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Attitude controllability analysis of an underactuated satellite with two reaction wheels and its control

In view of the fact that actuators of satellites often break down in long term missions, this paper tackles attitude control problems of satellites by two actuators, especially two reaction wheels, for a failsafe. The contributions of this work, compared with our previous works, are to consider not only kinematics but dynamics of the satellite and to handle arbitrary structure of the communication antenna and two wheels axes. Based on the analysis on equilibrium points, rotation movement and controllability, we divide the control problem into the following three cases. First, in the case that equilibrium points exist, we propose a controller to achieve arbitrary directions of the communication antenna without any rotation. Secondly, if there exists no equilibrium point, we give a sufficient condition and a control law to achieve the desired direction of the antenna, where the satellite remains to rotate around the desired axis. Finally, when neither the first case condition nor the second one is satisfied, it is known that we cannot keep the direction of the antenna in the desired direction, and we can control the direction periodically instead.