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Optimal Strip Attitude Command of Earth Observation Satellite using Differential Dynamic Programming

Seungyeop Han, Byeong-Un Jo, Koki Ho

Abstract

This paper addresses the optimal scan profile problem for strip imaging in an Earth observation satellite (EOS) equipped with a time-delay integration (TDI) camera. Modern TDI cameras can control image integration frequency during imaging operation, adding an additional degree of freedom (DOF) to the imaging operation. On the other hand, modern agile EOS is capable of imaging non-parallel ground targets, which require a substantial amount of angular velocity and angular acceleration during operation. We leverage this DOF to minimize various factors impacting image quality, such as angular velocity. Initially, we derive analytic expressions for angular velocity based on kinematic equations. These expressions are then used to formulate a constrained optimal control problem (OCP), which we solve using differential dynamic programming (DDP). We validate our approach through testing and comparison with reference methods across various practical scenarios. Simulation results demonstrate that our proposed method efficiently achieves near-optimal solutions without encountering non-convergence issues.

Optimal Strip Attitude Command of Earth Observation Satellite using Differential Dynamic Programming

Abstract

This paper addresses the optimal scan profile problem for strip imaging in an Earth observation satellite (EOS) equipped with a time-delay integration (TDI) camera. Modern TDI cameras can control image integration frequency during imaging operation, adding an additional degree of freedom (DOF) to the imaging operation. On the other hand, modern agile EOS is capable of imaging non-parallel ground targets, which require a substantial amount of angular velocity and angular acceleration during operation. We leverage this DOF to minimize various factors impacting image quality, such as angular velocity. Initially, we derive analytic expressions for angular velocity based on kinematic equations. These expressions are then used to formulate a constrained optimal control problem (OCP), which we solve using differential dynamic programming (DDP). We validate our approach through testing and comparison with reference methods across various practical scenarios. Simulation results demonstrate that our proposed method efficiently achieves near-optimal solutions without encountering non-convergence issues.
Paper Structure (17 sections, 51 equations, 12 figures, 1 table, 1 algorithm)

This paper contains 17 sections, 51 equations, 12 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Analytic Expression of General Strip Attitude Profile
  3. General Staring Attitude
  4. General Strip Attitude for TDI camera
  5. Target Position Model
  6. Satellite Orbit Model
  7. Constrained Optimal Control Problem and DDP
  8. Unconstrained Optimal Control Problem and the HJB equation
  9. Review of Differential Dynamic Programming
  10. DDP Updated Algorithm with Terminal Constraint
  11. Augmented Lagrangian Method for Path Constraint
  12. Optimal Strip Attitude Command Generation
  13. Simulation Result
  14. Optimal Scan Profile without $f_\text{CCD}$ constraints
  15. Optimal Scan Profile with $f_\text{CCD}$ constraints
  16. ...and 2 more sections

Figures (12)

  • Figure 1: Geometry of Staring Control.
  • Figure 2: Illustration of (a) matched (b) mismatched scan direction and scan rate errors
  • Figure 3: (a) Correctly aligned frame $\mathcal{D}$ and (b) relationship between $v_\text{LOS}$ and $v_\text{ccd}$
  • Figure 4: Target profile as a great circle of spherical earth model
  • Figure 5: Four STRIP scenarios: (a) parallel, (b) offset, (c) perpendicular, (d) reverse
  • ...and 7 more figures