Comparison of Control Approaches for Formation Flying of Two Identical Satellites in Low Earth Orbit

Abstract: Formation flying of satellites describes a mission in which a set of satellites arrange their position with respect to one another. In this paper, satellite formation flying guidance and control algorithms are investigated in terms of required velocity increment Delta-v, and tracking error for a Chief/Deputy satellite system. Different control methods covering continuous and impulsive laws are implemented and tested for Low Earth Orbit (LEO). Sliding Mode, Feedback Linearization and Model Predictive Controllers are compared to an Impulsive Feedback Law which tracks the mean orbital element differences. Sliding Mode and Feedback Linearization controllers use the same dynamic model which includes Earth Oblateness perturbations. On the other hand, Model Predictive Control with Multi-Objective Cost Function is based on the Clohessy–Wiltshire equations, which do not account for any perturbation and do not cover the eccentricity of the orbit. The comparison was done for two different missions both including Earth Oblateness effects only. A relative orbit mission, which was based on the Prisma Satellite Mission and a rendezvous mission, was implemented. The reference trajectory for the controllers was generated with Yamanaka and Ankersen’s state transition matrix, while a separate method was used for the Impulsive Law. In both of the missions, it was observed that the implemented Impulsive Law outperformed in terms of Delta-v, 1.2 to 3.5 times smaller than the continuous control approaches, while the continuous controllers had a smaller tracking error, 2 to 8.3 times less, both in terms of root mean square error and maximum error in the steady state. Finally, this study shows that the tracking error and Delta-v has inversely proportional relationship.