Multi Impulse Low Earth Orbit Maneuver Synthesis Through Thrust Measure Primer Vector Conditions and Piecewise Multiple Shooting

Abstract

This work sets out to apply primer vector theory to optimal impulse maneuvers in Low Earth Orbit (LEO) and adapt it to the types of perturbations encountered in this environment, which is not readily available in the literature. A review of the theory of optimal control and orbital maneuvering is made and in particular, primer vector theory is laid out in detail based on the extension of the thrust control to a measure, including its generalization to conservative and non-conservative perturbation models. An impulsive multiple shooting optimization scheme in Cartesian coordinates is presented, through a piecewise approach to the problem. Then, some maneuver scenarios with known solutions under the Keplerian model are solved under perturbed orbital dynamics with the help of the primer vector, and the resulting trajectories are compared. The perturbation models include a J2 model, representing the class of conservative perturbations by modeling Earth's nonspherical gravity field, and a J2+Drag model, representing the class of non-conservative perturbations by including the effects of atmospheric drag in LEO\@. For each model, some valid methods of primer vector calculation have been tried and validated between each other, and the primer vector is proven to be a useful tool in reducing the cost of orbital maneuvers.