  We consider the motion planning of an object in a Riemannian manifold where
the object is steered from an initial point to a final point utilizing optimal
control. Considering Pontryagin Minimization Principle we compute the Optimal
Controls needed for steering the object from initial to final point. The
Optimal Controls were solved with respect to time t and shown to have norm 1
which should be the case when the extremal trajectories, which are the
solutions of Pontryagin Principle, are arc length parametrized. The extremal
trajectories are supposed to be the geodesics on the Riemannian manifold. So we
compute the geodesic curvature and the Gaussian curvature of the Riemannian
structure.
