# Modeling and Control of Satellite Formations: A Survey
## 1 Introduction
The first demonstration of collision avoidance and orbit control for UWE-4 pico-satellites is presented in [PERSON] and [PERSON] [13]. A possible collision with a piece of space debris was avoided by UWE-4 by use of its orbit control capabilities for an evasive maneuver in early July 2020. This maneuver increased the miss distance from 822 m to more than 6000 m. The results, presented in [13] demonstrate perspectives for small spacecraft to comply with regulations on de-orbiting and capabilities for collision avoidance maneuvers. Ref. [PERSON] and [PERSON] [14] used the optimal and adaptive control techniques to develop the satellite formation flying-high precision guidance. The mentioned examples are related to the SFF missions and the formation flying guidance (FFG), which is considered as the generation of the reference trajectories used as an input for a formation agent's relative state tracking control law. The examples mentioned are related to the SFF missions and the formation flying guidance (FFG), which is considered as the generation of any reference trajectories used as an input for a formation agents' relative state tracking control law [1]. A detailed and informative review of the results on the control of spacecraft formations can also be found in the monograph [15], which presents fundamental problems and approaches related to group flights of spacecraft, provides information on the dynamics of satellite motion, considers methods of static optimization, feedback control, and filtration, the nonlinear models of the relative spacecraft motion, including the rendezvous of satellites, orbital perturbations and methods for their effect mitigating, as well as the methods for groups of spacecraft control algorithms development. To implement the given navigation laws by individual agents of the group, control algorithms are developed--both local control algorithms for each satellite separately, and algorithms based on the receipt by individual agents of data on the state (e.g., positions and velocities) of other satellites. This paper provides a comprehensive overview of spacecraft formation flight control (SFFC), covering design methods and stability results analysis for these coupled state control laws. Since the SFFC architecture defines a general approach to the development of a particular SFFC algorithm, it is reasonable to organize publications according to the formation architecture. Therefore, following the lines of the 2004 review on the subject [1], in the present paper, the SFFC literature is divided into three main types: Multiple-Input-Multiple-Output (MIMO), in which the formation is treated as a single entity with multiple inputs and multiple outputs; the leader-follower (LF) formation, in which individual spacecraft controllers are linked hierarchically; and a virtual framework as the virtual structure (VS) formation, in which spacecraft are treated as rigid bodies embedded in a common virtual rigid body, and the master/slave configuration. This survey is aimed to expand [1] and present modern results of recent years. When picking up papers for reviewing, the authors have largely been guided by the influence of the papers on other publications in the field. For example, works [16; 17; 18] by the time of the review submission received 237, 193, 156 citations, respectively, in the database Scopus. In addition, the selection of material in this work was undoubtedly influenced by the scientific interests of the authors, who apologize in advance to colleagues whose contributions were outside the main focus of this review. The rest of the paper is organized as follows. Section 2 deals with the MIMO formation architecture. The circle formation is described in Section 3, whilst Section 4 is devoted to leader-follower architecture. Concluding remarks of Section 5 finalize the paper. In general, the references inside each Section are given in chronological order.