Model selection for satellite formation flight reconfiguration

Mathematical relations are derived for two fuel-optimal cost functions for Satellite Formation Flight Reconfiguration (SFFR) based on two sets of Lawden's Equations (LEs), with respect to time and true anomaly respectively. It shows that the LEs with respect to time should be selected and cost function should be formulated with respect to time, when analytical solutions are not necessary. First, cost functions of these two LEs are compared, in cases of impulse thrust and continuous thrust. Then, fuel-optimal cost function for the continuous thrust is developed and two-point-boundary-value problem of SFFR is founded on the Pontriagin maximum principle. Then, initial co-state values are obtained by using a boundary iterative method, and the optimal control accelerations are determined. Finally, Numerical simulation illustrates the validity of the analysis and the performance of the algorithm.