The attitude control problem of a rigid spacecraft containing a redundant set of reaction wheels is investigated. The classical solution path determines a control solution which requires the smallest set of motor torques. With small micro spacecraft the available power or the energy consumption are critical factors. A locally optimal attitude control strategy is developed which minimizes the instantaneous electrical power requirements. Degenerate conditions with several fly wheel speeds being zero are also investigated. The new control is able to reduce the amount of power and energy required by about 10%, while only marginally increasing the average required torque.
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