A real-time 3-D trajectory planner for the leader-following formation control of autonomous vehicles is proposed. The planner relies on the definition of a trailer body whose hinge point is rigidly attached to the leader and assigns each follower to a distinct point of such a trailer. Convergence results for the trailer body reference frame are presented based on Lyapunov analysis, which guarantee that the planning can be independently implemented by n followers, with a common leader, as they asymptotically behave as n points of a unique trailer body. As such, the need for communication among followers is dispensable. The proposed strategy is divided into trajectory planning and trajectory tracking, the first problem being vehicle-independent. Experimental results obtained with quadrotor vehicles are presented, which demonstrate the richness and suitability of the planned trajectories.