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Safe trajectory tracking for the two-aircraft system

This paper presents a trajectory tracking scheme with safe collision conflict resolution for the case of two aircraft at a fixed altitude. The proposed scheme allows each aircraft to optimize its discretized trajectory independently with the use of limited position information from the other aircraft over a receding time horizon. The aircraft objective function, to be minimized over each time horizon, represents distance deviations from the flight plan discretized trajectory and the contribution of a barrier function that acts in the case of relative distance proximity between aircraft. Aircraft are modeled by a discrete kinematic model subject to bounds on velocity and angular velocity. The optimization is performed using a sequential quadratic programming method which allows for minimization of a scalar nonlinear function subject to multiple nonlinear equality constraints (kinematic model) and multiple inequality constraints (velocity constraints and safety conditions). For special symmetric cases where the proposed scheme fails (singular cases) a limit cycle method is implemented to modify segments of the flight plan desired trajectories leading to feasible solutions in terms of the optimization process.