An essential part of any spacecraft mission is the design, planning, and operation of robust and fuel-efficient trajectories that can fulfill mission requirements while coping with the harsh reality of the space environment. These trajectories are traditionally engineered in a two-step approach. First, orbits are designed in a deterministic fashion, assuming that the dynamics and state of the spacecraft are known with infinite accuracy. Secondly, the robustness of these initial conditions is tested against model uncertainties and knowledge errors using brute-force Monte Carlo simulations that explore different realizations of the uncertainty set. This two-step approach is not only time-consuming, but also contributes to slowing down the mission development process as the robustness of candidate orbits can only be assessed a-posteriori. This PhD project aims at implementing and developing novel stochastic continuation procedures that have the potential to revolutionize the trajectory design process by accounting for uncertainties from the very beginning of the design phase. Our idea is to study ‘moment maps’ of spacecraft distributions, i.e., maps of low-order moments of the satellite’s evolving density function using methods of numerical continuation, differential algebra and probabilistic programming. The goal is to directly calculate, up to a certain confidence level, regions of the phase space where the spacecraft’s distribution is expected to evolve depending on the time scales and uncertainties of a user-defined problem. The numerical procedures will be general by nature and therefore applicable to a variety of spacecraft missions, including ESA’s Hera, aiming towards the binary asteroid 65803 Didymos, and the JAXA-lead MMX, destined for Phobos. In both cases, the shapes of the target bodies and other dynamical parameters remain uncertain, thus hindering the confidence of mission designers in operating certain types of orbits ahead of arrival.
