ROBUST TRAJECTORY DESIGN FOR ASTEROID ORBITERS

In low gravity environments with large uncertainties, a robust orbit transfer may be preferred over a fuel-optimal transfer. Such a case exists in the orbital environment around small asteroids, where transfers can be achieved with maneuvers of relatively small magnitudes. However, these trajectories are also highly sensitive to maneuver execution errors and state uncertainties. This paper will investigate a parametric robust optimization method with applications to asteroid missions, where the robust-optimal solution will be the trajectory that minimizes the variance of error in a terminal constraint under state and control uncertainties. The proposed method requires analytically mapping state and control errors to a terminal constraint. A single-phase mapping solution will be developed for application to fully open-loop trajectories. Additionally, a multiple-phase mapping solution will be proposed for trajectories in which maneuvers are redesigned to correct state errors throughout the trajectory. Robust trajectories will be designed for three cases: orbit corrections about a small asteroid using the Clohessy-Wiltshire equations, orbit transfers in the two-body problem, and a heliocentric asteroid approach trajectory approximated with rectilinear motion.