Skip to main content
Log in

Motion planning for redundant multi-bodied planar kinematic snake robots

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

A Correction to this article was published on 26 July 2021

This article has been updated

Abstract

In this paper, the motion planning problem for planar snake-like robots with more than three links that is subjected to nonholonomic constraints is solved explicitly. In other words, for a given desired planar trajectory and a set of initial conditions of the snake, a unique feasible gait is generated to ensure that the origin of the snake robot’s body frame traverses that path. Additionally, the generated gait ensures that all the nonholonomic constraints are satisfied for all time.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Data availibility

Data sharing is not applicable to this article since no datasets were generated or analyzed during the current study.

Change history

References

  1. Ali, A., Yaqub, S., Usman, M., Zuhaib, K., Khan, M., Lee, J.-Y., Han, C.: Motion planning for a planar mechanical system with dissipative forces. Robot. Autonom. Syst. 107, 129–144 (2018)

    Article  Google Scholar 

  2. Bazzi, S., Shammas, E., Asmar, D., Mason, M.: Motion analysis of two-link nonholonomic swimmers. Nonlinear Dyn. 89(4), 2739–2751 (2017)

    Article  MathSciNet  Google Scholar 

  3. Bloch, A.: Nonholonomic Mechanics and Control. Springer (2003)

  4. Boyer, F., Porez, M.: Multibody system dynamics for bio-inspired locomotion: from geometric structures to computational aspects. Bioinspir. Biomim. 10(2), (2015)

  5. Chitta, S., Cheng, P., Frazzoli, E., Kumar, V.: Robotrikke: a novel undulatory locomotion system. In: IEEE International Conference on Robotics and Automation (2005)

  6. Dear, T., Buchanan, B., Abrajan-Guerrero, R., Kelly, S.D., Travers, M., Choset, H.: Locomotion of a multi-link non-holonomic snake robot with passive joints. Int. J. Robot. Res. 39(5), 598–616 (2020)

    Article  Google Scholar 

  7. Dear, T., Kelly, S., Travers, M., Choset, H.: The three-link nonholonomic snake as a hybrid kinodynamic system. In: American Control Conference, Boston, USA (2016)

  8. Dear, T., Kelly, S., Travers, M., Choset, H.: Locomotion of a multi-link nonholonomic snake robot. In: ASME Dynamic Systems and Control Conference, Virginia, USA (2017)

  9. Hatton, R., Choset, H.: Approximating displacement with the body velocity integral. In: Robotics: Science and Systems, Seattle, USA (2009)

  10. Hatton, R., Choset, H.: Optimizing coordinate choice for locomoting systems. In: IEEE International Conference on Robotics and Automation, Alaska, USA (2010)

  11. Hatton, R., Choset, H.: Geometric motion planning: the local connection, stokes’ theorem, and the importance of coordinate choice. Int. J. Robot. Res. 30(8), 988–1014 (2011)

    Article  Google Scholar 

  12. Hirose, S.: Biologically Inspired Robots (Snake-like Locomotor and Manipulator). Oxford University Press (1993)

  13. Itani, O., Shammas, E.: Motion planning for a redundant planar snake robot. In: IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Boston, USA (2020)

  14. Krishnaprasad, P., Tsakiris, D.: Oscillations, se(2)-snakes and motion control. In: IEEE Conference on Decision and Control (1995)

  15. Liljeback, P., Pettersen, K., Stavdahl, O., Gravdahl, J.: Snake robots locomotion in environments with obstacles. IEEE/ASME Trans. Mechatron. 17(6), 1158–1169 (2012)

    Article  Google Scholar 

  16. Marsden, J., Scheurle, J.: The reduced Euler–Lagrangian equations. Fields Inst. Commun. 1, 139–164 (1993)

    MATH  Google Scholar 

  17. Marsden, J., Montgomery, R., Ratiu, T.: Reduction, symmetry, and phases in mechanics. Memoirs Am. Math. Soc. 88(436), (1990)

  18. Ostrowski, J.: The Mechanics and Control of Undulatory Robotic Locomotion. Ph.D. Thesis, California Institute of Technology (1996)

  19. Shammas, E.: Generalized Motion Planning for Underactuated Mechanical Systems. Ph.D. Thesis, Carnegie Mellon University (2006)

  20. Shammas, E., Choset, H., Rizzi, A.: Natural gait generation techniques for principally kinematic mechanical systems. In: IEEE International Conference on Robotics and Automation, Orlando, Florida (2006)

  21. Shammas, E., Oliveira, M.: Exact motion planning solution for principally kinematic systems. In: International Conference on Intelligent Robots and Systems, San Francisco, USA (2011)

  22. Yona, T., Or, Y.: The wheeled three-link snake model: singularities in nonholonomic constraints and stick-slip hybrid dynamics induced by coulomb friction. Nonlinear Dyn. 95(3), 2307–2324 (2019)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the University Research Board at the American University of Beirut and the Munib and Angela Masri Institute of Energy and Natural Resources at the American University of Beirut.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Elie Shammas.

Ethics declarations

Conflict of interest

The authors declare that they have 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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Itani, O., Shammas, E. Motion planning for redundant multi-bodied planar kinematic snake robots. Nonlinear Dyn 104, 3845–3860 (2021). https://doi.org/10.1007/s11071-021-06515-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-06515-y

Keywords

Navigation