Based on the controlled mobility of UAV, an augmentation edge heuristic node movement control algorithm is proposed for the realization of the fault tolerant UAVs Ad Hoc networks. Memetic algorithm was developed to get a cheapest possible set of additional edges which make the given communication topology graph vertex-biconnected. With the augmentation edges as heuristics, the vertexes which the edges connected move towards each other to establish edges, the related nodes also move as the follower with the leader-follower movement control algorithm based on the consensus algorithm. After nodes moved, the changed network becomes vertex-biconnected so that the fault tolerant configuration is achieved. The simulation experiment results show that the proposed algorithm is effective, and the total distance metric is improved by comparison with the block movement algorithm and the contraction algorithm.