LAUSR

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