Loose flight means within bounded space envelopment for satellite swarm

Satellite swarms consist of a large number of low-cost satellites, with limited orbit control capability and low satellite swarm configuration requirements. Therefore, the traditional design and maintenance methods for high-precision control of satellite orbits and satellite swarm configurations cannot be easily adapted to meet the on-orbit operation requirements of satellite swarm. To address this problem, the looseness evaluation model and artificial potential field control model of satellite swarm are constructed to realize the loose flight of satellite swarm in bounded space envelopment. Firstly, the study developed an evaluation mathematical model of the looseness of a satellite swarm to evaluate the satellite swarm’s uniformity in bounded space envelopment. This model accounts for volume ratio, normalized standard deviation, and velocity offset of satellite swarm. Subsequently, a model that accounts for aspects such as virtual reference satellites, swarm members, space obstacles, was constructed to optimize the control force for a satellite swarm. This model, which is based on the artificial potential field, allows the satellite swarm to maintain loose flight and avoid obstacles in bounded space envelopment, thus ensuring the on-orbit safety of satellite swarm. Finally, the mathematical models constructed in this study was validated through numerical simulations.