Analytical Results to Fuel-optimal Spacecraft Formation Maneuver

Abstract

Abstract In this study, analytical results are obtained for fuel-optimal spacecraft formation maneuver, including initialization and reconfiguration. The method consists of two stages. The first is parameterization of the problem and a new form of the problem is developed for simplicity. Second, the out-of-plane and in-plane maneuver are studied with the help of a useful inequality introduced and proved, the lower bound of the fuel consumption and the corresponding constraints of the control forces are derived and obtained. The result shows that the minimum total fuel consumption depends on the relative size parameters, and that the existence of optimal control algorithms depends upon the initial conditions. Numerical simulation of application proved the validity and efficiency of the proposed method, which can also be utilized in the maneuver of PCF.