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Regul. Chaotic Dyn., 2013, Volume 18, Issue 1-2, Pages 126–143 (Mi rcd100)  

This article is cited in 23 scientific papers (total in 23 papers)

On the Dynamic Model and Motion Planning for a Spherical Rolling Robot Actuated by Orthogonal Internal Rotors

Mikhail Svinin, Akihiro Morinaga, Motoji Yamamoto

Mechanical Engineering Department, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan

Abstract: The paper deals with the dynamics of a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. The driving principle for such a robot exploits nonholonomic constraints to propel the rolling carrier. A full mathematical model as well as its reduced version are derived, and the inverse dynamics are addressed. It is shown that if the rotors are mounted on three orthogonal axes, any feasible kinematic trajectory of the rolling robot is dynamically realizable. For the case of only two rotors the conditions of controllability and dynamic realizability are established. It is shown that in moving the robot by tracing straight lines and circles in the contact plane the dynamically realizable trajectories are not represented by the circles on the sphere, which is a feature of the kinematic model of pure rolling. The implication of this fact to motion planning is explored under a case study. It is shown there that in maneuvering the robot by tracing circles on the sphere the dynamically realizable trajectories are essentially different from those resulted from kinematic models. The dynamic motion planning problem is then formulated in the optimal control settings, and properties of the optimal trajectories are illustrated under simulation.

Keywords: non-holonomic systems, rolling constraints, dynamics, motion planning

DOI: https://doi.org/10.1134/S1560354713010097

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 70E60, 70Q05, 70E18, 70E55, 49J15, 93C15
Received: 30.01.2013
Language: English

Citation: Mikhail Svinin, Akihiro Morinaga, Motoji Yamamoto, “On the Dynamic Model and Motion Planning for a Spherical Rolling Robot Actuated by Orthogonal Internal Rotors”, Regul. Chaotic Dyn., 18:1-2 (2013), 126–143

