In this paper, finite-time position consensus and collision avoidance problems are investigated for multi-AUV (autonomous underwater vehicle) systems. First, based on the homogeneous control method, finite-time position consensus algorithms are proposed for both leaderless and leader follower multi-AUV systems without considering collisions between the AUVs. Specifically, in the leader follower case, a novel distributed finite-time observer is developed for the followers to estimate the leader's velocity. Second, by constructing collision avoidance and connectivity maintenance functions, modified consensus algorithms containing corresponding gradient terms are presented for multi-AUV systems of both cases, which guarantee collision avoidance, connectivity maintenance, velocity matching, and consensus boundedness. Simulations demonstrate the effectiveness of the proposed control algorithms. (C) 2013 Elsevier Ltd. All rights reserved.