The complex nature of many astrodynamic systems often leads to high computational costs or degraded accuracy in the analysis and design of spacecraft missions, and the incorporation of uncertainty into the trajectory optimization process often becomes intractable. This research applies mathematical modeling techniques to reduce computational cost and improve tractability for design, optimization, uncertainty quantification (UQ) and sensitivity analysis (SA) in astrodynamic systems and develops a method for trajectory optimization under uncertainty (OUU).
This thesis demonstrates the use of surrogate regression models and polynomial chaos expansions for the purpose of design and UQ in the complex three-body system. Results are presented for the application of the models to the design of mid-field rendezvous maneuvers for spacecraft in three-body orbits. The models are shown to provide high accuracy with no a priori knowledge on the sample size required for convergence. Additionally, a method is developed for the direct incorporation of system uncertainties into the design process for the purpose of OUU and robust design; these methods are also applied to the rendezvous problem. It is shown that the models can be used for constrained optimization with orders of magnitude fewer samples than is required for a Monte Carlo approach to the same problem.
Finally, this research considers an application for which regression models are not well-suited, namely UQ for the kinetic deflection of potentially hazardous asteroids under the assumptions of real asteroid shape models and uncertainties in the impact trajectory and the surface material properties of the asteroid, which produce a non-smooth system response. An alternate set of models is presented that enables analytic computation of the uncertainties in the imparted momentum from impact. Use of these models for a survey of asteroids allows conclusions to be drawn on the effects of an asteroid\u27s shape on the ability to successfully divert the asteroid via kinetic impactor
