The analysis of air traffic growth expects a doubling in the flights number over the next 20 years. The Air Traffic Management (ATM) will therefore have to absorb this additional burden and to increase the airspace capacity, while ensuring at least equivalent standards of safety. The European project SESAR was initiated to propose solutions to this problem. It relies on a new concept of air traffic control, known as 4D (3D + time) trajectory planning, which consists in exploiting the new Flight Management System (FMS) abilities that ensure that the aircraft is at a given position at a given moment. For each flight, a reference trajectory, called Reference Business Trajectory (RBT), is requested by the operating airline. During the flight, conflict situations may nevertheless occur, in which two or several aircraft can dangerously approach each other. In this case, it is necessary to modify one or more trajectories to ensure that minimum separation standards (currently 5 Nm horizontally and 1000 ft vertically) are still satisfied. Moreover, it is desirable that proposed new trajectories deviate as little as possible from RBTs. Several methods have been tested to find an optimal solution to address this problem including genetic algorithm[1] and navigation function based approach[2]. The first approach can not guarantee a feasible (conflict-free) solution for a given time computing. The second one does not take into account the constraints imposed by ATM, such as bounded velocity.
