Multiple spacecraft formation control with O-D Method

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