Generation of Multiple-Revolution Many-Impulse Optimal Spacecraft Maneuvers

Abstract

Impulsive trajectories provide time- and [Formula: see text]-reachability insights. Two novel homotopy-based methods are proposed for generating optimal many-impulse, multirevolution maneuvers. The first method is based on the continuation over the specific impulse value, which is shown to enhance convergence performance of the resulting two-point boundary-value problems. The second method is based on the formulation of impulsive trajectories using a linear acceleration term. The two methods are used in a hybrid framework. The utility of the proposed methods is demonstrated on four problems: Two interplanetary trajectories 1) from Earth to Mars, 2) from Earth to asteroid Dionysus, 3) a planet-centric transfer maneuver from a geostationary transfer orbit (GTO) to geostationary orbit (GEO) consisting of 21 revolutions, and 4) a 50-revolution transfer from the considered GTO to a circular orbit at the first Lagrange point (L1) of the Earth–moon system. The last two problems leading to 18 and 50 impulses are tackled to give an optimal near-impulsive solution. The impulsive solution with 18 impulses is shown to satisfy Lawden’s conditions.