This paper proposes an optimal path type classification scheme for the three-point Dubins problem. It allows to directly extract the shortest path type from a Dubins set, evaluating only the relative initial and final configurations with the via point position using a suitable partition of the Cartesian plane. Two alternative approaches are proposed to address the problem: an analytical approach and a heuristic one. The latter was revealed to be much faster from a computational point of view. The proposed classification logic makes the path planning for the three-point Dubins problem much more effective and suitable for real-time applications. Numerical examples are provided to show the efficiency of the proposed strategy.

In this paper, a complete tool for real-time detection of atypical energy behaviors of airplanes is presented. The methodology extends in real time an existing offline process using Dubins trajectories as a predictor of the remaining distance to the runway threshold. Two major contributions are presented in this paper. First, a real-time measure of the aircraft energy behaviour is defined, indicating whether the aircraft is in good condition to intercept the extended runway centreline from its current position. Secondly, a 2D trajectory suggestion is given, allowing safe management of the approach path according to atypical criteria of historical data. Finally, this document proposes a comprehensive tool for air traffic controllers, which is a major step forward in understanding, becoming aware of and resolving critical situations that could lead to accidents.