Satellite Cluster Flight Using Guidance Trajectory and Model Predictive Control

This paper presents a model predictive control based framework that is used in conjunction with a polytope boundary constraint and the Hill-Clohessy-Wiltshire equations to maintain a desired formation of a cluster of spacecraft while also allowing freedom to maneuver within the allowable bounds. A fuel optimal guidance trajectory is generated and the model predictive control framework controls to this desired trajectory. The operational polytope boundaries enable the predictive framework of the model predictive control to be used to make small maneuvers to correct perturbations from its desired trajectory. The boundaries are designed such that no two agents have overlapping regions, allowing the vehicles to execute avoidance strategies without continually maintaining the trajectories of other agents. The model predictive control framework combined with the convex polytope boundary enables a scalable method that can support clusters of satellites in safely achieving mission objectives while minimizing fuel usage. As part of the implementation of this control scheme, this paper compares the fuel usage for a three spacecraft system. This work also compares the computation and fuel requirements for L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_1$$\end{document}, L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}, and L infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_\infty$$\end{document} norm formulations of the framework.