An optimal guidance approximation for quasi-circular orbital rendezvous

Abstract

Three-dimensional guidance about a time-optimal rendezvous flight path is examined within the framework of a quasi-circular orbital dynamics assumption. The guidance scheme, optimal in the same sense as the nominal trajectory, is based formally upon the approximate construction of a field of neighbouring optimal rendezvous paths, following a method developed by Kelley in an earlier paper1. For purposes of illustration, a class of reference trajectories, generated by a low magnitude, circumferentially directed thrust vector, has been adopted for the guidance analysis. Such trajectories are time optimal, under appropriate circumstances, for transfer between neighbouring co-planar circular orbits. The application considered permits an analytical representation of the extremal field which in turn leads to a closed form linear feedback control solution with time-varying gains. Some suggestions are also given for possible modifications which might enhance system accuracy and the range of operability during practical implementation of low-thrust rendezvous guidance.