New Minimum Infinity-Norm Solution and Rapid Eigenaxis Attitude Maneuvering of Spacecraft

This paper presents a new algorithm for determining the minimum infinity-norm, or L∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_\infty $$\end{document}-norm solution to a system of underdetermined consistent linear equations. This algorithm can be applied to enable rapid attitude maneuvering of spacecraft. Unlike previous algorithms that consider the dual optimization problem, the proposed algorithm solves the control problem directly using the inherent properties of the solution. Therefore, the algorithm is relatively straightforward, easy to understand and implement, and provides more insight into the nature of the problem. Using the proposed algorithm, the maximum torque of a reaction-wheel array along a given direction can be determined in real-time onboard, thus improving the spacecraft’s attitude agility compared with the widely used minimum L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_2$$\end{document}-norm solutions.