Stationkeeping on Unstable Orbits: Generalization to the Elliptic Restricted Three-Body Problem

摘要

We develop new methods for generating periodic orbits about the collinear libration points and for stabilizing motion on libration orbits using the general formalism of the elliptic restricted three-body problem (ER3BP), Calculation of periodic orbits is accomplished by formulating the ER3BP as a control problem This approach yields halo-like orbits that do not exist without applying active control, having arbitrarily small amplitudes. Linearization about the libration points in pulsating coordinates yields an unstable linear parameter-varying (LPV) system with periodic coefficients. We introduce a continuous acceleration control term into the state-space dynamics and use an LPV-generalized version of the pole-assignment technique to find linear periodic reference trajectories. The nonlinear terms of the equations of motion are then treated as periodic disturbances. A disturbance-accommodating control is used to track the libration-point reference orbit in the presence of nonlinear periodic disturbances. Simulation experiments show that stationkeeping is robust to propulsive dispersions.