman, P., Matia, Y., Gat, A.D.: Fluid mechanics of pneumatic soft robots. Soft Rob. 8(5), 519–530 (2021). https://doi.org/10.1089/soro.2020.0037
Matia, Y., Elimelech, T., Gat, A.D.: Leveraging internal viscous flow to extend the capabilities of beam-shaped soft robotic actuators. Soft Rob. 4(2), 126–134 (2017). https://doi.org/10.1089/soro.2016.0048
Salem, L., Gamus, B., Or, Y., Gat, A.D.: Leveraging viscous peeling to create and activate soft actuators and microfluidic devices. Soft Rob. 7(1), 76–84 (2020). https://doi.org/10.1089/soro.2019.0005
Zhao, R., Miao, M., Lu, J., Wang, Y., Li, D.: Formation control of multiple underwater robots based on ADMM distributed model predictive control. Ocean Eng. 257, 111585 (2022). https://doi.org/10.1016/j.oceaneng.2022.111585
Gamus, B., Salem, L., Ben-Haim, E., Gat, A.D., Or, Y.: Interaction between inertia, viscosity, and elasticity in soft robotic actuator with fluidic network. IEEE Trans. Rob. 34(1), 81–90 (2017). https://doi.org/10.1109/TRO.2017.2765679
Gamus, B., Salem, L., Gat, A.D., Or, Y.: Understanding inchworm crawling for soft-robotics. IEEE Robot. Autom. Lett. 5(2), 1397–1404 (2020). https://doi.org/10.1109/LRA.2020.2966407
Matia, Y., Gat, A.D.: Dynamics of elastic beams with embedded fluid-filled parallel-channel networks. Soft Rob. 2(1), 42–47 (2015). https://doi.org/10.1089/soro.2014.0020
Sun, F.M., Xu, X.S., Qi, Z.H.: Non-linear vibration and dynamic characteristic of fish-like robot controlled by GMM actuator. J. Intell. Mater. Syst. Struct. 20(12), 1503–1513 (2009). https://doi.org/10.1177/1045389X09105234
Karimi, A., Bamdad, M., Sina, S.A.: November. A Bio-Mimetic Three-Dimensional Design and Modeling of a Fish-Like Robot. In: 2022 10th RSI International Conference on Robotics and Mechatronics (ICRoM), pp. 236–241. IEEE (2022). https://doi.org/10.1109/ICRoM57054.2022.10025322
Haji, B.J., Bamdad, M.: Steady-state dynamic analysis of a nonlinear fluidic soft actuator. J. Vib. Control (2022). https://doi.org/10.1177/10775463211066995
Haji, B.J., Bamdad, M.: Nonlinear dynamic and stability analysis of soft fluidic robotic system with reduced computational cost. Mech. Adv. Mater. Struct. 30(23), 4862–4881 (2022). https://doi.org/10.1080/15376494.2022.2107741
Zhao, Q., Liu, S., Chen, J., He, G., Di, J., Zhao, L., Su, T., Zhang, M., Hou, Z.: Fast-moving piezoelectric micro-robotic fish with double caudal fins. Robot. Auton. Syst. 140, 103733 (2021). https://doi.org/10.1016/j.robot.2021.103733
Zhao, J., Gao, X., Xiao, Y., Wu, C., Wu, G., Wang, Z., Zhang, Y., Cui, F., Liu, W.: A fish-like underwater miniature robot capable of high-speed and controllable locomotion. IEEE Robot. Autom. Lett. (2024). https://doi.org/10.1109/LRA.2024.3372443
Li, Y., Liu, L., Wang, Y., Ren, C.: Hydrodynamic analysis and motion control of the Coanda-effect jet thruster for underwater robots. Ocean Eng. 266, 113096 (2022). https://doi.org/10.1016/j.oceaneng.2022.113096
Katzschmann, R.K., DelPreto, J., MacCurdy, R., Rus, D.: Exploration of underwater life with an acoustically controlled soft robotic fish. Sci. Robot. 3(16), 3449 (2018). https://doi.org/10.1126/scirobotics.aar3449
Bamdad, M., Feyzollahzadeh, M.: Computational efficient discrete time transfer matrix method for large deformation analysis of flexible manipulators. Mech. Based Des. Struct. Mach. 50(12), 4274–4296 (2022). https://doi.org/10.1080/15397734.2020.1830800
Feyzollahzadeh, M., Bamdad, M.: Vibration analysis of rotating beam with variable cross section using Riccati transfer matrix method. Struct. Eng. Mech., An Int’l J 70(2), 199–207 (2019). https://doi.org/10.12989/sem.2019.70.2.199
Chen, W., Xia, D., Liu, J.: August. Modular design and realization of a torpedo-shape robot fish. In: 2008 IEEE International Conference on Mechatronics and Automation, pp. 125–130. IEEE (2008). https://doi.org/10.1109/ICMA.2008.4798738
Lighthill, M.J.: Large-amplitude elongated-body theory of fish locomotion. Proc R Soc London. Ser. B Biol. Sci. 179(1055), 125–138 (1971). https://doi.org/10.1098/rspb.1971.0085
Mouloud, D., Samir, Z., Slimane, S.A., Mohamed, B., Djilali, B.: Numerical study of static instability of pipe conveying incompressible fluid under different boundary conditions. Am. J. Eng. Appl. Sci. 13(4), 736–47 (2020). https://doi.org/10.3844/ajeassp.2020.736.747
Lv, Z., Hao, W., Xiao, F., Chen, P., Liu, Z., Wang, Y.: Soft pneumatic actuator from particle reinforced silicone rubber: Simulation and experiments. J. Appl. Polym. Sci. 139(33), e52795 (2022). https://doi.org/10.1002/app.52795
Moon, D.H., Shin, S.H., Na, J.B., Han, S.Y.: Fluid-Structure Interaction Based on Meshless Local Petrov-Galerkin Method for Worm Soft Robot Analysis. Int. J. Precis. Eng. Manuf-Green Technol. 7(3), 727–742 (2020). https://doi.org/10.1007/s40684-019-00186-2
Acknowledgements
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
Author information
Authors and Affiliations
Contributions
Conceptualization and methodology, Mahdi Bamdad; simulation, analysis and writing-original draft preparation, Ahmad Karimi.; supervision, Mahdi Bamdad and Seyed Ali Sina.; review and editing, Francisco Cruz and Seyed Ali Sina; funding acquisition, Francisco Cruz. All authors have read and agreed to the published version of the manuscript.
Corresponding author
Ethics declarations
Ethics Approval
Not applicable.
Institutional Review Board Statement
The study in the paper did not involve humans or animals.
Consent to Participate
Not applicable.
Consent for Publication
Not applicable.
Conflicts of Interest
The authors declare no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
About this article
Cite this article
Bamdad, M., Karimi, A., Sina, S. et al. Modeling and Dynamic Analysis of Fish Robot with Soft Fluidic Actuation. J Intell Robot Syst 111, 2 (2025). https://doi.org/10.1007/s10846-024-02196-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10846-024-02196-y