Low-Thrust Real-Time Guidance Algorithm for Proximity Operations about an Asteroid

Abstract

This paper proposes a real-time implementable Lyapunov-based guidance algorithm for small-body proximity operations. The guidance solution accounts for the secular effects coming from the oblateness of the main body and for the non-impact condition between the latter one and the spacecraft. The first perturbation with respect to the two-body problem is implemented via an update of the Keplerian elements based on the secular precessing ellipse model, while the second one through a check on the radial distance at periapsis. Advantages are taken of the fact that real-time guidance algorithms require only the knowledge of the current state of the spacecraft and of the target. The proposed mission scenario implements an approximate model of 433 Eros as the main body and a low-thrust point mass spacecraft executing orbital transfers about it. It is shown that, for transfers lasting tens of days, ignoring the oblateness of the main body results in errors on the order of ten degrees for the right ascension of the ascending node, the mean anomaly, and the argument of periapsis. These errors are reduced by two orders of magnitude when the proposed guidance algorithm is applied.