Coupled dynamic modeling, identification and experimental validation of a hydraulically driven soft robotic arm

Abstract

Unlocking the high-performance potential of Hydraulically-Driven Soft Robotic Arms (HDSRAs) requires computationally tractable dynamic models that are both physically faithful and rigorously validated, a combination that remains a critical challenge. This paper addresses this gap by presenting a systematic framework for the modeling, identification, and multi-faceted validation of such systems. Central to the framework is an enhanced coupled dynamic model incorporating often-neglected physical phenomena, including stiffness coupling, Rayleigh damping, and pressure-dependent hydraulics. The framework’s value is then established through a cohesive suite of four targeted experimental studies. An ablation study first quantitatively confirms the necessity of each model enhancement. A comparative analysis subsequently demonstrates the model’s superior accuracy against representative existing methods. A model-based feedforward control experiment then proves the model’s practical utility by significantly improving trajectory tracking performance. Finally, a generalization study on a more complex tri-chamber arm confirms the framework’s scalability. This work delivers not just a model, but a fully validated, high-fidelity “digital twin” that provides a solid foundation for designing high-performance controllers for a broad class of HDSRAs.

Keywords

Soft robotics / Hydraulic actuation / Dynamic modeling / Coupled mechanics / Parameter identification

CRediT authorship contribution statement

Yu Lei: Writing – original draft, Software, Methodology, Formal analysis. Pengkun Du: Methodology, Conceptualization. Minghao Xie: Methodology, Investigation. Zheng Chen: Writing – review & editing, Supervision, Project administration, Funding acquisition. Jason Gu: Supervision.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work is supported by Zhejiang Provincial Natural Science Foundation of China (LR23E050001), the National Natural Science Foundation of China (52575076), and The Seed Fund Cultivation Project of Ocean College, Zhejiang University (2025LJ002).

References

[1] D. Rus, M.T. Tolley, Design, fabrication and control of soft robots, Nature 521 (7553) (2015) 467-475.

[2] S. Kim, C. Laschi, B. Trimmer, Soft robotics: A bioinspired evolution in robotics, Trends Biotechnol. 31 (5) (2013) 287-294.

[3] E.W. Hawkes, L.H. Blumenschein, J.D. Greer, A.M. Okamura, A soft robot that navigates its environment through growth, Sci. Robot. 1 (2) (2017) eaan3028.

[4] G. Chen, X. Yang, X. Zhang, H. Hu, Water hydraulic soft actuators for underwater autonomous robotic systems, Appl. Ocean Res. 109 (2021) 102551,https://doi.org/10.1016/j.apor.2021.102551,URL https://www.sciencedirect.com/science/article/pii/S0141118721000286.

[5] Q. Tan, Y. Chen, J. Liu, K. Zou, J. Yi, S. Liu, Z. Wang, Underwater crawling robot with hydraulic soft actuators, Front. Robot. AI, Volume 8 -, 2021 (2021), https://doi.org/10.3389/frobt.2021.688697,URL https://www.frontiersin.org/journals/robotics-and-ai/articles/10.3389/frobt.2021.688697.

[6] M. Runciman, E. Franco, J. Avery, F. Rodriguez y Baena, G. Mylonas, Model based position control of soft hydraulic actuators, 2023 IEEE International Conference on Robotics and Automation, ICRA, 2023, pp. 2676-2682, https://doi.org/10.1109/ICRA48891.2023.10161573.

[7] Z. Chen, B. Helian, Y. Zhou, M. Geimer, An integrated trajectory planning and motion control strategy of a variable rotational speed pump-controlled electro-hydraulic actuator, IEEE/ASME Trans. Mechatronics 28 (1) (2023) 588-597, https://doi.org/10.597.

[8] Z. Chen, S. Zhou, C. Shen, L. Lyu, J. Zhang, B. Yao, Observer-based adaptive robust precision motion control of a multi-joint hydraulic manipulator, IEEE/CAA J. Autom. Sin. 11 (5) (2024) 1213-1226.

[9] Y. Chen, Q. Sun, Q. Guo, Y. Gong, Dynamic modeling and experimental validation of a water hydraulic soft manipulator based on an improved Newton—Euler iterative method, Micromachines, 13 (1), (2022), http://dx.doi.org/10.3390/mi13010130, URL https://www.mdpi.com/2072-666X/13/1/130

[10] L.-W. Meng, X.-L. Xie, X.-H. Zhou, S.-Q. Liu, Z.-G. Hou, Design, optimization, and modeling of a hydraulic soft robot for chronic total occlusions, Biomimetics,9 (3), (2024), https://doi.org/10.3390/biomimetics9030163,URL https://www.mdpi.com/2313-7673/9/3/163.

