Skip to main content
SpringerLink
Log in

Path Tracking Control of a Spherical Robot with Pendulum-Like Driver

  • Conference paper
  • First Online:
Mathematical Modeling and Supercomputer Technologies (MMST 2023)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1914))

  • 101 Accesses

Abstract

We consider the path tracking problem for a rolling spherical robot on an arbitrary uneven surface. A full mathematical model of motion as well as its reduced version without slipping and twisting are derived. A state-feedback control laws that provide robot motion along a given trajectory are synthesized. The effectiveness of the proposed control laws is demonstrated by results of computer simulation.

D.V. Balandin is supported by the Ministry of Science and Higher Education of the Russian Federation, (Agreement 075-10-2021-093, Project RAI-RND-2126 Artificial intelligence methods and algorithms development for solving problems of dynamic manipulation in robotic applications). R.S. Biryukov and A.M. Tuzikov are supported by the Ministry of Science and Higher Education of the Russian Federation, project no. FSWR-2023-0034, and by the Research and Education Mathematical Center Mathematics for Future Technologies.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Balandin, D.V., Komarov, M.A., Osipov, G.V.: A motion control for a spherical robot with pendulum drive. J. Comput. Syst. Sci. Int. 52(4), 650–663 (2013). https://doi.org/10.1134/S1064230713040047

    Article  MathSciNet  Google Scholar 

  2. Hogan, F.R., Forbes, J.R., Barfoot, T.D.: Rolling stability of a power-generating tumbleweed rover. J. Spacecr. Rocket. 51(6), 1895–1905 (2014). https://doi.org/10.2514/1.A32883

    Article  Google Scholar 

  3. Hogan, F., Forbes, J.: Modeling of spherical robots rolling on generic surfaces. Modeling of spherical robots rolling on generic surfaces. Multibody Syst. Dyn. 35(1), 91–109 (2015). https://doi.org/10.1007/s11044-014-9438-3

  4. Ho, C.-H., Wu, C.-K., Tu, J.-Y., Hsu, S.-K.: Conceptual design of spherical vehicle system for future transportation. J. Autom. Control Eng. 3(3), 191–195 (2015). https://doi.org/10.12720/joace.3.3.191-195

  5. Bai, Y., Svinin, M., Yamamoto, M.: Adaptive trajectory tracking control for the ball-pendulum system with time-varying uncertainties. In: Proceeding of International Conference on Intelligent Robots and Systems (IROS, 2017), Vancouver, BC, Canada, 2017, pp. 2083–2090 (2017). https://doi.org/10.1109/IROS.2017.8206026

  6. Ivanova, T.B., Kilin, A.A., Pivovarova, E.N.: Controlled motion of a spherical robot with feedback. J. Dyn. Control Syst. 24(3), 497–510 (2018). https://doi.org/10.1007/s10883-017-9387-2

    Article  MathSciNet  Google Scholar 

  7. Chernousko, F.L., Bolotnik, N.N.: Dynamics of mobile systems with controlled configuration. Fizmatlit, Moscow (2022). (in Russian)

    Google Scholar 

  8. Kim, I.-K., Kim, J.-S., Goh, C.-S.: Theoretical and practical study of spherical motor without the winding overhang. In: Proceeding of International Electric Machines and Drives Conference (IEMDC 2007), Antalya, Turkey, 2007, pp. 1361–1365 (2007). https://doi.org/10.1109/IEMDC.2007.383627

  9. Li, Z., Jun, W.: The principle of work and essential technology of magnetic suspended spherical motor. In: 3d International Conference on Measuring Technology and Mechatronics Automation, Shanghai, China, 2011, pp. 898–901 (2011). https://doi.org/10.1109/ICMTMA.2011.796

  10. Lim, C.K., Yan, L., Chen, I.-M., Yang, G., Lin, W.,: A novel approach in generating 3-DOF motions. In: Proceedings of the IEEE International Conference Mechatronics and Automation, 2005, Niagara Falls, ON, Canada, 2005, pp. 1485–1490 (2005). https://doi.org/10.1109/ICMA.2005.1626775

  11. Balandin, D.V., Kogan, M.M.: Multi-objective generalized \(H_2\) control. Automatica 99(1), 317–322 (2019). https://doi.org/10.1016/j.automatica.2018.10.006

    Article  MathSciNet  Google Scholar 

  12. Balandin, D.V., Biryukov, R.S., Kogan, M.M.: Finite-horizon multi-objective generalized \(H_2\) control with transients. Automatica 106(8), 27–34 (2019). https://doi.org/10.1016/j.automatica.2019.04.023

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia

    Dmitry V. Balandin, Ruslan S. Biryukov & Alexander M. Tuzikov

Authors
  1. Dmitry V. Balandin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ruslan S. Biryukov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexander M. Tuzikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ruslan S. Biryukov .

Editor information

Editors and Affiliations

  1. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Dmitry Balandin

  2. Lobachevsky State University, Nizhny Novgorod, Russia

    Konstantin Barkalov

  3. Lobachevsky State University, Nizhny Novgorod, Russia

    Iosif Meyerov

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Balandin, D.V., Biryukov, R.S., Tuzikov, A.M. (2024). Path Tracking Control of a Spherical Robot with Pendulum-Like Driver. In: Balandin, D., Barkalov, K., Meyerov, I. (eds) Mathematical Modeling and Supercomputer Technologies. MMST 2023. Communications in Computer and Information Science, vol 1914. Springer, Cham. https://doi.org/10.1007/978-3-031-52470-7_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-52470-7_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-52469-1

  • Online ISBN: 978-3-031-52470-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation