<p>The assembly of large space structures requires reasonable trajectory planning of multiple satellites. In this work, the trajectory optimization design of a swarm satellite system (SSS) is studied for on-orbit assembly after separation and release from the spacecraft. Firstly, an orbital dynamic model of the SSS is established by utilizing the natural coordinate formulation (NCF). Secondly, a generalized control force model is applied to a single satellite via the combination of potential functions and a proportional differential (PD) controller. Then, a typical distributed auction algorithm (DAA) for optimal target assignment is presented. Finally, the trajectory optimization cases via the DAA are combined with the generalized avoidance forces to achieve collision-free motion. Dynamic simulation results show that the integrated approach proposed in this work provides a feasible choice for the on-orbit rapid assembly of the SSS.</p>