A method for defining a fall back route comprising of way points, for a mobile machine, in a 3D zone (ZNd) of displacement having convex zones (Zni, i=1 to 7) such that over a considered region (Hj, j=1 to 6) of a Z axis, said zones each describe a polygon in any plane perpendicular to a Z axis, said method being characterised in that it is implemented on a computer and in that it comprises the following steps i/ to ii/ relative to said region of the Z axis, in considering any plane perpendicular to the Z axis over said region:
- i/ defining a set of points (PBk, k=1 to 7), referred to as beacons points for the fall back route, such that the edges of the Voronoi diagram associated with said set of beacon points separate therebetween the polygons described by the convex zones in said plane;
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- ii/ in a database, associating with each way point of the fall back route and each beacon point of the route, an identifier of the convex zone to which said point belongs, coordinates of said point and for each beacon point, an identifier of the said region of the Z axis.