Abstract:
This paper is concerned with the motion of a helical body in an ideal fluid, which is controlled by rotating three internal rotors. It is proved that the motion of the body is always controllable by means of three rotors with noncoplanar axes of rotation. A condition whose satisfaction prevents controllability by means of two rotors is found. Control actions that allow the implementation of unbounded motion in an arbitrary direction are constructed. Conditions under which the motion of the body along an arbitrary smooth curve can be implemented by rotating the rotors are presented. For the optimal control problem, equations of sub-Riemannian geodesics on SE(3) are obtained.
Keywords:
ideal fluid, motion of a helical body, Kirchhoff equations, control of rotors, gaits, optimal control.
The work of E.V.Vetchanin and I. S.Mamaev (Introduction and Sections 1 and 2) was supported by the Russian Science Foundation (project No. 14-19-01303). The work of A. A.Kilin (Section 3 and Conclusion) was supported by the Russian oundation for Basic Research No. 14-01-00395-a and No. 15-08-09093-a.
Citation:
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
\Bibitem{VetKilMam16}
\by Evgeny V. Vetchanin, Alexander A. Kilin, Ivan S. Mamaev
\paper Control of the Motion of a Helical Body in a Fluid Using Rotors
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 7-8
\pages 874--884
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\crossref{https://doi.org/10.1134/S1560354716070108}
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Linking options:
https://www.mathnet.ru/eng/rcd233
https://www.mathnet.ru/eng/rcd/v21/i7/p874
This publication is cited in the following 7 articles:
A. V. Borisov, E. V. Vetchanin, I. S. Mamaev, “Motion of a smooth foil in a fluid under the action of external periodic forces. II”, Russ. J. Math. Phys., 27:1 (2020), 1–17
E. V. Vetchanin, “The Motion of a Balanced Circular Cylinder in an Ideal Fluid Under the Action of External Periodic Force and Torque”, Rus. J. Nonlin. Dyn., 15:1 (2019), 41–57
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
E. V. Vetchanin, V. A. Tenenev, A. A. Kilin, “Optimalnoe upravlenie dvizheniem v idealnoi zhidkosti tela s vintovoi simmetriei s vnutrennimi rotorami”, Kompyuternye issledovaniya i modelirovanie, 9:5 (2017), 741–759
E. V. Vetchanin, I. S. Mamaev, “Optimal control of the motion of a helical body in a liquid using rotors”, Russ. J. Math. Phys., 24:3 (2017), 399–411
Yury L. Karavaev, Alexander A. Kilin, Anton V. Klekovkin, “Experimental Investigations of the Controlled Motion of a Screwless Underwater Robot”, Regul. Chaotic Dyn., 21:7-8 (2016), 918–926
E. V. Vetchanin, A. A. Kilin, “Upravlenie dvizheniem neuravnoveshennogo tyazhelogo ellipsoida v zhidkosti s pomoschyu rotorov”, Nelineinaya dinam., 12:4 (2016), 663–674
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