Decentralized Differential Aerodynamic Control of Microsatellites Formation with Sunlight Reflectors

Abstract

The paper presents a study of decentralized control for a satellite formation flying mission that uses differential lift and drag to enforce the relative positioning requirements. All spacecraft are equipped with large sunlight reflectors so that, given the appropriate lighting conditions, the formation as a whole can be made visible from the Earth as a configurable pixel image in the sky. The paper analyzes the possibility of achieving a pre-defined lineup of the formation by implementing decentralized aerodynamic-based control through the orientation of sunlight reflectors relative to the incoming airflow. The required relative trajectories are so-called projected circular orbits which ensure the rotation of the image with the orbital period. The choice of the reference trajectory for each satellite is obtained by minimizing the total sum of relative trajectory residuals. The control law is based on the linear-quadratic regulator with the decentralized objective function of reducing the mean deviation of each satellite’s trajectory relative to the other satellites. The accuracy of the required image construction and convergence time depending on the initial conditions and orbit altitude are studied in the paper.

Keywords

• formation flying
• differential aerodynamic force
• decentralized control
• linear-quadratic regulator
• linear programming optimization