Abstract: For the collision-free formation control of large-scale spacecraft swarms in space, it is essential to rapidly generate safe transfer trajectories that avoid collisions. However, directly solving trajectory planning problems with complex constraints is often impractical, especially when the swarm consists of a large number of agents. In such cases, the number of collision avoidance constraints increases exponentially with the swarm size, posing significant computational challenges. To address this issue, this paper proposes a direct trajectory optimization algorithm based on virtual force fields. By designing a consensus-driven virtual force field, the algorithm directly adjusts and optimizes the discrete trajectories of the swarm members at the geometric level. Leveraging the differentially flat characteristics of spacecraft relative dynamics, the method generates continuous control trajectories without relying on conventional optimization solvers for complex trajectory planning. The proposed approach maintains computational complexity independent of the swarm size. It iteratively constructs approximately optimal, collision-free transfer trajectories via virtual force field updates, thereby overcoming the heavy communication overhead typically required in traditional distributed trajectory optimization methods. Furthermore, the virtual force field is formulated analytically and ensures consensus across the swarm during each iteration. Compared to conventional trajectory planning algorithms, the proposed method significantly reduces computational resource consumption while preserving near-optimal trajectory quality. Simulation results validate the effectiveness of the proposed control strategy.

Key words: spacecraft swarm, formation reconfiguration, virtual force field, trajectory planning, collision avoidance