Multiple Spacecraft Formation Control Using Theta-D Method

Multiple spacecraft formation control about the L2 libration point is investigated in this paper.The circular restricted three-body problem with Sun and Earth as the two primaries is utilized as a framework of study.The idea of virtual structure is considered as the architecture of multiple spacecraft formation. The center of the virtual rigid body follows a nominal Lissajous orbit around the L2 libration point. A nonlinear model is developed that describes the relative formation dynamics. This nonlinear control problem was addressed by employing a relatively new nonlinear control approach, called the Theta-D technique. This method is based on a series solution to the Hamilton_Jacobi_Bellman equation and gives a closed-form suboptimal feedback solution. Simulation results demonstrate that this controller is able to provide millimeter-level formation flying accuracy.