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We present a novel control scheme for multiple non-holonomic vehicles under uncertainty, which can guarantee collision avoidance while complying with constraints imposed on the vehicles. Dipolar navigation functions are used for decentralized conflict-free control, while model predictive control is used in a centralized manner in order to ensure that the resulting trajectories remain feasible with respect to the constraints present and to optimize the performance objectives. The model used is chosen to resemble air traffic control problems, with some uncertainty introduced in the system. The efficiency of the control strategy is demonstrated by realistic simulations.