Optimal Control Theory applied to interplanetary transfer for a Near-Earth Asteroid retrieval mission

The growing interest in exploiting extraterrestrial resources has spotlighted asteroid retrieval missions as a pivotal strategy for resource utilization and planetary defense. This study proposes a non-destructive retrieval approach by rendezvousing with Near-Earth Asteroids (NEA) and utilizing guided propulsion to move part of its mass closer to Earth in order to allow in-orbit production of spacecraft components without launching them from Earth making spacecraft construction less expensive. From the JPL Small Bodies Database, a refined selection of asteroids is idendtified through a Pareto front analysis that searches for bodies that have the best orbital parameters’ proximity to those matching the departure point, at the Sun-Earth Lagrange Point L2. Optimal low-thrust trajectories via indirect methods based on the Optimal Control Theory are determined for the spacecraft to rendezvous with the asteroids. Upon attachment, a matching the retrieved asteroid’s mass is introduced, and the mission transitions to seeking the quickest maneuvre to retreive the highest possible amount of asteroid mass back to strategic points in the Earth-Moon system such as the L4 or L5 Lagrangian points. The desired trajectory is calculated using a single-shooting method relying on the Pontryagin's Minimum Principle (PmP) to reduce the propellant mass spent and an autonomous switching function based on the bang-bang control to regulate the thrust without having previously specified the thrust and coasting arcs, this being possible thanks to the complexity of gravitational interactions among the considered celestial bodies. The dynamic modeling of planetary bodies’ positions relies on JPL DE441 ephemeris incorporating the gravitational influence of the Sun in a two-bodies system.