Automated Design of Optimal Finite Thrust Orbit Insertion with Ballistic Flyby Constraints

Abstract

An automated method is developed to generate a minimum-fuel, finite thrust orbit insertion sequence while simultaneously generating a flyby trajectory of the same body that satisfies pre- and postflyby conditions in a general force field with ephemeris-level dynamics. The initial estimate requires no user input, and an impulsive solution is automatically converted to an optimal finite thrust transfer. As part of the initial estimate, a new method of generating ephemeris-level single flyby free returns is presented. A hybrid method is implemented for the optimal control solution whereby the costates are added to the vector of free parameters and the cost function is minimized directly. Analytic gradients are derived to decrease computation time and aid convergence of the optimization algorithm. The method is successfully applied in the Earth–moon system with application to human spaceflight and in the Saturn–Titan system with application to robotic spaceflight.