Skip to main content
SpringerLink
Log in

Dynamic tail modeling and motion analysis of a beaver-like robot

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The beaver-like underwater robot can crawl and swim, playing a significant role in the exploration of amphibious environments. The robot's fan-shaped tail offers partial forward propulsion and enhances motion stability. However, a comprehensive method for modeling this tail motion is lacking. This paper introduces a segmented approach to dynamic modeling, building both propulsion and lift models for the robot's beaver-like tail. The approach integrates hydrodynamics with material mechanics to formulate a fan-shaped flexible dynamics theory. A performance index is established to quantify the tail's motion performance, offering a theoretical foundation for its evaluation. To validate the dynamic model and assess motion performance under varying swing amplitude coefficients, both simulations and experiments are undertaken. An optimal swing amplitude coefficient of 2 is identified, setting the stage for future developments in robotic motion control. This work may also advance dynamic modeling and analysis in other biomimetic underwater robots.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data availability

In the future, we will conduct more in-depth hydrodynamics research on beaver-like robot, and some data used in this paper will be involved. The data sets generated and analyzed during this study are not public, but can be obtained from the corresponding authors upon reasonable request.

References

  1. Yuh, J., West, M.: Underwater robotics. Adv. Robot. 15, 609–639 (2001)

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. Zhou, P.J., et al.: Overview of progress in development of the bionic underwater propulsion system. J. Biomim. Biomater. Biomed. Eng. 32, 9–19 (2017)

    Google Scholar 

  4. Cong, Y., Gu, C., Zhang, T., Gao, Y.: Underwater robot sensing technology: a survey. Fundam. Res. 1, 337–345 (2021)

    Article  Google Scholar 

  5. Costa, D., Palmieri, G., Palpacelli, M., Panebianco, L., Scaradozzi, D.: Design of a bio-inspired autonomous underwater robot. J. Intell. Robot. Syst. 91, 181–192 (2018)

    Article  Google Scholar 

  6. Yu, J., Wang, M., Dong, H., Zhang, Y., Wu, Z.: Motion control and motion coordination of bionic robotic fish: a review. J. Bionic Eng. 15, 579–598 (2018)

    Article  Google Scholar 

  7. Yao, C., Dong, W.: Method to calculate resistance of high-speed displacement ship taking the effect of dynamic sinkage and trim and fluid viscosity into account. J. Shanghai Jiaotong Univ. Sci. 17, 421–426 (2012)

    Article  Google Scholar 

  8. Chen, G., Zhao, Z., Wang, Z., Tu, J., Hu, H.: Swimming modeling and performance optimization of a fish-inspired underwater vehicle (FIUV). Ocean Eng. 271, 113748 (2023)

    Article  Google Scholar 

  9. Wang, T., Wang, Z., Zhang, B.: Mechanism design and experiment of a bionic turtle dredging robot. Machines 9, 86 (2021)

    Article  Google Scholar 

  10. Li, H., et al.: Design of the swimming system of a bionic jellyfish robot for seabed exploration. Appl. Ocean Res. 134, 103498 (2023)

    Article  Google Scholar 

  11. Chen G et al., Design and control of a novel bionic mantis shrimp robot. IEEE/ASME Transactions on Mechatronics 2023.

  12. Chen, G., Ti, X., Shi, L., Hu, H.: Design of beaver-like hind limb and analysis of two swimming gaits for underwater narrow space exploration. J. Intell. Robot. Syst. 104, 65 (2022)

    Article  Google Scholar 

  13. Chen, G., Tu, J., Ti, X., Wang, Z., Hu, H.: Hydrodynamic model of the beaver-like bendable webbed foot and paddling characteristics under different flow velocities. Ocean Eng. 234, 109179 (2021)

    Article  Google Scholar 

  14. Willis, J.: Modelling swimming aquatic animals in hydrodynamic models. Ecol. Model. 222, 3869–3887 (2011)

    Article  Google Scholar 

  15. Richards, C.T.: The kinematic determinants of anuran swimming performance: an inverse and forward dynamics approach. J. Exp. Biol. 211, 3181–3194 (2008)

    Article  Google Scholar 

  16. Richards, C.T., Clemente, C.J.: Built for rowing: frog muscle is tuned to limb morphology to power swimming. J. R. Soc. Interface. 10, 20130236 (2013)

    Article  Google Scholar 

  17. Li, R., et al.: A multi-body dynamics based numerical modelling tool for solving aquatic biomimetic problems. Bioinspir. Biomim. 13, 056001 (2018)

    Article  Google Scholar 

  18. Cui, Z., Gu, X., Li, K., Jiang, H.: CFD studies of the effects of waveform on swimming performance of carangiform fish. Appl. Sci. 7, 149 (2017)

    Article  Google Scholar 

  19. Ribak, G., Gurka, R.: The hydrodynamic performance of duck feet for submerged swimming resembles oars rather than delta-wings. Sci Rep-Uk 13, 16217 (2023)

