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ABAMGuid+: An Enhanced Aerocapture Guidance Framework using Augmented Bank Angle Modulation

Kyle A. Sonandres, Thomas R. Palazzo, Jonathan P. How

TL;DR

This work advances aerocapture guidance by developing ABAMGuid+ — a four-phase, ABAM-based controller that combines bang-bang longitudinal controls with continuous alpha-sigma modulation (CASM) in the terminal phase. It derives optimal-control solutions for both linear and quadratic aerodynamics, validates them with Gauss pseudospectral methods, and embeds the key insights into a real-time guidance algorithm that uses CASM to handle dispersions without solving full optimal-control problems online. Across nominal and off-nominal Uranus-entry scenarios, ABAMGuid+ achieves tighter exit-velocity targeting, smaller propellant penalties, and higher capture success, with Monte Carlo analyses showing substantial improvements over FNPAG and prior ABAMGuid. The results demonstrate the practical impact of augmenting bank angle with angle of attack control and of converting optimal trajectories into computationally efficient online guidance that robustly accommodates environmental uncertainties.

Abstract

Aerocapture consists of converting a hyperbolic approach trajectory into a captured target orbit utilizing the aerodynamic forces generated via a single pass through the atmosphere. Aerocapture guidance systems must be robust to significant environmental variations and modeling uncertainty, particularly regarding atmospheric properties and delivery conditions. Recent work has shown that enabling control over both bank angle and angle of attack, a strategy referred to as augmented bank angle modulation (ABAM), can improve robustness to entry state and atmospheric uncertainties. In this work, we derive optimal control solutions for an aerocapture vehicle using ABAM. We first formulate the problem using a linear aerodynamic model and derive closed-form optimal control profiles using Pontryagin's Minimum Principle. To increase modeling fidelity, we also consider a quadratic aerodynamic model and obtain the solution directly using the optimality conditions. Both formulations are solved numerically using Gauss pseudospectral methods (via GPOPS, a software tool for pseudospectral optimal control), to validate the analytic solutions. We then introduce a novel aerocapture guidance algorithm, ABAMGuid+, which indirectly minimizes propellant usage by mimicking the structure of the optimal control solution, enabling efficient guidance by avoiding the complexity of solving the full optimal control problem online. Extensive Monte Carlo simulations of a Uranus aerocapture mission demonstrate that ABAMGuid+ increases capture success rates and reduces post-capture propellant requirements relative to previous methods.

ABAMGuid+: An Enhanced Aerocapture Guidance Framework using Augmented Bank Angle Modulation

TL;DR

This work advances aerocapture guidance by developing ABAMGuid+ — a four-phase, ABAM-based controller that combines bang-bang longitudinal controls with continuous alpha-sigma modulation (CASM) in the terminal phase. It derives optimal-control solutions for both linear and quadratic aerodynamics, validates them with Gauss pseudospectral methods, and embeds the key insights into a real-time guidance algorithm that uses CASM to handle dispersions without solving full optimal-control problems online. Across nominal and off-nominal Uranus-entry scenarios, ABAMGuid+ achieves tighter exit-velocity targeting, smaller propellant penalties, and higher capture success, with Monte Carlo analyses showing substantial improvements over FNPAG and prior ABAMGuid. The results demonstrate the practical impact of augmenting bank angle with angle of attack control and of converting optimal trajectories into computationally efficient online guidance that robustly accommodates environmental uncertainties.

Abstract

Aerocapture consists of converting a hyperbolic approach trajectory into a captured target orbit utilizing the aerodynamic forces generated via a single pass through the atmosphere. Aerocapture guidance systems must be robust to significant environmental variations and modeling uncertainty, particularly regarding atmospheric properties and delivery conditions. Recent work has shown that enabling control over both bank angle and angle of attack, a strategy referred to as augmented bank angle modulation (ABAM), can improve robustness to entry state and atmospheric uncertainties. In this work, we derive optimal control solutions for an aerocapture vehicle using ABAM. We first formulate the problem using a linear aerodynamic model and derive closed-form optimal control profiles using Pontryagin's Minimum Principle. To increase modeling fidelity, we also consider a quadratic aerodynamic model and obtain the solution directly using the optimality conditions. Both formulations are solved numerically using Gauss pseudospectral methods (via GPOPS, a software tool for pseudospectral optimal control), to validate the analytic solutions. We then introduce a novel aerocapture guidance algorithm, ABAMGuid+, which indirectly minimizes propellant usage by mimicking the structure of the optimal control solution, enabling efficient guidance by avoiding the complexity of solving the full optimal control problem online. Extensive Monte Carlo simulations of a Uranus aerocapture mission demonstrate that ABAMGuid+ increases capture success rates and reduces post-capture propellant requirements relative to previous methods.
Paper Structure (21 sections, 2 theorems, 48 equations, 9 figures, 3 tables, 2 algorithms)

