EP1721124A1 - Curvilinear distance estimation method for a moving vehicle with limited maneuverability - Google Patents

Curvilinear distance estimation method for a moving vehicle with limited maneuverability

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Publication number
EP1721124A1
EP1721124A1 EP05707976A EP05707976A EP1721124A1 EP 1721124 A1 EP1721124 A1 EP 1721124A1 EP 05707976 A EP05707976 A EP 05707976A EP 05707976 A EP05707976 A EP 05707976A EP 1721124 A1 EP1721124 A1 EP 1721124A1
Authority
EP
European Patent Office
Prior art keywords
mobile
aircraft
distance
instantaneous position
pixel
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP05707976A
Other languages
German (de)
French (fr)
Inventor
Elias Thales Intellectual Property BITAR
Nicolas Thales Intellectual Property MARTY
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Thales SA
Original Assignee
Thales SA
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Filing date
Publication date
Application filed by Thales SA filed Critical Thales SA
Publication of EP1721124A1 publication Critical patent/EP1721124A1/en
Withdrawn legal-status Critical Current

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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C5/00—Measuring height; Measuring distances transverse to line of sight; Levelling between separated points; Surveyors' levels
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/38—Electronic maps specially adapted for navigation; Updating thereof
    • G01C21/3863—Structures of map data
    • G01C21/387—Organisation of map data, e.g. version management or database structures
    • G01C21/3881—Tile-based structures

Definitions

  • the invention relates to terrain navigation and more particularly to estimates of curvilinear distance taking into account possible obstacles to be circumvented.
  • the applicant has already proposed, in a French patent application filed on 9/29/2003, under the number 0311320, a method of estimating the distances, relative to a reference point, of the points of a map extracted from 'a terrain elevation database.
  • This process implements a distance transform by propagation and accommodates obstacles to be circumvented, the shape of which can change over time, such as reliefs seen by an aircraft having a vertical flight profile imposed with variations in altitude. which make that the same threatening relief at a certain moment is no longer at another or vice versa.
  • the distance transform by propagation is used to establish a distance map covering a more or less large area where a mobile is moving and having the instantaneous position of the mobile as the origin of distance measurements.
  • This distance map which is not intended to be displayed, is used to draw a geographic map which is displayed and represents the area of evolution divided into regions shown in false colors and delimited according to the possibility of mobile to cross them and the time it would take to reach them when they are passable, for example red for insurmountable obstacles, yellow for regions distant from access and green for regions close to access.
  • the distance estimates made during the establishment of the distance map take into account the obstacles to be circumvented and the evolution of the threat they represent for the mobile depending on the degree of accomplishment of its mission, they do not take account of the maneuverability of the mobile so that the distance estimates made lack realism for certain points located in the close vicinity of the mobile. Indeed, in particular in the case of an aircraft, the distance estimates are carried out in the same way, whether the point in question is placed in front of or behind the aircraft, while the aircraft can reach without difficulty a point placed in front of it but must make a full turn on itself to reach a point behind it, full turn whose scale depends on its ability to turn, on the side where the turn is started: leeward side or windward side, and the intensity of the crosswind.
  • the object of the present invention is to ensure the consistency and the realism of the estimates of curvilinear distance, obtained by the method described in the aforementioned French patent application or by another method, by prohibiting them from being measured on paths outside of the '' reaching the mobile carrying out navigation on the ground as requiring maneuvers beyond its possibilities.
  • z one called the evolution zone, in which a map of distances covering the evolution zone and having an origin of distance measurements close to the instantaneous position of the mobile, characterized in that it consists, when drawing up the distance map, of completing any obstacles to be circumvented by an additional obstacle to be circumvented which is linked to the mobile and placed in its vicinity, and which includes expanses of the close vicinity of the mobile, considered as inaccessible for the mobile because of the limits of its maneuverability. . ⁇ ,
  • the additional obstacle is of concave shape and disposed in the vicinity of the instantaneous position of the mobile so that its concavity is turned in the direction of movement of the mobile and includes the instantaneous position of the mobile.
  • the additional obstacle has a U-shape, the opening of the U being turned in the direction of movement of the mobile and encompassing the instantaneous position of the mobile.
  • the additional obstacle has the shape of a half-moon, the opening of the half-moon being turned in the direction of movement of the mobile and encompassing the instantaneous position of the mobile.
  • the additional obstacle has a shape with two butterfly wing lobes, placed on either side of the instantaneous position of the mobile and having a common tangent oriented in the direction of movement of the mobile.
  • the contour of the additional obstacle comprises parts corresponding to the projections on the ground of two circular trajectories linked to the aircraft, admitting a common external tangent at the level of the aircraft, oriented in the direction of the movement of the mobile and having a radius equal to the radius of curvature of the tightest turn allowed for the aircraft at the time considered.
  • the contour of the additional obstacle comprises parts of cycloids corresponding to the projections on the ground of two circular trajectories linked to the aircraft, having a radius equal to the radius of curvature the tightest turn allowed for the aircraft at the time.
  • the contour of the additional obstacle consists of two cycloid lobes limited to their parts going from their starting point, which is the instantaneous position of the aircraft, to their second intersection with straight lines going from the instantaneous position of the aircraft to virtual positions on the cycloid lobes corresponding for the aircraft to an arbitrary angle of change of course.
  • the contour of the additional obstacle when the mobile is an aircraft subjected to a crosswind, the contour of the additional obstacle consists of two cycloid lobes limited to their parts going from their starting point, which is the instantaneous position of the aircraft, to their second intersection with straight lines going from the instantaneous position of the aircraft to virtual positions on the cycloid lobes corresponding for the aircraft to a course change angle of 180 degrees.
  • the contour of the additional obstacle has two parts in cycloid lobe responding to the system of parametric equations:
  • TAS being the amplitude of the air speed of the aircraft
  • ⁇ ra ⁇ being the roll angle of the aircraft during the maneuver
  • ⁇ being a factor depending on the initial conditions
  • ⁇ being a coefficient equal to +1 for a turn at right and -1 for a left turn
  • C j Long + ⁇ .R. cos ( ⁇ g )
  • C Yg Lat - R.sin (y g )
  • ⁇ g ⁇ JJeading + kH long being the longitude of the instantaneous position of the aircraft, lat being the latitude of the instantaneous position of the aircraft, and heading being the heading of the aircraft.
  • the additional obstacle taking account of the limits of maneuverability of the mobile is deprived of the surface of an angular sector starting from the mobile and having its opening turned in the direction of movement of the mobile.
  • the distance map is in the form of a grid of cells corresponding to the elements of a terrain elevation database meshing the terrain of evolution of the mobile
  • the additional obstacle taking into account the limits of maneuverability of the mobile is deprived of the cells covered in whole or in part by an angular sector starting from the mobile and having its opening turned in the direction of the mobile.
  • the distance map results from the application, to the pixels of an image formed by a map taken from a terrain elevation database, of a distance transform which uses a chamfer mask listing the distances of a pixel in analysis from the nearest pixels called pixels of the neighborhood and which has axes of propagation oriented like the directions of the pixels of the neighborhood with respect to the pixel in analysis in the chamfer mask, the additional obstacle being account of the mobility of the aircraft is deprived of an angular sector starting from a pixel close to the mobile, taken as the origin of the distance measurements, and having its opening oriented along the axis of propagation closest to the direction of the mobile movement.
  • the distance map results from the application, to the pixels of an image formed by a map taken from a terrain elevation database, of a distance transform which uses a chamfer mask listing the distances of a pixel in analysis from the nearest pixels called pixels of the neighborhood and which has axes of propagation oriented like the directions of the pixels of the neighborhood with respect to the pixel in analysis in the chamfer mask, the additional obstacle being account of the mobility of the aircraft is deprived of an angular sector starting from a pixel near u mobile, taken for origin from the measurements of distance, corresponding to the angular sector oriented along the axis of propagation closest to the direction of movement of the mobile and delimited by bisectors of the angles formed by the axes of propagation.
  • a figure 1 represents an example of distance map covering an area where a mobile evolves and having the position of the mobile as the origin of the distance measurements
  • a figure 2 represents an example of chamfer mask usable by a distance transform by propagation
  • Figures 3a and 3b show the cells of the chamfer mask illustrated in Figure 2, which are used in a scan pass in lexicographic order and in a scan pass according to the lexicographic order inve rse
  • - a figure 4 represents a part of map of distances centered on the instantaneous position of the mobile showing the position and a possible form of an additional obstacle placed according to the invention so that the estimates of distance made in the distance map take into account the maneuverability limitations of the mobile
  • - a figure 5 illustrates the existing relationships between e the route and the course followed by an aircraft
  • - a figure 6 illustrates, in an air coordinate system linked to an aircraft
  • a distance map on an evolution zone is formed by the set of values of the distances of the points placed at the nodes of a regular mesh of the evolution zone compared to a point of the zone taken for origin of the measurements of distance.
  • it can be presented in the form of a table of values whose boxes correspond to a division of the evolution zone into cells centered on the nodes of the mesh.
  • the regular mesh adopted is often that of the points of a terrain elevation database covering the area of evolution.
  • the point of the zone taken as the origin of the distance measurements is the node of the mesh closest to the projection on the ground of the instantaneous position of the mobile.
  • Distance maps are often made using a propagation distance transform also known as a chamfer distance transform.
  • Chamfer distance transforms first appeared in image analysis to estimate distances between objects. Gunilla Borgefors describes examples, in her article "Distance Transformation in Digital Images.” published in the journal: Computer Vision, Graphics and Image Processing, Vol. 34 pp. 344-378 in February 1986.
  • the distance between two points on a surface is the minimum length of all the possible routes on the surface starting from one of the points and ending at the other.
  • a distance transform by propagation estimates the distance of a pixel called "goal" pixel with respect to a pixel called “source” pixel by gradually building up, starting from the source pixel, the shortest possible path following the mesh of pixels and ending at the target pixel, and using the distances found for the image pixels already analyzed and a table called chamfer mask listing the values of the distances between a pixel and his close neighbors.
  • a chamfer mask is in the form of a table with an arrangement of boxes reproducing the pattern of a pixel surrounded by its close neighbors.
  • a box assigned the value 0 identifies the pixel taken as the origin of the distances listed in the table.
  • Around this central box are agglomerated peripheral boxes filled with non-zero proximity distance values and repeating the arrangement of the pixels in the vicinity of a pixel supposed to occupy the central box.
  • the proximity distance value appearing in a peripheral box is that of the distance separating a pixel occupying the position of the peripheral box concerned, from a pixel occupying the position of the central box. Note that the proximity distance values are distributed in concentric circles.
  • a first circle of four boxes corresponding to the four pixels of first row, _ which i are closest to the pixel of the central box, either on the same line or on the same column, are assigned a value of proximity distance D1.
  • the chamfer mask can cover a more or less extended neighborhood of the pixel of the central box by listing the values of the proximity distances of a more or less large number of concentric circles of pixels of the neighborhood. It can be reduced to the first two circles formed by the pixels in the vicinity of a pixel occupying the central box as in the example of the distance maps of FIGS.
  • Borgefors gives, at the first proximity distance D1 which corresponds to a rung on the abscissa or on the ordinate and also to the multiplicative factor of scale, the value 3 and, at the second proximity distance which corresponds to the root of the sum of the squares of the rungs on the abscissa and on the ordinate ⁇ JX 2 + y 2 , the value 5.
  • a chamfer mask retaining the first three circles, therefore of dimensions 5x5, it gives, at the distance D1 which corresponds to the scaling factor, the value 5, to the distance D2, the value 7 which is an approximation of 5/2, and at distance D3 the value 11 which is an approximation of 5 ⁇ 5.
  • the progressive construction of the shortest possible path going to a target pixel starting from a source pixel and following the mesh of the pixels is done by a regular scanning of the pixels of the image by means of the chamfer mask. Initially, the pixels of the image are seen; assign an infinite distance value, making it a number large enough to exceed all the values of the measurable distances in the image, except for the source pixel which is assigned a zero distance value. Then the initial distance values assigned to the goal points are updated during the scanning of the image by the chamfer mask, an update consisting in replacing a distance value assigned to a goal point, by a new one. lower value resulting from an estimate of distance made on the occasion of a new application of the chamfer mask at the target point considered.
  • a distance estimate by applying the chamfer mask to a target pixel consists in listing all the paths going from this target pixel to the source pixel and passing through a pixel in the vicinity of the target pixel whose distance has already been estimated during the same scan. , to search among the routes listed, the shortest route (s) and to adopt the length of the shortest route (s) as an estimate of distance.
  • the progressive search for the shortest possible paths starting from a source pixel and going to the different goal pixels of the image gives rise to a phenomenon of propagation in directions of the pixels which are the closest neighbors of the pixel under analysis and whose distances are listed in the chamfer mask.
  • the directions of the closest neighbors of a pixel which do not vary are considered as axes of propagation of the d istance transform with chamfer mask which often takes even, the name of distance transforms by propagation.
  • the scanning order of the pixels in the image influences the reliability of the distance estimates and their updates because the paths taken into account depend on them.
