Constraint Control of Nonholonomic Mechanical Systems

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

48 pages, 9 figures

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