Optimal drag-based collision avoidance: Balancing miss distance and orbital decay

The increasing number of objects in Low Earth Orbit makes active collision avoidance imperative for satellites operating in this region. For satellites non equipped with propulsion systems, the collision risk can be mitigated by exploiting the active modulation of aerodynamic forces through the ballistic coefficient. This article proposes a novel and high-fidelity optimal control approach for collision avoidance via aerodynamic drag modulation for an unpropelled SmallSat. Central to this approach is a cost function that jointly maximizes the miss distance while minimizing orbital decay during the maneuver. Moreover, the proposed approach has been rigorously tested through its application to the real-world scenario of the SOURCE satellite, slated for launch in 2025. For the satellite under investigation and a maneuver altitude of 350km, an in-track separation distance of around 22km can be accomplished within a warning time of 24h, which is large enough to conclude that the collision was successfully avoided. As a downside, however, this results in an additional loss in the semi-major axis of 165m and thus a reduced lifetime of the satellite. This balance between separation distance and additional loss in altitude can be flexibly adjusted by the user, which is demonstrated extensively in the article by means of a parameter study. Compared to the widespread use of chemical propulsion systems, this strategy naturally demands longer warning times due to the significantly lower available forces, and also radial offsets to the potential collision object cannot be in this case. Nevertheless, it offers a very promising alternative for active collision avoidance, especially for low-altitude applications.