Escape from the Earth–Moon system constitutes the first step of deep space exploration. Under stringent propellant constraints, achieving a highly efficient and low-energy escape trajectory is critical to mission success. To reduce fuel consumption, high specific impulse electric propulsion is often employed, and lunar gravity assists (LGA) is leveraged to further increase energy. However, the inherent sensitivity of low-thrust and lunar gravity assists poses a significant challenge to trajectory optimization. In this context, this paper presents a design method for low-thrust lunar gravity assist escape trajectories. The spacecraft transfers from a given geostationary transfer orbit (GTO) to the Moon, subsequently performs a lunar gravity assist to increase its energy, and ultimately achieves the required escape velocity with minimal fuel consumption. To mitigate the sensitivity of trajectory optimization, a time regularization scheme is introduced. Subsequently, a design and optimization method combining a rapid lunar flyby point search framework and a direct collocation method for low-thrust optimization is subsequently established.

Specifically, the problem is modeled within the circular restricted three-body problem (CRTBP). A time regularization scheme is integrated into the dynamics to handle the strong sensitivity of the lunar gravity assist. This technique adaptively scales the time evolution rate by mapping the time to a new pseudo-time, effectively reducing the sensitivity and improving optimization convergence during the gravity assist phase. Building upon the established model, a comprehensive framework for initial trajectory generation is developed. Recognizing the significant influence of flyby point on both the escape energy and the trajectory configuration, its selection is prioritized as the crucial first step. A hybrid search framework combining two-body analytical approximations and three-body numerical integrations is constructed, enabling the rapid identification of the flyby point that maximizes the post-flyby escape energy. With the flyby point identified, the GTO-to-Moon and post-flyby escape trajectories are computed individually. These segments are then patched together, to form a complete, continuous trajectory that serves as the initial guess. Subsequently, the low-thrust lunar gravity assist escape trajectory is optimized using a direct collocation method. The optimization seeks to minimize fuel consumption while satisfying the constraints on safe lunar flyby altitude and escape conditions. In conclusion, a comprehensive low-thrust lunar gravity assist escape trajectory design and optimization framework is presented for deep space exploration missions. Numerical results validate that the proposed methodology significantly enhances the robustness and convergence performance of low-thrust trajectory optimization in the multi-body regime.