Fully distributed formation flying control of multiple spacecraft by observer-based linear output protocols

This article addresses the problem of formation flying control for multiple spacecraft in the presence of undirected graphs. The study assumes that only relative output information among spacecraft is available. Leveraging the linearized Clohessy-Wiltshire equations, the article introduces two novel distributed observer-based linear static output protocols, along with their reduced-order counterparts. The parameters of the gains are meticulously selected by constructing a Lyapunov function that comprises a positive semidefinite term and two integral terms, commonly employed in absolute stability theory. The most significant advantages of this article are that the designed protocols are linear and work in a fully distributed manner, that is, they do not need the a priori global information of the network topology (namely, the spectrum of the associated Laplacian matrix) and can thus achieve formation flying for any undirected communication graph with an arbitrary number of spacecraft. Numerical simulations show the effectiveness of the proposed approaches.