Atmospheric Density-Compensating Model Predictive Control for Targeted Reentry of Drag-Modulated Spacecraft

TL;DR

This work tackles the challenge of reentry targeting for drag-modulated small spacecraft under atmospheric-density uncertainty by combining an extended Kalman filter that estimates density prediction errors with a model predictive controller that robustly tracks a nominal guidance trajectory. The EKF augments the state with a density-error term and uses GPS-relative measurements to produce a real-time estimate of $\Delta\rho$, which is fed into a time-varying MPC that penalizes changes in the ballistic coefficient and accounts for disturbance effects over a prediction horizon. A Monte Carlo study with historical space-weather data demonstrates that the framework achieves near-trajectory fidelity, with 98.4% of runs staying within 100 km of the guidance and a mean entry-interface tracking error of 12.1 km when density errors are estimated. The results show significant improvements over a density-unaware controller and establish the method’s viability for reliable, drag-based reentry of small satellites while highlighting the practical limits under extreme space-weather events.

Abstract

This paper presents an estimation and control framework that enables the targeted reentry of a drag-modulated spacecraft in the presence of atmospheric density uncertainty. In particular, an extended Kalman filter (EKF) is used to estimate the in-flight density errors relative to the atmospheric density used to generate the nominal guidance trajectory. This information is leveraged within a model predictive control (MPC) strategy to improve tracking performance, reduce control effort, and increase robustness to actuator saturation compared to the state-of-the-art approach. The estimation and control framework is tested in a Monte Carlo simulation campaign with historical space weather data. These simulation efforts demonstrate that the proposed framework is able to stay within 100 km of the guidance trajectory at all points in time for 98.4% of cases. The remaining 1.6% of cases were pushed away from the guidance by large density errors, many due to significant solar storms and flares, that could not physically be compensated for by the drag control device. For the successful cases, the proposed framework was able to guide the spacecraft to the desired location at the entry interface altitude with a mean error of 12.1 km and 99.7% of cases below 100 km.

Figures (12)

• Figure 1: The directions of the local vertical, local horizontal frame.
• Figure 2: Orbital decays of spacecraft with (a) constant ballistic coefficients and (b) a change in ballistic coefficient at a $t_{swap}$ of approximately 12 days.
• Figure 3: Nominal ballistic coefficients for 250 trajectories with randomly sampled initial conditions and desired entry interface locations compared to the feasible range.
• Figure 4: Block diagram depicting the simulation of estimation and control algorithms and the spacecraft dynamics.
• Figure 5: Monte Carlo results of the final guidance position errors as (a) a histogram and (b) a cumulative distribution function zoomed in on the errors below $25$ km.