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- Article in a journal -

Area
Mechanical Engineering

Author(s)

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.

 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" }