  • the lexicographic orders include reverse lexicographic (scanning pixels of the image line by line from bottom to top and, within a line, from right to left), transposed lexicographic (scanning pixels of the image column by column of left to right and, within a column, from top to bottom), the reverse transposed lexicographic (pixel scanning by columns from right to left and within a column from bottom to top) satisfy this regularity condition and more generally all scans in which rows and columns are scanned from right to left or left to right.
  • Borgefors recommends double scanning the pixels of the image, once in lexicographic order and once in reverse lexicographic order.
  • FIG. 3a shows, in the case of a scanning pass in lexicographic order going from the upper left corner to the lower right corner of the image, the boxes of the chamfer mask of FIG. 1 used to list the paths going from d 'a target pixel placed on the central box (box indexed by 0) at the source pixel passing through a neighboring pixel whose distance has already been estimated during the same scan. There are eight of these boxes, located in the upper left of the chamfer mask. There are therefore eight paths listed for the search for the shortest whose length is taken to estimate the distance.
  • FIG. 3b shows, in the case of a scanning pass in reverse lexicographic order going from the lower right corner to the upper left corner of the image, the boxes of the chamfer mask of FIG.
  • the distance map shown in FIG. 1 is a simplified example facilitating the understanding of the problem which the invention addresses. This distance map covers an area with two obstacles impassable 10 and 11, where a mobile is supposed to be at point S and move in the direction of the arrow. It was established using the simplest of the distance transforms proposed by Gunilla Borgefors, using a chamfer mask of dimension 3x3 with two neighborhood distances 3,
  • the distance estimates are made independently of the movement of the mobile and do not take into account the inability of the mobile to follow certain routes for reasons of maneuverability.
  • this adaptation journey distorts the distance estimate because it can make the actual journey traveled by the mobile clearly longer than the minimum length path used to estimate the distance. This is particularly the case for points located in the close vicinity of the mobile but in directions distant from that of its momentary movement. For example, in the example of a distance map illustrated in FIG.
  • This new insurmountable obstacle 20 is linked to the mobile and arranged in its vicinity close. It is concave in shape, the cell (point S) containing the instantaneous position of the mobile being placed in its concavity turned in the direction of movement of the mobile. It has a general half-moon or U-shape.
  • This new insurmountable obstacle 20, which moves with the mobile, completes the obstacles to be circumvented (10, 11 Figure 1) and forces the transformation of distance to be removed, in its search lengths of the shortest paths, paths out of range of the mobile due to its limited maneuverability. For an aircraft, this is to prohibit unrealistic U-turns, excessively sharp turns and even to take into account local wind conditions.
  • this new insurmountable obstacle 20 linked to the aircraft and to the direction of its movement relative to the map therefore by report to the ground by listing the cells of the distance map which are placed in the vicinity of the aircraft while being inaccessible to it by a direct route due to its limited maneuverability.
  • the local wind must be taken into account. Indeed, as shown in FIG.
  • the direction on the ground of the movement of an aircraft which is that of its ground speed GS oriented along its route (track in English) of unit vector t, corresponds to the direction of the vector sum of the air speed vector TAS of the aircraft, oriented according to its heading (heading in Anglo-Saxon) of unit vector h, and of the wind speed WS (wind speed in Anglo-Saxon) oriented according to a unit vector ⁇ v . Without wind, as shown in FIG.
  • the cells of the distance map placed in the vicinity of the aircraft while being directly inaccessible to it are those contained within two circles 30, 31 passing through the position of the aircraft, having a common tangent oriented along the heading of the aircraft (vector Y) and a radius R corresponding to the smallest acceptable turning radius at the time.
  • the initial position condition is:
  • the initial speed condition is:
  • the aircraft follows the tracks on the ground of the two circles (30, 31 FIG. 5) only the time necessary for a change of course and course maneuver.
  • the transition time to change course depends on the angular speed of the aircraft and therefore on its roll angle.
  • the cells contained in the contour are selected for the obstacle, neglecting those located in front of the initial position of the aircraft, in the direction of its movement.
  • One way of selecting for the obstacle the cells contained in a contour which has been determined beforehand by avoiding the cells situated in front of the initial position of the aircraft, in the direction of its movement consists, as shown in FIG. 8 , to take only those entirely located in the contour and not to consider those which are only partially contained therein.
  • To list the cells contained in a closed contour we can, as shown in Figure 9, choose a cell X that we know inside the contour, have the contour described by a moving point Z and assimilate the cells crossed by the line segment XZ to the cells contained in the contour.
  • the angular sector of delimitation of the cells left free to propagate is chosen to be that of the angular sectors delimited, by the bisectors of the angles formed by the axes of propagation plotted at the level of the pixel closest to the current position of the aircraft, taken as source pixel, origin for distance measurements, having the orientation closest to that of the movement of the aircraft.
  • FIG. 10 shows part of the beam of the propagation axes defined by the pixels of the image concerned by the upper right quarter of the chamfer mask of FIG. 2 applied to the pixel COO taken as the origin of the distance measurements since it is assumed to be the closest the current position of the aircraft.
  • first row pixels C01 and C10 next to the pixel in COO analysis on the same row or the same column
  • second row pixel C11 next to the pixel in COO analysis on the first diagonal
  • third row pixels C12 and C21 immediate neighbors of the pixel in COO analysis but neither on the same line, nor on the same column and neither on the same diagonal thereof.
  • the various orientations of these first, second and third rank pixels C01, C10, C11, C12, C21, immediate neighbors of the pixel in COO analysis define the only possible directions of propagation for the distance transform in the upper right quarter of the mask. chamfer in fact the northeast quarter for a map image with the top facing north and the right facing east.
  • the direction D0 of the propagation of the pixel COO in analysis towards the pixel C10 of first rank on the same column serves as angular reference and corresponds, in the language of chess, to a movement of a tower.
  • the direction D1 of the propagation of the pixel COO in analysis towards the third row pixel C21 arranged on different row, column and diagonal is angularly the closest to the direction DO.
  • the direction D2 of the propagation of the pixel COO in analysis towards the pixel C11 of second rank on the same diagonal is a little further apart. In the absence of anisotropy of the map image, it makes an angle of 45 degrees relative to the reference direction DO. It corresponds in the language of chess to a movement of a madman.
  • the direction D3 of the propagation of the pixel COO in analysis towards the third row pixel C12 arranged on different row, column and diagonal is even further apart. In the absence of anisotropy of the image, it makes an angle of 63.5 degrees relative to the reference direction DO. In the language of chess it corresponds to a movement of a rider.
  • direction D4 of the propagation of the COO pixel in analysis towards the first rank pixel C01 on the same line is the most distant and makes an angle of 90 degrees relative to the reference direction D. It corresponds in the language of the game of failure to move a tower.
  • the bisectors of the angles formed by these five directions of propagation D0, D1, D2, D3 and D4 cut in the upper right quarter of the chamfer mask five circular sectors centered on the pixel COO in analysis and turned in the five directions of propagation namely : - an angular sector called C10 turn because it is oriented towards the pixel C10, in the direction D0 corresponding to the movement of a tower, - an angular sector called C21 jumper because it is oriented towards the pixel C21, in the corresponding direction D1 to the movement of a jumper, - an angular sector called C11 crazy because it is oriented towards the pixel C11, in the direction D2 corresponding to the movement of a madman, - an angular sector called C12 jumper because it is oriented towards the pixel C12 , in the direction D3 corresponding to the movement of a jumper, and - an angular sector called C01 turn because it is oriented towards the pixel C01, in the direction D4
  • the unit vector of the ordinate axis before stretching YEart remains equal to the unit vector Y G ⁇ C I after stretching while the unit vector of the abscissa axis before stretching XEarth is found, after stretching, dilated in the proportion of 1 / cos (Latitude): ⁇ YGrid Y Earth Gric_ cos (Latitude)
  • the method of estimating curvilinear distance takes account of the vertical flight profile, the contours of the obstacles to be circumvented being updated as a function of the time of route of the routes tested when searching for the shortest routes, the lengths of which are taken to estimate distances, in order to take account of the altitude reached at each instant deduced from the vertical profile of the flight.

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Databases & Information Systems (AREA)
  • Automation & Control Theory (AREA)
  • Radar Systems Or Details Thereof (AREA)
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Abstract

In the distance maps used to facilitate the navigation of moving vehicles such as aircraft, the estimated distances take into account obstacles to be avoided but do not take into account the maneuverability of the moving vehicle. The adaptive trajectory required by the moving vehicle in order to take the right direction is not taken into account such that certain distance estimations for accessible points placed in the vicinity of the moving vehicle are unrealistic. According to the invention, in order to make a distance map more realistic, a concave shaped obstacle linked to the moving vehicle is added to the rear of the position of the moving vehicle, forcing distance estimations to avoid an area which is inaccessible for the moving vehicle for reason of maneuverability.

Description

PROCEDE D'ESTIMATION DE DISTANCE CURVILIGNE POUR MOBILE A MANOEUVRABILITE LIMITEEMETHOD FOR ESTIMATING CURVILINE DISTANCE FOR MOBILE WITH LIMITED MANEUVERABILITY
L'invention concerne la navigation de terrain et plus particulièrement les estimations de distance curviligne prenant en compte d'éventuels obstacles à contourner. La demanderesse a déjà proposé, dans une demande de brevet français déposée le 26/9/2003, sous le n°0311320, un procédé d'estimation des distances, par rapport à un point de référence, des points d'une carte extraite d'une base de données d'élévation du terrain. Ce procédé met en œuvre une transformée de distance par propagation et s'accommode d'obstacles à contourner dont la forme peut évoluer au cours du temps, comme des reliefs vus par un aéronef ayant un profil vertical de vol imposé avec des variations d'altitude qui font qu'un même relief menaçant à un certain moment ne l'est plus à un autre ou inversement. La transformée de distance par propagation sert à établir une carte de distances couvrant une zone plus ou moins grande où évolue un mobile et ayant la position instantanée du mobile pour origine des mesures de distance. Cette carte de distances, qui n'est pas destinée à être affichée, est utilisée pour tracer une carte géographique qui, elle, est affichée et représente la zone d'évolution découpée en régions montrées en fausses couleurs et délimitées en fonction de la possibilité du mobile à les franchir et du temps que celui-ci mettrait à les atteindre lorsqu'elles sont franchissables, par exemple rouge pour des obstacles infranchissables, jaune pour des régions lointaines d'accès et verte pour les régions proches d'accès. Si les estimations de distance faites lors de l'établissement de la carte de distances prennent en compte les obstacles à contourner et évolution de la menace qu'ils représentent pour le mobile en fonction du degré d'accomplissement de sa mission, elles ne tiennent pas compte de la manœuvrabilité du mobile si bien que les estimations de distance faites manquent de réalisme pour certains points situés dans le proche voisinage du mobile. En effet, notamment dans le cas d'un aéronef, les estimations de distance sont menées de la même manière, que le point considéré soit placé devant ou derrière l'aéronef, alors que l'aéronef peut atteindre sans encombre un point placé devant lui mais doit faire un tour complet sur lui- même pour atteindre un point placé derrière lui, tour complet dont l'ampleur dépend de sa capacité à virer, du côté où est entamé le virage : côté sous le vent ou côté contre le vent, et de l'intensité du vent de travers.The invention relates to terrain navigation and more particularly to estimates of curvilinear distance taking into account possible obstacles to be circumvented. The applicant has already proposed, in a French patent application filed on 9/29/2003, under the number 0311320, a method of estimating the distances, relative to a reference point, of the points of a map extracted from 'a terrain elevation database. This process implements a distance transform by propagation and accommodates obstacles to be circumvented, the shape of which can change over time, such as reliefs seen by an aircraft having a vertical flight profile imposed with variations in altitude. which make that the same threatening relief at a certain moment is no longer at another or vice versa. The distance transform by propagation is used to establish a distance map covering a more or less large area where a mobile is moving and having the instantaneous position of the mobile as the origin of distance measurements. This distance map, which is not intended to be displayed, is used to draw a geographic map which is displayed and represents the area of evolution divided into regions shown in false colors and delimited according to the possibility of mobile to cross them and the time it would take to reach them when they are passable, for example red for insurmountable obstacles, yellow for regions distant from access and green for regions close to access. If the distance estimates made during the establishment of the distance map take into account the obstacles to be circumvented and the evolution of the threat they represent for the mobile depending on the degree of accomplishment of its mission, they do not take account of the maneuverability of the mobile so that the distance estimates made lack realism for certain points located in the close vicinity of the mobile. Indeed, in particular in the case of an aircraft, the distance estimates are carried out in the same way, whether the point in question is placed in front of or behind the aircraft, while the aircraft can reach without difficulty a point placed in front of it but must make a full turn on itself to reach a point behind it, full turn whose scale depends on its ability to turn, on the side where the turn is started: leeward side or windward side, and the intensity of the crosswind.
