Design of Periodic Orbits for Formation Flying around a Halo Orbit

A formation flying around a halo orbit is discussed in this paper. We aim to form a natural and closed formation flying around a halo orbit to reduce fuel consumption. A method to form a periodic orbit using a monodromy matrix derived by linearizing the equation of motion of spacecraft is proposed, where the complex eigenvalues of the monodromy matrix and their corresponding eigenvectors are used to form multiple orbiting formations. Using the proposed method, it is confirmed that the formation in which a chief moves around the halo orbit a certain number of times and a deputy returns to its same relative position can be constructed with almost zero velocity increment. We also discuss the design of formation trajectories when adding velocity increments. The validity of the proposed method is confirmed by numerical calculations.