Robust Aerocapture Trajectory Optimization Under Atmospheric Density Uncertainty

Aerocapture maneuvers can significantly increase mission design flexibility. Although prior work based on the longitudinal dynamics has established that a bang/bang control profile using bank angle modulation is optimal for minimizing the postaerocapture insertion [Formula: see text], the optimal solution is sensitive to atmospheric uncertainties. This study investigates robust three-degrees-of-freedom (i.e., lateral/longitudinal) aerocapture trajectories under atmospheric density variations. The primer vector theory reveals that the coupled lateral/longitudinal dynamics results in a regularized bang/bang profile. First, using direct collocation, a nonstandard formulation of the desensitized aerocapture problem is developed that reduces the problem dimension using the global sensitivity analysis and enhances numerical accuracy in cost evaluation through state augmentation. The proposed desensitized optimization framework is applied to derive robust trajectories, which maintains a regularized bang/bang profile, with more than one switch in bank angle. The key finding of this paper is that aerocapture trajectories can be made more robust to atmospheric density uncertainty by employing a predominantly liftdown bank profile with multiple bank angle switches, which reduces the final time of the aerocapture maneuver and minimizes the time spent within the uncertain atmosphere. This analysis is supported through Monte Carlo simulations of an Earth aerocapture application.