Satellite attitude control systems often use reaction wheels as their primary method of pointing control. Four reaction wheel systems arc popular as they provide redundancy in the event of actuator failure. The reaction wheels are often orientated in the shape of a tetrahedron (equal angles between all orientation vectors), a tripod (3 wheels along the primary axes, and one at 45° to these axes), or a pyramid (all wheels at right angles on the {^above letter x}- {^above letter y} plane, and inclined towards z), as these provide simpler decoupling of reaction wheel torques to satellite body torques. In this paper, first the orientation of wheels in a tetrahedron, tripod and pyramidal based four reaction wheel control systems for a small satcllitc, such as a 3-unit Cubcsat, is optimised to maximise the available decoupled acceleration per axis in the event of a single reaction wheel failure. Results show a moderate improvement in available decoupled acceleration per axis can be achieved using a pyramidal orientation that is offset compared to the conventional arrangement, and the pyramidal configuration outperforms the others is all situations. Secondly, the optimisation is repeated with the reaction wheel orientations allowed to move freely with respect to each other. Results show a very minor improvement in available decoupled acceleration per axis can be achieved during fault conditions.
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