Model predictive control switching strategy for safe small satellite cluster formation flight

This paper presents the development and analysis of a spacecraft formation flying architecture. The desired state of each spacecraft is maintained using a model predictive control-based control framework that is based on the Hill–Clohessy–Wiltshire equations and a polytope boundary constraint as a switching surface. This framework can be used to maintain the desired cluster formation while also guaranteeing internal cluster flight. The polytope boundaries are designed, such that no two agents have overlapping regions, allowing the vehicles to execute avoidance strategies without continually maintaining the trajectories of other agents. The model predictive control framework combined with the convex polytope boundary enables a scalable method that can support clusters of satellites to coordinate to safely achieve mission objectives while minimizing fuel usage. As part of the implementation of this control scheme, the authors created two spacecraft formation flying control approaches. The first approach uses fewer, large maneuvers to control a spacecraft to the center of a keep-in-volume. The second approach allows the spacecraft to perform many small maneuvers to stay just inside the boundary of the keep-in-volume. This paper compares the fuel cost savings of these two approaches. The results presented in this paper demonstrate that the first approach produces the lower total fuel usage, but if a lower amount of fuel per maneuver is required, then the second approach should be used. This work also compares the computation requirements and fuel usage for \(\hbox {L}_1\), \(\hbox {L}_2\), and \(\hbox {L}_\infty \) norms formulations of the framework, the \(\hbox {L}_1\) and \(\hbox {L}_2\) norms require the least amount of fuel usage, while the \(\hbox {L}_2\) requires the least amount of computation time.