Skip to main content

Modeling Soft Swimming Robots using Discrete Elastic Rod Method

  • Chapter
  • First Online:
Bioinspired Sensing, Actuation, and Control in Underwater Soft Robotic Systems

Abstract

Soft swimming robots are primarily composed of elastically deformable materials, which typically make up the robot’s body, limbs, and/or fins. Such robots can swim by moving their limbs, flapping their fins, or undulating their body in order to control thrust and direction. This chapter presents a technique to model these soft swimming robots using a computational framework based on the method of discrete elastic rods (DER). This approach to soft robot simulation draws inspiration from methods to simulate slender structures that are widely used in the computer graphics community. In this framework, the soft robot limbs or fins are treated as flexible rods that deflect in response to internal actuation and surface tractions from contacting bodies and the surrounding fluid. Here, we apply this model to the special case of a seastar-inspired robot composed of radiating limbs that produce motion through bending and hydrodynamic drag. We begin with an overview of the DER-based framework and then present simulation results for forward swimming and turning.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. S.I. Rich, R.J. Wood, C. Majidi, Untethered soft robotics. Nature Electron. 1(2), 102 (2018)

    Google Scholar 

  2. R.K. Katzschmann, A.D. Marchese, D. Rus, Hydraulic autonomous soft robotic fish for 3d swimming, in Experimental Robotics (Springer, New York, 2016), pp. 405–420

    Google Scholar 

  3. X. Tan, D. Kim, N. Usher, D. Laboy, J. Jackson, A. Kapetanovic, J. Rapai, B. Sabadus, X. Zhou, An autonomous robotic fish for mobile sensing, in Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, New York, 2006), pp. 5424–5429

    Book  Google Scholar 

  4. T. Li, G. Li, Y. Liang, T. Cheng, J. Dai, X. Yang, B. Liu, Z. Zeng, Z. Huang, Y. Luo, et al., Fast-moving soft electronic fish. Sci. Adv. 3(4), e1602045 (2017)

    Google Scholar 

  5. M.D. Bartlett, N. Kazem, M.J. Powell-Palm, X. Huang, W. Sun, J.A. Malen, C. Majidi, High thermal conductivity in soft elastomers with elongated liquid metal inclusions. Proc. Natl. Acad. Sci. 114(9), 2143–2148 (2017)

    Article  Google Scholar 

  6. C. Duriez, Control of elastic soft robots based on real-time finite element method, in Proceedings of the 2013 IEEE International Conference on Robotics and Automation (IEEE, New York, 2013), pp. 3982–3987

    Book  Google Scholar 

  7. G. Runge, A. Raatz, A framework for the automated design and modelling of soft robotic systems. CIRP Annals 66(1), 9–12 (2017)

    Article  Google Scholar 

  8. O. Goury, C. Duriez, Fast, generic, and reliable control and simulation of soft robots using model order reduction. IEEE Trans. Robot. 34(6), 1565–1576 (2018)

    Article  Google Scholar 

  9. J. Chenevier, D. GonzĂ¡lez, J.V. Aguado, F. Chinesta, E. Cueto, Reduced-order modeling of soft robots. PloS One 13(2), e0192052 (2018)

    Google Scholar 

  10. J. Hiller, H. Lipson, Dynamic simulation of soft multimaterial 3d-printed objects. Soft Robot. 1(1), 88–101 (2014)

    Article  Google Scholar 

  11. N. Cheney, J. Bongard, H. Lipson, Evolving soft robots in tight spaces, in Proceedings of the 2015 annual conference on Genetic and Evolutionary Computation (ACM, New York, 2015), pp. 935–942

    Google Scholar 

  12. X. Zhou, C. Majidi, O.M. O’Reilly, Soft hands: an analysis of some gripping mechanisms in soft robot design. Int. J. Solids Struct. 64, 155–165 (2015)

    Article  Google Scholar 

  13. S. Grazioso, G. Di Gironimo, B. Siciliano, A geometrically exact model for soft continuum robots: the finite element deformation space formulation. Soft Robot. 6(6), 790–811 (2018)

    Article  Google Scholar 

  14. F. Renda, F. Giorgio-Serchi, F. Boyer, C. Laschi, J. Dias, L. Seneviratne, A unified multi-soft-body dynamic model for underwater soft robots. Int. J. Robot. Res. 37(6), 648–666 (2018)

    Article  Google Scholar 

  15. M.K. Jawed, A. Novelia, O.M. O’Reilly, A primer on the Kinematics of Discrete Elastic Rods. Springer Briefs in Applied Sciences and Technology (Springer, Berlin, 2018)

    Google Scholar 

  16. M. Bergou, M. Wardetzky, S. Robinson, B. Audoly, E. Grinspun, Discrete elastic rods. ACM Trans. Graph. 27(3), 63 (2008)

    Google Scholar 

  17. M. Bergou, B. Audoly, E. Vouga, M. Wardetzky, E. Grinspun, Discrete viscous threads. ACM Trans. Graph. 29(4), 116 (2010)

