Multi-Aircraft Optimal 4D In-Flight Trajectory Planning Based On Embedded Optimal Control

Abstract

The main goal of this dissertation is the in-flight 4D trajectory planning problem for multiple aircraft in converging and intersecting routes in the presence of multicell storms in development. The problem is solved using nonlinear model predictive control based on hybrid optimal control with logical constraints in disjunctive form which arise in modelling passage through waypoints, distance-based and time-based separation constraints, decision making processes, conflict resolution policies, no-fly zones, obstacles or storms avoidance. Enforcing separation between aircraft, passage through waypoints, and obstacle or storm avoidance are especially demanding in terms of modelling efforts. Indeed, in general, the first one requires the introduction of auxiliary integer variables in the model, for the second one a multiphase optimal control approach is used, and for the last ones geometric approximations of the obstacles or storms are usually introduced. Multiple phases increase model complexity and the presence of integer variables in the model has the drawback of combinatorial complexity of the corresponding mixed-integer optimal control problem. In this work, an embedding approach is employed to tackle the hybrid optimal control problems, that is, to transform logical constraints in disjunctive form into inequality and equality constraints which involve only continuous auxiliary variables. In this way, the hybrid optimal control problem is converted into a smooth optimal control problem which is solved using traditional techniques, thereby reducing the computational complexity of finding the solution. Moreover, the evolution of the storms is handled using the nonlinear model predictive control scheme, which iteratively re-plans the trajectories as a new estimation of the state of the storms is available. The presence of this feedback mechanism in this trajectory planning scheme makes it substantially different from openloop trajectory planning methods. Since it is intended for trajectory planning with very short time horizon before the departure or during the flight, it has been herein called online trajectory planning. The effectiveness of the approach is demonstrated through several realistic numerical experiments by computing the optimal trajectories of multiple aircraft in converging and intersecting arrival routes with time-based separation constraints, distance-based separation constraints, operational constraints, and storms avoidance constraints.