La présente invention a pour but d'assurer la cohérence et le réalisme des estimations de distance curviligne, obtenues par le procédé décrit dans la demande de brevet français précitée ou par un autre procédé, en leur interdisant d'être mesurées sur des trajets hors d'atteinte du mobile effectuant la navigation de terrain car exigeant des manœuvres dépassant ses possibilités.The object of the present invention is to ensure the consistency and the realism of the estimates of curvilinear distance, obtained by the method described in the aforementioned French patent application or by another method, by prohibiting them from being measured on paths outside of the '' reaching the mobile carrying out navigation on the ground as requiring maneuvers beyond its possibilities.
Elle a pour objet un procédé d'estimation de distance curviligne au sein d'une zone où évolue un mobile à manœuvrabilité limitée et qui renferme des obstacles éventuels à contourner, z:one dite zone d'évolution, dans lequel est établie une carte de distances couvrant la zone d'évolution et ayant une origine des mesures de distance proche de la position instantanée du mobile, caractérisé en ce qu'il consiste, lors de l'établissement de la carte de distances, à compléter les obstacles éventuels à contourner par un obstacle supplémentaire à contourner qui est lié au mobile et placé dans son voisinage, et qui englobe des étendues du proche voisinage du mobile, considérées comme inaccessibles pour le mobile du fait des limites de sa manœuvrabilité. .Λ,It relates to a method of estimating a curvilinear distance within an area where a mobile with limited maneuverability evolves and which contains possible obstacles to be circumvented, z: one called the evolution zone, in which a map of distances covering the evolution zone and having an origin of distance measurements close to the instantaneous position of the mobile, characterized in that it consists, when drawing up the distance map, of completing any obstacles to be circumvented by an additional obstacle to be circumvented which is linked to the mobile and placed in its vicinity, and which includes expanses of the close vicinity of the mobile, considered as inaccessible for the mobile because of the limits of its maneuverability. . Λ ,
Avantageusement, l'obstacle supplémentaire est de forme concave et disposé dans le voisinage de la position instantanée du mobile de manière que sa concavité soit tournée dans la direction du déplacement du mobile et englobe la position instantanée du mobile.Advantageously, the additional obstacle is of concave shape and disposed in the vicinity of the instantaneous position of the mobile so that its concavity is turned in the direction of movement of the mobile and includes the instantaneous position of the mobile.
Avantageusement, l'obstacle supplémentaire a une forme en U, l'ouverture du U étant tournée dans la direction du déplacement du mobile et englobant la position instantanée du mobile.Advantageously, the additional obstacle has a U-shape, the opening of the U being turned in the direction of movement of the mobile and encompassing the instantaneous position of the mobile.
Avantageusement, l'obstacle supplémentaire a une forme de demi-lune, l'ouverture de la demi-lune étant tournée dans la direction de déplacement du mobile et englobant la position instantanée du mobile. Avantageusement, l'obstacle supplémentaire a une forme à deux lobes en aile de papillon, placés de part et d'autre de la position instantanée du mobile et ayant une tangente commune orientée dans la direction de déplacement du mobile.Advantageously, the additional obstacle has the shape of a half-moon, the opening of the half-moon being turned in the direction of movement of the mobile and encompassing the instantaneous position of the mobile. Advantageously, the additional obstacle has a shape with two butterfly wing lobes, placed on either side of the instantaneous position of the mobile and having a common tangent oriented in the direction of movement of the mobile.
Avantageusement, lorsque le mobile est un aéronef, le contour de l'obstacle supplémentaire comporte des parties correspondant aux projections au sol de deux trajectoires circulaires liées à l'aéronef, admettant une tangente extérieure commune au niveau de l'aéronef, orientée dans la direction du mouvement du mobile et ayant un rayon égal au rayon de courbure du virage le plus serré admis pour l'aéronef au moment considéré.Advantageously, when the mobile is an aircraft, the contour of the additional obstacle comprises parts corresponding to the projections on the ground of two circular trajectories linked to the aircraft, admitting a common external tangent at the level of the aircraft, oriented in the direction of the movement of the mobile and having a radius equal to the radius of curvature of the tightest turn allowed for the aircraft at the time considered.
Avantageusement, lorsque le mobile est un aéronef soumis à un vent de travers, le contour de l'obstacle supplémentaire comporte des parties de cycloïdes correspondant aux projections au sol de deux trajectoires circulaires liées à l'aéronef, ayant un rayon égal au rayon de courbure du virage le plus serré admis pour l'aéronef au moment considéré.Advantageously, when the mobile is an aircraft subjected to a cross wind, the contour of the additional obstacle comprises parts of cycloids corresponding to the projections on the ground of two circular trajectories linked to the aircraft, having a radius equal to the radius of curvature the tightest turn allowed for the aircraft at the time.
Avantageusement, lorsque le mobile est un aéronef soumis à un vent de travers, le contour de l'obstacle supplémentaire consiste en deux lobes de cycloïde limités à leurs parties allant de leur point de départ, qui est la position instantanée de l'aéronef, à leur deuxième intersection avec des droites allant de la position instantanée de l'aéronef à des positions virtuelles sur les lobes de cycloïdes correspondant pour l'aéronef à un angle de changement do route arbitraire.Advantageously, when the mobile is an aircraft subjected to a crosswind, the contour of the additional obstacle consists of two cycloid lobes limited to their parts going from their starting point, which is the instantaneous position of the aircraft, to their second intersection with straight lines going from the instantaneous position of the aircraft to virtual positions on the cycloid lobes corresponding for the aircraft to an arbitrary angle of change of course.
Avantageusement, lorsque le mobile est un aéronef soumis à un vent de travers, le contour de l'obstacle supplémentaire consiste en deux lobes de cycloïde limités à leurs parties allant de leur point de départ, qui est la position instantanée de l'aéronef, à leur deuxième intersection avec des droites allant de la position instantanée de l'aéronef à des positions virtuelles sur les lobes de cycloïdes correspondant pour l'aéronef à un angle de changement de route de 180 degrés. Avantageusement, lorsque le mobile est un aéronef soumis à un vent de travers et la carte de distances établie dans un repère géographique utilisant les longitudes et les latitudes, le contour de l'obstacle supplémentaire présente deux parties en lobe de cycloïde répondant au système d'équations paramétriques :Advantageously, when the mobile is an aircraft subjected to a crosswind, the contour of the additional obstacle consists of two cycloid lobes limited to their parts going from their starting point, which is the instantaneous position of the aircraft, to their second intersection with straight lines going from the instantaneous position of the aircraft to virtual positions on the cycloid lobes corresponding for the aircraft to a course change angle of 180 degrees. Advantageously, when the mobile is an aircraft subjected to a crosswind and the distance map established in a geographical reference using the longitudes and the latitudes, the contour of the additional obstacle has two parts in cycloid lobe responding to the system of parametric equations:
x et y étant les coordonnées abscisse et ordonnée d'un point dans le repère géographique de la carte de distances, rWSx étant le vecteur vent exprimé dans le repère géographique de la wsY carte de distances, avec TAS2 R = £- tan φ„„ TAS _ g-.tanφro„ w = R TAS x and y being the abscissa and ordered coordinates of a point in the geographical coordinate system of the distance map, r WS x being the wind vector expressed in the geographical coordinate system of the ws Y distance map, with TAS 2 R = £ - tan φ „„ TAS _ g-.tanφ ro „w = R TAS
TAS étant Vamplitude de la vitesse air de l'aéronef, φraιι étant l'angle de roulis de l'aéronef pendant la manœuvre, γ étant un facteur dépendant des conditions initiales, δ étant un coefficient égal à +1 pour un virage à droite et -1 pour un virage à gauche, et avec Cj = Long + δ .R. cos(γ g ) CYg = Lat - R.sin(y g) γ g = δ JJeading + k.H long étant la longitude de la position instantanée de l'aéronef, lat étant la latitude de la position instantanée de l'aéronef, et heading étant le cap de l'aéronef. Avantageusement, l'obstacle supplémentaire tenant compte des limites de manœuvrabilité du mobile est privé de la surface d'un secteur angulaire partant du mobile et ayant son ouverture tournée dans la direction du mouvement du mobile.TAS being the amplitude of the air speed of the aircraft, φ ra ιι being the roll angle of the aircraft during the maneuver, γ being a factor depending on the initial conditions, δ being a coefficient equal to +1 for a turn at right and -1 for a left turn, and with C j = Long + δ .R. cos (γ g ) C Yg = Lat - R.sin (y g ) γ g = δ JJeading + kH long being the longitude of the instantaneous position of the aircraft, lat being the latitude of the instantaneous position of the aircraft, and heading being the heading of the aircraft. Advantageously, the additional obstacle taking account of the limits of maneuverability of the mobile is deprived of the surface of an angular sector starting from the mobile and having its opening turned in the direction of movement of the mobile.
Avantageusement, lorsque la carte de distances se présente sous la forme d'une grille de cellules correspondant aux éléments d'une base de données d'élévation du terrain maillant le terrain d'évolution du mobile, l'obstacle supplémentaire tenant compte des limites de manœuvrabilité du mobile est privé des cellules recouvertes en totalité ou en partie par un secteur angulaire partant du mobile et ayant son ouverture tournée dans la direction du mobile.Advantageously, when the distance map is in the form of a grid of cells corresponding to the elements of a terrain elevation database meshing the terrain of evolution of the mobile, the additional obstacle taking into account the limits of maneuverability of the mobile is deprived of the cells covered in whole or in part by an angular sector starting from the mobile and having its opening turned in the direction of the mobile.
Avantageusement, lorsque la carte de distances résulte de l'application, aux pixels d'une image formée par une carte tirée d'une base de données d'élévation du terrain, d'une transformée de distance qui utilise un masque de chanfrein répertoriant les distances d'un pixel en analyse par rapport aux pixels les plus proches dits pixels du voisinage et qui a des axes de propagation orientés comme les directions des pixels du voisinage par rapport au pixel en analyse dans le masque de chanfrein, l'obstacle supplémentaire tenant compte de la mobilité de l'aéronef est privé d'un secteur angulaire partant d'un pixel proche d u mobile, pris pour origine des mesures de distance, et ayant son ouverture orientée selon l'axe de propagation le plus proche de la direction du mouvement du mobile.Advantageously, when the distance map results from the application, to the pixels of an image formed by a map taken from a terrain elevation database, of a distance transform which uses a chamfer mask listing the distances of a pixel in analysis from the nearest pixels called pixels of the neighborhood and which has axes of propagation oriented like the directions of the pixels of the neighborhood with respect to the pixel in analysis in the chamfer mask, the additional obstacle being account of the mobility of the aircraft is deprived of an angular sector starting from a pixel close to the mobile, taken as the origin of the distance measurements, and having its opening oriented along the axis of propagation closest to the direction of the mobile movement.
Avantageusement, lorsque la carte de distances résulte de l'application, aux pixels d'une image formée par une carte tirée d'une base de données d'élévation du terrain, d'une transformée de distance qui utilise un masque de chanfrein répertoriant les distances d'un pixel en analyse par rapport aux pixels les plus proches dits pixels du voisinage et qui a des axes de propagation orientés comme les directions des pixels du voisinage par rapport au pixel en analyse dans le masque de chanfrein, l'obstacle supplémentaire tenant compte de la mobilité de l'aéronef est privé d'un secteur angulaire partant d'un pixel proche u mobile, pris pour origine des mesures de distance, correspondant au secteur angulaire orienté selon l'axe de propagation le plus proche de la direction du mouvement du mobile et délimité par des bissectrices des angles formés par les axes de propagation.Advantageously, when the distance map results from the application, to the pixels of an image formed by a map taken from a terrain elevation database, of a distance transform which uses a chamfer mask listing the distances of a pixel in analysis from the nearest pixels called pixels of the neighborhood and which has axes of propagation oriented like the directions of the pixels of the neighborhood with respect to the pixel in analysis in the chamfer mask, the additional obstacle being account of the mobility of the aircraft is deprived of an angular sector starting from a pixel near u mobile, taken for origin from the measurements of distance, corresponding to the angular sector oriented along the axis of propagation closest to the direction of movement of the mobile and delimited by bisectors of the angles formed by the axes of propagation.
