Low-Thrust Many-Revolution Transfer between Near Rectilinear Halo Orbit and Low Lunar Orbit Using Hybrid Differential Dynamic Programming

TL;DR

This work develops a Sundman-transformed HDDP framework to design low-thrust, many-revolution transfers between a Low Lunar Orbit and a Near Rectilinear Halo Orbit under lunar perturbations. It integrates an automated continuation of dynamics from the two-body problem toward the circular restricted three-body problem within a Moon-centered inertial frame, enabling robust convergence from a poor initial guess. The approach yields a 50.5-revolution LLO-to-NRHO transfer with about 19.2 kg of propellant, using a bang-bang control structure and requiring substantial computational effort (≈4000 iterations, ≈35 hours on a high-end CPU). This method provides a generalizable pathway to reliably compute long-duration CR3BP transfers and can extend to other multi-revolution, low-thrust orbital transfers in similar celestial settings.

Abstract

Low-thrust, many-revolution transfers between near-rectilinear halo orbits and low lunar orbits are challenging due to the many-revolutions and is further complicated by three-body perturbation. To address these challenges, we extend hybrid differential dynamic programming by enhancing with a continuation of dynamical system. The optimization begins with the Sundman-transformed two-body problem and gradually transitions to the Sundman-transformed circular restricted three-body problem expressed in the moon-centered inertial frame. Numerical examples demonstrate the robust convergence of our method, where optimal transfers from low lunar orbit to near-rectilinear halo orbit are obtained with a poor initial guess of low lunar orbit.

Figures (6)

• Figure 1: LLO at alt=5000 km
• Figure 2: NRHO and targeting single point of the NRHO in rotational frame
• Figure 3: Coordinate
• Figure 4: optimal transfer of LLO to NRHO in CR3BP, 0.30N
• Figure 5: optimal control of LLO to NRHO in CR3BP, 0.3N