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Regul. Chaotic Dyn., 2015, Volume 20, Issue 2, Pages 134–152 (Mi rcd17)  

This article is cited in 31 scientific papers (total in 31 papers)

The Dynamics and Control of a Spherical Robot with an Internal Omniwheel Platform

Yury L. Karavaeva, Alexander A. Kilinb

a M. T. Kalashnikov Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069 Russia
b Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia

Abstract: This paper deals with the problem of a spherical robot propelled by an internal omniwheel platform and rolling without slipping on a plane. The problem of control of spherical robot motion along an arbitrary trajectory is solved within the framework of a kinematic model and a dynamic model. A number of particular cases of motion are identified, and their stability is investigated. An algorithm for constructing elementary maneuvers (gaits) providing the transition from one steady-state motion to another is presented for the dynamic model. A number of experiments have been carried out confirming the adequacy of the proposed kinematic model.

Keywords: spherical robot, kinematic model, dynamic model, nonholonomic constraint, omniwheel.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005 and performed in Steklov Mathematical Institute of Russian Academy of Sciences.


DOI: https://doi.org/10.1134/S1560354715020033

References: PDF file   HTML file

Bibliographic databases:

MSC: 93B18, 93B52
Received: 19.01.2014
Accepted:27.02.2015
Language:

Citation: 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

Citation in format AMSBIB
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\by Yury L. Karavaev, Alexander A. Kilin
\paper The Dynamics and Control of a Spherical Robot with an Internal Omniwheel Platform
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 2
\pages 134--152
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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. Alexander V. Sakharov, “Rotation of the Body with Movable Internal Masses Around the Center of Mass on a Rough Plane”, Regul. Chaotic Dyn., 20:4 (2015), 428–440  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    2. Alexander P. Ivanov, “On the Control of a Robot Ball Using Two Omniwheels”, Regul. Chaotic Dyn., 20:4 (2015), 441–448  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    3. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “The Jacobi Integral in Nonholonomic Mechanics”, Regul. Chaotic Dyn., 20:3 (2015), 383–400  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    4. 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
    5. Alexander A. Kilin, Elena N. Pivovarova, Tatyana B. Ivanova, “Spherical Robot of Combined Type: Dynamics and Control”, Regul. Chaotic Dyn., 20:6 (2015), 716–728  mathnet  crossref  mathscinet  adsnasa
    6. E. N. Pivovarova, A. V. Klekovkin, “Vliyanie treniya kacheniya na upravlyaemoe dvizhenie robota-kolesa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:4 (2015), 583–592  mathnet  elib
    7. A. A. Kilin, Yu. L. Karavaev, “Eksperimentalnye issledovaniya dinamiki sfericheskogo robota kombinirovannogo tipa”, Nelineinaya dinam., 11:4 (2015), 721–734  mathnet
    8. Alexey V. Borisov, Yury L. Karavaev, Ivan S. Mamaev, Nadezhda N. Erdakova, Tatyana B. Ivanova, Valery V. Tarasov, “Experimental Investigation of the Motion of a Body with an Axisymmetric Base Sliding on a Rough Plane”, Regul. Chaotic Dyn., 20:5 (2015), 518–541  mathnet  crossref  mathscinet  zmath
    9. 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
    10. Yu. L. Karavaev, A. A. Kilin, “Nonholonomic dynamics and control of a spherical robot with an internal omniwheel platform: theory and experiments”, Proc. Steklov Inst. Math., 295 (2016), 158–167  mathnet  crossref  crossref  mathscinet  isi  elib
    11. Alexey V. Borisov, Sergey P. Kuznetsov, “Regular and Chaotic Motions of a Chaplygin Sleigh under Periodic Pulsed Torque Impacts”, Regul. Chaotic Dyn., 21:7-8 (2016), 792–803  mathnet  crossref
