Decentralized Formation and Constellation Stability Design Requirements Using Differential Mean Orbit Elements

Abstract

Over the past few years, there has been an increased interest in large constellation architectures for different applications and services within the aerospace industry. Inherently, the growing attention to these complex systems comes with a desire for mission robustness and safety. Therefore, the aim of this paper is to enable a framework of necessary conditions to guarantee stability for formations with low levels of communication as well as low knowledge of control policies between users and formations with coordinated or uncoordinated impulsive maneuvers. A weighted formation barycenter and formation slots are presented to define the formation problem. Graph theory results are leveraged to demonstrate convergence on the consensus of the formation barycenter. Sufficient stability conditions are developed for different scenarios, and their performances are measured though a proposed formation error Lyapunov function. Analysis using the proposed Lyapunov formation error function shows that a democratic weighting scheme minimizes the formation error. An impulsive controller is presented to test the developed stability conditions. Simulations show the application of an impulsive decentralized control approach with sufficient stability conditions for different constellation scenarios; and it is validated that a democratic formation minimizes the formation error.