[11] D. Trivedi, C.D. Rahn, W.M. Kier, I.D. Walker, Soft robotics: Biological inspiration, state of the art, and future research, Appl. Bionics Biomech. 5 (3) (2008) 99-117.

[12] R.J. Webster, B.A. Jones, Design and kinematic modeling of constant curvature continuum robots: A review, Int. J. Robot. Res. 29 (13) (2010) 1661-1683.

[13] C. Armanini, F. Boyer, A.T. Mathew, C. Duriez, F. Renda, Soft robots modeling: A structured overview, IEEE Trans. Robot. 39 (3) (2023) 1728-1748.

[14] Q. Xie, T. Wang, S. Zhu, Simplified dynamical model and experimental verification of an underwater hydraulic soft robotic arm, Smart Mater. Struct. 31 (7) (2022) 075011, https://doi.org/10.1088/1361-665X/ac736f.

[15] L. Lindenroth, J. Back, A. Schoisengeier, Y. Noh, H. Würdemann, K. Althoefer, H. Liu, Stiffness-based modelling of a hydraulically-actuated soft robotics manipulator, 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS, 2016, pp. 2458-2463, https://doi.org/10.1109/IROS.2016.7759383.

[16] E. Coevoet, T.M. Téné, Q. Peyron, S. Zaharia, J. Dequidt, C. Duriez, Software toolkit for modeling, simulation, and control of soft robots, Adv. Robot. 31 (22) (2017) 1208-1224.

[17] P. Schegg, C. Duriez, Review on generic methods for mechanical modeling, simulation and control of soft robots, PLoS One 17 (1) (2022) e0251059.

[18] F. Renda, F. Boyer, J. Dias, L. Seneviratne, Discrete cosserat approach for multisection soft manipulator dynamics, IEEE Trans. Robot. 34 (6) (2018) 1518-1533.

[19] S. Liu, J. Jiao, N. Ding, T. Mei, Dynamic modeling incorporating water damping for a fiber-reinforced soft actuator based on Euler–Bernoulli and cosserat rod theories, IEEE/ASME Trans. Mechatronics 30 (1) (2025) 403-413, https://doi.org/10.413.

[20] Q. Xie, T. Wang, S. Zhu, Simplified dynamical model and experimental verification of an underwater hydraulic soft robotic arm, Smart Mater. Struct. 31 (7) (2022) 075011, https://doi.org/10.1088/1361-665X/ac736f.

[21] B.J. Caasenbrood, A.Y. Pogromsky, H. Nijmeijer, Control-oriented models for hyperelastic soft robots through differential geometry of curves, Soft Robot. 9 (1) (2022) 68-87.

[22] V. Falkenhahn, T. Mahl, A. Hildebrandt, R. Neumann, O. Sawodny, Dynamic modeling of bellows-actuated continuum robots using the Euler–Lagrange formalism, IEEE Trans. Robot. 31 (6) (2015) 1483-1496.

[23] M. Xie, Z. Liu, L. Sun, Dynamical modeling and control of soft robots with non-constant curvature deformation, IEEE Robot. Autom. Lett. 7 (2) (2022) 5029-5036.

[24] C. Wang, C. Liu, Y. Zhang, J. Zhao, J. Liu, Dynamic modeling and experimental validation of a water hydraulic soft manipulator based on an improved Newton–Euler iterative method, Sensors 22 (3) (2022) 1222.

[25] L. Ljung, System Identification: Theory for the User, Prentice Hall, (1999).

[26] Q. Xie, Y. Zhang, T. Wang, S. Zhu, Dynamic response prediction of hydraulic soft robotic arms based on LSTM neural network, Proc. Inst. Mech. Eng. I 237 (7) (2023) 1251-1265, https://doi.org/10.1265.

[27] C. Della Santina, R.K. Katzschmann, A. Bicchi, D. Rus, Dynamic control of soft robots interacting with the environment, 2018 IEEE International Conference on Soft Robotics, RoboSoft, IEEE, 2018, pp. 24-28.

[28] P. Polygerinos, Z. Wang, J.T.B. Overvelde, K.C. Galloway, R.J. Wood, K. Bertoldi, C.J. Walsh, Modeling of soft fiber-reinforced bending actuators, IEEE Trans. Robot. 31 (3) (2015) 778-789, https://doi.org/10.789.

[29] V. Cacucciolo, F. Renda, E. Poccia, C. Laschi, M. Cianchetti, Modelling the nonlinear response of fibre-reinforced bending fluidic actuators, Smart Mater. Struct. 25 (10) (2016) 105020.

[30] Y. Lei, P. Du, M. Xie, Z. Chen, J. Gu, Prototype design and experimental test for a hydraulic-driven soft robotic arm, Procedia Comput. Sci. 250 (2024) 88-94,Proceedings of the 2024 International Conference on Biomimetic Intelligence and Robotics.