Energy preserving low-thrust guidance for orbit transfers in KS variables

A Lyapunov-based approach is presented to design finite-thrust closed-loop guidance schemes in a two-body model, to perform any general orbit transfer. The design is performed in the Kustaanheimo–Stiefel (KS) model, a regularized two-body framework. The KS model aids in the design of the guidance schemes, but the new guidance solutions can be explicitly characterized in the regular two-body model. The control scheme covers two main phases: first, a matching of the semi-major axis of the target orbit; and second, a matching of the remaining desired orbital elements by holding energy constant. No constraint is imposed on the magnitude of the thrust; however, an emphasis is placed on low-thrust examples.