An Adjoint-Based Method for Continuous Thrust Relative Maneuver Computation in the Restricted Three-Body Problem

A method for computing continuous-thrust maneuvers for relative motion control in the restricted three-body problem (R3BP) is proposed. The maneuvers are computed with respect to a local-vertical local-horizon (LVLH) frame centered at the target. The relative dynamics in such scenario is characterized by time-varying parameters associated to the target orbital motion and to the LVLH frame orientation. Therefore, classical methods used for rendezvous in near-Earth orbits, based on linear time-invariant descriptions of the relative motion, cannot be adopted. To address the timevarying nature of the relative motion in the R3BP we leverage the adjoint system theory tools. More specifically, the adjoint system associated to the relative dynamics equations is used for computing and assessing the feasibility of continuous-thrust maneuvers for reaching a predefined position with respect to the target. The method proposed is tested on a rendezvous scenario in the Earth-Moon case, with a target on a near-rectilinear halo orbit. The test case is inspired by future international space exploration missions revolving around building and exploiting a crew-tended cis-lunar space station, known as Lunar Orbital Platform-Gateway.