On the Construction of Variational Integrators for Optimal Control of Nonholonomic Mechanical Systems

In this paper we derive variational integrators for optimal control problems of nonholonomic mechanical systems. We rewrite the system as a constrained second-order variational problem, that is, as a problem where the Lagrangian and constraints are defined in terms of the position, velocity and the acceleration of the system. Instead of discretizing directly the equations of motion, we discretize the corresponding Hamilton’s principle of critical action to derive a geometric integrator. We use the classical Lagrange multipliers method for constrained problems to derive this numerical scheme. An optimal control problem of a nonholonomic particle is given to illustrate the contents of the work.