D'autres caractéristiques et avantages de l'invention ressortiront d'un mode de réalisation donné à titre d'exemple. Cette description sera faite en regard du dessin dans lequel : - une figure 1 représente un exemple de carte de distances couvrant une zone où évolue un mobile et ayant la position du mobile comme origine des mesures de distance, - une figure 2 représente un exemple de masque de chanfrein utilisable par une transformée de distance par propagation, - des figures 3a et 3b montrent les cellules du masque de chanfrein illustré à la figure 2, qui sont utilisées dans une passe de balayage selon l'ordre lexicographique et dans une passe de balayage selon l'ordre lexicographique inve rse, - une figure 4 représente une partie de carte de distances centrée sur la position instantanée du mobile montrant la position et une forme possible d'un obstacle supplémentaire placé conformément à l'invention pour que les estimations de distance faites dans la carte de distances tiennent compte des limitations de manœuvrabilité du mobile, - une figure 5 illustre les relations existantes entre la route et le cap suivis par un aéronef, - une figure 6 illustre, dans un repère air lié à un aéronef, les domaines de forme circulai re, qui sont inaccessibles pour l'aéronef en raison des limites de sa manœuvrabilité, - une figure 7 montre la trace au sol des domaines d'inaccessibilité représentés à la figure 1, - une figure 8 représente une partie de carte de distances centrée sur la position instantanée du mobile montrant la position et une autre forme possible d'un obstacle supplémentaire placé conformément à l'invention pour que les estimations de distance faites dans la carte de distances tiennent compte des limitations de manœuvrabilité du mobile, - une figure 9 illustre une façon de répertorier les cellules de la carte de distances appartenant à l'obstacle supplémentaire placé conformément à l'invention, - une figure 10 illustre les directions et secteurs angulaires définis par un masque de chanfrein tel que celui de la figure 2, - des figures 11 et 12 illustrent les problèmes posés par l'anisotropie affectant une carte extraite d'une base de données d'élévation du terrain à maillage régulier en latitude et longitude, et - une figure 13 montre l'effet d'une correction de l'anisotropie par étirement sur une carte extraite d'une base de données d'élévation du terrain à maillage régulier en latitude et longitude après correction de l'anisotropie.Other characteristics and advantages of the invention will emerge from an embodiment given by way of example. This description will be made with reference to the drawing in which: - a figure 1 represents an example of distance map covering an area where a mobile evolves and having the position of the mobile as the origin of the distance measurements, - a figure 2 represents an example of chamfer mask usable by a distance transform by propagation, - Figures 3a and 3b show the cells of the chamfer mask illustrated in Figure 2, which are used in a scan pass in lexicographic order and in a scan pass according to the lexicographic order inve rse, - a figure 4 represents a part of map of distances centered on the instantaneous position of the mobile showing the position and a possible form of an additional obstacle placed according to the invention so that the estimates of distance made in the distance map take into account the maneuverability limitations of the mobile, - a figure 5 illustrates the existing relationships between e the route and the course followed by an aircraft, - a figure 6 illustrates, in an air coordinate system linked to an aircraft, the areas of circular shape, which are inaccessible for the aircraft due to the limits of its maneuverability, - a Figure 7 shows the ground trace of the inaccessibility areas shown in Figure 1, - Figure 8 shows a portion of the distance map centered on the instantaneous position of the mobile showing the position and another possible form of an additional obstacle placed in accordance with the invention so that the distance estimates made in the distance map take into account the limitations of maneuverability of the mobile, - Figure 9 illustrates a way of listing the cells of the distance map belonging to the additional obstacle placed in accordance with the invention, - Figure 10 illustrates the directions and angular sectors defined by a chamfer mask such as that of the Figure 2, - Figures 11 and 12 illustrate the problems posed by the anisotropy affecting a map extracted from a terrain elevation database with regular mesh in latitude and longitude, and - a Figure 13 shows the effect of '' correction of anisotropy by stretching on a map extracted from a terrain elevation database with regular mesh in latitude and longitude after correction of anisotropy.
Une carte de distances sur une zone d'évolution est formée de l'ensemble des valeurs des distances des points placés aux nœuds d'un maillage régulier de la zone d'évolution par rapport à un point de la zone pris pour origine des mesures de distance. Comme montré à la figure 1, elle peut être présentée sous la forme d'un tableau de valeurs dont les cases correspondent à un découpage de la zone d'évolution en cellules centrées sur les nœuds du maillage. Le maillage régulier adopté est souvent celui des points d'une base de données d'élévation du terrain couvrant la zone d'évolution. Le point de la zone pris pour origine des mesures de distance est le nœud du maillage le plus proche de la projection au sol de la position instantanée du mobile. Les cartes de distances sont souvent réalisées en utilisant une transformée de distance par propagation également connue sous la dénomination de transformée de distance de chanfrein. Les transformées de distance de chanfrein sont apparues initialement en analyse d'image pour estimer des distances entre objets. Gunilla Borgefors en décrit des exemples, dans son article intitulé " Distance Transformation in Digital Images." paru dans la revue : Computer Vision, Graphics and Image Processing, Vol. 34 pp. 344-378 en février 1986. La distance d'entre deux points d'une surface est la longueur minimale de tous les parcours possibles sur la surface partant de l'un des points et aboutissant à l'autre. Dans une image formée de pixels répartis selon un maillage régulier de lignes, colonnes et diagonales, une transformée de distance par propagation estime la distance d'un pixel dit pixel "but" par rapport à un pixel dit pixel "source" en construisant progressivement, en partant du pixel source, le plus court trajet possible suivant le maillage des pixels et aboutissant au pixel but, et en s'aidant des distances trouvées pour les pixels de l'image déjà analysés et d'un tableau dit masque de chanfrein répertoriant les valeurs des distances entre un pixel et ses proches voisins. Comme montré à la figure 2, un masque de chanfrein se présente sous la forme d'un tableau avec une disposition de cases reproduisant le motif d'un pixel entouré de ses proches voisins. Au c ntre du motif, une case affectée de la valeur 0 repère le pixel pris pour origine des distances répertoriées dans le tableau. Autour de cette case centrale, s'agglomèrent des cases périphériques remplies de valeurs de distance de proximité non nulles et reprenant la disposition des pixels du voisinage d'un pixel supposé occuper la case centrale. La valeur de distance de proximité figurant dans une case périphérique est celle de la distance séparant un pixel occupant la position de la case périphérique concernée, d'un pixiel occupant la position de la case centrale. On remarque que les valeurs de distance de proximité se répartissent en cercles concentriques. Un premier cercle de quatre cases correspondant aux quatre pixels de premier rang,_ qu i sont les plus proches du pixel de la case centrale, soit sur la même ligne, soit sur la même colonne, sont affectées d'une valeur de distance de proximité D1. Un deuxième cercle de quatre cases correspondant aux quatre pixels de deuxième rang, qui sont pixels les plus proches du pixel de la case centrale placés sur les diagonales, sont affectées d'une valeur de distance de proximité D2. Un troisième cercle de huit cases correspondant aux huit pixels de troisième rang, qui sont les plus proches du pixel de la case centrale tout en restant en dehors de la ligne, de la colonne et des diagonales occupées par le pixel de la case centrale, sont affectées d'une valeur de distance de proximité D3. Le masque de chanfrein peut couvrir un voisinage plus ou moins étendu du pixel de la case centrale en répertoriant les valeurs des distances de proximité d'un nombre plus ou moins important de cercles concentriques de pixels du voisinage. Il peut être réduit aux deux premiers cercles formés par les pixels du voisinage d'un pixel occupant la case centrale comme dans l'exemple des cartes de distances des figures 1 ou être étendu au-delà des trois premiers cercles formés par les pixels du voisinage du pixel de la case centrale. Il est habituel de s'arrêter à trois premiers cercles comme pour le masque de chanfrein montré à la figure 2. Ce n'est que dans un but de simplification que l'on s'est arrêté au deux premiers cercles pour la carte de distances de la figure 1. Les valeurs des distances de proximité D1, D2, D3 qui correspondent à des distances euclidiennes sont exprimées dans une échelle dont le facteur multiplicatif autorise l'emploi de nombres entiers au prix d'une certaine approximation. C'est ainsi que G . Borgefors adopte une échelle correspondant à un facteur multiplicatif 3 ou 5. Dans le cas d'un masque de chanfrein retenant les deux premiers cercles de valeurs de distance de proximité, donc de dimensions 3x3, G. Borgefors donne, à la première distance de proximité D1 qui correspond à un échelon en abscisse ou en ordonnées et également au facteur multiplicatif d'échelle, la valeur 3 et, à la deuxième distance de proximité qui correspond à la racine de la somme des carrés des échelons en abscisse et en ordonnée ΛJX2 +y2 , la valeur 5. Dans le cas d'un masque de chanfrein retenant les trois premiers cercles, donc de dimensions 5x5, elle donne, à la distance D1 qui correspond au facteur multiplicatif d'échelle, la valeur 5, à la distance D2, la valeur 7 qui est une approximation de 5 /2 , et à la distance D3 la valeur 11 qui est une approximation de 5^5 . La construction progressive du plus court trajet possible allant à un pixel but en partant d'un pixel source et en suivant le maillage des pixels se fait par un balayage régulier des pixels de l'image au moyen du masque de chanfrein. Initialement, les pixels de l'image se voient; affecter une valeur de distance infinie, en fait un nombre suffisamment élevé pour dépasser toutes les valeurs des distances mesurables dans l'image, à l'exception du pixel source qui se voit affecter une valeur de distance nulle. Puis les valeurs initiales de distance affectées aux points but sont mises à jour au cours du balayage de l'image par le masque de chanfrein, une mise à jour consistant à remplacer une valeur de distance attribuée à un poi nt but, par une nouvelle valeur moindre résultant d'une estimation de distance faite à l'occasion d'une nouvelle application du masque de chanfrein au point but considéré. Une estimation de distance par application du masque de chanfrein à un pixel but consiste à répertorier tous les trajets allant de ce pixel but au pixel source et passant par un pixel du voisinage du pixel but dont la distance a déjà été estimée au cours du même balayage, à rechercher parmi les trajets répertoriés, le ou les trajets les plus courts et à adopter la longueur du ou des trajets les plus courts comme estimation de distance. Cela se fait en plaçant le pixel but dont on veut estimer la d ïstance dans la case centrale du masque de chanfrein, en sélectionnant les cases périphériques du masque de chanfrein correspondant à des pixels du voisinage dont la distance vient d'être mise à jour, en calculant les longueurs des trajets les plus courts reliant le pixel but à mettre à jour au pixel source en passant par un des pixels sélectionnés du voisinage, par addition de la valeur de distance affectée au pixel du voisinage concerné et de la valeur de distance de proximité donnée par le masque de chanfrein, et à adopter, comme estimation de distance, le minimum des valeurs de longueur de trajet obtenues et de l'ancienne valeur de distance affectée au pixel en cours d'analyse. Au niveau d'un pixel en analyse par le masque de chanfrein, la recherche progressive des plus courts trajets possibles partant d'un pixel source et allant aux différents pixels but de l'image donne lieu à un phénomène de propagation en directions des pixels qui sont les voisins les plus proches du pixel en analyse et dont les distances sont répertoriées dans le masque de chanfrein. Dans le cas d'une répartition régulière des ixels de l'image, les directions des plus proches voisins d'un pixel ne variant pas sont considérées comme des axes de propagation de la transformée de d istance à masque de chanfrein qui prend souvent elle-même, l'appellation de transformées de distance par propagation. L'ordre de balayage des pixels de l'image influe sur la fiabi lité des estimations de distance et de leurs mises à jour car les trajets pris en compte en dépendent. En fait, il est soumis à une contrainte de régularité qui "fait que si les pixels de l'image sont repérés selon l'ordre lexicographique (pixels classés dans un ordre croissant ligne par ligne en partant du haut de l'image et en progressant vers le bas de l'image, et de gauche à droite au sein d'une ligne), et si un pixel p a été analysé avant un pixel q alors un pixel p+x doit être analysé avant le pixel q+x. Les ordres lexicographique, lexicographique inverse (balayage des pixels de l'image ligne par ligne de bas en haut et, au sein d'une ligne, de droite à gauche), lexicographique transposé (balayage des pixels de l'image colonne par colonne de gauche à droite et, au sein d'une colonne, de haut en bas), lexicographique transposé inverse (balayage des pixels par colonnes de droite à gauche et au sein d'une colonne de bas en haut) satisfont cette condition de régularité et plus généralement tous les balayages dans lesquels les lignes et colonnes sont