Orbit Maintenance for Quasi-Periodic Orbit in Earth-Moon System

This paper investigates the orbit maintenance approach for the quasi-periodic orbit about libration points. Because of the highly unstable dynamical environment, a tiny deviation will lead spacecraft to be far away from the mission orbit. Floquet mode analysis incorporates the dynamical systems theory for the controller design. Unfortunately, Floquet mode method is difficult to be applied to a quasi-periodic orbit because the monodromy matrix is not well-defined so that the invariant manifolds cannot be determined to create the stationkeeping controller. To solve the problem, a new orbit maintenance strategy named covariance-based approach is proposed, integrated with an autonomous orbit determination. Based on the property that the maximum orbit uncertainty direction will converge to the direction of the unstable manifold of a local orbit, the controller is reformed by using the eigenstructure of the state covariance, which is isochronously computed by the orbit-determination process, to substitute for the monodromy matrix. Application to the orbit maintenance of a Lissajous orbit about Earth-Moon L2 verifies the feasibility of our method and also investigates parameters that influence the overall stabilization and consumption cost.