Low-thrust Trajectory Optimization in the Circular Restricted Three Body Problem

The use of multi-body dynamics and dynamical systems theory for trajectory design has become increasingly prevalent to space mission design. One common multi-body dynamics model is the Circular Restricted Three-Body Problem (CR3BP), which describes the motion of a test particle under the influence of two massive primary bodies. The CR3BP yields a multitude of dynamical structures that can be leveraged for trajectory design, including libration point orbits (LPOs), invariant manifolds, and heteroclinic connections. These structures can be used to design low-energy transfers and low-thrust trajectory design for small spacecraft, such as CubeSats. Particularly, these dynamical structures can inform trajectory optimization methods to identify fuel-optimal transfers between LPOs within the CR3BP.Hybrid differential dynamic programming is used here to nd optimal low-thrust trajectories in the CR3BP. It is a modication of dynamic programming that aims to minimize a cost function in a dynamical environment, and uses quadratic expansions of the cost and the dynamics to circumvent the limitations inherent in dynamic programming. Using heteroclinic connections as a starting point, single-phase hybrid differential dynamic programming is used in this thesis to find fuel-optimal transfers between Lyapunov orbits in the Earth-Moon CR3BP and between halo orbits in the Sun-Earth CR3BP. A continuation process is used in the Sun-Earth CR3BP which uses preceding optimized trajectories to find optimal transfers to increasingly large target halo orbits.Single-phase hybrid differential dynamic programming is shown to be a robust and effective optimization approach in the CR3BP when combined with dynamical systems theory techniques, and is able to successfully find many optimal transfers for a CubeSat between Sun-Earth halo orbits.