Deep-Space Spacecraft Formation Flying using Θ-D Control

A new control technique for deep-space spacecraft formation flying is proposed in this paper. The circular restricted three-body problem with Sun and Earth as the two primaries is utilized as a framework of study and two satellite formation flying is considered. The leader satellite is stationkept in the nominal 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 new nonlinear control approach, called the θ- D technique. This method is based upon the optimal control concept and gives a closed-form suboptimal feedback solution. In this approach the Hamiltonian-Jacobi-Bellman (HJB) equation is solved approximately by adding some perturbations to the cost function. The controller is designed such that the relative position error between the two satellites is maintained within one centimeter accuracy. The numerical results from employing this method demonstrate the potential of this method.