Advertisement

Note on Signature of Trident Mechanisms with Distribution Growth Vector (4,7)

  • Stanislav FrolíkEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11472)

Abstract

We recall some basic concepts of differential geometry and control theory and their application in robotics, namely we describe so called generalized trident snake robot with four control parameters. Indeed, we are working with a model that combines a robotic snake and Doubin car. We determine the controlling distribution and describe its properties. Consequently, we determine the signature corresponding to the mechanisms with four controlling parameters. This is essential for analysis of the underlying algebraic structure and allows us to choose suitable control model.

Keywords

Non-holonomic system Trident robot Differential geometry Signature 

Notes

Acknowledgement

This research was supported by a grant of the Czech Science Foundation no. 17-21360S, “Advances in Snake-like Robot Control” and by a Grant No. FSI-S-17-4464.

References

  1. 1.
    Agracev, A., Barilari, D., Boscain, U.: Introduction to Riemannian and sub-Riemannian geometry. Preprint SISSA (2016)Google Scholar
  2. 2.
    De Zanet, C.: Generic one-step bracket-generating distributions of rank four. Archivum Mathematicum 51(5), 257–264 (2015)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Hrdina, J.: Local controllability of trident snake robot based on sub-Riemannian extremals. Note di Matematica 37(suppl. 1), 93–102 (2017)MathSciNetGoogle Scholar
  4. 4.
    Návrat, A., Vašík, P.: On geometric control models of a robotic snake. Note di Matematica 37, 119–129 (2017)MathSciNetGoogle Scholar
  5. 5.
    Hrdina, J., Návrat, A., Vašík, P., Matoušek, R.: CGA-based robotic snake control. Adv. Appl. Clifford Algebr. 27, 621–632 (2017)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hrdina, J., Návrat, A., Vašík, P., Matoušek, R.: Geometric control of the trident snake robot based on CGA. Adv. Appl. Clifford Algebr. 27, 621–632 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Hrdina, J., Návrat, A., Vašík, P.: Control of 3-link robotic snake based on conformal geometric algebra. Adv. Appl. Clifford Algebr. 26, 1069–1080 (2016).  https://doi.org/10.1007/s00006-015-0621-2MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ishikawa, M.: Trident snake robot: locomotion analysis and control. In: NOL-COS, IFAC Symposium on Nonlinear Control Systems, vol. 6 (2004)Google Scholar
  9. 9.
    Ishikawa, M., Minami, Y., Sugie, T.: Development and control experiment of the trident snake robot. IEEE/ASME Trans. Mechatron. 15(1), 9 (2010)CrossRefGoogle Scholar
  10. 10.
    Montgomery, R.: A Tour of Subriemannian Geometries, Their Geodesics and Applications. Mathematical Surveys and Monographs, p. 259. AMS, Providence (2002)Google Scholar
  11. 11.
    Murray, R.M., Zexiang, L., Sastry, S.S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)Google Scholar
  12. 12.
    Pietrowska, Z., Tchoń, K.: Dynamics and motion planning of trident snake robot. J. Intell. Robot. Syst. 75(1), 17–28 (2014)CrossRefGoogle Scholar
  13. 13.
    Selig, J.M.: Geometric Fundamentals of Robotics. Monographs in Computer Science. Springer, New York (2004).  https://doi.org/10.1007/b138859CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringBrno University of TechnologyBrnoCzech Republic

Personalised recommendations