EP-3671695-B1 - METHOD AND DEVICE FOR PLANNING FLIGHT TRAJECTORIES

EP3671695B1EP 3671695 B1EP3671695 B1EP 3671695B1EP-3671695-B1

Inventors

de Riese, Mathias

Dates

Publication Date: 20260506
Application Date: 20181221

Claims (14)

Method for planning flight trajectories for at least two aircraft aiming to subsequently approach a predefined reference point, wherein - each aircraft travels along a flight route according to an individual flight trajectory, such that a first aircraft travels along a first flight route according to a first flight trajectory and a second aircraft travels along a second flight route according to a second flight trajectory, wherein - at least the second flight trajectory is set or adjusted such that at least one predetermined minimum separation between the two aircraft approaching the predefined destination according to their respective flight trajectories is ensured and - the predetermined minimum separation is ensured throughout the whole flight trajectories by setting or adjusting an adjustable trajectory parameter ( θ ) of the second flight trajectory, characterized in that - an arrival time difference ( θ ) defining a time difference between the first and the second aircraft to reach the predefined reference point is determined as the adjustable trajectory parameter of the second flight trajectory, wherein - the position of the aircraft at any point in time within a trajectory segment between two nodes is modelled by a position function or - the time of the aircraft at any location within the trajectory segment between two nodes is modelled by a time function, wherein - a first distance function ( D A ( t )) and a second distance function ( D B (t, θ )) are each defined as analytical expressions for each trajectory segment of the first and second trajectory respectively, and - a separation function (S(t, θ )) is defined as an analytical expression for each time interval where segments of the first and second trajectories overlap, and - a point in time of the minimum of the separation function ( t min ( θ )) is determined as at least one analytical expression for each overlapping time interval, wherein the analytical expression depends on the adjustable trajectory parameter ( θ ) of the second flight trajectory, - the at least one determination function ( θ ( σ )) is determined as analytical expression based on each analytical expression of the point in time ( t min ( θ )), - determining the adjustable trajectory parameter ( θ ) of the second flight trajectory using the at least one determination function such that the value of the minimum separation of the corresponding overlapping time interval will never be below the predetermined minimum separation ( σ ), and in addition or alternatively - the separation function S ( t , θ ) is defined as: S t θ = D A t − D B t θ . with: - t as the time, - θ defining as the adjustable trajectory parameter a time difference between the points of time for the first and the second aircraft to reach the predefined reference point, - D A ( t ) defining the first distance function as an analytic expression for the distance of the first aircraft to the predefined reference point being dependent on time, and preferably not being dependent on the distance (θ) between the first and the second aircraft at the predefined reference point, and - D B ( t,θ ) defining the second distance function as an analytic expression for the distance of the second aircraft to the predefined reference point being dependent on time and being dependent on the distance (θ) between the first and the second aircraft at the predefined reference point.
Method according to claim 1, wherein the predefined reference point is a predefined destination.
Method according to claim 1 or claim 2, wherein - the first flight trajectory is associated to a preceding aircraft approaching the reference point before a following aircraft, - the second flight trajectory is associated to the following aircraft reaching the reference point subsequently after the preceding aircraft, - the second flight trajectory, at least part of it, is calculated or adjusted based - on the first trajectory and - on the minimum separation such that the second flight trajectory ensures the minimum separation with respect to the first trajectory.
Method according to any of the preceding claims, wherein - each flight trajectory comprising at least one of - a plurality of nodes, wherein each node is defined at least by - a node location defining the location of the node - a node time defining a point in time for the respective aircraft to reach the node location, and optionally - a flight speed of the respective aircraft at the node, and - at least one trajectory segment connecting a preceding node and a following node, and in particular - each flight trajectory comprises a plurality of trajectory segments.
Method according to any of the preceding claims, wherein - the position function or the time function respectively - is given by a polynomial function and/or - comprises or is based on a predefined constant acceleration assuming a constant acceleration of the aircraft travelling along the respective trajectory segment.
Method according to any of the preceding claims, wherein - a last node of each flight trajectory defines the destination at a runway and/or - a first node of each flight trajectory defines a starting point at a runway and/or - at least the first flight trajectory and the second flight trajectory use the same route but at different time and in particular - with individual flight speeds.
Method according to any of the preceding claims, wherein for each flight trajectory and each trajectory segment n it is defined a distance D over ground with respect to a predefined reference location, in particular the predefined reference point or the final destination, by the equation depending on time t: D t = D n t − t n = 1 2 a n t − t n 2 + v n t − t n + d n , wherein: - D n defines for trajectory segment n a distance D over ground to the predefined reference location, - d n defines the distance of the following node of the trajectory segment n to the predefined reference location, - a n defines a constant acceleration of the aircraft throughout the trajectory segment n, of the aircraft, - v n defines the speed of the aircraft at the following node of the trajectory segment n, and - t n defines the point in time at which the aircraft reaches the following node of the trajectory segment n, wherein d n , a n , v n , and t n , each forms a characteristic parameter of the trajectory segment.
Method according to any of the preceding claims, wherein the setting or adjusting of at least the second flight trajectory uses at least one determination function, for determining the adjustable trajectory parameter ( θ ) of the second flight trajectory , and the determination function is calculated based on - a separation function defining a separation between the two aircraft travelling according to the first and the second trajectory, at least for part of their travel and/or at least for a part of the first and a part of the second trajectory, and - the separation function depends on the first and second flight trajectories and - the separation function depends on the adjustable trajectory parameter ( θ ) of the second flight trajectory, wherein - the at least one determination function is calculated by - determining a point in time of a local minimum of the separation function as an analytical expression and wherein, the separation function is dependent on time and - the point in time of the minimum of the separation function is inserted into the separation function such that an analytical expression for the separation function at the minimum results which is independent of time, and - the resulting separation function at the minimum is set equal to the predetermined minimum separation ( σ ) and resolved for the adjustable trajectory parameter ( θ ), wherein - in particular the separation function S(t, θ) is defined as: S t θ = D A t − D B t θ . with: - t as the time, - θ defining as the adjustable trajectory parameter a time difference between the points of time for the first and the second aircraft to reach the predefined reference point, - D A ( t ) defining an analytic expression for the distance of the first aircraft to the predefined reference point being dependent on time, and preferably not being dependent on the time difference ( θ ) between the first and the second aircraft at the predefined reference point, and - D B (t, θ ) defining an analytic expression for the distance of the second aircraft to the predefined reference point being dependent on time and being dependent on the time difference ( θ ) between the first and the second aircraft at the predefined reference point.
