Hybrid Optimization Technique for Earth-Moon Transfer Trajectories Human and Cargo Missions to the Lunar Gateway

This thesis addresses the issue of low-energy transfers between low Earth orbit (LEO) and near rectilinear halo orbits (NRHO) within the Earth–Moon system. The focus is on supporting the Lunar Gateway within NASA’s Artemis program. The cislunar domain is presented as an ideal environment for testing technologies, establishing logistics hubs, and enabling future Mars missions. Trajectory optimization is constrained by the Kourou launch site in French Guiana as the departure point, which has strict altitude and inclination constraints. These limitations significantly impact the feasibility of different trajectories. The optimization process employs a combination of two approaches. First, a Genetic Algorithm (GA) scans the solution space to identify promising trajectories. Then, a sequential quadratic programming (SQP) method uses the SNOPT solver to fine-tune these trajectories. Since the cis-lunar area is highly unstable, the trajectories reach a specific point along the NRHO. The European Space Operations Centre (ESOC) and NASA's Spacecraft, Planet, Instrument, C-Matrix, Events (SPICE) tool provide precise ephemerides to calculate this point. Simplified models were also tested to gain a panoramic view of the problem. In particular, we employed the Circular Restricted Three-Body Problem (CR3BP) with a single-shooting method. While not as precise as the high-fidelity n-body model, the CR3BP is useful for gaining an initial understanding of how the solution space behaves. It also helps identify primary sensitivities before conducting more complex simulations. Since dealing with altitude and inclination constraints simultaneously can be challenging, a multiple-shooting setup was used. The trajectory was split into nodes, each with a discrete impulse and flexible segment duration. This setup significantly improves the solutions and makes the trajectory more adjustable. Additionally, the GA+SNOPT hybrid optimization technique was applied to refine the solution. The work was later expanded by varying the departure date over the course of a year. This allowed for the identification of better launch windows along the NRHO. Some adjustments were also made to avoid clustering impulses too closely together, such as modifying the bounds of the variables governing the duration of individual segments. These improvements reduced the number of maneuvers required, allowing for lower fuel consumption. Other types of trajectories, such as Weak Stability Boundary (WSB) trajectories, were employed to identify routes with minimal delta-V. Overall, the results demonstrate that combining the two optimization methods effectively identifies low-cost trajectories.