Design of Natural Loose Formation Flying around Halo Orbits

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Two spacecraft or more are assumed to be in a state of loose formation flying around a collinear Lagrangian point in the Sun-Earth circular restricted three-body problem (CR3BP) system. The orbit reference of choice for the leader is a halo orbit, and the followers are assumed to follow nearby and be constrained either geometrically or in size. This type of formation could be useful in the future for constructing space ports, space telescopes, astronomical spacecraft requiring sun shields and, with greater numbers, spacecraft swarm missions. The formation design method is constructed by firstly seeking the local coordinate system from the monodromy matrix through extraction of the independent bases that span the space of the halo orbit. To nullify diverging and converging motion, we confine the relative motion to within the periodic subspaces. We observe two modes of relative motion within these subspaces, long-term and short-term motion. In this study, we approximate the long-term motion by deriving a discrete formulation of independent directions based on the eigenvectors of the monodromy matrix, while for the short-term motion we approximate the fundamental set solutions using Fourier series and additional linear functions. Since the size of the formation discussed is significantly smaller than that of the halo orbit, the formation design method can fundamentally be stated as a process of linearly combining these approximations to achieve the desired formation. Consequently, use of this approach transforms formation design from a differential equation problem into an algebraic one, and furthermore enables the long-term and short-term motion design problems to be handled either jointly or separately. A set of design examples is presented to demonstrate the validity of the design method.
2012-07-04

Design of Natural Loose Formation Flying around Halo Orbits

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