Station-keeping about sun-mars three-dimensional quasi-periodic collinear libration point trajectories

Space missions designed to operate along three-dimensional quasi-periodic orbits in the proximity of the collinear libration points have been proposed since the late 60s. Because of the intrinsic instability of collinear libration point orbits, guidance laws for station-keeping must be developed to maintain the spacecraft sufficiently near the nominal path. We propose the design of a station-keeping strategy suitable for three-dimensional Lissajous libration point orbits in the Sun-Mars system. Due to the nonnegligible eccentricity of Mars orbit, the dynamical framework of the elliptic restricted three-body problem (ER3BP) is considered. Using Hamiltonian formalism and canonical transformations, the linear dynamics associated with the ER3BP in the neighborhood of the SunMars collinear libration points is reduced to a compact representation. Using this approach, trajectories asymptotic to the Lissajous orbit can be represented by a single linear function, depending only on the four in-plane state variables, driving the design of the feedback guidance law. Suitability and performance of the station-keeping strategy at hand is verified by means of numerical analysis, performed by integrating the nonlinear equations of motion. Its compatibility with available low-thrust devices is investigated as well, and this leads to identifying potentially critical scenarios