Method according to any of the preceding claims, wherein - a or the separation function is determined as an analytic expression, - the separation function is given - as the difference of the distance function D A ( t ) of the first trajectory and the distance function D B (t, θ ) of the second trajectory, or - as the difference of a trajectory segment of the first trajectory and a trajectory segment of the second trajectory - the separation function is differentiated with respect to time in order to find a or the minimum, - the differentiated separation function is used to find an analytical expression for the point in time at which the separation function has its minimum, - the analytical expression of time is inserted into the separation function and the separation function is set equal to the predetermined minimum separation ( σ ) in order to find a function depending on the predetermined minimum separation ( σ ) and being independent of time and resolving it in order to receive the at least one determination function, wherein - the determination function is dependent on the predetermined minimum separation (σ).
Method according to any of the preceding claims, wherein - a or the at least one determination function, is successively applied to a current pair of two current trajectory segments of the first and second trajectory, - the at least one determination function comprises at last one related characteristic parameter each corresponding to a characteristic parameter of the two trajectory segments , in particular at least one constant acceleration of at least one of the two trajectory segments, - successively applying the at least one determination function is performed by setting the value of each related characteristic parameter of the determination function to the value of the corresponding characteristic parameter of the respective trajectory segment in order to determine a value of the adjustable trajectory parameter ( θ ) of the second flight trajectory.
Method according to any of the preceding claims, wherein - in a first step determining an initial minimal value for the adjustable trajectory parameter ( θ ), and - in a second step determining a or the current pair of trajectory segments comprising a first segment of the first trajectory and a first segment of the second trajectory, wherein the following node of the first trajectory segment defines the destination at a runway and the second trajectory segment contains the point separated by the predetermined minimum separation ( σ ) from the runway, - in a third step applying a or the determination function to the current pair of trajectory segments for determining or changing the minimal value of the adjustable trajectory parameter ( θ ) of the second flight trajectory, - in a fourth step determining a new current pair of trajectory segments in particular based on the so far determined minimal value of the adjustable trajectory parameter ( θ ), - in a fifth step repeating third and fourth steps until a minimal value, in particular the smallest value, for the adjustable trajectory parameter ( θ ) of the second flight trajectory is found such that the predetermined minimum separation ( σ ) is ensured for the complete second trajectory with respect to the first trajectory, wherein in particular - the adjustable trajectory parameter ( θ ) is the arrival time difference, wherein preferably in the fourth step the new current pair of trajectory segments is determined by - exchanging for the first trajectory and/or the second trajectory each - the current trajectory segment by a new current trajectory segment, wherein - the current trajectory segment and the new current trajectory segment are connected by having a common node and - the new trajectory segments of both trajectories overlap in the time domain and wherein - the first and the second trajectory segments are exchanged both at the same time only if the common node connecting the current and the new trajectory segments have the same node time for the first and the second trajectory, and/or in the third step - applying the determination function to the current pair of trajectory segments is restricted to an overlapping area, wherein the overlapping area is defined by a time interval that covers both trajectory segments of the current pair of trajectories, and/or in the first step - the adjustable trajectory parameter ( θ ) of the second flight trajectory is set as a starting point such that the predetermined minimum separation between the first and second trajectory occurs at the point in time when the aircraft according to the first trajectory lands, and wherein in particular, the initial minimum value of the adjustable trajectory parameter ( θ ) is calculated as a flight duration of the second aircraft for a final part of its flight trajectory of a length equal to the predetermined minimum separation before reaching the predefined reference point, in particular the runway.
Method according to any of the preceding claims, wherein - the first trajectory is given as a fixed trajectory and - the second trajectory is set or adjusted such, that the at least one predetermined minimum separation between the two aircraft is ensured, and - the adjustable trajectory parameter ( θ ) of the second flight trajectory is adjusted such that the second flight trajectory is shifted with respect to the first flight trajectory in order to thereby ensure the predetermined minimum separation between the first and second flight trajectory.
Device for planning flight trajectories for at least two aircraft aiming to subsequently approach a predefined reference point, comprising a processing unit, in particular a microprocessor, adapted to perform the planning of the flight trajectories, wherein - each aircraft travels along a flight route according to an individual flight trajectory, such that a first aircraft travels along a first flight route according to a first flight trajectory and a second aircraft travels along a second flight route according to a second flight trajectory, wherein - at least the second flight trajectory is set or adjusted such that at least one predetermined minimum separation between the two aircraft approaching the predefined destination according to their respective flight trajectories is ensured and - the predetermined minimum separation is ensured throughout the whole flight trajectories by setting or adjusting an adjustable trajectory parameter ( θ ) of the first or second flight trajectory, characterized in that a method according to at least one of claims 1 to 12 is implemented on the processing unit.
Computer program prepared to perform a method according any of claims 1 to 12 when executed on a computer.

