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Regul. Chaotic Dyn., 2015, Volume 20, Issue 6, Pages 716–728 (Mi rcd40)  

This article is cited in 18 scientific papers (total in 18 papers)

Spherical Robot of Combined Type: Dynamics and Control

Alexander A. Kilina, Elena N. Pivovarovaa, Tatyana B. Ivanovab

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

Abstract: This paper is concerned with free and controlled motions of a spherical robot of combined type moving by displacing the center of mass and by changing the internal gyrostatic momentum. Equations of motion for the nonholonomic model are obtained and their first integrals are found. Fixed points of the reduced system are found in the absence of control actions. It is shown that they correspond to the motion of the spherical robot in a straight line and in a circle. A control algorithm for the motion of the spherical robot along an arbitrary trajectory is presented. A set of elementary maneuvers (gaits) is obtained which allow one to transfer the spherical robot from any initial point to any end point.

Keywords: spherical robot, control, nonholonomic constraint, combined mechanism

Funding Agency Grant Number
Russian Foundation for Basic Research 15-08-09261-a
Ministry of Education and Science of the Russian Federation MK-2171.2014.1
Russian Science Foundation 14-19-01303
The work of A. A. Kilin was supported by the RFBR grant no. 15-08-09261-a. The work of E. N. Pivovarova was carried out within the framework of the grant of the President of the Russian Federation for the Support of Young Candidates of Science (MK-2171.2014.1). The work of T. B. Ivanova (Section 3) was supported by the RSF grant no. 14-19-01303.


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MSC: 37J60, 70E18, 70F25
Received: 17.09.2015

Citation: 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

Citation in format AMSBIB
\by Alexander A. Kilin, Elena N. Pivovarova, Tatyana B. Ivanova
\paper Spherical Robot of Combined Type: Dynamics and Control
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 6
\pages 716--728

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    This publication is cited in the following articles:
    1. A. A. Kilin, Yu. L. Karavaev, “Eksperimentalnye issledovaniya dinamiki sfericheskogo robota kombinirovannogo tipa”, Nelineinaya dinam., 11:4 (2015), 721–734  mathnet
    2. 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
    3. E. V. Vetchanin, A. A. Kilin, “Controlled motion of a rigid body with internal mechanisms in an ideal incompressible fluid”, Proc. Steklov Inst. Math., 295 (2016), 302–332  mathnet  crossref  crossref  mathscinet  isi  elib
    4. 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
    5. 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
    6. Yu. L. Karavaev, A. V. Klekovkin, A. A. Kilin, “Dinamicheskaya model treniya kacheniya sfericheskikh tel po ploskosti bez proskalzyvaniya”, Nelineinaya dinam., 13:4 (2017), 599–609  mathnet  crossref  elib
    7. E. N. Pivovarova, “Issledovanie ustoichivosti statsionarnykh dvizhenii sferorobota kombinirovannogo tipa”, Nelineinaya dinam., 13:4 (2017), 611–623  mathnet  crossref  elib
    8. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration”, Regul. Chaotic Dyn., 22:8 (2017), 955–975  mathnet  crossref
    9. 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
    10. 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
    11. 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
    12. 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
    13. A. V. Borisov, I. S. Mamaev, E. V. Vetchanin, “Dynamics of a Smooth Profile in a Medium with Friction in the Presence of Parametric Excitation”, Regul. Chaotic Dyn., 23:4 (2018), 480–502  mathnet  crossref  mathscinet
    14. A. A. Kilin, E. N. Pivovarova, “Integrable Nonsmooth Nonholonomic Dynamics of a Rubber Wheel with Sharp Edges”, Regul. Chaotic Dyn., 23:7-8 (2018), 887–907  mathnet  crossref
    15. V. Putkaradze, S. Rogers, “On the dynamics of a rolling ball actuated by internal point masses”, Meccanica, 53:15 (2018), 3839–3868  crossref  mathscinet  isi  scopus
    16. 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
    17. A. A. Kilin, T. B. Ivanova, E. N. Pivovarova, “Control of the rolling motion of a spherical robot on an inclined plane”, Dokl. Phys., 63:10 (2018), 435–440  mathnet  crossref  crossref  isi  elib  scopus
    18. 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  crossref  crossref  isi  elib  elib  scopus
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