    12. T. Mazitov, P. Bozek, A. Abramov, Yu. Nikitin, I. Abramov, “Using bee algorithm in the problem of mapping”, International Conference on Manufacturing Engineering and Materials, ICMEM 2016, Procedia Engineering, 149, eds. S. Hloch, G. Krolczyk, Elsevier Science BV, 2016, 305–312  crossref  isi  scopus
    13. B. P. DeJong, K. Yelamarthi, B. Bloxsom, “A four-pendulum omnidirectional spherical robot: design analysis and comparison”, Proceedings of the ASME International Mechanical Engineering Congress and Exposition (2015), v. 4a, Amer. Soc. Mechanical Engineers, 2016, V04AT04A019  isi
    14. Mehdi Roozegar, Mohammad J. Mahjoob, Moosa Ayati, “Adaptive Estimation of Nonlinear Parameters of a Nonholonomic Spherical Robot Using a Modified Fuzzy-based Speed Gradient Algorithm”, Regul. Chaotic Dyn., 22:3 (2017), 226–238  mathnet  crossref  mathscinet
    15. Alexander A. Kilin, Elena N. Pivovarova, “The Rolling Motion of a Truncated Ball Without Slipping and Spinning on a Plane”, Regul. Chaotic Dyn., 22:3 (2017), 298–317  mathnet  crossref  mathscinet
    16. 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
    17. E. N. Pivovarova, “Issledovanie ustoichivosti statsionarnykh dvizhenii sferorobota kombinirovannogo tipa”, Nelineinaya dinam., 13:4 (2017), 611–623  mathnet  crossref  elib
    18. A. Kilin, P. Bozek, Yu. Karavaev, A. Klekovkin, V. Shestakov, “Experimental investigations of a highly maneuverable mobile omniwheel robot”, Int. J. Adv. Robot. Syst., 14:6 (2017), 1729881417744570  crossref  isi  scopus
    19. T. W. U. Madhushani, D. H. S. Maithripala, J. V. Wijayakulasooriya, J. M. Berg, “Semi-globally exponential trajectory tracking for a class of spherical robots”, Automatica, 85 (2017), 327–338  crossref  mathscinet  zmath  isi  scopus
    20. E. V. Vetchanin, A. A. Kilin, “Control of body motion in an ideal fluid using the internal mass and the rotor in the presence of circulation around the body”, J. Dyn. Control Syst., 23:2 (2017), 435–458  crossref  mathscinet  zmath  isi  scopus
    21. M. Roozegar, M. J. Mahjoob, “Modelling and control of a non-holonomic pendulum-driven spherical robot moving on an inclined plane: simulation and experimental results”, IET Contr. Theory Appl., 11:4 (2017), 541–549  crossref  mathscinet  isi  scopus
    22. T. W. U. Madhushani, D. H. S. Maithripala, J. M. Berg, “Feedback regularization and geometric PID control for trajectory tracking of mechanical systems: hoop robots on an inclined plane”, Proceedings of the American Control Conference, 2017 American Control Conference (ACC), IEEE, 2017, 3938–3943  crossref  isi
    23. T. J. Ylikorpi, A. J. Halme, P. J. Forsman, “Dynamic modeling and obstacle-crossing capability of flexible pendulum-driven ball-shaped robots”, Robot. Auton. Syst., 87 (2017), 269–280  crossref  isi  scopus
    24. P. S. Carvalho, M. J. Rodrigues, “The centre of mass of a ‘flying’ body revealed by a computational model”, Eur. J. Phys., 38:1 (2017), 015002  crossref  isi  scopus
    25. A. Nayak, R. N. Banavar, D. H. S. Maithripala, “Almost-global tracking for a rigid body with internal rotors”, Eur. J. Control, 42 (2018), 59–66  crossref  mathscinet  zmath  isi  scopus
    26. 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
    27. T. Liptak, I. Virgala, M. L'ubica, A. Galajdova, P. Tuleja, L. Koukolova, J. Varga, M. Sukop, “Modeling and control of two-link snake”, Int. J. Adv. Robot. Syst., 15:2 (2018), 1729881418760638  crossref  isi  scopus
    28. M. M. Svinin, M. Yamamoto, Ya. Bai, “Dynamics-Based Motion Planning for a Pendulum-Actuated Spherical Rolling Robot”, Regul. Chaotic Dyn., 23:4 (2018), 372–388  mathnet  crossref  mathscinet
    29. A. A. Kilin, E. N. Pivovarova, “Chaplygin top with a periodic gyrostatic moment”, Russ. J. Math. Phys., 25:4 (2018), 509–524  crossref  mathscinet  zmath  isi  scopus
    30. A. A. Kilin, T. B. Ivanova, E. N. Pivovarova, “Controlled Motion of a Spherical Robot of Pendulum Type on An Inclined Plane”, Dokl. Phys., 63:7 (2018), 302–306  mathnet  mathnet  crossref  crossref  isi  elib  scopus
    31. Vitaliy Fedonyuk, Phanindra Tallapragada, “The Dynamics of a Chaplygin Sleigh with an Elastic Internal Rotor”, Regul. Chaotic Dyn., 24:1 (2019), 114–126  mathnet  crossref
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