Maximum Torque and Momentum Envelopes for Reaction Wheel Arrays

Spacecraft reaction wheel maneuvers are limited by the maximum torque and/or angular momentum that the wheels can provide. For an n-wheel configuration, the torque or momentum envelope can be obtained by projecting the n-dimensional hypercube, representing the domain boundary of individual wheel torques or momenta, into three dimensional space via the 3xn matrix of wheel axes. In this paper, the properties of the projected hypercube are discussed, and algorithms are proposed for determining this maximal torque or momentum envelope for general wheel configurations. Practical strategies for distributing a prescribed torque or momentum among the n wheels are presented, with special emphasis on configurations of four, five, and six wheels.