Low-Thrust Variable-Specific-Impulse Transfers and Guidance to Unstable Periodic Orbits

Abstract

The use of a power-limited, variable-specific-impulse propulsion system to transfer a vehicle from the smaller primary to an arbitrary circular restricted three-body trajectory and the subsequent guidance along all phases of the complete trajectory is investigated. As a practical application, the transfer of a spacecraft with a finite-burn propulsion system from a low Earth orbit to the stable manifold associated with halo and vertical figure-eight orbits at the interior collinear libration point of the sun-Earth/moon system is considered. We find that an indirect method coupled with an adjoint control transformation yields a robust and efficient solution method to construct these transfers. State-feedback linearization for guidance along the powered arcs is able to adjust the control to cancel a range of sinusoidal perturbations. The dynamics of the spacecraft in the sun-Earth/moon system is approximated as a circular restricted three-body problem.