CN109507877B - Aircraft trajectory planning safety evaluation method - Google Patents
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Abstract
The invention discloses a safety evaluation method for aircraft trajectory planning, which utilizes a plane ray method to process dropped remains and a forbidden landing area in the rocket launching process, and processes the intersection problem of a trajectory and a space forbidden flight area through bounding box collision detection and space separation axis determination, thereby realizing safety evaluation and trajectory availability detection before rocket launching. The method greatly improves the accuracy of judgment, simplifies calculation and improves efficiency.
Description
Technical Field
The invention relates to a safety evaluation method for aircraft trajectory planning, and belongs to the technical field of rocket trajectory planning and wreckage safety evaluation in the aviation and aerospace field.
Background
The debris falling area is a possible falling point area formed on the ground by the free falling motion of each stage of rocket of the ballistic missile after the work is finished and the rocket body is separated from the main rocket body. The no-landing area is a preset area on the ground, which may be composed of cities, industrial areas, military areas and the like. The debris falling area safety analysis process can be modeled as intersection judgment of a plurality of areas on the earth cambered surface and probability of falling into a non-falling area, because of improvement of the range of the existing medium-long distance missile and rocket, influence of the earth radian is required to be considered in the calculation and intersection judgment of the debris falling area and the non-falling area, meanwhile, a distribution law of the debris falling area is required to be considered, and the point is required to be considered in the calculation of the intersection probability.
When the intersection of a plurality of regions of the earth cambered surface is judged, if a two-dimensional coordinate is directly constructed by longitude and latitude coordinates, because the longitude and latitude distribution is not uniform in practice, the error ratio is likely to be smaller under the condition that the range is smaller (for example, less than 10km), but in practical application, the span of the range is larger, sometimes the range can reach hundreds of kilometers, and under the condition, if the unevenness of the longitude and latitude coordinates is ignored, the judgment result is not credible, so that an efficient and accurate projection rule is required to be adopted to project the points on the earth cambered surface to a two-dimensional plane for intersection judgment. During probability calculation, generally, debris falling in a debris falling area can be in mean distribution or normal distribution, normal distribution in the two distribution laws is more consistent with practical conditions, rocket debris can make inclined projectile motion within a certain time after separation of a projectile body and is influenced by uncertainty and is more consistent with structural characteristics of normal distribution, but probability calculation of two-dimensional normal distribution is often low in efficiency and troublesome in realization, and therefore certain optimization is required under the condition of no precision loss.
The safety analysis of the track space area mainly considers whether a ballistic missile flight corridor passes through a space area near the earth surface, wherein the space area comprises an enemy air defense area, a no-fly area and the like. Modeling the problem as a mathematical problem may be understood as determining whether two spatial cubes intersect. The detection of the spatial convex polyhedron usually adopts a method of replacing an original object with an approximate geometric body so as to improve the efficiency and simplify the operation, the selection of the type of the bounding box is the key of a hierarchical bounding box method, and the bounding box for the detection of the collision is generally restricted by simplicity and compactness. Commonly used Bounding boxes are the Axis-Aligned Bounding Box AABB (Axis-Aligned Bounding Box, AABB for short), the Sphere Bounding Box (Sphere), the directional Bounding Box OBB (Oriented Bounding Box, OBB for short), and the k-caps (Dis-tangent-Oriented polyesters, Dops for short). The direction bounding volume is specifically defined and solved: the square bounding box for a given object is defined as the smallest cuboid containing the object and arbitrarily oriented with respect to the coordinate axes. The computational key to the directional bounding volume is to find the best direction and determine the minimum size of the bounding box that encloses the object in that direction. Therefore, the method for calculating the direction bounding volume in the general application occasion mainly utilizes the first-order and second-order statistical characteristics of the vertex coordinates to firstly calculate the mean value mu of the vertex distribution, and then calculates the covariance matrix C by taking the mean value mu as the center of the bounding box. The covariance matrix C is a real symmetric matrix, three eigenvectors of which are orthogonal, and which can be used as a base after normalization to determine the direction of the direction bounding volume, and the maximum value and the minimum value of the vertex of each element in the three axial directions of the base are respectively calculated to determine the size of the direction bounding volume.
The above method for determining whether there is an intersection between three dimensions is widely used in civil fields, such as engineering and mechanical modeling, game engine production, and the like. The method has certain high efficiency and better portability, and has the best effect under the constraint of compactness and complexity. But also have problems such as loss of precision (relative to the target body, which has certain advantages over conventional bounding balls and axis alignment bounding bodies), higher complexity, etc.
