In the context of Flying Ad hoc NETworks (FANET), this paper proposes a controlled mobility routing scheme to efficiently tracking a Moving Point of Interest (MPI). Once the MPI has been localized and its position reported to a ground station (GS), the best path in terms of number of Unmanned Aerial Vehicles (UAVs) participating in the routing and their positions is computed in a centralized way and the UAVs chosen for the routing are informed about the positions to move to. Upon the construction of the path between the MPI and the GS, the UAVs involved in the routing move in order to track the MPI movements without losing connectivity with the GS. The proposed scheme minimizes the energy consumption while enhancing the performance of the FANET by increasing the throughput and reducing the delay, thus allowing FANET designers to foresee QoS constrained applications.