Abstract: This paper studies formation control design and stability analysis for a system of double-integrator agents with directed communication links, in which the agents' motions are restricted to a set of given curves. The agents' dynamics and the given curves are all described in a fixed system of rectangular coordinates. Path functions are introduced to design path-following control system and then incorporated into arc-length functions to design formation protocol for guaranteeing consensus of both positions and velocities of agents along their desired paths based on the nominated formation. By graph theory, it is proved that the designed formation control system is asymptotically stable if the directed graph associated with the communication topology has a globally reachable node. The directed coordinated strategy proposed in this paper is applicable to optimal data collecting in an area.