NGO-Based Orbits Optimization for Impulsive Transfers between DRO and Halo Orbits

Abstract

This research investigates the design of fuel-saving orbital transfer trajectories for spacecraft departing from distant retrograde orbits (DRO) toward Halo orbits around the Earth-Moon L2 libration point. Relevant trajectory designs hold practical value for future lunar space station projects and deep space exploration undertakings. Previous research commonly adopted indirect modeling methods or classic evolutionary algorithms to acquire transfer solutions, yet these techniques show limited performance in multi-body dynamic systems, particularly unsatisfactory convergence efficiency. To address this defect, this paper proposes an improved direct optimization strategy based on the Northern Goshawk Optimization (NGO) algorithm. All numerical analyses are conducted within the circular restricted three-body problem (CR3BP) framework, which accurately reflects gravitational features in cislunar space while avoiding overly complicated calculation processes. The departing and target orbits are discretized mathematically, and the whole transfer mission is defined as a constrained nonlinear optimization problem aiming to minimize total velocity variation. The adopted algorithm balances global exploration and local exploitation rather than prioritizing a single search mode. This balanced mechanism effectively lowers the risk of falling into local optimal solutions, a prevalent flaw of conventional optimization methods. Precise dynamic modeling is also implemented: canonical transformation is applied to reorganize dynamic governing equations for simpler computation, and differential correction technology is utilized to optimize preliminary trajectory results generated by NGO iteration. Multiple tests with diverse initial values and mission constraints are carried out to verify the method’s stability. Simulation results prove that the proposed strategy maintains steady performance under external interference and stably yields qualified feasible trajectories. Overall, the Northern Goshawk Optimization algorithm proves applicable for high-precision orbital transfer optimization. This study also provides valuable references for low-energy trajectory planning in cislunar space.