Abstract:
In this paper we consider the control of a dynamically asymmetric balanced ball on a plane in the case of slipping at the contact point. Necessary conditions under which a control is possible are obtained. Specific algorithms of control along a given trajectory are constructed.
This work was supported by Analytic Departmental Target Program “Development of Scientific
Potential of Higher Schools” for 2012–2014, no.1.1248.2011, the Grant of the President of the
Russian Federation for Support of Leading Scientific Schools NSh-2964.2014.1, the grant of the
President of the Russian Federation for the Support of Young Doctors of Science (MD-2324.2013.1)
and Candidates of Science (MK-2171.2014.1).
Citation:
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
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\by Tatiana B. Ivanova, Elena N. Pivovarova
\paper Comments on the Paper by A.V. Borisov, A.A. Kilin, I.S. Mamaev "How to Control the Chaplygin Ball Using Rotors. II"
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 1
\pages 140--143
\mathnet{http://mi.mathnet.ru/rcd145}
\crossref{https://doi.org/10.1134/S1560354714010092}
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This publication is cited in the following 16 articles:
Yu. L. Karavaev, “Spherical Robots:
An Up-to-Date Overview of Designs and Features”, Rus. J. Nonlin. Dyn., 18:4 (2022), 709–750
Alexander A. Kilin, Elena N. Pivovarova, “Motion control of the spherical robot rolling on a vibrating plane”, Applied Mathematical Modelling, 109 (2022), 492
Vakhtang Putkaradze, Stuart M. Rogers, “On the Normal Force and Static Friction Acting on a Rolling Ball Actuated by Internal Point Masses”, Regul. Chaotic Dyn., 24:2 (2019), 145–170
T. B. Ivanova, A. A. Kilin, E. N. Pivovarova, “Controlled motion of a spherical robot with feedback. II”, J. Dyn. Control Syst., 25:1 (2019), 1–16
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
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
A. V. Borisov, E. V. Vetchanin, A. A. Kilin, “Control of the Motion of a Triaxial Ellipsoid in a Fluid Using Rotors”, Math. Notes, 102:4 (2017), 455–464
Alexey V. Borisov, Ivan S. Mamaev, “Adiabatic Invariants, Diffusion and Acceleration in Rigid Body Dynamics”, Regul. Chaotic Dyn., 21:2 (2016), 232–248
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
Evgeny V. Vetchanin, Alexander A. Kilin, Ivan S. Mamaev, “Control of the Motion of a Helical Body in a Fluid Using Rotors”, Regul. Chaotic Dyn., 21:7-8 (2016), 874–884
E. V. Vetchanin, A. A. Kilin, “Upravlenie dvizheniem neuravnoveshennogo tyazhelogo ellipsoida v zhidkosti s pomoschyu rotorov”, Nelineinaya dinam., 12:4 (2016), 663–674
V. Kozlov, “The phenomenon of reversal in the Euler–Poincaré–Suslov nonholonomic systems”, J. Dyn. Control Syst., 22:4 (2016), 713–724
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
I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Hamiltonization of elementary nonholonomic systems”, Russ. J. Math. Phys., 22:4 (2015), 444–453
Yu. L. Karavaev, A. A. Kilin, “Dinamika sferorobota s vnutrennei omnikolesnoi platformoi”, Nelineinaya dinam., 11:1 (2015), 187–204
Yizhar Or, “Painlevé’s Paradox and Dynamic Jamming in Simple Models of Passive Dynamic Walking”, Regul. Chaotic Dyn., 19:1 (2014), 64–80
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