Variational discretization for optimal control problems of nonholonomic mechanical systems

This paper explores the construction of geometric and variational methods for the optimal control of nonholonomic mechanical systems, and the construction of variational integrators for this class of optimal control problems. Given a cost function, the optimal control problem is understood as a constrained higher-order variational problem. Through a variational discretization of a Lagrangian defined in a submanifold of the tangent space of the constraint distribution, we obtain the discrete Euler-Lagrange equations for the nonholonomic optimal control problem. The optimal control of a Chaplygin sleigh is presented as an illustrative example.