balayées de droite à gauche ou de gauche à droite. G. Borgefors préconise un double balayage des pixels de l'image, une fois dans l'ordre lexicographique et une autre dans l'ordre lexicographique inverse. La figure 3a montre, dans le cas d'une passe de balayage selon l'ordre lexicographique allant du coin supérieur gauche au coin inférieur droit de l'image, les cases du masque de chanfrein de la figure 1 utilisées pour répertorier les trajets allant d'un pixel but placé sur la case centrale (case indexée par 0) au pixel source en passant par un pixel du voisinage dont la distance a déjà fait l'objet d'une estimation au cours du même balayage. Ces cases sont au nombre de huit, disposées dans la partie supérieure gauche du masque de chanfrein. Il y a donc huit trajets répertoriés pour la recherche du plus court dont la longueur est prise pour estimation de la distance. La figure 3b montre, dans le cas d'une passe de balayage selon l'ordre lexicographique inverse allant du coin inférieur droit au coin supérieur gauche de l'image, les cases du masque de chanfrein de la figure 1 utilisées pour répertorier les trajets allant d'un pixel but placé sur la case centrale (case indexée par 0) au pixel source en passant par un pixel du voisinage dont la distance a déjà fait l'objet d'une estimation au cours du même balayage. Ces cases sont complémentaires de celles de la figure 2a. Elles sont également au nombre de huit mais disposées dans la partie inférieure droite du masque de chanfrein. Il y a donc encore huit trajets répertoriés pour la recherche du plus court dont la longueur est prise pour estimation de la distance. La carte de distances montrée à la figure 1 est un exemple simplifié facilitant la compréhension du problème auquel s'attaque l'invention. Cette carte de distances couvre une zone avec deux obstacles infranchissables 10 et 11 , où évolue un mobile sensé être au point S et se déplacer dans le sens de la flèche. Elle a été établie à l'aide de la plus simple des transformées de distance proposées par Gunilla Borgefors, utilisant un masque de chanfrein de dimension 3x3 avec deux distances de voisinage 3,A distance map on an evolution zone is formed by the set of values of the distances of the points placed at the nodes of a regular mesh of the evolution zone compared to a point of the zone taken for origin of the measurements of distance. As shown in Figure 1, it can be presented in the form of a table of values whose boxes correspond to a division of the evolution zone into cells centered on the nodes of the mesh. The regular mesh adopted is often that of the points of a terrain elevation database covering the area of evolution. The point of the zone taken as the origin of the distance measurements is the node of the mesh closest to the projection on the ground of the instantaneous position of the mobile. Distance maps are often made using a propagation distance transform also known as a chamfer distance transform. Chamfer distance transforms first appeared in image analysis to estimate distances between objects. Gunilla Borgefors describes examples, in her article "Distance Transformation in Digital Images." published in the journal: Computer Vision, Graphics and Image Processing, Vol. 34 pp. 344-378 in February 1986. The distance between two points on a surface is the minimum length of all the possible routes on the surface starting from one of the points and ending at the other. In an image formed by distributed pixels according to a regular mesh of lines, columns and diagonals, a distance transform by propagation estimates the distance of a pixel called "goal" pixel with respect to a pixel called "source" pixel by gradually building up, starting from the source pixel, the shortest possible path following the mesh of pixels and ending at the target pixel, and using the distances found for the image pixels already analyzed and a table called chamfer mask listing the values of the distances between a pixel and his close neighbors. As shown in Figure 2, a chamfer mask is in the form of a table with an arrangement of boxes reproducing the pattern of a pixel surrounded by its close neighbors. At the center of the pattern, a box assigned the value 0 identifies the pixel taken as the origin of the distances listed in the table. Around this central box are agglomerated peripheral boxes filled with non-zero proximity distance values and repeating the arrangement of the pixels in the vicinity of a pixel supposed to occupy the central box. The proximity distance value appearing in a peripheral box is that of the distance separating a pixel occupying the position of the peripheral box concerned, from a pixel occupying the position of the central box. Note that the proximity distance values are distributed in concentric circles. A first circle of four boxes corresponding to the four pixels of first row, _ which i are closest to the pixel of the central box, either on the same line or on the same column, are assigned a value of proximity distance D1. A second circle of four boxes corresponding to the four pixels of second rank, which are pixels closest to the pixel of the central box placed on the diagonals, are assigned a proximity distance value D2. A third circle of eight boxes corresponding to the eight pixels of third row, which are closest to the pixel of the central box while remaining outside the line, the column and the diagonals occupied by the pixel of the central box, are assigned a proximity distance value D3. The chamfer mask can cover a more or less extended neighborhood of the pixel of the central box by listing the values of the proximity distances of a more or less large number of concentric circles of pixels of the neighborhood. It can be reduced to the first two circles formed by the pixels in the vicinity of a pixel occupying the central box as in the example of the distance maps of FIGS. 1 or be extended beyond the first three circles formed by the pixels in the vicinity of the pixel in the central box. It is usual to stop at the first three circles as for the chamfer mask shown in Figure 2. It is only for the sake of simplicity that we stopped at the first two circles for the distance map in Figure 1. The values of proximity distances D1, D2, D3 which correspond to Euclidean distances are expressed in a scale whose multiplicative factor allows the use of whole numbers at the cost of a certain approximation. This is how G. Borgefors adopts a scale corresponding to a multiplicative factor 3 or 5. In the case of a chamfer mask retaining the first two circles of proximity distance values, therefore of dimensions 3x3, G. Borgefors gives, at the first proximity distance D1 which corresponds to a rung on the abscissa or on the ordinate and also to the multiplicative factor of scale, the value 3 and, at the second proximity distance which corresponds to the root of the sum of the squares of the rungs on the abscissa and on the ordinate ΛJX 2 + y 2 , the value 5. In the case of a chamfer mask retaining the first three circles, therefore of dimensions 5x5, it gives, at the distance D1 which corresponds to the scaling factor, the value 5, to the distance D2, the value 7 which is an approximation of 5/2, and at distance D3 the value 11 which is an approximation of 5 ^ 5. The progressive construction of the shortest possible path going to a target pixel starting from a source pixel and following the mesh of the pixels is done by a regular scanning of the pixels of the image by means of the chamfer mask. Initially, the pixels of the image are seen; assign an infinite distance value, making it a number large enough to exceed all the values of the measurable distances in the image, except for the source pixel which is assigned a zero distance value. Then the initial distance values assigned to the goal points are updated during the scanning of the image by the chamfer mask, an update consisting in replacing a distance value assigned to a goal point, by a new one. lower value resulting from an estimate of distance made on the occasion of a new application of the chamfer mask at the target point considered. A distance estimate by applying the chamfer mask to a target pixel consists in listing all the paths going from this target pixel to the source pixel and passing through a pixel in the vicinity of the target pixel whose distance has already been estimated during the same scan. , to search among the routes listed, the shortest route (s) and to adopt the length of the shortest route (s) as an estimate of distance. This is done by placing the goal pixel whose extent we want to estimate in the central box of the chamfer mask, by selecting the peripheral boxes of the chamfer mask corresponding to neighboring pixels whose distance has just been updated, by calculating the lengths of the shortest paths connecting the goal pixel to be updated to the source pixel passing through one of the selected pixels of the neighborhood, by adding the distance value assigned to the pixel of the neighborhood concerned and the distance value of proximity given by the chamfer mask, and to adopt, as distance estimate, the minimum of the path length values obtained and the old distance value assigned to the pixel being analyzed. At the level of a pixel analyzed by the chamfer mask, the progressive search for the shortest possible paths starting from a source pixel and going to the different goal pixels of the image gives rise to a phenomenon of propagation in directions of the pixels which are the closest neighbors of the pixel under analysis and whose distances are listed in the chamfer mask. In the case of a regular distribution of the ixels of the image, the directions of the closest neighbors of a pixel which do not vary are considered as axes of propagation of the d istance transform with chamfer mask which often takes even, the name of distance transforms by propagation. The scanning order of the pixels in the image influences the reliability of the distance estimates and their updates because the paths taken into account depend on them. In fact, it is subject to a regularity constraint which "means that if the pixels of the image are identified according to the lexicographic order (pixels classified in an ascending order line by line starting from the top of the image and progressing towards the bottom of the image, and from left to right within a line), and if a pixel p has been analyzed before a pixel q then a pixel p + x must be analyzed before the pixel q + x. The lexicographic orders, reverse lexicographic (scanning pixels of the image line by line from bottom to top and, within a line, from right to left), transposed lexicographic (scanning pixels of the image column by column of left to right and, within a column, from top to bottom), the reverse transposed lexicographic (pixel scanning by columns from right to left and within a column from bottom to top) satisfy this regularity condition and more generally all scans in which rows and columns are scanned from right to left or left to right. G. Borgefors recommends double scanning the pixels of the image, once in lexicographic order and once in reverse lexicographic order. FIG. 3a shows, in the case of a scanning pass in lexicographic order going from the upper left corner to the lower right corner of the image, the boxes of the chamfer mask of FIG. 1 used to list the paths going from d 'a target pixel placed on the central box (box indexed by 0) at the source pixel passing through a neighboring pixel whose distance has already been estimated during the same scan. There are eight of these boxes, located in the upper left of the chamfer mask. There are therefore eight paths listed for the search for the shortest whose length is taken to estimate the distance. FIG. 3b shows, in the case of a scanning pass in reverse lexicographic order going from the lower right corner to the upper left corner of the image, the boxes of the chamfer mask of FIG. 1 used to list the paths going from a goal pixel placed in the central box (box indexed by 0) to the source pixel, passing through a neighboring pixel, the distance of which has already been estimated during the same scan. These boxes are complementary to those in Figure 2a. They are also eight in number but arranged in the lower right part of the chamfer mask. There are therefore still eight paths listed for the search for the shortest whose length is taken to estimate the distance. The distance map shown in FIG. 1 is a simplified example facilitating the understanding of the problem which the invention addresses. This distance map covers an area with two obstacles impassable 10 and 11, where a mobile is supposed to be at point S and move in the direction of the arrow. It was established using the simplest of the distance transforms proposed by Gunilla Borgefors, using a chamfer mask of dimension 3x3 with two neighborhood distances 3,
5 4. Les estimations de distance sont faites indépendamment du mouvement du mobile et ne tiennent pas compte de l'incapacité du mobile à suivre certains parcours pour des raisons de manœuvrabilité. Lorsqu'un mobile doit effectuer un parcours d'adaptation pour se mettre en situation de0 pouvoir rejoindre un point de la carte de distances, ce parcours d'adaptation fausse l'estimation de distance car il peut rendre le trajet effectif parcouru par le mobile nettement plus long que le trajet de longueur minimale ayant servi à l'estimation de distance. C'est particulièrement le cas pour les points situés dans le proche voisinage du mobile mais dans des directions éloignées de5 celle de son mouvement du moment. Par exemple, dans l'exemple de carte de distances illustré à la figure 1, les cellules 13 et 14 qui sont les plus proches voisines de la cellule occupée par la position instantanée du mobile (point S) ont la même estimation de distance 3 alors que l'une est dans la direction du mouvement du mobile (flèche) et l'autre dans la direction0 inverse. Si l'on considère que le mobile est un aéronef, il parvient sans5 4. The distance estimates are made independently of the movement of the mobile and do not take into account the inability of the mobile to follow certain routes for reasons of maneuverability. When a mobile has to make an adaptation journey in order to be able to reach a point on the distance map, this adaptation journey distorts the distance estimate because it can make the actual journey traveled by the mobile clearly longer than the minimum length path used to estimate the distance. This is particularly the case for points located in the close vicinity of the mobile but in directions distant from that of its momentary movement. For example, in the example of a distance map illustrated in FIG. 1, cells 13 and 14 which are the closest neighbors to the cell occupied by the instantaneous position of the mobile (point S) have the same estimate of distance 3 then that one is in the direction of movement of the mobile (arrow) and the other in the reverse direction0. If we consider that the mobile is an aircraft, it arrives without
