Abstract
Formation control of multiple spacecraft flying in deep space about the L2 libration point is investigated. Dynamics of the spacecraft is formulated as a circular restricted three-body problem with Sun and Earth as the two primaries. A virtual structure (VS) concept is used as a framework for multiple spacecraft formation in which the centre of the virtual rigid body is assumed to follow a nominal orbit around the L2 libration point. Control is applied to each individual spacecraft so as to keep a constant relative distance from the centre of the VS. The relative formation dynamics is nonlinear and control of this system is carried out using a relatively new suboptimal control technique called as thetas–D technique. The thetas–D method provides approximate analytical solution to the Hamilton–Jacobi–Bellman equation. As it is a feedback control and in a closed form, it is implementable. Simulation results demonstrate that this controller is able to provide millimeter level formation flying accuracy.
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