Modified Bezier curve for 4D reference trajectory definition under flight profile constraint

International audience; The task of establishing properly spaced landing sequences is quite demanding for air traffic controllers in heavy traffic conditions. Indeed, air traffic controllers combine two or more streams into a single stream before landing by means of radar vectoring and speed instructions. This high level task of sequencing aircraft is not currently communicated to the pilot. Instead, controller translate it into clearances to the pilot, typically radar vectoring and speed instructions. In this paper, the task of merging an aircraft over a specified meter fix is addressed through a novel ?Set Reference Path? procedure in which the air traffic controller may clear an aircraft to merge at a specified meter fix at a given time. This paper focuses on the definition of a reference path for time-based operations at meter fix. It includes path stretching operations, which occur when the aircraft is predicted to overfly too early a meter fix with respect to other traffic flow constraints. This paper presents a new approach to generate a reference path with length and endpoint constraints based on modified Bezier curves. Compared to reference trajectories based on straight lines and circle arcs, which are usual in the aviation community, the proposed approach allows for smooth control cues and avoids the scheduling between straight lines and circle arcs segments. The proposed design is followed by illustrative examples which show the effectiveness of the proposed approach.