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This study investigates consensus problems for networks of second-order agents, where each agent can only access the relative position information from its neighbours. We first introduce two new protocols with and without time-delay. Then we provide a convergence analysis in three cases: (a) networks with fixed topology; (b) networks with switching topology; (c) networks with switching topology and time-delays. Several conditions are presented to make all agents asymptotically reach consensus while accomplishing some tasks such as moving to a common value and moving together with a constant velocity or with a constant acceleration. Finally, simulation results are provided to demonstrate the effectiveness of our theoretical results.