<»,. encombre à la cellule 13, puisqu'il n'a aucune manœuvre à effectuer pour l'atteindre. A l'inverse, il lui est difficile d'atteindre la cellule 14 car il lui faut faire un tour complet avant de pouvoir envisager de la rejoindre. L'obligation d'effectuer ce tour complet pour des raisons de manœuvrabilité rend5 irréaliste l'estimation de distance de la cellule 14. Plus généralement, les estimations de distance faites en prenant en compte des trajets de longueur minimale inaccessibles au mobile en raison de sa manœuvrabilité limitée sont rendues plus ou' moins irréalistes en fonction de l'importance relative de la longueur du trajet d'adaptation qui a0 été négligé. Pour éviter cet inconvénient, on propose, comme représenté à la figure 4, d'ajouter aux obstacles infranchissables (10, 11 figure 1) un nouvel obstacle infranchissable 20, répertoriant les cellules de la carte de distances inaccessibles au mobile du fait de ses limites de manœuvrabilité. Ce nouvel5 obstacle infranchissable 20, est lié au mobile et disposé dans son voisinage proche. Il est de forme concave, la cellule (point S) contenant la position instantanée du mobile étant placée dans sa concavité tournée dans la direction du déplacement du mobile. Il présente une forme générale en demi- lune ou en U. Ce nouvel obstacle infranchissable 20, qui se déplace avec le mobile, complète les obstacles à contourner (10, 11 figure 1) et oblige la transformation de distance à écarter, dans sa recherche des longueurs des plus courts chemins, les chemins hors de portée du mobile du fait de sa manœuvrabilité limitée. Pour un aéronef, il s'agit d'interdire les demi-tours irréalistes, les virages trop accentués et même de tenir compte des conditions locales de vent. Pour rendre une carte de distances encore plus réaliste dans le cas d'un aéronef, il est intéressant de préciser davantage la forme de ce nouvel obstacle infranchissable 20 lié à l'aéronef et à la direction de son mouvement par rapport à la carte donc par rapport au sol en répertoriant les cellules de la carte de distances qui sont placées au voisinage de l'aéronef tout en lui étant inaccessibles par un trajet direct du fait de sa manœuvrabilité limitée. Pour repérer les cellules de la carte de distances proches de l'aéronef mais inaccessibles de celui-ci par un trajet direct du fait des limites de sa manœuvrabilité il faut tenir compte du vent local. En effet, comme montré à la figure 5, la direction au sol du mouvement d'un aéronef, qui est celle de sa vitesse sol GS orientée selon sa route (track en anglo-saxon) de vecteur unitaire t , correspond à la direction de la somme vectorielle du vecteur vitesse air TAS de l'aéronef, orienté selon son cap (heading en anglo-saxon) de vecteur unitaire h , et de la vitesse du vent WS (wind speed en anglo-saxon) orientée selon un vecteur unitaire ïv . Sans vent, comme montré à la figure 6, les cellules de la carte de distances placées dans le voisinage de l'aéronef tout en lui étant inaccessibles directement, sont celles contenues à l'intérieur de deux cercles 30, 31 passant par la position de l'aéronef, ayant une tangente commune orientée selon le cap de l'aéronef (vecteur Y) et un rayon R correspondant au plus petit rayon de virage acceptable sur le moment. Ces cercles 30, 31 , qui représentent les trajectoires en virage les plus serrées autorisées, d'un côté ou de l'autre, pour l'aéronef, répondent au système d'équations paramétriques : < " ,. obstructs cell 13, since it has no maneuver to perform to reach it. Conversely, it is difficult for him to reach cell 14 because he must make a full turn before he can consider joining it. The obligation to complete this complete turn for reasons of maneuverability makes the estimate of distance from cell 14 unrealistic. More generally, the distance estimates made by taking into account journeys of minimum length inaccessible to the mobile due to its Limited maneuverability is made more or less unrealistic depending on the relative importance of the length of the adaptation path which has been neglected. To avoid this drawback, it is proposed, as shown in FIG. 4, to add to the impassable obstacles (10, 11 FIG. 1) a new impassable obstacle 20, listing the cells of the distance map inaccessible to the mobile due to its limits. maneuverability. This new insurmountable obstacle 20, is linked to the mobile and arranged in its vicinity close. It is concave in shape, the cell (point S) containing the instantaneous position of the mobile being placed in its concavity turned in the direction of movement of the mobile. It has a general half-moon or U-shape. This new insurmountable obstacle 20, which moves with the mobile, completes the obstacles to be circumvented (10, 11 Figure 1) and forces the transformation of distance to be removed, in its search lengths of the shortest paths, paths out of range of the mobile due to its limited maneuverability. For an aircraft, this is to prohibit unrealistic U-turns, excessively sharp turns and even to take into account local wind conditions. To make a distance map even more realistic in the case of an aircraft, it is advantageous to further specify the shape of this new insurmountable obstacle 20 linked to the aircraft and to the direction of its movement relative to the map, therefore by report to the ground by listing the cells of the distance map which are placed in the vicinity of the aircraft while being inaccessible to it by a direct route due to its limited maneuverability. To locate the cells of the distance map close to the aircraft but inaccessible from it by a direct route due to the limits of its maneuverability, the local wind must be taken into account. Indeed, as shown in FIG. 5, the direction on the ground of the movement of an aircraft, which is that of its ground speed GS oriented along its route (track in English) of unit vector t, corresponds to the direction of the vector sum of the air speed vector TAS of the aircraft, oriented according to its heading (heading in Anglo-Saxon) of unit vector h, and of the wind speed WS (wind speed in Anglo-Saxon) oriented according to a unit vector ïv . Without wind, as shown in FIG. 6, the cells of the distance map placed in the vicinity of the aircraft while being directly inaccessible to it, are those contained within two circles 30, 31 passing through the position of the aircraft, having a common tangent oriented along the heading of the aircraft (vector Y) and a radius R corresponding to the smallest acceptable turning radius at the time. These circles 30, 31, which represent the tightest turning trajectories authorized, on one side or the other, for the aircraft, respond to the system of parametric equations:
avec TAS2 R = - £- anφroB TAS g.tanφ w = rail R TAS φroιι étant l'angle de roulis de l'aéronef pendant la manœuvre, γ étant un facteur dépendant des conditions initiales, δ étant un coefficient égal à +1 pour un virage à droite et -1 pour un virage à gauche.with TAS 2 R = - £ - anφ roB TAS g.tanφ w = rail R TAS φ ro ιι being the roll angle of the aircraft during the maneuver, γ being a factor depending on the initial conditions, δ being an equal coefficient at +1 for a right turn and -1 for a left turn.
La vitesse air de l'aéronef, lorsqu'il parcourt ces cercles s'écrit alors: En supposant le vent constant en vitesse et en direction, les cercles 30, 31 laissent au sol une trace en forme de cycloïde. Le système d'équations paramétriques de cette trace, peut être obtenue par intégration du système d'équations paramétriques de la vitesse air de parcours sur les cercles. Lorsque l'on tient compte du vent, le système (1) d'équations paramétriques de la vitesse de l'aéronef, exprimé dans un repère sol X Y dont l'axe des ordonnées Y est orienté selon le cap de l'aéronef, devient : wsxΛ étant le vecteur vent wsv The air speed of the aircraft, when it traverses these circles is then written: Assuming the wind constant in speed and direction, the circles 30, 31 leave a cycloid-shaped trace on the ground. The system of parametric equations of this trace, can be obtained by integration of the system of parametric equations of the air speed of course on the circles. When the wind is taken into account, the system (1) of parametric equations for the speed of the aircraft, expressed in a ground coordinate system XY whose Y axis is oriented along the heading of the aircraft, becomes : ws x Λ being the wind vector ws v
Par intégration, on obtient, dans ce repère sol, le système d'équations paramétriques de la trace : XΛ fWSx .t - δ .R. cos(wt + γ ) + Cx Λ (0 = X WSY .t + R. sin(wt + γ ) + Cγ By integration, we obtain, in this ground coordinate system, the system of parametric equations of the trace: XΛ f WS x .t - δ .R. cos (wt + γ) + C x Λ (0 = X WS Y .t + R. sin (wt + γ) + C γ
Cx et Cy étant des constantes d'intégration qui dépendent du repère considéré.C x and C y being integration constants which depend on the reference frame considered.
Dans un repère air Xh Y dont l'axe des ordonnées Y est orienté selon le cap (heading) de l'aéronef le système d'équations paramétriques (1 ) devient :In an air coordinate system Xh Y whose Y axis is oriented according to the heading of the aircraft, the system of parametric equations (1) becomes:
Par intégration, il donne, dans ce repère air, le système d'équations paramétriques de la trace :By integration, it gives, in this air coordinate system, the system of parametric equations of the trace:
La condition initiale de position est :The initial position condition is:
car l'aéronef est initialement au centre du repère. La condition initiale de vitesse est : because the aircraft is initially at the center of the coordinate system. The initial speed condition is:
car l'aéronef a un vecteur vitesse orienté initialement selon l'axe de route t . A l'instant initial t=0, le système d'équation (3) donne pour vitesse air initiale : Jι La condition de vitesse initiale (relation 6) implique :because the aircraft has a speed vector initially oriented along the course axis t. At the initial instant t = 0, the equation system (3) gives the initial air speed: Jι The initial speed condition (relation 6) implies:
En tenant compte de ces relations (7) dans le système d'équations (4), il vient :Taking into account these relations (7) in the system of equations (4), it comes:
et la condition de position initiale (relation 5) implique C 'Xrah =δ.R. cγ =oand the condition of initial position (relation 5) implies C 'X ra h = δ.R. c γ = o
Dans un repère sol XtYt, dont l'axe des ordonnées Yt est orienté selon la route (track) de l'aéronef, le système d'équations paramétriques (1) devient :In a ground coordinate system XtY t , whose ordinate axis Y t is oriented along the track (track) of the aircraft, the system of parametric equations (1) becomes:
Par intégration, il donne, dans ce repère sol, le système d'équations paramétriques de la trace :By integration, it gives, in this ground coordinate system, the system of parametric equations of the trace:
WSXt.t - δ _R.cos(wt +γ,) + Cxt WSYt.t + R.sin(wt +yt) + CYt \?J*WS Xt .t - δ _R.cos (wt + γ,) + C xt WS Yt .t + R.sin (wt + y t ) + C Yt \? J *
La condition de position initiale :The initial position condition:
exprimant que l'aéronef est initialement au centre du repère, et celle de vitesse initiale : expressing that the aircraft is initially at the center of the reference frame, and that of initial speed:
exprimant que l'aéronef a un vecteur vitesse orienté initialement selon l'axe de route t conduisent aux valeurs de constantes d'intégration : CX) =δJl.cos(yt) Cκ = -R.sin(γ<) yt = -δ . Track — Heading)expressing that the aircraft has a speed vector initially oriented along the course axis t lead to the values of integration constants: C X) = δJl.cos (y t ) C κ = -R.sin (γ < ) y t = -δ. Track - Heading)
Dans le repère géographique XgYg, utilisé par la carte de distances, le système d'équations paramétriques (1) devient :In the geographic coordinate system X g Y g , used by the distance map, the system of parametric equations (1) becomes:
Par intégration, il donne, dans ce repère géographique, le système d'équations paramétriques de la trace :By integration, it gives, in this geographic coordinate system, the system of parametric equations of the trace:
Λ WSXg.t-h.R.cos(wt+yg) + CJ \y Jg WSYg.t+R.sin(wtx-yg) + CYg Λ WS Xg .th.R.cos (wt + y g ) + C J \ y Jg WS Yg .t + R.sin (wtx-y g ) + C Yg
La condition de position initiale : et la condition de vitesse initiale : conduisent aux valeurs de constantes d'intégration CXt = δ.R.cos(yg)The initial position condition: and the initial speed condition: lead to the values of integration constants C Xt = δ.R.cos (y g )
CYt = -R.sm(y g) tan gyg ) = -δ . tasι(Heading) ou encore C^ = Long + δ .R. cos(γ g ) CYg = Lat - R.sw(y g) γ = δ Jffeading + k.UC Yt = -R.sm (y g ) tan gy g ) = -δ. tasι (Heading) or C ^ = Long + δ .R. cos (γ g ) C Yg = Lat - R.sw (y g ) γ = δ Jffeading + kU
En fait, l'aéronef ne suit les traces au sol des deux cercles (30, 31 figure 5) que le temps nécessaire à une manœuvre de changement de route et de cap. Le temps de transition pour changer de cap dépend de la vitesse angulaire de l'avion et donc de son angle de roulis.In fact, the aircraft follows the tracks on the ground of the two circles (30, 31 FIG. 5) only the time necessary for a change of course and course maneuver. The transition time to change course depends on the angular speed of the aircraft and therefore on its roll angle.
