Optimal uses of reaction wheels in the pyramid configuration using a new minimum infinity-norm solution

In this study, simple methods are presented to improve the agility performance of a spacecraft with four reaction wheels in the pyramid configuration. A new and simple method is proposed to determine the momentum and the torque envelopes, which are defined as the maximum momentum and torque capacities of the wheel array, respectively. Then, based on the geometry of the envelopes, the best shape of the pyramid configuration needed to deliver optimal agility performance is discussed. In this paper, new methods are also proposed to optimally distribute three-dimensional torque and momentum commands, to the individual reaction wheels. The developed methods are based on the use of novel algorithms to solve minimum infinity-norm, or L∞L∞-norm, problems. These algorithms can easily be implemented with minimal modification of conventional ones, but yield considerable improvement of agility performance in numerical examples.