Sample-Based Robust Uncertainty Propagation for Entry Vehicles

Abstract

This paper introduces a new approach for uncertainty quantification and propagation applicable to entry vehicle trajectories,suitable for use in trajectory optimization and computation of approximate invariant funnels. Because of the lack of precise knowledge of the atmospheres of other solar system bodies, traditional entry trajectory design methods rely on extensive Monte Carlo simulations, leading to accurate results but at high labor and computational costs. Other conventional methods can be faster but require assumptions on the probability distributions of dispersion parameters. The approach developed in this paper represents uncertainties in the system using conservative ellipsoidal bounds. A sample-based strategy inspired by the Unscented Kalman Filter is used to propagate the dynamics and uncertainties around the nominal trajectory. The method is demonstrated on the Duffing oscillator and then applied to a Mars entry vehicle problem using both three-degree-of-freedom and six-degree-of-freedom dynamical models. Its performance is compared with traditional uncertainty quantification methods.