Constraint Control of Nonholonomic Mechanical Systems

Vakhtang Putkaradze, Stuart Rogers

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 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 SO(3). We show that it is possible to control the system using the constraint ξ(t) and demonstrate numerical examples in which the system tracks quite complex trajectories such as a spiral.

Original languageEnglish (US)
Pages (from-to)193-234
Number of pages42
JournalJournal of Nonlinear Science
Issue number1
StatePublished - Feb 1 2018

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media, LLC.


  • Nonholonomic mechanics
  • Optimal control
  • Suslov’s problem


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