Single axis pointing for underactuated spacecraft with a residual angular momentum

The problem of aiming a generic body-fixed axis along an inertially fixed direction is dealt with for an underactuated spacecraft in the presence of a non-zero residual angular momentum, when only two reaction wheels can exchange angular momentum with the spacecraft platform. An analytical condition for the feasibility of the desired pointing is derived first, together with a closed-form solution for the corresponding attitude with zero platform angular rate. A nonlinear controller is then developed in the framework of singular perturbation theory, enforcing a two-timescale response to the system. Convergence to the desired attitude, when the pointing direction falls within admissible limits, is then proved for rest-to-rest maneuvers and randomly generated initial tumbling conditions for a configuration representative of a small-size satellite.