Optimal control of underactuated nonholonomic mechanical systems

In this paper we use a nonholonomic affine connection formulation to study an optimal control problem for a class of nonholonomic, under-actuated mechanical systems. The class of nonholonomic systems we study in this paper includes, in particular, wheeled-type vehicles, which are important for many robotic locomotion systems. We illustrate our ideas by considering a simple example on a three-dimensional manifold