Underactuated Spacecraft Switching Law for Two Reaction Wheels and Constant Angular Momentum

This paper develops a switching feedback controller for the attitude of an underactuated spacecraft that exploits two internal control torques provided by reaction wheels. The problem is challenging; for example, even in the zero total angular momentum case, no smooth or even continuous time-invariant feedback law for stabilizing a desired orientation exists. The method introduced here exploits the separation of the system states into inner-loop base variables and outer-loop fiber variables. The base variables track periodic reference trajectories, the amplitude of which is governed by parameters that are adjusted to induce an appropriate change in the fiber variables. Under suitable assumptions on the total angular momentum, this controller stabilizes an equilibrium that corresponds to a desired inertially fixed orientation. If the desired attitude violates the assumption on angular momentum, then controlled oscillations in a neighborhood around the target orientation are induced by the switching controller. The control scheme is based on several approximations and is designed for relatively small maneuvers close to the desired attitude in a vicinity which may be achieved by thruster-based control schemes. Simulation results demonstrate that the switching feedback law provides good performance in controlling the attitude of an underactuated spacecraft.