Multiple Aircrafts Trajectory Optimization In Free Flight Model

Free flight is an emerging paradigm in Air Traffic Management (ATM). Conflict detection and resolution is the heart of any free flight concept. The problem of optimal cooperative three-dimensional conflict resolution involving multiple aircraft is addressed by the rigorous numerical trajectory optimization methods. The conflict problem is posed as an optimal control problem of finding trajectories that minimize a certain objective function while the safe separation between each aircraft pair is maintained. The initial and final positions of the aircraft are known and aircraft models with detailed nonlinear point-mass dynamics are considered. The protection zone around the aircraft is modeled to be cylindrical in shape. The optimal control problem is converted to a finite dimensional nonlinear program by the use of collocation on finite elements. The NLP is solved by the use of an interior point algorithm that incorporates a novel line search method.The main research contents and contributions are as follows:1. On the basis of a reliable initialization strategy that yields a feasible solution on simple model, an advanced initialization strategy via recursion is proposed. Through this strategy, the problem of three-dimensional conflict resolution of multiple aircraft is converted to a problem which has similar formulation with former problem but with less number of aircrafts.2. There are still some shortcomings in current algorithm of simultaneous approach. One of which is simultaneous approach making the constraints to be strictly met on collocation points, but constraints could not be met on non-collocation points. A subdividing finite elements strategy via error estimate on non-collocation point is proposed to this problem. The proposed method could obtain a fine collocation plan of collocation points while still maintaining low computational complexity. Numerical results demonstrate the effectiveness of the proposed approach.3. An ellipsoidal protection zone is proposed to replace the cylindrical protection zone in the free flight conflict resolution model. As the cylindrical protection zone introduces extra numerical elements and numerical instabilities, it leads to the increasing model complexity and computational cost. The ellipsoidal protection zone could reduce the difficulty in solving the resulting NLP problem. Through this strategy, the size of discretized problem can be controlled, and the dynamic problem can be solved accurately. The performance of the proposed approach is demonstrated.