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

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.

💡 Research Summary

This paper presents a novel integrated estimation and control framework designed to enable the precise targeted reentry of drag-modulated spacecraft (like CubeSats) in the presence of significant atmospheric density uncertainty. The core challenge addressed is that the aerodynamic drag force, which is harnessed for deorbiting, depends critically on atmospheric density—a parameter that is highly variable and difficult to predict accurately due to solar activity and other space weather phenomena.

The proposed solution is a two-layer strategy combining real-time estimation with advanced control. First, an Extended Kalman Filter (EKF) is employed to estimate the in-flight atmospheric density error. Using GPS measurements of the spacecraft’s position and velocity relative to a pre-computed nominal guidance trajectory, the EKF estimates a scale factor that corrects the nominal density model used for planning. This provides the controller with crucial, adaptive knowledge of the environmental disturbance.

Second, this density estimate is fed into a refined Model Predictive Control (MPC) law. The MPC uses a linear time-varying (LTV) model of the spacecraft’s error dynamics relative to the guidance trajectory, which is continuously updated using the latest density estimate. At each control step, the MPC solves a finite-horizon optimization problem to determine the optimal adjustment to the spacecraft’s ballistic coefficient (via a drag device like an ExoBrake). The control objective is twofold: minimize trajectory tracking error while also penalizing changes in the ballistic coefficient, thereby reducing control effort and actuator wear—a practical consideration for resource-constrained small satellites.

The paper details improvements over prior work, including the integration of LTV dynamics for more accurate prediction and a modified guidance trajectory generation process that centers the nominal ballistic coefficients away from actuator saturation limits, providing more control authority.

The performance of the entire EKF-MPC framework is rigorously validated through an extensive Monte Carlo simulation campaign. Instead of using simple statistical density dispersions, the simulations incorporate density variations derived from historical space weather data, making the test scenarios highly realistic. Results demonstrate robust performance: in 98.4% of simulated cases, the spacecraft remained within 100 km of the guidance trajectory throughout its entire descent. For these successful cases, the mean landing error at the entry interface was 12.1 km, with 99.7% of cases achieving an error below 100 km. The remaining 1.6% of failures were attributed to extreme density errors (e.g., from major solar storms) that exceeded the physical compensation capabilities of the assumed drag device, highlighting the system’s practical limits.

In summary, this research provides a comprehensive and practical solution for accurate deorbiting. It bridges the gap between theoretical control design and real-world operation by integrating real-time environmental estimation with a predictive controller that explicitly handles constraints, ultimately promising enhanced mission capabilities for small satellites in areas like responsible end-of-life disposal and targeted payload return.