Citation in format AMSBIB
\Bibitem{SviMorYam13}
\by Mikhail Svinin, Akihiro Morinaga, Motoji Yamamoto
\paper On the Dynamic Model and Motion Planning for a Spherical Rolling Robot Actuated by Orthogonal Internal Rotors
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 1-2
\pages 126--143
\mathnet{http://mi.mathnet.ru/rcd100}
\crossref{https://doi.org/10.1134/S1560354713010097}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3040987}
\zmath{https://zbmath.org/?q=an:1272.70049}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000317623400009}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Kak upravlyat sharom Chaplygina pri pomoschi rotorov. II”, Nelineinaya dinam., 9:1 (2013), 59–76  mathnet
    2. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “How to Control the Chaplygin Ball Using Rotors. II”, Regul. Chaotic Dyn., 18:1-2 (2013), 144–158  mathnet  crossref  mathscinet  zmath
    3. M. Svinin, A. Morinaga, M. Yamamoto, “On the geometric phase approach to motion planning for a spherical rolling robot in dynamic formulation”, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE International Conference on Intelligent Robots and Systems, ed. N. Amato, IEEE, 2013, 2413–2418  isi
    4. A. V. Borisov, I. S. Mamaev, A. V. Tsiganov, “Non-holonomic dynamics and Poisson geometry”, Russian Math. Surveys, 69:3 (2014), 481–538  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. T. B. Ivanova, E. N. Pivovarova, “Kommentarii k state A. V. Borisova, A. A. Kilina, I. S. Mamaeva «Kak upravlyat sharom Chaplygina pri pomoschi rotorov. II»”, Nelineinaya dinam., 10:1 (2014), 127–132  mathnet
    6. A. Morinaga, M. Svinin, M. Yamamoto, “A motion planning strategy for a spherical rolling robot driven by two internal rotors”, IEEE Trans. Robot., 30:4 (2014), 993–1002  crossref  isi  scopus
    7. Tatiana B. Ivanova, Elena N. Pivovarova, “Comments on the Paper by A.V. Borisov, A.A. Kilin, I.S. Mamaev “How to Control the Chaplygin Ball Using Rotors. II””, Regul. Chaotic Dyn., 19:1 (2014), 140–143  mathnet  crossref  mathscinet  zmath
    8. Yu. L. Karavaev, A. A. Kilin, “Dinamika sferorobota s vnutrennei omnikolesnoi platformoi”, Nelineinaya dinam., 11:1 (2015), 187–204  mathnet  elib
    9. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Dynamics and Control of an Omniwheel Vehicle”, Regul. Chaotic Dyn., 20:2 (2015), 153–172  mathnet  crossref  mathscinet  zmath  adsnasa
    10. Valery V. Kozlov, “The Dynamics of Systems with Servoconstraints. II”, Regul. Chaotic Dyn., 20:4 (2015), 401–427  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    11. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Hamiltonization of elementary nonholonomic systems”, Russ. J. Math. Phys., 22:4 (2015), 444–453  crossref  mathscinet  zmath  isi  scopus
    12. S. Ferraro, F. Jimenez, D. Martin de Diego, “New developments on the geometric nonholonomic integrator”, Nonlinearity, 28:4 (2015), 871–900  crossref  mathscinet  zmath  isi  scopus
    13. A. Morinaga, M. Svinin, M. Yamamoto, “On the iterative steering of a rolling robot actuated by internal rotors”, Analysis, Modelling, Optimization, and Numerical Techniques, Springer Proceedings in Mathematics & Statistics, 121, eds. G. Tost, O. Vasilieva, Springer, 2015, 205–218  crossref  mathscinet  zmath  isi  scopus
    14. M. Svinin, Ya. Bai, M. Yamamoto, “Dynamic model and motion planning for a pendulum-actuated spherical rolling robot”, 2015 IEEE International Conference on Robotics and Automation (ICRA), IEEE Computer Soc., 2015, 656–661  isi
    15. Yury L. Karavaev, Alexander A. Kilin, “The Dynamics and Control of a Spherical Robot with an Internal Omniwheel Platform”, Regul. Chaotic Dyn., 20:2 (2015), 134–152  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    16. Alexey V. Borisov, Ivan S. Mamaev, “Adiabatic Invariants, Diffusion and Acceleration in Rigid Body Dynamics”, Regul. Chaotic Dyn., 21:2 (2016), 232–248  mathnet  crossref  mathscinet  zmath  elib
    17. V. Kozlov, “The phenomenon of reversal in the Euler–Poincaré–Suslov nonholonomic systems”, J. Dyn. Control Syst., 22:4 (2016), 713–724  crossref  mathscinet  zmath  isi  scopus
    18. S. Gajbhiye, R. N. Banavar, “Geometric tracking control for a nonholonomic system: a spherical robot”, IFAC-PapersOnLine, 49:18 (2016), 820–825  crossref  mathscinet  isi  scopus
    19. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    20. H. Kang, C. Liu, Ya.-B. Jia, “Inverse dynamics and energy optimal trajectories for a wheeled mobile robot”, Int. J. Mech. Sci., 134 (2017), 576–588  crossref  isi  scopus
    21. M. R. Azizi, J. Keighobadi, “Point stabilization of nonholonomic spherical mobile robot using nonlinear model predictive control”, Robot. Auton. Syst., 98 (2017), 347–359  crossref  isi  scopus
    22. T. B. Ivanova, A. A. Kilin, E. N. Pivovarova, “Controlled motion of a spherical robot with feedback. I”, J. Dyn. Control Syst., 24:3 (2018), 497–510  crossref  mathscinet  zmath  isi  scopus
    23. Yang Bai, Mikhail Svinin, Motoji Yamamoto, “Dynamics-Based Motion Planning for a Pendulum-Actuated Spherical Rolling Robot”, Regul. Chaotic Dyn., 23:4 (2018), 372–388  mathnet  crossref  mathscinet
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