Improved Directional State Transition Tensors for Accurate Aerocapture Performance Analysis

TL;DR

The paper addresses the challenge of nonconservative, highly nonlinear aerocapture dynamics by extending state transition tensors (STTs) to directional state transition tensors (DSTTs) that operate in reduced latent spaces. It introduces augmented higher-order Cauchy Green tensors (HOCGTs) and their selective (sCGT) and QoI-based (qCGT) variants to identify dynamically sensitive directions for perturbation propagation and quantity-of-interest tracking. Results show that DSTTs constructed along these dynamics-informed directions achieve lower approximation errors and improved propagation accuracy, particularly near peak dynamic pressure, compared with traditional DSTTs and higher-dimensional representations. The approach enables robust, onboard-capable uncertainty propagation for aerocapture guidance and navigation, with potential extensions to complex QoIs and non-Gaussian state distributions.

Abstract

Aerocapture is a unique challenge for semi-analytical propagation because its nonconservative dynamics lead to force magnitudes that vary substantially across the trajectory. State transition tensors (STTs), higher-order Taylor series expansions of the solution flow, have been widely used as a computationally efficient semi-analytical propagation method for orbital scenarios, but have not previously been applied to aerocapture. However, obtaining the higher-order STTs requires integrating exponentially more equations. Directional state transition tensors (DSTTs) mitigate this cost by projecting the state into a reduced-dimension basis. This work develops novel dynamics analysis techniques to identify effective bases for this reduction, including augmented higher-order Cauchy Green tensors tailored to quantities of interest such as apoapsis radius. Results show that DSTTs constructed along these bases significantly reduce computational cost while maintaining accuracy in apoapsis and energy prediction. In particular, certain of these DSTTs outperform traditional DSTTs in nonlinear perturbation propagation for key state subsets and quantities of interest. These results establish STTs and DSTTs as practical tools for aerocapture performance analysis to enable robust guidance and navigation.

Figures (11)

• Figure 1: Dynamic pressure profile for the nominal trajectory.
• Figure 2: Eigenvectors for the maximum eigenvalue for each decomposed dynamics second-order CGT from $(t_{k+1}, t_k)$.
• Figure 3: Angle between dominant decomposed dynamics CGT eigenvector and all overall CGT eigenvectors.
• Figure 4: Eigenvectors of the maximum eigenvalue for different HOCGT constructions from $(t_{k+1}, t_k)$. The sCGTs select position, velocity, and flight path angle; the $\varepsilon$-qCGTs are in terms of energy.
• Figure 5: Top two eigenvalues of the third-order HOCGTs found from SS-HOPM for $(t_{k+1}, t_k)$