Robust Entry Vehicle Guidance with Sampling-Based Invariant Funnels

TL;DR

This paper introduces a novel set-based, sampling-based sum-of-squares method for robustly guiding entry vehicles, improving landing accuracy without relying on probabilistic assumptions.

Contribution

It develops a new invariant funnel computation technique that enhances robustness in entry guidance by avoiding probabilistic models and using set-based uncertainty bounds.

Findings

Computed tight invariant funnels for Mars entry model

Achieved increased landing accuracy with thermal constraint adherence

Demonstrated robustness without probabilistic assumptions

Abstract

Managing uncertainty is a fundamental and critical issue in spacecraft entry guidance. This paper presents a novel approach for uncertainty propagation during entry, descent and landing that relies on a new sum-of-squares robust verification technique. Unlike risk-based and probabilistic approaches, our technique does not rely on any probabilistic assumptions. It uses a set-based description to bound uncertainties and disturbances like vehicle and atmospheric parameters and winds. The approach leverages a recently developed sampling-based version of sum-of-squares programming to compute regions of finite time invariance, commonly referred to as "invariant funnels". We apply this approach to a three-degree-of-freedom entry vehicle model and test it using a Mars Science Laboratory reference trajectory. We compute tight approximations of robust invariant funnels that are guaranteed to reach a goal region with increased landing accuracy while respecting realistic thermal constraints.