This paper contains 21 sections, 2 theorems, 48 equations, 9 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Augmented Bank Angle Modulation Aerocapture Problem Formulation
  3. General ABAM Aerocapture Problem
  4. Exit Velocity Targeting Reformulation
  5. Longitudinal Problem Statement
  6. Aerodynamic Modeling
  7. Optimal Control Solutions
  8. Linear Aerodynamic Model
  9. Quadratic Aerodynamic Model
  10. Numerical Verification and Comparison
  11. Guidance Algorithm Design
  12. Four-Phase Formulation
  13. Continuous Alpha-Sigma Modulation
  14. Guidance Performance in Varying Entry Scenarios
  15. Simulation Methodology
  16. ...and 6 more sections

Key Result

Theorem 1

Assume that the optimal bank angle for the two-input case (ABAM) is given by $\sigma^* = \sigma^*_\text{BAM}$, as in Definition def: sigma bam. Then the optimal angle of attack profile, $\alpha^*: \mathbb{R} \rightarrow \{ \alpha_\textrm{min}, ~ \alpha_\textrm{max} \}$, is determined by where $H_\alpha = H_{\alpha, \textrm{up}}$ during lift-up flight, and $H_\alpha = H_{\alpha, \textrm{down}}$ du

Figures (9)

  • Figure 1: Aerocapture maneuver. The spacecraft enters along a hyperbolic trajectory (1), entering the target planet's atmosphere at the atmospheric entry interface (2). The guidance system actively controls the vehicle once sufficient control authority is detected (3), continuing until the end of active guidance (4). The vehicle exits the atmosphere (5) in an elliptical orbit. Subsequent maneuvers, periapsis raise (6) and apoapsis correction (7), establish the desired orbit.
  • Figure 2: Linear (blue) and quadratic (black) $C_D$ approximations versus true aerodynamics (red) as a function of angle of attack (left panel). The right panel displays error percentage versus truth over the $\alpha$ range. The linear model well approximates the true nonlinear aerodynamics, and the quadratic model is nearly identical to truth.
  • Figure 3: GPOPS results. Black vertical dashed lines correspond to $\alpha$ switching times, and red vertical dashed lines correspond to $\sigma$ switching times. With both models, the analytic and numerical solutions are consistent: in Fig. \ref{['fig: linear gpops']}, analytic switching times (zero crossings and curve intersection in top panel) align closely with the switching behavior in the GPOPS control profiles. In Fig \ref{['fig: quadratic gpops']}, the analytic control profiles (top panel) and bank angle switch (red dashed line) match the GPOPS control profiles.
  • Figure 4: Illustration of the four-phase control structure used in ABAMGuid+. The nominal profile consists of three bang-bang switching phases, followed by an unsaturated terminal phase to account for trajectory dispersions. The dashed orange line represents the profile used in our previous method (ABAMGuid), which maintains a saturated angle of attack in the final phase. ABAMGuid+ has enhanced ability to respond to terminal phase dispersions by performing unsaturated control of both channels.
  • Figure 5: Nominal trajectory ($\gamma$ = -10.79 degrees) results for each algorithm. The altitude vs. velocity profile (top-left) and evolution of orbital eccentricity (top-right) illustrate that each trajectory converges on the target exit velocity and orbital eccentricity. The $\sigma$ and $\alpha$ profiles over time are shown in the bottom-left and bottom-right panels, respectively.
  • ...and 4 more figures

Theorems & Definitions (13)

  • Definition 1
  • Definition 2
  • Theorem 1
  • proof
  • Remark 1
  • Remark 2
  • Remark 3
  • Definition 3
  • Definition 4
  • Theorem 2
  • ...and 3 more