Averaged relative states for spacecraft formation control in the presence of J2 disturbances

The method of controlling a spacecraft formation using mean relative states as the inputs is an effective technique if control actuation is sought to be reduced. In this paper, we extend the efficacy of this method by including the linearized J2 terms in the system dynamics and derive the linear mapping between the actual and the mean relative states. The resultant control equation has J2 related gains that are shown to improve the tracking of the states and increase system performance for a phase plane-based controller performing formation maneuvering.

► We derive mean relative in-plane states of two formation flying (FF) spacecraft.
► Linearized J2 perturbations are included in the system dynamics.
► We establish a phase plane control strategy using the J2 dynamics.
► The J2-enabled controller exhibits improved tracking accuracy during FF maneuvers.