Elliptical formation control based on relative orbit elements

A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model. In-plane and out-of-plane motions can be completely decoupled, which benefits elliptical formation design. The inverse transformation of the state transition matrix is derived to study the relative orbit control strategy. Impulsive feedback control laws are developed for both in-plane and out-of-plane relative motions. Control of in-plane and out-of-plane relative motions can be completely decoupled using the ROE-based feedback control law. A tangential impulsive control method is proposed to study the relationship of fuel consumption and maneuvering positions. An optimal analytical along-track impulsive control strategy is then derived. Different typical orbit maneuvers, including formation establishment, reconfiguration, long-distance maneuvers, and formation keeping, are taken as examples to demonstrate the performance of the proposed control laws. The effects of relative measurement errors are also considered to validate the high accuracy of the proposed control method.