Efficient initialization and optimization of translunar direct-abort trajectory under reentry constraints

Emergency return constitutes a critical procedure for ensuring astronaut safety, with direct abort offering the shortest return time among abort strategies. Optimization models for direct-abort trajectories are developed under two representative scenarios, accompanied by a solution strategy that guarantees rapid and robust convergence. For the time optimal case, an in plane direct-abort trajectory is designed to minimize return time subject to ΔV and flight-path angle constraints. Simulation results demonstrate that trajectories initiated from different abort points converge to virtually identical terminal reentry positions in the inertial frame, with variations in orbit plane reentry points remaining within approximately 1° under tight ΔV limits. For the landing restricted case, additional constraints on reentry location and velocity direction are imposed to shape the trajectory, and convergence of the resulting optimization problem is shown to be highly sensitive to the initial guess. An initialization method is introduced that decouples flight-path angle and landing site constraints by exploiting characteristic behaviors of in plane direct-abort solutions, thereby enabling fast and reliable convergence. Simulations reveal multiple feasible abort trajectories with distinct ΔV requirements for a given abort point. Moreover, within a specified reentry window, aborts executed over a continuous time interval yield closely clustered reentry epochs, while delaying the abort toward the window's end incurs progressively higher ΔV requirements. High fidelity dynamics simulations further validate the convergence performance and computational efficiency of the proposed approach.