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Journal of Dynamical and Control Systems

, Volume 24, Issue 3, pp 497–510 | Cite as

Controlled Motion of a Spherical Robot with Feedback. I

  • Tatyana B. Ivanova
  • Alexander A. Kilin
  • Elena N. Pivovarova
Article

Abstract

In this paper, we develop a model of a controlled spherical robot with an axisymmetric pendulum-type actuator with a feedback system suppressing the pendulum’s oscillations at the final stage of motion. According to the proposed approach, the feedback depends on phase variables (the current position and velocities) and does not depend on the type of trajectory. We present integrals of motion and partial solutions, analyze their stability, and give examples of computer simulation of motion using feedback to illustrate compensation of the pendulum’s oscillations.

Keywords

Spherical robot Nonholonomic constraint Control Feedback 

Mathematics Subject Classification (2010)

70F25 70Q05 93D15 

Notes

Acknowledgements

The authors extend their gratitude to A. V. Borisov, I. S. Mamaev and Yu. L. Karavaev for fruitful discussions of the results obtained.

The work of T. B. Ivanova (Sections 1 and 2) was carried out within the framework of the state assignment to the Ministry of Education and Science of Russia (1.2404.2017/4.6) and was supported by a grant of RFBR (15-08-09261-a). The work of A. A. Kilin (Section 3) was carried out at MIPT under project 5–100 for state support for leading universities of the Russian Federation. The work of E. N. Pivovarova (Section 4) was supported by the grant of RSF (15-12-20035).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  • Tatyana B. Ivanova
    • 1
  • Alexander A. Kilin
    • 2
  • Elena N. Pivovarova
    • 1
  1. 1.Udmurt State UniversityIzhevskRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyRussia

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