Redundant Reaction Wheel Torque Distribution Yielding Instantaneous L2 Power-Optimal Spacecraft Attitude Control

The attitude-control problem of a rigid spacecraft containing a redundant set of reaction wheels is investigated. Particularly with small spacecraft the available power is very limited due to the small surface area to radiate excess heat. A power-optimal reaction wheel motor torque distribution strategy is developed that minimizes the instantaneous electrical power requirements. Power regeneration from slowing down the wheels is not considered in this work. The new torque distribution is developed as a modification to the traditional minimum-torque solution. Degenerate conditions in which at least one rotor has zero speed are investigated, as well as particular symmetric wheel speed configurations. The new control is able to reduce the amount of mechanical power and energy required by about 10―20%, while only marginally increasing the average required torque.