Model predictive control for formation flying based on D’Amico relative orbital elements

The desire to fly small spacecraft close together has been a topic of increasing interest over the past several years. This paper presents the development and analysis of a model predictive control based framework that is used with the D’Amico relative orbital elements (ROEs) to maintain the desired trajectories of a cluster of spacecraft while also allowing freedom to maneuver within some allowable bounds. Switching surfaces based on the ROE constraints contain the full state of the system, allowing for fuel reduction over other approaches that use the Hill—Clohessy—Wiltshire equations. The formation and boundary constraints are designed such that no two agents have overlapping regions, allowing the vehicles to maintain safety of fl ight without continually maintaining the trajectories of other agents. This framework allows for a scalable method that can support clusters of satellites to safely achieve mission objectives while minimizing fuel usage. This paper provides simulated results of the framework for a three spacecraft formation that demonstrates a 67% fuel reduction when compared to previous approaches.