The paper discusses the problem of flight trajectory synthesis that is conducted to prevent potential conflict situations between two aircraft in air traffic. A method of multi-objective sequential synthesis of conflict-free flight trajectories is developed. This method provides the synthesis of Pareto conflict-free trajectories using multi-criteria dynamic programming and selection of the optimal trajectory. The paper also considers the principles of discretization concerning states and controls to apply dynamic programming. An analysis of the proposed method is performed using computer simulation.
A number of probabilistic methods for aircraft conflict evaluation are presented. The analytical method is shown. The probability method that enables taking into account the features of stochastic dynamics of motion and the new compositional method of conflict probability evaluation are proposed. The feature of this method is that analytical solution is made using the predicted uncertainty areas of each aircraft position separately, making it possible to manage the position uncertainty and to apply for a wider range of scenarios. The multi-criteria decision-making for conflicts resolution is discussed. Optimality criteria and constraints for conflict resolution are defined. The generic multi-criteria model of conflict-free trajectories selection and the methods of resolution of two- and multi-aircraft conflicts have been developed. These methods provide the synthesis of conflict-free trajectories using different aircraft maneuvers according to criteria of flight regularity, economy, and maneuvering complexity using the multi-criteria dynamic programming.