A trajectory design and optimization framework for transfers from the Earth to the Earth-Moon triangular L4 point

Abstract

• A synthetic computation procedure for transfer families using tangential velocity increments is presented. • A fast optimization method for direct transfer is constructed based on primer vector theory. • The necessary optimality conditions for a transfer utilizing powered lunar gravity assist under a minimum swing-by height constraint are deriver. • An optimization procedure for the optimal transfer utilizing powered lunar gravity assist is presented. The triangular libration points in the Earth-Moon system are considered to be potential candidates for future space missions because of their unique positions and dynamics. This paper presents a comprehensive transfer trajectory design and optimization framework for transfers from the Earth to L 4 in the Earth-Moon system, including direct transfer and transfer utilizing powered lunar gravity assist. In this framework, first, a synthetic procedure combining an initial guess, a differential correction algorithm and numerical continuation for generating tangential transfer families is illustrated. Subsequently, the optimization models for optimal transfer trajectories with the minimum velocity increment requirement are constructed. For direct transfer, the optimal direct transfer trajectory is obtained using primer vector theory. For the optimal transfer utilizing powered lunar gravity assist under a minimum swing-by height constraint, the necessary optimality conditions are found through optimal control theory, and an optimization procedure that allows for numerical convergence to the optimal solution is constructed. Numerical results indicate that the proposed transfer trajectory design and optimization framework has sufficient effectiveness to provide various transfer trajectories associated with different insertion points and fuel-optimal transfers.