Geometries of single-input locally accessible control systems

The description of a nonlinear control system as an exterior differential system suggests an interesting connection between locally accessible control systems and the existence of a natural geometry associated to the control system. The classification of single-input locally accessible control systems leads to a canonical construction of a (pseudo-) Riemannian metric on the state space. Conditions for the existence of such a metric are derived and the construction is illustrated in a simple example.