Satellite formation flying control of the relative trajectory shape and size using lorentz forces - Amaro, Gonçalo da Costa (2022)
Propellantless control approaches for small satellite formation flying represent a special interest and an important advantage for space industry nowadays. A formation flying control algorithm using the Lorentz force for LowEarth Orbits to achieve a trajectory with required shape and size is proposed in this dissertation. The Lorentz force is produced as the result of interaction between the Earth’s magnetic field and an electrically charged spacecraft. Achieving the required trajectories represents a challenge since the control is the variation of the satellite’s charge value. This control mechanism simplicity cannot provide full controllability. A Lyapunovbased control is developed for elimination of the initial relative drift after launch and it is aimed for reaching a required relative trajectory with predefined shape and size. The control algorithm is constructed to correct different parameters of the relative trajectory at different relative positions. The required amplitudes for close relative trajectories for inplane and outofplane motion as well as the relative drift and shift of elliptical relative orbits are controllable using Lorentz force. Due to the absence of full controllability, the algorithm is incapable to correct the inplane and outofplane motion phases, once these parameters are defined by the deployment conditions and therefore arbitrary. The proposed control allows the convergence to the trajectory with required shape and size. Centralized and decentralized control approaches are implemented and their performance is studied. The centralized approach considers two satellites formation formed by an electrically neutral leader satellite moving on a circular LEO and a follower which actively controls its orbital motion by changing its charge in order to remain in close vicinity of the leader. Formation flying consisting of more than two satellites with chargechanging capability can also be controlled by the proposed algorithm using a decentralized approach. This work also considers the control of satellite swarm trajectories in a sphereshaped formation. Numerical simulation of the relative motion is used to study performance of the control algorithm. It implements the model of the geomagnetic field as a tilted dipole. The repulsive collision avoidance control is proposed for the case when the system elements are inside a dangerous proximity area. The convergence time and final trajectory accuracy are evaluated for different simulation parameters and conditions.