Design of Loose Spacecraft Formation Flying around Halo Orbits

Two spacecraft or more are assumed to be in a state of loose formation flying arounda collinear Lagrangian point in the Sun-Earth Circular Restricted Three-Body Problem(CRTBP) system. The orbit reference of choice for the leader is a Halo orbit and thefollowers are assumed to follow nearby and be constrained either geometrically or insize. This type of formation could be useful in the future for constructing space ports,space telescopes, astronomical spacecraft requiring sun shields and, with greater num-bers, spacecraft swarm missions. The formation design method is constructed by firstlyseeking the local coordinate system from the monodromy matrix through extraction ofthe independent bases which span the space of the Halo orbit. To nullify diverging andconverging motion, we confine the relative motion to within the periodic subspaces. Twotypes of formations are studied in this thesis, natural loose formations and periodic looseformations with impulsive control. For natural formations, two modes of relative motionwithin these subspaces, long-term and short-term motions. In this study, the long-termmotion is approximated by deriving a discrete formulation of independent directionsbased on the eigenvectors of the monodromy matrix, while for the short-term motionthe fundamental set solutions are modeled using Fourier series and additional linear func-tions. Since the size of the formation discussed is significantly smaller than that of theHalo orbit, the formation design method can fundamentally be stated as a process oflinearly combining these approximations to achieve the desired formation. Consequently,use of this approach transforms formation design from a differential equation probleminto an algebraic one, and furthermore enables the long-term and short-term motiondesign problems to be handled either jointly or separately. To increase design degree offreedom impulsive control is introduced to the formation problem. The use of single, twoand three impulses are specially discussed in detail. Design examples, both for naturaland with impulsive control formation are presented to demonstrate the validity of thedesign method. Keywords: Restricted Circular Three-Body Problem, Loose FormationFlying, Halo Orbits, Impulsive Contro