Regular and Chaotic Dynamics

, Volume 21, Issue 7–8, pp 874–884 | Cite as

Control of the motion of a helical body in a fluid using rotors

  • Evgeny V. Vetchanin
  • Alexander A. Kilin
  • Ivan S. Mamaev
Nonlinear Dynamics & Mobile Robotics

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 

MSC2010 numbers

70Q05 70Hxx 76Bxx 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • Evgeny V. Vetchanin
    • 1
  • Alexander A. Kilin
    • 2
  • Ivan S. Mamaev
    • 1
  1. 1.Izhevsk State Technical UniversityIzhevskRussia
  2. 2.Udmurt State UniversityIzhevskRussia

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