A Theoretical Framework for the Stable Operation of Autonomous Spacecraft Formations in the Hill-Clohessy-Wiltshire Frame

The dynamic stability of a swarm is an essential consideration in the design of autonomous formation flying spacecraft. In this paper, we begin by using an illustrative example to create a geometric framework utilizing spacecraft formations in Hill-Clohessy-Wiltshire frame. We use this geometric structure to develop theoretical results to analyze swarm stability in a general three-dimensional space and show how stable swarm members can lead to instabilities. We also discuss an adaptive key-component controller as a means to regulate relative error dynamics in highly sensed swarm environments where a fixed gain controller can be difficult to design. Finally, we use a simulation to present and validate our theoretical framework for swarm stability.