Smooth Flight Trajectory Planning in the Presence of No-Fly Zones and Obstacles

This paper describes a novel procedure to generate continuously differentiable optimal flight trajectories in the presence of arbitrarily shaped no-fly zones and obstacles having a fixed position in time. The operational flight scenario is first discretized with 9 finite dimensional grid of positions-directions pairs. A weighted and oriented graph is then defined for which the nodes are the earlier mentioned grid points and for which the arcs correspond to minimum length trajectories compliant with obstacle avoidance constraints. Arcs are obtained via solving convex quadratic programming optimization problems that can also account for geometrical constraints such as trajectory curvature limitations. The problem of finding an optimal trajectory be tween two nodes of the so-called core paths graph is then solved via a minimum cost path search algorithm. In a real-time application perspective, the generation of the core paths graph is computationally cumbersome. Moreover, the aircraft position and direction rarely coincide with one of the graph nodes. However, if the graph is built offline and stored, the definition of an optimal trajectory connecting any points of the space domain requires a reduced computational effort. The particular case of piecewise polynomial trajectories minimizing a flight path's length, compliant with constraints on curvature and flight-path angles, is fully developed. Two- and three-dimensional examples are discussed to show the applicability as well as the effectiveness of the technique.