Safety Control for Satellite Formation Flying via High-Order Control Barrier Functions

In satellite formation flying, maintaining a predefined safety distance between the reference satellite and its accompanying satellites is critical to prevent collisions—a requirement that traditional control methods fail to satisfy. This paper proposes a novel safety control algorithm that enforces the relative position constraint as a formal safety condition. Specifically, we construct a high-order control barrier function (HOCBF) tailored to the dynamics of satellite formations, which defines a safety set that guarantees collision avoidance. By formulating and solving a quadratic programming problem embedded with the HOCBF, we obtain a safe controller that ensures the forward invariance of the safety set. Simulation results demonstrate that our controller effectively maintains the required safety distance and prevents collisions under various disturbance scenarios, outperforming conventional methods in terms of response speed and robustness. These findings confirm the practical advantages of the proposed approach for safe satellite formation flying.