Space swarms,enabled by the miniaturization of spacecraft,have the potential capability to lower costs,increase efficiencies,and broaden the horizons of space missions.The formation con-trol problem of large-scale spacecraft swarms flying around an elliptic orbit is considered.The objective is to drive the entire formation to produce a specified spatial pattern.The relative motion between agents becomes complicated as the number of agents increases.Hence,a density-based method is adopted,which concerns the density evolution of the entire swarm instead of the trajec-tories of individuals.The density-based method manipulates the density evolution with Partial Dif-ferential Equations (PDEs).This density-based control in this work has two aspects,global pattern control of the whole swarm and local collision-avoidance between nearby agents.The global behav-ior of the swarm is driven via designing velocity fields.For each spacecraft,the Q-guidance steering law is adopted to track the desired velocity with accelerations in a distributed manner.However,the final stable velocity field is required to be zero in the classical density-based approach,which appears as an obstacle from the viewpoint of astrodynamics since the periodic relative motion is always time-varying.To solve this issue,a novel transformation is constructed based on the periodic solutions of Tschauner-Hempel (TH) equations.The relative motion in Cartesian coordinates is then transformed into a new coordinate system,which permits zero-velocity in a stable configura-tion.The local behavior of the swarm,such as achieving collision avoidance,is achieved via a carefully-designed local density estimation algorithm.Numerical simulations are provided to demonstrate the performance of this approach.