A new minimum infinity-norm solution: With application to capacity analysis of spacecraft reaction wheels

In this study, a new algorithm is presented to find a minimum infinity-norm, or L_∞-norm, solution of an underdetermined linear equations system. Contrary to the previous algorithms, which in fact solve its `dual optimization problem´ instead of the problem itself, the newly proposed one directly solves the minimum L_∞-norm problem using properties of the solution. Therefore, it is more straightforward, easy to understand, and deepening our understanding of the problem. In order to show the usability of the proposed algorithm, the present paper also includes an example of its applications to the capacity analysis of spacecraft reaction wheels. The algorithm can be used to define the torque/momentum envelopes, which are the maximum torque/momentum capacities of the reaction wheels, respectively. The resultant envelopes then can be used to determine the optimal specification requirements of the reaction wheels to achieve mission requirements.