    Google Scholar 

  18. Z. Shen, J. Huang, W. Chen, H. Bao, Geometrically exact simulation of inextensible ribbon, in Computer Graphics Forum, vol. 34 (Wiley, New York, 2015), pp. 145–154

    Google Scholar 

  19. D. Baraff, A. Witkin, Large steps in cloth simulation, in Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques (ACM, New York, 1998), pp. 43–54

    Google Scholar 

  20. E. Grinspun, A.N. Hirani, M. Desbrun, P. Schröder, Discrete shells, in Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (Eurographics Association, Aire-la-Ville, 2003), pp. 62–67

    Google Scholar 

  21. J. Panetta, M. Konaković-Luković, F. Isvoranu, E. Bouleau, M. Pauly, X-shells: a new class of deployable beam structures. ACM Trans. Graphics (TOG) 38(4), 83 (2019)

    Google Scholar 

  22. B. Audoly, N. Clauvelin, P.-T. Brun, M. Bergou, E. Grinspun, M. Wardetzky, A discrete geometric approach for simulating the dynamics of thin viscous threads. J. Comput. Phys. 253, 18–49 (2013)

    Article  MathSciNet  Google Scholar 

  23. C. Batty, A. Uribe, B. Audoly, E. Grinspun, Discrete viscous sheets, in ACM Transactions on Graphics, vol. 31 (ACM, New York, 2012), p. 113

    Google Scholar 

  24. N.N. Goldberg, X. Huang, C. Majidi, A. Novelia, O.M. O’Reilly, D.A. Paley, W.L. Scott, On planar discrete elastic rod models for the locomotion of soft robots. Soft Robot. 6(5), 595–610 (2019)

    Article  Google Scholar 

  25. G. Kirchhoff, Ueber das gleichgewicht und die bewegung eines unendlich dĂ¼nnen elastischen stabes. J. Reine. Angew. Math. 56, 285–313 (1859)

    MathSciNet  Google Scholar 

  26. M.K. Jawed, F. Da, J. Joo, E. Grinspun, P.M. Reis, Coiling of elastic rods on rigid substrates. Proc. Natl. Acad. Sci. 111(41), 14663–14668 (2014)

    Article  Google Scholar 

  27. M.K. Jawed, N.K. Khouri, F. Da, E. Grinspun, P.M. Reis, Propulsion and instability of a flexible helical rod rotating in a viscous fluid. Phys. Rev. Lett. 115(16), 168101 (2015)

    Google Scholar 

  28. L. Zhang, J.J. Abbott, L. Dong, K.E. Peyer, B.E. Kratochvil, H. Zhang, C. Bergeles, B.J. Nelson, Characterizing the swimming properties of artificial bacterial flagella. Nano Lett. 9(10), 3663–3667 (2009)

    Article  Google Scholar 

  29. Y. Modarres-Sadeghi, M. PaĂ¯doussis, C. Semler, A nonlinear model for an extensible slender flexible cylinder subjected to axial flow. J. Fluids Struct. 21(5–7), 609–627 (2005)

    Article  Google Scholar 

  30. M. Mallick, A. Kumar, N. Tamboli, A. Kulkarni, P. Sati, V. Devi, S. Chandar, Study on drag coefficient for the flow past a cylinder. Int. J. Civil Eng. Res. 5(4), 301–306 (2014)

    Google Scholar 

  31. W. Huang, M.K. Jawed, Newmark-beta method in discrete elastic rods algorithm to avoid energy dissipation. J. Appl. Mech. 86(8), 084501 (2019)

    Google Scholar 

  32. X. Huang, K. Kumar, M.K. Jawed, A. Mohammadi Nasab, Z. Ye, W. Shan, C. Majidi, Highly dynamic shape memory alloy actuator for fast moving soft robots. Adv. Mater. Technol. 4(4), 1800540 (2019)

    Google Scholar 

  33. X. Huang, K. Kumar, M. Jawed, Z. Ye, C. Majidi, Soft electrically actuated quadruped (SEAQ)-integrating a flex circuit board and elastomeric limbs for versatile mobility. IEEE Robot. Autom. Lett. 4(3), 2415-2422 (2019)

    Article  Google Scholar 

  34. X. Huang, K. Kumar, M.K. Jawed, A.M. Nasab, Z. Ye, W. Shan, C. Majidi, Chasing biomimetic locomotion speeds: Creating untethered soft robots with shape memory alloy actuators. Sci. Robot. 3(25), 7557 (2018)

    Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge support from the Office of Naval Research (award #N00014-17-1-2063; Program Manager: Dr. Tom McKenna).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Carmel Majidi .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Huang, W., Patterson, Z., Majidi, C., Jawed, M.K. (2021). Modeling Soft Swimming Robots using Discrete Elastic Rod Method. In: Paley, D.A., Wereley, N.M. (eds) Bioinspired Sensing, Actuation, and Control in Underwater Soft Robotic Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-50476-2_13

Download citation

Publish with us

Policies and ethics