Disclosure of Invention
The technical problem to be solved is as follows:
aiming at the defects in the prior art, the invention provides an aircraft trajectory planning safety evaluation method, which aims at the problems of ground debris falling areas and forbidden falling areas, reasonable conversion and projection are carried out on the basis of initial data to eliminate the influence of the radian of the earth, and the reliability of safety judgment is improved; when the problem of normal distribution probability calculation is processed, a similar segmentation idea is adopted, the areas are divided into blocks, values are assigned and then added to simplify the calculation process, and the efficiency is improved; certain conversion is carried out on the ballistic data, and a better intersection test stereo is obtained with the minimum precision loss; and determining the center of the enclosure by adopting a projection-based algorithm so as to improve the compactness to the maximum extent and obtain the enclosure stereo of the minimum flight-forbidden region.
The technical scheme adopted for solving the technical problem is as follows:
an aircraft trajectory planning safety assessment method is characterized in that: the method comprises the following steps:
(1) selecting a first point of a polygon in the debris falling area as a tangent point to make a tangent plane;
(2) projecting the debris falling area and the non-falling area to the tangent plane;
(3) determining the intersection point of the debris falling area and the forbidden falling area by using a correlation algorithm of plane geometry;
(4) combining the debris falling area according to certain logic, wherein the forbidden falling area and the intersection point form an intersection area, namely a dangerous area;
(5) establishing an external rectangle for the polygon of the debris falling area and establishing a two-dimensional normal distribution law by taking the rectangular area as a reference;
(6) dividing the rectangular area into NxN small blocks to be recorded as unit areas, and calculating and storing corresponding probability of each unit area according to coordinates;
(7) calculating the number of unit areas contained in the debris falling area, summing the number of the unit areas and recording the sum as P1, calculating the number of the unit areas contained in the intersection area and summing the number as P2, wherein P2/P1 is the intersection probability of the debris falling area and the non-falling area;
(8) sequentially selecting two adjacent points on the trajectory as datum points, and solving a separation axis;
(9) the two points are connected by one axis, namely an axis, and the other axis is parallel to a certain plane of the geocentric coordinate system and is vertical to the axis;
(10) solving a third axis according to the definition that the separating shafts are mutually vertical;
(11) acquiring the radius of the surrounding solid according to the uncertainty of the ballistic trajectory;
(12) selecting an origin of geocentric coordinates or a certain vertex of a polyhedron as a reference point;
(13) projecting each vertex of the polyhedron in three axial vector directions, and storing projection values;
(14) screening the minimum and maximum projection values in each direction and making a difference, wherein the difference is the minimum surrounding solid radius;
(15) based on the radius, establishing projection equations of the coordinates of the central point in three directions, and solving the equations;
(16) and judging whether an intersection exists according to the separation axis theorem after the surrounding solid of the aircraft trajectory and the flight forbidden region is obtained.
Further, the algorithm related to the plane geometry in the step (3) is ray method, straddle experiment or fast exclusion experiment.
Further, N is more than or equal to 100 in the step (6).
Compared with the prior art, the invention has the following beneficial effects:
according to the method, the plane and the solid geometry are applied to rocket wreckage and trajectory safety analysis in the aerospace field, deformation and adaptability improvement are performed according to specific conditions aiming at an original algorithm, the judgment accuracy is improved, the calculation is simplified, and the efficiency is improved;
1. by the method, the complexity of processing on the spherical surface is avoided and the precision is considered at the same time by the projection of the debris falling area and the forbidden falling area, the error is reduced, the judgment accuracy is improved, and the purpose of quickly judging whether the debris falling area and the forbidden falling area are intersected or not and acquiring an intersection area is realized;
2. when the intersection probability is processed, equivalent replacement processing is carried out on the more complex two-dimensional normal distribution, and integration is replaced by a fixed value among cells, so that the accuracy and the accuracy are both considered, the calculation is simplified, the efficiency is improved, and the intersection probability of the debris falling area and the forbidden falling area is accurately obtained;
3. in the aspect of conversion of the ballistic model, the method avoids the mode of dividing the cylindrical surface and replacing the cylindrical surface with a polygon, so that the calculation process is simplified, the loss of precision is reduced, and the ballistic model is classified under the same geometric parameters with the flight forbidden area, thereby being beneficial to the subsequent calculation and test;
4. the method optimizes the compactness of the radius and the center point, greatly improves the judgment precision and accuracy, and can avoid the situation of no solution caused by overlarge margin during the safety judgment of the rocket trajectory and the space flight-forbidden area to a certain extent.
Drawings
FIG. 1 is a schematic diagram of a method for evaluating the security of a debris falling area and a forbidden falling area and calculating the intersection probability.
Fig. 2 is a schematic diagram of a rocket trajectory and flight-forbidden zone safety assessment method.
