Hybrid Differential Dynamic Programming in the Circular Restricted Three-Body Problem

Abstract

This paper presents the application of differential dynamic programming to low-thrust trajectory optimization in the three-body problem along with supporting techniques. A penalty method is suggested for path inequality constraints and used to enforce a minimum radius constraint. Time variable formulations are presented for the flight time and a moving target. The latter is used to access all points along a desired periodic orbit as valid terminal states. Multiphase differential dynamic programming is applied to discontinuous initial guesses that combine segments of different periodic orbits. Numerical examples include multirevolution transfers between distant retrograde orbits, a heteroclinic transfer between planar Lyapunov orbits, and transfers between L1 and L2 halo orbits in the Earth–moon circular restricted three-body problem.