In this paper, we study the fixed-time cooperative tracking control problem for multi-robot systems with doubleintegrator dynamics. First, a novel distributed observer is proposed for each follower to estimate the leader state in a fixed time, then a local tracking controller based on sliding mode technique is proposed such that the estimated leader state is tracked in a fixed time. Both cases of a stationary leader and a dynamic leader are investigated. Since nonholonomic dynamics can better describe the mobile robots in reality, we further extend the results to achieve fixed-time cooperative tracking for multi-robot systems with nonholonomic dynamics. Different from the conventional finite-time cooperative tracking strategies, the fixed-time approach in this work guarantees that an upper bound of settling time can be prescribed without dependence on initial states of robots, which provides additional system information in advance. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.