Low Thrust Trajectory Optimization in Cislunar and Translunar Space

Low-thrust propulsion technologies such as electric propulsion and solar sails are key to enabling many space missions which would be impractical with chemical propulsion. With exhaust velocities 10x higher than chemical rockets, electric propulsion systems can deliver a spacecraft to its target state for a fraction of the fuel. Due to the low thrust, the control must remain active for weeks or even years. When three-body dynamics are considered, the change in dynamics over the course of a trajectory can be extreme. This greatly complicates low-thrust mission design and navigation in cislunar and translunar space, making it an area of active research. Deterministic strategies for trajectory design and optimization solve a series of linearized problems. In regimes with simple or slowly-varying dynamics, the linearization holds “true enough”, and existing algorithms can easily arrive at a solution. However, three-body environments readily provide real cases where the linearization for all but the most carefully-chosen problem descriptions break down. The objectives for this research come directly from the limitations of the current state of the art. Modifications to existing algorithms are presented which improve convergence, especially when good initial guesses are not available. Initial work was also completed to enhance spacecraft onboard navigation capabilities, through the use of artificial neural networks for optimal trajectory correction. The approach begins with one optimal low-thrust transfer. Then, thousands of transfers in the neighborhood of the nominal transfer are optimized. These transfers are described in the language of indirect optimal control, with the optimal control given as a function of Lawden’s primer vector. We see that for a slightly different initial condition, the states and the costates both follow a slightly different trajectory to the target. A feedforward artificial neural network is trained to map the difference in states to the difference in costates, with a high degree of accuracy. The novel application of neural networks pioneered in this research sets the stage for spacecraft that can navigate themselves autonomously in the presence of errors. Future spacecraft may use this technique to optimally correct their trajectories without ground contacts. Neural network navigation is demonstrated in two simplified dynamical environments: two-body heliocentric gravity, and the Earth-Moon circular restricted three body problem. Transition of the results to NASA and/or industry flight projects is being explored.