Strategy for Optimal, Long-Term Stationkeeping of Libration Point Orbits in the Earth-Moon System

Lagrangian coherent structures in various map representations for application to multi-body gravitational regimes

“…The computation of FTLE values adds some context for the ARTEMIS maneuver strategy. Previous analysis by Folta et al [5,7], as well as Pavlak and Howell [26], demonstrates that the optimal, plane-constrained stationkeeping maneuvers during the Lyapunov phases of the ARTEMIS trajectory correlate strongly with the stable direction recovered from an approximate monodromy matrix (M) associated with revolutions of the trajectory. The optimal maneuver direction for a stationkeeping cycle aligns with the position projection of the stable eigenvector computed from an approximation to the monodromy matrix.…”

Applying Dynamical Systems Theory to Optimize Libration Point Orbit Stationkeeping Maneuvers for WIND

“…= partial derivative matrix of the CR3BP equations of motion with respect to the six element state b = y-intercept for a line = vector from larger primary, m 1 , to the spacecraft, m 3 DF(X) = partial derivative matrix of the free variables, X, with respect to the constraints, F(X) d = scalar distance from the larger primary, m 1 , to the spacecraft, m 3 ̅ = nondimensional vector from the larger primary, m 1 , to the spacecraft, m 3 D 1 = distance from m 1 ,m 2 barycenter to larger primary, m 1 D 2 = distance from m 1 ,m 2 barycenter to smaller primary, m 2 F(X) = constraint equations for fixed-time multiple shooting algorithm ̅ = equations of motion for the spacecraft in the CR3BP = dimensional gravitational constant l * = characteristic length m * = characteristic mass m 1 = mass of the larger primary m 2 = mass of the smaller primary m 3 = mass of the spacecraft (zero) n = number of patch points ̅ = dimensional position vector of m 3 with respect to the system barycenter = vector from smaller primary, m 2 , to the spacecraft, m 3 r = scalar distance from the smaller primary, m 2 , to the spacecraft, m 3 ̅ = nondimensional vector from the smaller primary, m 2 , to the spacecraft, m 3 s = slope of a line t = time = maneuver magnitude θ = orientation of rotating frame relative to inertial frame μ = nondimensional mass ratio ̅ = nondimensional position vector of m 3 with respect to the system barycenter τ = nondimensional time φ = state transition matrix = differentiation with respect to time…”

“…This maneuver design strategy has been intuitive, but as several previous studies have shown [2][3][4] , this is not the most efficient method for stationkeeping of libration point orbits (LPO) in terms of Δv, and therefore fuel. This work will present the application of dynamical systems to compute the maneuver direction which minimizes Δv for any position in WIND's orbit, discuss the implementation of this new maneuver design process into operations, and show results for the first two MCCs which were performed using this methodology.…”

A Modified Targeting Strategy for Station-Keeping of Libration Point Orbits in the Real Earth-Moon System

“…In 2010, several station-keeping strategies are considered for application to ATREMIS by Folta et al [7] and two approaches are examined to investigate the station-keeping problem in the Earth-Moon system in a full ephemeris model. Pavlak [8] introduced a numerical process of constructing nominal orbits around the Earth-Moon libration points in a highfidelity model based on LPOs generated in the CRTBP model, and later Pavlak and Howell [9] proposed a nearoptimal station-keeping method for long-term stationkeeping in the Earth-Moon system. An adaptive robust controller for a spacecraft with unknown mass and boundary of perturbation forces is proposed by M. Xu and S. Xu [10] to deal with the station-keeping control for halo orbits around Sun-Earth L 1 .…”