Publication: Constraint Control of Nonholonomic Mechanical Systems
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Constraint Control of Nonholonomic Mechanical Systems

- Article in a journal -
 

Area
Mechanical Engineering

Author(s)
Vakhtang Putkaradze , Stuart Rogers

Published in
Journal of Nonlinear Science

Year
2018

Abstract
We derive an optimal control formulation for a nonholonomic mechanical system using the nonholonomic constraint itself as the control. We focus on Suslov's problem, which is defined as the motion of a rigid body with a vanishing projection of the body frame angular velocity on a given direction $$\backslashvarvec{\backslashxi }$$ ξ . We derive the optimal control formulation, first for an arbitrary group, and then in the classical realization of Suslov's problem for the rotation group $$\backslashtextit{SO}(3)$$ SO ( 3 ) . We show that it is possible to control the system using the constraint $$\backslashvarvec{\backslashxi }(t)$$ ξ ( t ) and demonstrate numerical examples in which the system tracks quite complex trajectories such as a spiral.

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BibTeX
@ARTICLE{
         Putkaradze2018CCo,
       author = "Putkaradze, Vakhtang and Rogers, Stuart",
       title = "Constraint Control of Nonholonomic Mechanical Systems",
       journal = "Journal of Nonlinear Science",
       pages = "193--234",
       abstract = "We derive an optimal control formulation for a nonholonomic mechanical system using
         the nonholonomic constraint itself as the control. We focus on Suslov's problem, which is
         defined as the motion of a rigid body with a vanishing projection of the body frame angular velocity
         on a given direction {\$}{\$}{\backslash}varvec{\{}{\backslash}xi
         {\}}{\$}{\$} $\xi$ . We derive the optimal control formulation, first for an
         arbitrary group, and then in the classical realization of Suslov's problem for the rotation
         group {\$}{\$}{\backslash}textit{\{}SO{\}}(3){\$}{\$} SO ( 3 ) .
         We show that it is possible to control the system using the constraint
         {\$}{\$}{\backslash}varvec{\{}{\backslash}xi {\}}(t){\$}{\$}
         $\xi$ ( t ) and demonstrate numerical examples in which the system tracks quite complex
         trajectories such as a spiral.",
       issn = "1432-1467",
       doi = "10.1007/s00332-017-9406-1",
       url = "https://doi.org/10.1007/s00332-017-9406-1",
       year = "2018",
       volume = "28",
       number = "1",
       ad_area = "Mechanical Engineering",
       ad_tools = "ADiGator"
}


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