    Article  Google Scholar 

  20. Huang, J., Wang, T., Lueth, T.C., Liang, J., Yang, X.: CFD based investigation on the hydroplaning mechanism of a Cormorant’s webbed foot propulsion. IEEE Access 8, 31551–31561 (2020)

    Article  Google Scholar 

  21. Akovali, G.: Plastic materials: polyvinyl chloride (PVC), pp. 23–53. Elsevier, Toxicity of building materials (2012)

    Google Scholar 

  22. Perrone, N., Kao, R.: A general finite difference method for arbitrary meshes. Comput. Struct. 5, 45–57 (1975)

    Article  MathSciNet  Google Scholar 

  23. Palacios, R., Murua, J., Cook, R.: Structural and aerodynamic models in nonlinear flight dynamics of very flexible aircraft. Aiaa J 48, 2648–2659 (2010)

    Article  Google Scholar 

  24. Schilder, J., Dwarshuis, K., Ellenbroek, M., de Boer, A.: The tangent stiffness matrix for an absolute interface coordinates floating frame of reference formulation. Multibody Syst Dyn 47, 243–263 (2019)

    Article  MathSciNet  Google Scholar 

  25. Li, L., Li, G., Li, R., Xiao, Q., Liu, H.: Multi-fin kinematics and hydrodynamics in pufferfish steady swimming. Ocean Eng. 158, 111–122 (2018)

    Article  Google Scholar 

  26. Chen, G., et al.: Modeling of swimming posture dynamics for a beaver-like robot. Ocean Eng. 279, 114550 (2023)

    Article  Google Scholar 

  27. Yue C, Guo S, Li M, ANSYS FLUENT-based modeling and hydrodynamic analysis for a spherical underwater robot, 2013 IEEE International Conference on Mechatronics and Automation, IEEE; 2013. pp. 1577–1581.

  28. Meng Q, Li Y, Gu Y, Dynamic mesh-based analysis of irradiance characteristics of solar simulator, Optical System Alignment, Tolerancing, and Verification VIII, vol. 9195SPIE; 2014. pp. 137–148.

  29. Nazir, Z., Su, Y., Wang, Z.: A CFD based investigation of the unsteady hydrodynamic coefficients of 3-D fins in viscous flow. J. Mar. Sci. Appl. 9, 250–255 (2010)

    Article  Google Scholar 

  30. Hou, Q., Ding, S., Yu, X., Mei, K.: A super-twisting-like fractional controller for SPMSM drive system. Ieee T Ind Electron 69, 9376–9384 (2021)

    Article  Google Scholar 

  31. Ding, S., Hou, Q., Wang, H.: Disturbance-observer-based second-order sliding mode controller for speed control of PMSM drives. Ieee T Energy Conver 38, 100–110 (2022)

    Article  Google Scholar 

  32. Li Y, Deep reinforcement learning: An overview. arXiv preprint arXiv:1701.07274 2017.

Download references

Acknowledgements

This work was financially supported by National Natural Science Foundation of China (Nos. 52275037, 51875528, and 41506116), Zhejiang Provincial Natural Science Foundation of China (No. LR24E050002), the Key Research and Development Project of Zhejiang Province (No. 2023C03015), the Key Research and Development Project of Ningxia Hui Autonomous Region (No. 2023BDE03002).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Gang Chen, Yidong Xu, Zhenyu Wang, Chen Chen & Xinxue Chai

  2. Faculty of Intelligent Manufacturing, Jiaxing Vocational & Technical College, Jiaxing, 314000, China

    Jiajun Tu

  3. School of Computer Science and Electronic Engineering, University of Essex, Colchester, CO4 3SQ, UK

    Gang Chen & Huosheng Hu

  4. Shaoxing SMIC Manufacturing Co., Ltd., Shaoxing, 312000, China

    Yuhang Xu

  5. Zhejiang CathayBot Technology Co., Ltd., Jinhua, 321035, China

    Jingjing Zhang & Jianwei Shi

Authors
  1. Gang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yidong Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhenyu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiajun Tu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Huosheng Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Chen Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Yuhang Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Xinxue Chai
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Jingjing Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Jianwei Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gang Chen.

Ethics declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

See Figs. 

Fig. 13
figure 13

Propulsion and lift curves of the tail of the beaver-like robot with different amplitude coefficients when f = 1

Full size image

13 and

Fig. 14
figure 14

Propulsion and lift curves of the tail of the beaver-like robot with different amplitude coefficients when f = 4

Full size image

14.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, G., Xu, Y., Wang, Z. et al. Dynamic tail modeling and motion analysis of a beaver-like robot. Nonlinear Dyn 112, 6859–6875 (2024). https://doi.org/10.1007/s11071-024-09446-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-024-09446-6

Keywords

Search

Navigation