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Star-Tracker-Constrained Attitude MPC for CubeSats

Dominik Beňo, Patrik Valábek, Martin Hromčík, Martin Klaučo

Abstract

This paper presents an online linear model predictive control (MPC) framework for slew maneuvers that maintains star-tracker availability during ground-target tracking. The nonlinear rigid-body dynamics and geometric exclusion constraints are analytically linearized about the current state estimate at each control step, yielding a time-varying linear MPC formulation cast as a standard quadratic program (QP). This structure is compatible with established aerospace flight-software practices and offers a computational profile with lower online complexity than comparable nonlinear MPC schemes. The controller incorporates angular-rate, actuator, and star-tracker exclusion constraints over a receding horizon. Performance is assessed in high-fidelity nonlinear model-in-the-loop simulations using NASA's "42" spacecraft dynamics simulator, including a Monte Carlo campaign over varying target geometries and inertia perturbations.

Star-Tracker-Constrained Attitude MPC for CubeSats

Abstract

This paper presents an online linear model predictive control (MPC) framework for slew maneuvers that maintains star-tracker availability during ground-target tracking. The nonlinear rigid-body dynamics and geometric exclusion constraints are analytically linearized about the current state estimate at each control step, yielding a time-varying linear MPC formulation cast as a standard quadratic program (QP). This structure is compatible with established aerospace flight-software practices and offers a computational profile with lower online complexity than comparable nonlinear MPC schemes. The controller incorporates angular-rate, actuator, and star-tracker exclusion constraints over a receding horizon. Performance is assessed in high-fidelity nonlinear model-in-the-loop simulations using NASA's "42" spacecraft dynamics simulator, including a Monte Carlo campaign over varying target geometries and inertia perturbations.

Paper Structure

This paper contains 22 sections, 23 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Motivation
  3. Contribution
  4. Problem statement
  5. Spacecraft model
  6. Geometry description
  7. Model predictive controller design
  8. Model of the Satellite
  9. State dynamics
  10. Geometric output linearization
  11. Design of the State and Disturbance Observer
  12. MPC design
  13. Nonlinear simulation
  14. Simulation environment
  15. Simulation scenario description
  16. ...and 7 more sections

Figures (4)

  • Figure 3: Angular-rate trajectories with rate limits. Solid blue: Linear MPC. Dashed green: nonlinear optimization. Dotted purple: naive solution. Black dashed lines: rate constraints.
  • Figure 4: Body torque trajectories with actuator limits. Solid blue: Linear MPC. Dashed green: nonlinear optimization. Dotted purple: naive solution. Black dashed lines: actuator constraints.
  • Figure 5: Instrument $\boldsymbol{v}_\mathrm{ins}^\mathcal{N}$ and star-tracker boresight $\boldsymbol{v}_\mathrm{str}^\mathcal{N}$ (expressed in the inertial frame $\mathcal{N}$) visualization during the maneuver. Black point represents the vector direction at the maneuver start, and the cross represents the star-tracker boresight at time $t$. The black dashed line stands for $\boldsymbol{v}_\mathrm{trg}^\mathcal{N}$. The red set represents the nadir exclusion zone, and the yellow set represents the sun exclusion zone. Solid blue: Linear MPC. Dashed green: nonlinear optimization. Dotted purple: naive solution.
  • Figure 6: Number of QP solver iterations at each control step for the linear MPC controller.