# Modeling and Control of Satellite Formations: A Survey
## 4 Leader-Follower Formation Architecture
For a constellation of satellites, a formation adjuster is proposed that includes a position adjuster for the formation of the desired precise formation and a position adjuster for aligning the positions of the satellites. It is shown that errors in trajectory tracking and orientation of the entire closed-loop control system can converge to a given neighborhood of the origin in a finite time. Simulation results are presented to demonstrate the benefits of the proposed formation control scheme. In [142], trajectory analysis, mission design, and the control law for several microsatellites for joint traversal of the spacecraft are considered. The problem of the cooperative movement of a group of satellites along an elliptical trajectory, i.e. cooperative circumnavigation, (CCN) is first defined to bring the group of microsatellites to a predetermined plane ellipse relative to the host spacecraft while maintaining the geometric configuration of the formation. Then, a CCN control law is proposed, in which artificial potential functions and the Laplace affine matrix are applied to fulfill the requirements of the CCN mission. Simulation results are presented to show the feasibility of this approach. In [143], a joint navigation approach for unmanned aerial vehicles (UAVs) is presented, which makes it possible to reliably and accurately determine the orientation of the main aircraft flying in formation with other UAVs (alternates, slaves). The proposed method is based on a closely related extended Kalman filter using the spatial diversity of measurements from global navigation satellite systems (GNSS) and vision systems integrated with data from inertial and magnetic sensors. The main focus is on the external environment, and the innovative idea is to extend the attitude estimation approaches based on multiple GNSS antennas to a multipurpose system where differential GNSS and UAV visual tracking of UAVs are used to create a virtual auxiliary navigation sensor. The processing concept and architecture are described with an emphasis on an ECP measurement update phase that is applicable to any number of collaborating proxies and to different GNSS processing architectures. The effectiveness of the proposed method is evaluated by experimental tests using two multi-rotors and two fixed ground antennas, one of which is used as a ground reference point for the analysis of pointing accuracy. The results show the feasibility of the developed approach in terms of accuracy and providing drift-free estimates in real-time or in post-processing scenarios. A group of four satellites forming a tetrahedron is discussed in [144]. The task is to maintain relative orbits so that the tetrahedron retains its shape and size over time according to the introduced criterion. The problem of constructing relative reference orbits of satellites is solved, which, within the framework of the linear HCW model, ensure the preservation of the tetrahedron parameters in the absence of control. In the framework of the Schweigart-Sedwick linear model [91, 92], which takes into account the influence of the second harmonic of the geopotential, as well as in the framework of a nonlinear motion model with the second harmonic, algorithms are proposed for constructing uniaxial motion control of satellites oriented along the Earth's magnetic field, which ensure the maintenance of relative orbits. In [145], the task of controlling a group of four satellites in a low near-circular Earth orbit is considered. The satellites form a tetrahedron of a certain shape and size. The initial data were selected in such a way that the change in the shape and size of this tetrahedron during the movement of satellites in orbit was minimal. The choice of the initial data was carried out analytically and then numerically refined. [PERSON] et al. [146] presented an approach to solving a class of problems arising in the development of satellite swarms. The key issue addressed in this article is \"simultaneous\" fusion and orbit control to achieve swarm configuration.