Description

Method and device for planning flight trajectories The present invention is directed to a method for planning flight trajectories for at least two aircraft aiming to subsequently approach a predefined reference point, in particular a predefined destination such as a runway. The present invention is also directed to a corresponding planning device for planning such flight trajectories and the invention is directed to a corresponding computer program. One of the main tasks in Air Traffic Control (ATC) is to keep aircraft properly separated. This defines the background for all Air Traffic Management (ATM) services, many of which rely on forecasts provided by trajectory predictions. This problem of keeping aircraft properly separated is also directed to arrival flights of aircraft at the same airport and in particular at the same runway. And accordingly, the separation is directed to a distance between the at least two aircraft and also to the time difference between these with respect to the same reference point. Nowadays appropriate separations are incorporated by air traffic management tools such as an Arrival Manager (AMAN) at one point, e.g. the landing runway. Such concepts assume that that point, i.e. the landing runway is the most critical point, i.e. that at the landing runway two aircraft have the closest approach, i.e. the smallest separation. However, if the first aircraft of such two aircraft approaches the runway with a higher speed than the other aircraft the closest approach of both aircraft may not be at the landing runway. One possibility to address this problem might be to ensure separations at several discrete points. That might be an improvement for advanced tools. However, in this case the minimum separation may not be ensured on continuous parts of the route. To ensure separations on continuous parts of the route one possibility might be assuming common speed profiles along these parts. I.e. if the separation is ensured at two adjacent points such separation may also be assumed on the part between these two points if the speed of both aircraft is constant and the faster aircraft is not overtaking the slower aircraft. However, usually a separation on continuous parts of the route which two flights have in common is only indirectly guaranteed by assuming common speed profiles along these parts. To further improve such air traffic management, trajectory prediction incorporates more and more details to increase the precision. This also takes into account that there's frequently more and more air traffic to be managed. There is a trend to design airspaces to be more flexible to allow efficient usage. Such developments lead to trajectories with individual and detailed speed profiles. Accordingly, it might soon become insufficient for an AMAN to assume common speed profiles or explicitly ensure separations only at discrete points. The US application US 2018/0240348 A1 is directed to methods and systems for probabil-istic spacing advisory tool. Accordingly, a predicted trajectory for each of flights of a plurality of flights to a target area is suggested including calculating a desired spacing for at least one of the points along a reference flight path. Accordingly, there is a target spacing suggested which is a distance between a second flight and a second meter point when the first flight passes a first meter point. Accordingly one object of the present invention is to suggest a solution addressing at least one of the above identified problems. In particular the object is ensuring separation along continuous stretches based on a pair of trajectories with individual speed profiles. It is at least an object of the present invention to provide an alternative solution with respect to the solutions known in the prior art. According to the invention a method for planning flight trajectories according to claim 1 is suggested. Accordingly, the method is directed for planning flight trajectories for at least two aircraft aiming to subsequently approach a predefined reference point. Such predefined reference point may in particular be a predefined destination, such as the runway of an arrival airport. A flight trajectory is basically a flight route or flight path with additional information, in particular the time or points in time at which the corresponding aircraft reaches particular points of the route or the flight path. Accordingly, a flight trajectory defines where the aircraft flies and when. It might in addition comprise information on how fast the aircraft flies at each point of its trajectory. Each aircraft travels along a flight route according to an individual flight trajectory, such that a first aircraft travels along a first flight route according to a first flight trajectory and a second aircraft travels along a second flight route according to a second flight trajectory. The first and second flight routes can be different or can be partly or completely the same. Based on that at least th