The problem of trajectory planning for formation variation of unmanned ground vehicles (UGVs) is challenging due to the coupled non-collision constraints that apply to multiple vehicles. To address this issue, an innovative frame-work based on the alternating direction method of multipliers (ADMM) is proposed in this paper. The framework decouples complex constraints into two categories: individual constraints and mutual constraints. The former category involves dynamic, formation, and static obstacle constraints, which can be solved in parallel by each vehicle. Convex feasible set (CFS) algorithm is employed in this paper to simplify the static obstacle constraints. The latter category deals with collision avoidance among vehicles during the variation process and can be solved by nonlinear solvers. The convergence of the ADMM for the optimization problem is proved in this paper. Compared with solving the entire problem directly, the proposed framework reduces computation time and improves the quality of solution.