Control properties of underactuated vehicles

This paper studies control properties of the dynamics of underactuated vehicles (e.g. underactuated surface vessels, underwater vehicles, aeroplanes or spacecraft). The unactuated dynamics implies constraints on the accelerations. Both the necessary and sufficient conditions for these constraints to be second-order nonholonomic, first-order nonholonomic or holonomic are developed. It is shown that underactuated vehicles with a gravitational field where the elements corresponding to the unactuated dynamics are zero, are not C¹ asymptotically stabilizable to a single equilibrium