H2 -Hλ T transition w avec : TAS £.tanφro„ w = R TASH 2 -H λ T transition w with: TAS £ .tanφ ro „w = R TAS
Le changement de route (track) dépend en plus des conditions de vent. Le cap (heading) final s'écritThe change of route also depends on the wind conditions. The final heading is written
Track fiml 2.(£ + l)II Heading w = Track βnal 2.£.π Track fiml 2. (£ + l) II Heading w = Track βnal 2. £ .π
et la duré du temps de transition pour changer de route : Heading ^ - Heading ini \ transition wand the duration of the transition time to change route: Heading ^ - Heading ini \ transition w
En final, pour déterminer les cellules de la carte de distances appartenant à l'obstacle infranchissable (20 figure 4) car considérées comme inaccessibles pour l'aéronef du fait de sa manœuvrabilité limitée, on trace, comme montré à la figure 7, un contour fermé formé des deux parties 40, 40' des traces au sol des deux cercles (30, 31 figure 5) partant de la position initiale de l'aéronef (point S) jusqu'aux points P, P' correspondant à un changement de route donné, par exemple, 180° et des deux droites 41, 41' joignant les extrémités P, P' des deux parties de trace 40, 40' à la position initiale de l'aéronef (point S). Cela donne à l'obstacle infranchissable lié à l'aéronef, une forme à deux lobes en aile de papillon. Une fois le contour déterminé, on sélectionne pour l'obstacle, les cellules contenues dans le contour en négligeant celles situées au devant de la position initiale de l'aéronef, dans le sens de son déplacement. Une manière de sélectionner pour l'obstacle les cellules contenues dans un contour qui a été déterminé au préalable en évitant les cellules situées au devant de la position initiale de l'aéronef, dans le sens de son déplacement consiste, comme représenté à la figure 8, à ne prendre que celles entièrement située dans le contour et à ne pas considérer celles qui n'y sont que partiellement contenues. Pour répertorier les cellules contenues dans un contour fermé, on peut, comme représenté à la figure 9, choisir une cellule X que l'on sait à l'intérieur du contour, faire décrire le contour par un point mobile Z et assimiler les cellules traversées par le segment de droite XZ aux cellules contenues dans le contour. Pour améliorer la propagation d'une transformée de distance à masque de chanfrein et obtenir plus rapidement, par balayage, des estimations de distance stables sur l'ensemble des cellules de la carte de la zone représentée, il est avantageux d'exclure de l'obstacle supplémentaire lié à l'aéronef pour tenir compte de sa manœuvrabilité, les cellules de la carte appartenant en totalité ou en partie à un secteur angulaire partant de la position actuelle de l'aéronef et ayant son ouverture tournée en direction de la route suivie par l'aéronef. En effet, le fait de dégager de tout obstacle ces cellules permet de laisser libres, au niveau de la position actuelle de l'aéronef et donc du pixel pris pour origine des mesures de distance, un ou plusieurs axes de propagation de la transformée de distance de chanfrein ayant des orientations proches de celle du mouvement de l'aéronef, ce qui augmente les possibilités de tracé, au voisinage de la position actuelle de l'aéronef, donc du pixel source, pour les chemins allant des pixels but au pixel source et renforce les chances de trouver rapidement un trajet de longueur minimale au cours du balayage effectué par le masque de chanfrein. Le secteur angulaire de délimitation des cellules laissées libres de propagation est choisi comme étant celui des secteurs angulaires délimités, par les bissectrices des angles formés par les axes de propagation tracés au niveau du pixel le plus proche de la position actuelle de l'aéronef, pris comme pixel source, origine pour les mesures de distance, ayant l'orientation la plus proche de celle du mouvement de l'aéronef. La figure 10 montre une partie du faisceau des axes de propagation définie par les pixels de l'image concernés par le quart haut droit du masque de chanfrein de la figure 2 appliqué au pixel COO pris comme origine des mesures de distance car supposé le plus proche de la position actuelle de l'aéronef. On y distingue les pixels de premier rang C01 et C10 voisins immédiats du pixel en analyse COO sur la même ligne ou la même colonne, le pixel de deuxième rang C11 voisin immédiat du pixel en analyse COO sur la première diagonale, les pixels de troisième rang C12 et C21 voisins immédiats du pixel en analyse COO mais ni sur une même ligne, ni sur une même colonne et ni sur une même diagonale de celui-ci. Les diverses orientations de ces pixels de premier, deuxième et troisième rangs C01, C10, C11, C12, C21 , voisins immédiats du pixel en analyse COO définissent les seules directions possibles de propagation pour la transformée de distance dans le quart haut droit du masque de chanfrein en fait le quart nord est pour une image de carte dont le haut est tourné vers le nord et la droite vers l'est. Ces cinq directions de propagation représentées sur la figure 10 par des traits appuyés et fléchés se complètent par symétries horizontale et verticale. La direction D0 de la propagation du pixel COO en analyse vers le pixel C10 de premier rang sur la même colonne sert de référence angulaire et correspond, dans le langage du jeu d'échec, à un mouvement d'une tour. La direction D1 de la propagation du pixel COO en analyse vers le pixel de troisième rang C21 disposé sur des ligne, colonne et diagonale différentes est angulairement la plus proche de la direction DO. Avec un maillage régulier des pixels, c'est-à-dire en l'absence d'anisotropie de l'image de carte, elle fait un angle de 26,5 degrés par rapport à cette dernière et correspond dans le langage du jeu d'échec à un mouvement d'un cavalier. La direction D2 de la propagation du pixel COO en analyse vers le pixel C11 de deuxième rang sur la même diagonale est un peu plus écartée. En l'absence d'anisotropie de l'image de carte, elle fait un angle de 45 degrés par rapport à la direction de référence DO. Elle correspond dans le langage du jeu d'échec à un mouvement d'un fou. La direction D3 de la propagation du pixel COO en analyse vers le pixel de troisième rang C12 disposé sur des ligne, colonne et diagonale différentes est encore plus écartée. En l'absence d'anisotropie de l'image, elle fait un angle de 63,5 degrés par rapport à la direction de référence DO. Elle correspond dans le langage du jeu d'échec à un mouvement d'un cavalier. Enfin la direction D4 de la propagation du pixel COO en analyse vers le pixel de premier rang C01 sur la même ligne est la plus écartée et fait un angle de 90 degrés par rapport à la direction de référence D. Elle correspond dans le langage du jeu d'échec à un mouvement d'une tour. Les bissectrices des angles formés par ces cinq directions de propagation D0, D1, D2, D3 et D4 découpent dans le quart haut droit du masque de chanfrein cinq secteurs circulaires centrés sur le pixel COO en analyse et tournés dans les cinq directions de propagation à savoir : - un secteur angulaire dit C10 tour car il est orienté vers le pixel C10, selon la direction D0 correspondant au mouvement d'une tour, - un secteur angulaire dit C21 cavalier car il est orienté vers le pixel C21, selon la direction D1 correspondant au mouvement d'un cavalier, - un secteur angulaire dit C11 fou car il est orienté vers le pixel C11 , selon la direction D2 correspondant au mouvement d'un fou, - un secteur angulaire dit C12 cavalier car il est orienté vers le pixel C12, selon la direction D3 correspondant au mouvement d'un cavalier, et - un secteur angulaire dit C01 tour car il est orienté vers le pixel C01 , selon la direction D4 correspondant au mouvement d'une tour. Le tableau suivant répertorie ces cinq secteurs angulaires :Finally, to determine the cells of the distance map belonging to the insurmountable obstacle (20 figure 4) because considered as inaccessible for the aircraft because of its limited maneuverability, we draw, as shown in figure 7, a contour closed formed of the two parts 40, 40 ′ of the traces on the ground of the two circles (30, 31 in FIG. 5) starting from the initial position of the aircraft (point S) up to points P, P 'corresponding to a change of route given, for example, 180 ° and the two straight lines 41, 41 'joining the ends P, P' of the two parts of the track 40, 40 'to the initial position of the aircraft (point S). This gives the insurmountable obstacle linked to the aircraft, a shape with two butterfly wing lobes. Once the contour has been determined, the cells contained in the contour are selected for the obstacle, neglecting those located in front of the initial position of the aircraft, in the direction of its movement. One way of selecting for the obstacle the cells contained in a contour which has been determined beforehand by avoiding the cells situated in front of the initial position of the aircraft, in the direction of its movement consists, as shown in FIG. 8 , to take only those entirely located in the contour and not to consider those which are only partially contained therein. To list the cells contained in a closed contour, we can, as shown in Figure 9, choose a cell X that we know inside the contour, have the contour described by a moving point Z and assimilate the cells crossed by the line segment XZ to the cells contained in the contour. To improve the propagation of a chamfer mask distance transform and more quickly obtain, by scanning, stable distance estimates on all the cells of the map of the represented area, it is advantageous to exclude from the additional obstacle linked to the aircraft to take account of its maneuverability, the cells of the map belonging in whole or in part to an angular sector starting from the current position of the aircraft and having its opening turned towards the route followed by the aircraft. Indeed, the fact of removing from any obstacle these cells makes it possible to leave free, at the level of the current position of the aircraft and therefore of the pixel taken as the origin of the distance measurements, one or more axes of propagation of the chamfer distance transform having orientations close to that of the movement of the aircraft, which increases the possibilities of drawing, in the vicinity of the current position of the aircraft, therefore of the source pixel, for the paths going from the target pixels to the source pixel and reinforces the chances of quickly finding a path of minimum length during the sweep carried out by the chamfer mask. The angular sector of delimitation of the cells left free to propagate is chosen to be that of the angular sectors delimited, by the bisectors of the angles formed by the axes of propagation plotted at the level of the pixel closest to the current position of the aircraft, taken as source pixel, origin for distance measurements, having the orientation closest to that of the movement of the aircraft. FIG. 10 shows part of the beam of the propagation axes defined by the pixels of the image concerned by the upper right quarter of the chamfer mask of FIG. 2 applied to the pixel COO taken as the origin of the distance measurements since it is assumed to be the closest the current position of the aircraft. We distinguish the first row pixels C01 and C10 next to the pixel in COO analysis on the same row or the same column, the second row pixel C11 next to the pixel in COO analysis on the first diagonal, the third row pixels C12 and C21 immediate neighbors of the pixel in COO analysis but neither on the same line, nor on the same column and neither on the same diagonal thereof. The various orientations of these first, second and third rank pixels C01, C10, C11, C12, C21, immediate neighbors of the pixel in COO analysis define the only possible directions of propagation for the distance transform in the upper right quarter of the mask. chamfer in fact the northeast quarter for a map image with the top facing north and the right facing east. These five directions of propagation represented in FIG. 10 by strong and arrowed lines complement each other by horizontal and vertical symmetries. The direction D0 of the propagation of the pixel COO in analysis towards the pixel C10 of first rank on the same column serves as angular reference and corresponds, in the language of chess, to a movement of a tower. The direction D1 of the propagation of the pixel COO in analysis towards the third row pixel C21 arranged on different row, column and diagonal is angularly the closest to the direction DO. With a regular mesh of pixels, that is to say in the absence of anisotropy of the map image, it makes an angle of 26.5 degrees relative to the latter and corresponds in the language of the game d failure of a jumper's movement. The direction D2 of the propagation of the pixel COO in analysis towards the pixel C11 of second rank on the same diagonal is a little further apart. In the absence of anisotropy of the map image, it makes an angle of 45 degrees relative to the reference direction DO. It corresponds in the language of chess to a movement of a madman. The direction D3 of the propagation of the pixel COO in analysis towards the third row pixel C12 arranged on different row, column and diagonal is even further apart. In the absence of anisotropy of the image, it makes an angle of 63.5 degrees relative to the reference direction DO. In the language of chess it corresponds to a movement of a rider. Finally the direction D4 of the propagation of the COO pixel in analysis towards the first rank pixel C01 on the same line is the most distant and makes an angle of 90 degrees relative to the reference direction D. It corresponds in the language of the game of failure to move a tower. The bisectors of the angles formed by these five directions of propagation D0, D1, D2, D3 and D4 cut in the upper right quarter of the chamfer mask five circular sectors centered on the pixel COO in analysis and turned in the five directions of propagation namely : - an angular sector called C10 turn because it is oriented towards the pixel C10, in the direction D0 corresponding to the movement of a tower, - an angular sector called C21 jumper because it is oriented towards the pixel C21, in the corresponding direction D1 to the movement of a jumper, - an angular sector called C11 crazy because it is oriented towards the pixel C11, in the direction D2 corresponding to the movement of a madman, - an angular sector called C12 jumper because it is oriented towards the pixel C12 , in the direction D3 corresponding to the movement of a jumper, and - an angular sector called C01 turn because it is oriented towards the pixel C01, in the direction D4 corresponding to the movement of a tower. The following table lists these five angular sectors:
Ainsi, avec un aéronef en mouvement en direction du quart haut droit de la carte, on choisit celui de ces cinq secteurs angulaires dont l'orientation correspond au mieux à celle de la route de l'aéronef. Dans le cas d'une l'image de carte extraite d'une base de données d'élévation du terrain à maillage régulier en longitude et en latitude de la surface terrestre, il est préférable de tenir compte de l'anisotropie introduite par le resserrement progressif des méridiens en directions des pôles. En effet, comme le montrent les figures 11 et 12, une telle carte présente un maillage de cellules de largeur variable, passant d'une forme carrée au niveau de la latitude 0° (figure 11 ) à une forme nettement rectangulaire au niveau de la latitude 53° (figure 12) impliquant qu'un aéronef suivant une même orientation de route (track) à la même vitesse sol ne franchit pas les mêmes cellules dans le même temps. Pour tenir compte de cette anisotropie dont l'importance varie en fonction de la latitude, on propose d'étirer artificiellement la carte pour ramener son maillage de cellules à une forme carrée. Comme montré à la figure 13, le vecteur unitaire de l'axe des ordonnées du repère d'orientation n'est pas touché par cet etirement réalisé dans une direction qui lui est perpendiculaire. Le vecteur unitaire de l'axe des ordonnées avant etirement YEart reste égal au vecteur unitaire YGΠCI après etirement tandis que le vecteur unitaire de l'axe des abscisses avant etirement XEarth se retrouve, après etirement, dilaté dans la proportion de 1/cos(Latitude) : Λ YGrid Y Earth Gric_ cos(Latitude)Thus, with an aircraft moving in the direction of the top right quarter of the map, one chooses that of these five angular sectors whose orientation corresponds best to that of the route of the aircraft. In the case of a map image extracted from a terrain elevation database with regular mesh in longitude and latitude of the earth's surface, it is preferable to take into account the anisotropy introduced by the tightening progressive meridians in direction of the poles. Indeed, as shown in FIGS. 11 and 12, such a map has a mesh of cells of variable width, passing from a square shape at the level of the 0 ° latitude (FIG. 11) to a clearly rectangular shape at the level of the 53 ° latitude (Figure 12) implying that an aircraft following the same route orientation (track) at the same ground speed does not cross the same cells at the same time. To take account of this anisotropy, the importance of which varies according to the latitude, it is proposed to artificially stretch the map to reduce its mesh of cells to a square shape. As shown in FIG. 13, the unit vector of the axis of the ordinates of the orientation frame is not affected by this stretching carried out in a direction which is perpendicular thereto. The unit vector of the ordinate axis before stretching YEart remains equal to the unit vector Y GΠC I after stretching while the unit vector of the abscissa axis before stretching XEarth is found, after stretching, dilated in the proportion of 1 / cos (Latitude): Λ YGrid Y Earth Gric_ cos (Latitude)
Il en résulte que la nouvelle orientation de la route de l'aéronef à prendre en considération après l'étirement (TrackOnGrid) est liée à l'orientation réelle de la route de l'aéronef (Track) par la relation :As a result, the new orientation of the aircraft route to be taken into account after the stretch (TrackOnGrid) is linked to the actual orientation of the aircraft route (Track) by the relation:
TrackOnGrid TrackOnGrid
Bien évidemment, lorsqu'il est appliqué à des aéronefs, le procédé d'estimation de distance curviligne qui vient d'être décrit, tient compte du profil vertical de vol, les contours des obstacles à contourner étant mis à jour en fonction du temps de parcours des trajets testés lors de la recherche des plus courts chemins dont les longueurs sont prises pour estimations des distances, afin de tenir compte de l'altitude atteinte à chaque instant déduite du profil vertical du vol. Obviously, when applied to aircraft, the method of estimating curvilinear distance which has just been described, takes account of the vertical flight profile, the contours of the obstacles to be circumvented being updated as a function of the time of route of the routes tested when searching for the shortest routes, the lengths of which are taken to estimate distances, in order to take account of the altitude reached at each instant deduced from the vertical profile of the flight.

