Sensitivity of Optimal Midcourse Correction Scheduling for Robust Cislunar Trajectory Design

A new approach to optimal trajectory design is the determination of optimal trajectories that are robust to initial trajectory dispersions, navigation errors, maneuver execution errors, and environment modeling errors. This paper investigates the sensitivity of cislunar robust optimal trajectory design to launch date, duration of navigation measurement passes, and navigation measurement frequency. For a given cislunar trajectory from translunar injection (TLI) to lunar orbit insertion (LOI), the optimal locations of midcourse corrections, also known as trajectory correction maneuvers (TCM) are determined by minimizing the final 3-σ ∆v subject to a final 3-σ position dispersion constraint for a given launch date, specified measurement pass duration prior to each maneuver, and measurement frequency. Optical navigation (OpNav) is assumed, and OpNav field-of-view (FOV) and lighting constraints are employed. These constraints turn out to be important elements of the problem. The sensitivity of the optimal TCM locations are then investigated by varying the launch date, duration of OpNav measurement passes, and the OpNav measurement frequency, and then re-optimizing the locations of the TCMs. Given the problem parameters provided herein, results show that while the optimal TCM locations with respect to TLI vary greatly from one launch date to another, their locations with respect to LOI are nearly invariant over a 2-month launch window. Results also show that in all cases the optimal location of the last TCM is found to be at the point where the OpNav lunar FOV constraint is first violated. For all other TCMs, OpNav measurement pass duration and measurement frequency can have a moderate to large affect on the optimal TCM locations.