Robust Cislunar Trajectory Optimization in the Presence of Stochastic Errors.

The focus of this research is the optimization of impulsive maneuvers in the circular restricted three body problem with stochastic error sources. Two and three impulse transfer trajectories with corrective maneuvers are designed to minimize an upper statistical bound for total Δ V , including the sum of nominal impulsive Δ V plus the 3 σ upper bound for corrections. Error sources include an initial state dispersion, maneuver execution error, and random white disturbances modeled as process noise. Direct optimization is performed via nonlinear programming. At each step in the nonlinear program, the optimal location and number of trajectory correction maneuvers (TCM) is determined, simultaneously satisfying a set of position dispersion constraints along the trajectory. Analytical gradients of the nominal maneuver magnitude and trace of the TCM covariance are provided to the nonlinear program to avoid finite differencing and associated numerical errors. Partial derivatives of the TCM covariance require the propagation of second-order state transition tensors. This work incorporates process noise into the optimization problem by propagating the effect of the accumulated process noise covariance. As a result, populating analytical gradients requires the partial derivative of the accumulated process noise covariance, called the accumulated process noise covariance state sensitivity tensor, which is propagated similar to state transition tensors. Robust trajectory scenarios analyzed include a three impulse trajectory from low-Earth orbit (LEO) to a near-rectilinear halo orbit (NRHO), and a two impulse NRHO rendezvous. [ABSTRACT FROM AUTHOR]