Optimal reconfiguration of satellites in formation

The goal of this study is to compute and analyze the optimal reconfiguration of an n-spacecraft formation where the distances between the spacecraft are small compared to the radius of the reference orbit Using the Clohessy-Wiltshire relative equations of motion, an optimal low-thrust continuous transfer scheme with no upper or lower bounds on thrust acceleration is chosen to simplify the analysis. The equations of motion are then reparameterized so that a more geometrically intuitive form of the Clohessy-Wiltshire equations is achieved. Given a set of transfer conditions, the optimal starting position for a single maneuver is derived. Based on the analytical solution to the performance index of a single transfer, this theory is extended to the full reconfiguration problem, which calls for a threefold optimization in terms of the dynamics and control of individual satellites, the order of reassignment, and the relative orientation of the final formation. A generalized technique is presented to optimize an arbitrary n-spacecraft reconfiguration. Three simplified cost functions for both the in-plane and out-of-plane reconfigurations are derived for phasing change only maneuvers, phasing change only where satellites move on various relative ellipse sizes, and phasing change maneuvers coupled with small changes in the size of the relative ellipse. A simple example is presented that demonstrates the application of the suggested solution technique.