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Aerocapture Guidance for Augmented Bank Angle Modulation

Kyle Sonandres, Thomas Palazzo, Jonathan P. How

TL;DR

The paper tackles Uranus aerocapture by introducing augmented bank angle modulation (ABAM), a two-input control framework using bank angle $\sigma$ and angle of attack $\alpha$ to improve apoapsis targeting. It derives optimal ABAM profiles via Pontryagin's Minimum Principle, validating these insights with Gauss pseudospectral optimization in GPOPS, and distills them into ABAMGuid for online guidance. Monte Carlo testing with a high-fidelity Uranus atmosphere model shows ABAMGuid can significantly reduce the required post-aerocapture $\Delta V$ (up to ~29.5% at the 99th percentile) and dramatically lower failure rates under conservative entry conditions, compared to FNPAG. The work demonstrates ABAM's potential to enhance aerocapture performance and mission robustness, while noting computational considerations and avenues for future improvements such as lateral guidance and heating/load constraints.

Abstract

This paper presents an optimal control solution for an aerocapture vehicle with two control inputs, bank angle and angle of attack, referred to as augmented bank angle modulation (ABAM). We derive the optimal control profiles using Pontryagin's Minimum Principle, validate the result numerically using the Gauss pseudospectral method (implemented in GPOPS), and introduce a novel guidance algorithm, ABAMGuid, for in-flight decision making. High-fidelity Monte Carlo simulations of a Uranus aerocapture mission demonstrate that ABAMGuid can greatly improve capture success rates and reduce the propellant needed for orbital correction following the atmospheric pass.

Aerocapture Guidance for Augmented Bank Angle Modulation

TL;DR

The paper tackles Uranus aerocapture by introducing augmented bank angle modulation (ABAM), a two-input control framework using bank angle and angle of attack to improve apoapsis targeting. It derives optimal ABAM profiles via Pontryagin's Minimum Principle, validating these insights with Gauss pseudospectral optimization in GPOPS, and distills them into ABAMGuid for online guidance. Monte Carlo testing with a high-fidelity Uranus atmosphere model shows ABAMGuid can significantly reduce the required post-aerocapture (up to ~29.5% at the 99th percentile) and dramatically lower failure rates under conservative entry conditions, compared to FNPAG. The work demonstrates ABAM's potential to enhance aerocapture performance and mission robustness, while noting computational considerations and avenues for future improvements such as lateral guidance and heating/load constraints.

Abstract

This paper presents an optimal control solution for an aerocapture vehicle with two control inputs, bank angle and angle of attack, referred to as augmented bank angle modulation (ABAM). We derive the optimal control profiles using Pontryagin's Minimum Principle, validate the result numerically using the Gauss pseudospectral method (implemented in GPOPS), and introduce a novel guidance algorithm, ABAMGuid, for in-flight decision making. High-fidelity Monte Carlo simulations of a Uranus aerocapture mission demonstrate that ABAMGuid can greatly improve capture success rates and reduce the propellant needed for orbital correction following the atmospheric pass.

Paper Structure

This paper contains 15 sections, 1 theorem, 25 equations, 2 figures, 3 tables.

Table of Contents

  1. INTRODUCTION
  2. OPTIMAL CONTROL PROBLEM
  3. Equations of Motion
  4. Control Variables
  5. Constraints and Objectives
  6. Assumptions and Simplification
  7. Optimal Control Derivation
  8. Numerical Analysis using GPOPS
  9. AEROCAPTURE GUIDANCE ALGORITHM
  10. A Four-Phase Algorithm
  11. Lateral Guidance, Constraints, and Uncertainty
  12. SIMULATION RESULTS
  13. Simulation Methodology
  14. Results
  15. CONCLUSIONS

Key Result

Theorem 1

Assume that for the two input case (ABAM), $\sigma^* = \sigma^*_\text{BAM}$, as in Definition def: sigma bam. Then during lift-up flight, $\alpha^* = \alpha_{\textrm{min}}$ if $H_{\alpha, \text{up}} > 0$, and $\alpha^* = \alpha_{\textrm{max}}$ if $H_{\alpha, \text{up}} < 0$. During lift-down flight,

Figures (2)

  • Figure 1: Switching functions (top row), optimal bank angle (center row) and angle of attack (bottom row) profiles. Switching functions plotted from GPOPS state and estimated costate output, controls plotted from GPOPS control solution. Left column corresponds to the nominal entry flight path angle (EFPA) case, center column corresponds to a shallow EFPA case, and right column corresponds to a steep EFPA case. Black vertical dashed lines correspond to $\alpha$ switching times and red vertical dashed lines correspond to $\sigma$ switching times.
  • Figure 2: MC simulation peak g-load (top row) and outcome (bottom) results as functions of entry flight path angle with conservative entry states. Black points indicate passing runs and red circles indicate failures. The vertical dashed lines are placed such that there is a $\geq$ 95% success rate at a given EFPA between the lines, with red corresponding to FNPAG, and black to ABAMGuid. Top right corresponds to ABAMGuid, top left to FNPAG.

Theorems & Definitions (6)

  • Definition 1
  • Theorem 1
  • proof
  • Remark 1
  • Remark 2
  • Remark 3