Sequential Convex Trajectory Planning for Space-Debris Conjunction Mitigation in Satellite Formations

The growing density of space debris in Low Earth Orbit poses significant risks to Distributed Space Systems (DSSs), where multiple satellites operate in close proximity. Conventional single-satellite collision avoidance maneuvers do not account for internal formation safety and may induce secondary conjunction risks. This work presents a formation-level trajectory optimization framework for short-term conjunction mitigation that jointly addresses external debris avoidance and inter-satellite collision prevention. The proposed Space-Debris Evasion with Internal-Collision-Avoidance (SDEICA) method formulates the problem as a sequential convex programming scheme. A probabilistic debris keep-out region is modeled as an elliptical collision tube derived from the relative position covariance at the Time of Closest Approach (TCA) and convexified via tangent-plane approximation. Internal safety constraints are incorporated through successive linearization of inter-satellite separation conditions. The framework is evaluated on 1197 conjunction scenarios derived from ESA Collision-Avoidance Challenge data for a three-satellite formation. Results demonstrate a systematic reduction in the probability of collision below the operational threshold of 10−5 in all cases, within numerical tolerance, eliminating intersatellite distance violations, maintaining bounded formation deviation, and requiring only moderate control effort. The median computational time is 17.12 s per scenario. These findings indicate that sequential convex optimization provides a practical approach for coordinated, fuel-efficient collision avoidance in satellite formations operating in increasingly congested orbital environments.