In this paper, we address the problem of driving a group of agents towards a consensus point when the agents have a discrete-time single-or double-integrator dynamics and the communication network is time-varying. We propose decentralized model predictive control schemes that take into account constraints on the agents' input and show that they guarantee consensus under mild assumptions. Since the global cost does not decrease monotonically, it cannot be used as a Lyapunov function for proving convergence to consensus. For this reason, our proofs exploit geometric properties of the optimal path followed by individual agents.