Approximately optimal manoeuvre strategy for aero-assisted space mission

Abstract An innovative aerodynamically assisted spacecraft manoeuvre strategy is introduced in this study which benefits from the higher order powers of the state variables as the feedback signal for online calculation of trajectory correction commands. The proposed manoeuvre policy is exploited from nonlinear optimal control theory formulation by incorporating a novel form of High Order Expansions method which results in an approximately optimal manoeuvre commands in practice. To extract such a manoeuvre policy, a specific approach of dealing with High Order Expansions method, namely Vectorised High Order Expansions, is illustrated comprehensively. Then, the implementation of this method is described to extract the solution of general optimal control problems by use of sensitivity variables. By means of this novel approach, the higher order manoeuvre policy is designed for the aero-assisted mission up to and including the 8th order expansions to better reveal the quality of the proposed approach. The performance of the proposed method is investigated by the means of planar point mass simulations; the results are compared with a state dependent Riccati equation method and the numerical open loop solution of the problem, and the quality of the higher order terms is investigated.