Periodic forcing, dynamics and control of underactuated spacecraft and underwater vehicles

In this paper we describe spacecraft and underwater vehicle dynamics with small-amplitude, periodically time-varying forcing. The dynamic descriptions are derived so that they can be used to prescribe forcing laws for controlling the motion of these systems when they are underactuated, i.e., when the number of force inputs is less than the dimension of the configuration space. The use of periodic force inputs is motivated by the demonstrated success of using periodic velocity inputs in the associated nonholonomic kinematic spacecraft and underwater vehicle motion control problems, e.g., controlling underactuated spacecraft driven with internal rotors and underwater vehicles at low Reynolds number. By now addressing dynamic as well as kinematic response, we provide results that are useful in many practical problems in which the system cannot be modelled as purely kinematic, e.g., controlling underactuated spacecraft driven with gas jets and underwater vehicles at high Reynolds number.