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Terminal Soft Landing Guidance Law Using Analytic Gravity Turn Trajectory

Seungyeop Han, Byeong-Un Jo, Koki Ho

TL;DR

The paper addresses pinpoint terminal landing under descent by designing a guidance law that leverages an analytic gravity-turn solution to generate a reference velocity toward the landing site. A nonlinear velocity-tracking controller follows this reference in finite time, with a robust, collision-avoidant extension that preserves a concave-down trajectory for obstacle clearance. It introduces a time-to-go based feedback, a gravity-turn-based reference, and a saturation-aware thrust command to ensure feasibility under bounds. Comparative simulations show fuel efficiency close to optimal performance, with strong robustness to disturbances demonstrated via Monte Carlo analyses. The approach offers a computationally light, analytically characterized alternative to online optimization for onboard EDL guidance.

Abstract

This paper presents an innovative terminal landing guidance law that utilizes an analytic solution derived from the gravity turn trajectory. The characteristics of the derived solution are thoroughly investigated, and the solution is employed to generate a reference velocity vector that satisfies terminal landing conditions. A nonlinear control law is applied to effectively track the reference velocity vector within a finite time, and its robustness against disturbances is studied. Furthermore, the guidance law is expanded to incorporate ground collision avoidance by considering the shape of the gravity turn trajectory. The proposed method's fuel efficiency, robustness, and practicality are demonstrated through comprehensive numerical simulations, and its performance is compared with existing methods.

Terminal Soft Landing Guidance Law Using Analytic Gravity Turn Trajectory

TL;DR

The paper addresses pinpoint terminal landing under descent by designing a guidance law that leverages an analytic gravity-turn solution to generate a reference velocity toward the landing site. A nonlinear velocity-tracking controller follows this reference in finite time, with a robust, collision-avoidant extension that preserves a concave-down trajectory for obstacle clearance. It introduces a time-to-go based feedback, a gravity-turn-based reference, and a saturation-aware thrust command to ensure feasibility under bounds. Comparative simulations show fuel efficiency close to optimal performance, with strong robustness to disturbances demonstrated via Monte Carlo analyses. The approach offers a computationally light, analytically characterized alternative to online optimization for onboard EDL guidance.

Abstract

This paper presents an innovative terminal landing guidance law that utilizes an analytic solution derived from the gravity turn trajectory. The characteristics of the derived solution are thoroughly investigated, and the solution is employed to generate a reference velocity vector that satisfies terminal landing conditions. A nonlinear control law is applied to effectively track the reference velocity vector within a finite time, and its robustness against disturbances is studied. Furthermore, the guidance law is expanded to incorporate ground collision avoidance by considering the shape of the gravity turn trajectory. The proposed method's fuel efficiency, robustness, and practicality are demonstrated through comprehensive numerical simulations, and its performance is compared with existing methods.
Paper Structure (20 sections, 84 equations, 12 figures, 4 tables)

This paper contains 20 sections, 84 equations, 12 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Analytic Solution of Planar Gravity Turn Trajectory
  3. Analytic Solution of Powered Descent Gravity Turn Trajectory
  4. Characteristics of Powered Descent Gravity-Turn Trajectory
  5. Velocity Vector for Terminal Landing
  6. Uniqueness and Existence of Velocity Vector
  7. Properties of Velocity Vector
  8. Terminal Landing Guidance Law
  9. Equation of motion for the lander
  10. Velocity Tracking Control Law
  11. Characteristics of Velocity Tracking Control Law
  12. Selection of Control Parameters
  13. Ground Collision Avoidance Logic
  14. Thrust Command Saturation Logic
  15. Summary of Landing Guidance Law
  16. ...and 5 more sections

Figures (12)

  • Figure 1: (a) Sample velocity vector field and (b) velocity vector along the line with different $\beta$
  • Figure 2: Engagement geometry and guidance frame
  • Figure 3: Collision Avoidance Geometry (a) A cone constraint (b) Side view of the tangent plane
  • Figure 4: Summation of two vector $\textbf{x}+\textbf{z}$ using 'fit' function, where $\textbf{z} = \text{fit}(\textbf{x}, \textbf{y}, c)$.
  • Figure 5: Results of Scenario 1 (a) Trajectory (b) Throttle Level (c) Flight-Path Angle (d) Elevation angle $\theta_u$
  • ...and 7 more figures