In this paper, we consider the problem of decentralized cohesive motion control of a formation of autonomous vehicles or robots moving in three dimensions, where the formation is required to move from its initial setting (defined by the positions of the agents in the formation) to a final desired setting and, during thismotion, maintain its formation geometry defined by the initial distances between the agent pairs. We propose a distributed control scheme to solve this problem utilizing the notions of graph rigidity and persistence as well as techniques of virtual target tracking and smooth switching. The distributed control scheme is developed by modeling the agent kinematics as single-velocity integrator; nevertheless, extension to the cases with practical kinematic and dynamic models of fixed-wing autonomous aerial vehicles and quadrotors is discussed. In this context, we examine the maintenance of geometric formation of a swarm of autonomous flight vehicles. The developed coordination and control schemes are verified via a number of simulations.