  We study the tracking of a trajectory for a nonholonomic system by recasting
the problem as an optimal control problem. The cost function is chosen to
minimize the error in positions and velocities between the trajectory of a
nonholonomic system and the desired reference trajectory evolving on the
distribution which defines the nonholonomic constraints. We prepose a geometric
framework since it describes the class of nonlinear systems under study in a
coordinate-free framework. Necessary conditions for the existence of extrema
are determined by the Pontryagin Minimum Principle. A nonholonomic fully
actuated particle is used as a benchmark example to show how the proposed
method is applied.