Claims

REVENDICATIONS
1. Procédé d'estimation de distance curviligne au sein d'une zone où évolue un mobile à manœuvrabilité limitée et qui renferme des obstacles éventuels à contourner, zone dite zone d'évolution, dans lequel est établie une carte de distances couvrant la zone d'évolution et ayant pour origine des mesures de distance la position instantanée (S) du mobile, caractérisé en ce qu'il consiste, lors de l'établissement de la carte de distances, à compléter les obstacles éventuels à contourner (10, 11) par un obstacle supplémentaire à contourner (20) placé au voisinage du mobile et lié au mobile, répertoriant des étendues du proche voisinage du mobile, considérées comme inaccessibles pour le mobile du fait de sa manœuvrabilité limitée. 1. Method for estimating a curvilinear distance within an area where a mobile with limited maneuverability operates and which contains possible obstacles to be circumvented, an area known as the evolution area, in which a distance map covering the area d '' evolution and originating from distance measurements the instantaneous position (S) of the mobile, characterized in that it consists, during the establishment of the distance map, in completing any obstacles to be circumvented (10, 11) by an additional obstacle to be circumvented (20) placed in the vicinity of the mobile and linked to the mobile, listing areas in the immediate vicinity of the mobile, considered as inaccessible for the mobile because of its limited maneuverability.
2. Procédé selon la revendication 1 , caractérisé en ce que l'obstacle supplémentaire (20) est de forme concave et disposé dans le voisinage de la position instantanée (S) du mobile de manière que sa concavité soit tournée dans la direction du déplacement du mobile et englobe la position instantanée (S) du mobile.2. Method according to claim 1, characterized in that the additional obstacle (20) is of concave shape and arranged in the vicinity of the instantaneous position (S) of the mobile so that its concavity is turned in the direction of movement of the mobile and includes the instantaneous position (S) of the mobile.
3. Procédé selon la revendication 1 , caractérisé en ce que l'obstacle supplémentaire (20) a une forme en U, l'ouverture du U étant tournée dans la direction du déplacement du mobile et englobant la position instantanée (S) du mobile3. Method according to claim 1, characterized in that the additional obstacle (20) has a U-shape, the opening of the U being rotated in the direction of movement of the mobile and encompassing the instantaneous position (S) of the mobile
4. Procédé selon la revendication 1 , caractérisé en ce que l'obstacle supplémentaire a une forme de demi-lune, l'ouverture de la demi- lune étant tournée dans la direction de déplacement du mobile et englobant la position instantanée (S) du mobile.4. Method according to claim 1, characterized in that the additional obstacle has the shape of a half-moon, the opening of the half-moon being turned in the direction of movement of the mobile and including the instantaneous position (S) of the mobile.
5. Procédé selon la revendication 1 , caractérisé en ce que l'obstacle supplémentaire (figures 7, 87, 9) a une forme à deux lobes en aile de papillon, placés de part et d'autre de la position instantanée (S) du mobile et ayant une tangente commune orientée dans la direction de déplacement du mobile. 5. Method according to claim 1, characterized in that the additional obstacle (Figures 7, 87, 9) has a shape with two lobes in butterfly wing, placed on either side of the instantaneous position (S) of the mobile and having a common tangent oriented in the direction of movement of the mobile.
6. Procédé selon la revendication 1, caractérisé en ce que, lorsque le mobile est un aéronef, le contour de l'obstacle supplémentaire comporte des parties correspondant aux projections au sol de deux cercles (30, 31 ) liés à l'aéronef, ayant un rayon égal au rayon de courbure du virage le plus serré admis pour l'aéronef au moment considéré.6. Method according to claim 1, characterized in that, when the mobile is an aircraft, the contour of the additional obstacle comprises parts corresponding to the projections on the ground of two circles (30, 31) linked to the aircraft, having a radius equal to the radius of curvature of the tightest turn allowed for the aircraft at the time considered.
7. Procédé selon la revendication 1 , caractérisé en ce que, lorsque le mobile est un aéronef soumis à un vent de travers, le contour de l'obstacle supplémentaire comporte des parties de cycloïde (figure 7) correspondant aux projections au sol de deux cercles (30, 31) liés à l'aéronef, ayant un rayon égal au rayon de courbure du virage le plus serré admis pour l'aéronef au moment considéré.7. Method according to claim 1, characterized in that, when the mobile is an aircraft subjected to a cross wind, the contour of the additional obstacle comprises cycloid parts (FIG. 7) corresponding to the projections on the ground of two circles (30, 31) linked to the aircraft, having a radius equal to the radius of curvature of the tightest turn allowed for the aircraft at the time considered.
8. Procédé selon la revendication 1 , caractérisé en ce que, lorsque le mobile est un aéronef soumis à un vent de travers, le contour de l'obstacle supplémentaire consiste en deux lobes de cycloïde (40, 40") limités à leurs parties allant de leur point de départ, qui est la position instantanée (S) de l'aéronef, à leur deuxième intersection (P, P') avec des droites (41 , 41 ') allant de la position instantanée (S) de l'aéronef à des positions virtuelles (P, P') sur les lobes de cycloïdes ( 40, 40') correspondant pour l'aéronef à un angle de changement de route arbitraire.8. Method according to claim 1, characterized in that, when the mobile is an aircraft subjected to a cross wind, the contour of the additional obstacle consists of two cycloid lobes (40, 40 ") limited to their parts going from their starting point, which is the instantaneous position (S) of the aircraft, at their second intersection (P, P ') with straight lines (41, 41') going from the instantaneous position (S) of the aircraft at virtual positions (P, P ') on the cycloid lobes (40, 40') corresponding for the aircraft to an arbitrary course change angle.
9. Procédé selon la revendication 1, caractérisé en ce que, lorsque le mobile est un aéronef soumis à un vent de travers, le contour de l'obstacle supplémentaire consiste en deux lobes de cycloïde (40, 40') limités à leurs parties allant de leur point de départ, qui est la position instantanée (S) de l'aéronef, à leur deuxième intersection (P, P') avec des droites (41 , 41') allant de la position instantanée (S) de l'aéronef à des positions virtuelles (P, P') sur les lobes de cycloïdes correspondant pour l'aéronef à un angle de changement de route de 180 degrés.9. Method according to claim 1, characterized in that, when the mobile is an aircraft subjected to a cross wind, the contour of the additional obstacle consists of two cycloid lobes (40, 40 ') limited to their parts going from their starting point, which is the instantaneous position (S) of the aircraft, at their second intersection (P, P ') with straight lines (41, 41') going from the instantaneous position (S) of the aircraft at virtual positions (P, P ') on the cycloid lobes corresponding for the aircraft to a course change angle of 180 degrees.
10. Procédé selon la revendication 1 , caractérisé en ce que, lorsque le mobile est un aéronef soumis à un vent de travers et la carte de distances établie dans un repère géographique utilisant les longitudes et les latitudes, le contour de l'obstacle supplémentaire (figure 7) présente deux parties (40, 40') en lobes de cycloïde répondant au système d'équations paramétriques : fxλ WSXg.t-δ.R.cos(wt+yg) + CXg ') V Λ WSYg .t + R. sin(wt + γ g ) + CYg x et y étant les coordonnées abscisse et ordonnée d'un point dans le repère géographique de la carte de distances, étant le vecteur vent exprimé dans le repère géographique de la10. Method according to claim 1, characterized in that, when the mobile is an aircraft subjected to a cross wind and the distance map established in a geographical reference using the longitudes and the latitudes, the contour of the additional obstacle ( figure 7) presents two parts (40, 40 ') in cycloid lobes corresponding to the system of parametric equations: fxλ WS Xg .t-δ.R.cos (wt + y g ) + C Xg ' ) V Λ WS Yg .t + R. sin (wt + γ g ) + C Yg x and y being the abscissa and ordered coordinates of a point in the geographical coordinate system of the distance map, being the wind vector expressed in the geographical coordinate system of the
carte de distances, avec TAS2 R =- #- tan φro„ TAS £.tanφroβ w = R TASdistance map, with TAS 2 R = - # - tan φ ro „TAS £ .tanφ roβ w = R TAS
TAS étant l'amplitude de la vitesse air de l'aéronef, φr0ιι étant l'angle de roulis de l'aéronef pendant la manœuvre, γ étant un facteur dépendant des conditions initiales, δ étant un coefficient égal à +1 pour un virage à droite et -1 pour un virage à gauche, et avec C^ ^ Long + 8Λ.cos(yg) CYg = Lat - R.sia(y g) y g ='δ Heading + kll long étant la longitude de la position instantanée de l'aéronef, lat étant la latitude de la position instantanée de l'aéronef, et heading étant le cap de l'aéronef.TAS being the amplitude of the air speed of the aircraft, φ r0 ιι being the roll angle of the aircraft during the maneuver, γ being a factor depending on the initial conditions, δ being a coefficient equal to +1 for a right turn and -1 for a left turn, and with C ^ ^ Long + 8Λ.cos (y g ) C Yg = Lat - R.sia (y g ) y g = 'δ Heading + kll long being the longitude of the instantaneous position of the aircraft, lat being the latitude of the instantaneous position of the aircraft, and heading being the heading of the aircraft.
11. Procédé selon la revendication 1 , caractérisé en ce que l'obstacle supplémentaire tenant compte des limites de manœuvrabilité du mobile est privé de la surface d'un secteur angulaire libre partant du mobile et ayant son ouverture tournée dans la direction du mouvement du mobile.11. Method according to claim 1, characterized in that the additional obstacle taking into account the maneuverability limits of the mobile is deprived of the surface of a free angular sector starting from the mobile and having its opening turned in the direction of movement of the mobile.
12. Procédé selon la revendication 11, caractérisé en ce que, lorsque la carte de distances se présente sous la forme d'une grille de cellules correspondant aux éléments d'une base de données d'élévation du terrain maillant le terrain d'évolution du mobile, l'obstacle supplémentaire tenant compte des limites de manœuvrabilité du mobile est privé des cellules recouvertes en totalité ou en partie le secteur angulaire libre.12. Method according to claim 11, characterized in that, when the distance map is in the form of a grid of cells corresponding to the elements of a terrain elevation database meshing the terrain of evolution of the mobile, the additional obstacle taking into account the maneuverability limits of the mobile is deprived of the cells covered in whole or in part the free angular sector.
13. Procédé selon la revendication 11, caractérisé en ce que, lorsque la carte de distances résulte de l'application, aux pixels d'une image formée par une carte tirée d'une base de données d'élévation du terrain, d'une transformée de distance qui utilise un masque de chanfrein répertoriant les distances d'un pixel en analyse par rapport aux pixels les plus proches dits pixels du voisinage et qui a des axes de propagation (DO, D1, D2, D3, D4) orientés comme les directions des pixels du voisinage par rapport au pixel en analyse dans le masque de chanfrein, le secteur angulaire libre a son ouverture orientée selon l'axe de propagation (DO, D1, D2, D3 ou D4) le plus proche de la direction du mouvement du mobile.13. Method according to claim 11, characterized in that, when the distance map results from the application, to the pixels of an image formed by a map drawn from a terrain elevation database, of a distance transform which uses a chamfer mask listing the distances of a pixel in analysis with respect to the nearest pixels known as neighboring pixels and which has propagation axes (DO, D1, D2, D3, D4) oriented as directions of the pixels of the neighborhood with respect to the pixel analyzed in the chamfer mask, the free angular sector has its opening oriented along the axis of propagation (DO, D1, D2, D3 or D4) closest to the direction of movement of the mobile.
14. Procédé selon la revendication 12, caractérisé en ce que le secteur angulaire libre de propagation est délimité par des bissectrices des angles formés par les axes de propagation (D0, D1, D2, D3, D4). 14. Method according to claim 12, characterized in that the angular sector free of propagation is delimited by bisectors of the angles formed by the axes of propagation (D0, D1, D2, D3, D4).
EP05707976A 2004-03-05 2005-02-09 Curvilinear distance estimation method for a moving vehicle with limited maneuverability Withdrawn EP1721124A1 (en)

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IL177287A0 (en) 2006-12-10
WO2005095888A1 (en) 2005-10-13

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