Control laws for minimum orbital changes -the satellite retrieval problem

Satellite retrieval following failure of an upper stage may require expending the unused propellants by firing the engine. If the satellite is already in a Shuttle-accessible orbit, then the thrust must be controlled such that the changes in orbital elements (primarily semi-major axis, eccentricity, and inclination) are minimized. This paper develops a set of blended extremal controls that minimizes changes in semi-major axis and eccentricity; under the assumption of a spherical gravity field, in-plane thrusting results in zero inclination change. The method requires the solution of a nonlinear programming problem, using as optimization variables the engine ignition time and a set of weighting factors to blend the contributions of the extremal controls. Three example cases for typical engine capabilities indicate that acceptable solutions are possible, with reasonable requirements on thrust steering.