# Modeling and Control of Satellite Formations: A Survey
## 3 Circle Formation Architecture
Each unit performs its own calculations based on the data obtained either as measurements or on the basis of the data transmitted from the entire group. In a decentralized architecture, there is no central entity to unify results. Hierarchical--includes hybrids of the above two architectures. The large spacecraft group can be divided into smaller ones, each with its own architecture and grading system. The simulation results given in [101] show that the decentralized reduced-order filter leads to simultaneous close to optimal estimates, as well as to the balance of communication and computational resources between the spacecraft. In addition, [PERSON] and [PERSON] [101] presented a hierarchical architecture for embedding decentralized assessment systems when scaling a problem for a large number of spacecraft in a group, as well as a necessary condition for a communication topology that guarantees the stability of the operation of simultaneously parallel computers and controllers. The purpose of the research presented in [102] is an analysis of the dynamics of orientation and control of a connected satellite formation moving where the connected nodes are modeled as extended rigid bodies. Ref. [102] uses a three-in-a-row structure, and the general formula for the equations of motion of the system is obtained using the Lagrange method. The motions of the associated satellite system are analyzed in a three-dimensional coordinate system in outer space. The System Dependent Riccati Equation Regulator (SDRE) is used to eliminate orientation errors. The stability region for an SDRE-driven coupled satellite system is estimated numerically to show the global asymptotic robustness of the steering method. Centralized and decentralized approaches are applied to a dynamic system to compare targeting performance. It was found that the SDRE works well with both centralized and decentralized approaches to control the orientation of linked satellites in the formation of motion. The design of a formation flying orbit control system for LEO satellites based on the SDRE control approach may be also found in [103]. In [104], the problem of controlling the motion of an electromagnetic formation using the finite time method is investigated. The principle of electromagnetic formation flight (EMFF) uses magnetic fields electrically generated by all satellites, which then allows you to control the relative degrees of freedom. In EMFF, each satellite is equipped with three orthogonal magnetic coils and three orthogonal flywheels [105]. Figure 1: Illustration of a group of three Coulomb spacecraft orbiting in deep space around the center of mass of their cluster. [PERSON] and [PERSON] [104] presented an electromagnetic force model and analyzes the effect of the Earth's magnetic field on EMFF satellites. Then, the equations of relative motion and the method for describing the general formation are established. The robust sliding mode controller is designed to track the trajectory in the presence of model uncertainties and external noise. The proposed controller, which combines the advantages of linear and terminal sliding mode control, can guarantee the convergence of tracking errors in a finite time, and not in an asymptotic sense. By constructing a specific Lyapunov function, the closed-loop system is proved to be globally stable and convergent. Numerical simulations of the maintenance and formation reconfiguration are then presented to show the efficiency of the designed controller. Optimal reconfigurations of the Coulomb formation of two spacecraft are found in [106] using nonlinear optimal control methods. The aim of reconfigurations is to maneuver two spacecraft between two charged equilibrium configurations. Four optimality criteria are considered: minimum time, minimum separation acceleration, minimum use of fuel for an electric motor, and minimum power consumption. Reconfiguration between equilibria is first considered by changing the desired dilution distance.