Fig. 3 is a schematic projection of the earth's curved surface.
Fig. 4 is a schematic view of intersection region acquisition.
Fig. 5 is a two-dimensional normal distribution function.
FIG. 6 is a probability distribution diagram of a debris landing area.
FIG. 7 is a probability distribution of a debris landing area and a forbidden landing area
Fig. 8 is a schematic diagram of the safety determination of the rocket trajectory and the flight-forbidden region.
Figure 9 is a schematic view of a rocket ballistic enclosure.
Fig. 10 is a schematic diagram of a ground flight-avoiding area surrounding stereo construction.
FIG. 11 is a schematic view of a bounding volume center point error.
Fig. 12 is a schematic diagram of the determination of the optimal center point of the surrounding solid.
Fig. 13 is a schematic projection view of a surrounding stereographic center point.
Fig. 14 is a schematic diagram of rocket trajectory and ground flight-forbidden zone safety evaluation.
Figure 15 is a schematic diagram of rocket trajectory and flight-forbidden zone planning.
Detailed Description
1. And (3) carrying out safety evaluation on the debris falling area and the forbidden falling area:
when the safety of the debris falling area is judged, spherical data with longitude and latitude as coordinates are input, firstly, the spherical data are mapped onto a plane, and the judgment is carried out through relevant geometric operation in the plane. By adopting a projection transformation mapping mode, obviously, when the projection surface is approximately parallel to the arc surface surrounded by the debris falling area, the error caused by projection is smaller. Therefore, a point can be arbitrarily selected from the arc surface where the debris falling area is located, and the tangent plane of the point is selected from the spherical surface as a projection plane, so that higher projection precision can be ensured.
Making any point B ═ x on the sphereB,yB,zB) And a vertical line to the tangent plane, wherein the vertical foot on the tangent plane is a vertical projection point B' of the point B on the tangent plane.
The tangent plane point method is that A ═ x0,y0,z0)，
The projected point B' coordinates are calculated as follows:
as can be seen from fig. 3, the projection of the spherical surface to the tangent plane does not correspond to one completely, and there are always two points on the spherical surface whose projection points on the tangent plane coincide, and these two points are distributed in two different hemispheres of the earth. Since we do not need to project the entire earth onto a plane, at most only the "nearest" half of the earth will be projected.
In practice, it is not possible to set the distance D from any point on the spherical surface to the tangent plane, e.g. for point B
A threshold value D may be setmaxWhen D > DmaxNo projection is needed, so that a "bowl-shaped" area centered on point a on the sphere is projected. DmaxThe selection can be determined according to the maximum D value of the projection of each boundary point of the debris falling area, and D is selectedmaxPreferably, the k value is within 3-10 as a proportionality coefficient kD, and needs to be determined according to the actual size scale of the debris falling area. During projection, if a projection of a boundary point in an avoidance area satisfies that D is less than or equal to DmaxThe entire avoidance area is projected.
Processing the projected debris falling area and the flight-forbidden area by adopting some algorithms of plane geometry to obtain an intersection area, and the specific steps are as follows:
(1) determining the intersection point of two polygonal areas and the polygon vertex in the areas by using a quick exclusion experiment, a straddle experiment and a ray method, wherein if the areas have no intersection point, the evaluation result is safe without a subsequent calculation step;
(2) the polygon of the intersection region can be obtained by combining the above points according to a certain logic sequence, as shown in the following figure:
in the blue region a2b2c2d2As a reference, from b2Start, b2a2And a1f1Intersect at k1And b is2At a1b1c1d1f1Inside, f1At a2b2c2d2Internally, so store b in order2，k1，f1Three points, a second2d2And f1d1，d1c1Intersect at k2，k3And f is1At a2b2c2d2Internally, so store f1，k2，k3Three points, according to which the points b can be obtained in sequence2,k1,f1,k2,k3,k4；
(3) And (3) sequentially splicing the points acquired according to the algorithm in the step (2) to acquire an intersected polygonal area. 2. Intersection probability calculation
The two-dimensional normal distribution is a two-dimensional probability distribution on a plane, and the probability in the double integral region D is:
taking fig. 5 as an example, it can be seen that the probability of the two-dimensional normal distribution can be understood as follows: if an integral area D in the XY plane is vertically upwards stretched and the volume of a space cube enclosed by the density curved surface is VDIf the total volume V formed by the volume and density curved surface and the XY plane is V, the probability of the integration region D is
This is also a practical sense of double integration.
The approximate calculation method adopted by the invention adopts the thought, the integral region D is supposed to be subdivided into countless small grids, the area of each small grid is gridArea, one characteristic point is selected in each small grid, and the probability density f (x) corresponding to the characteristic point is calculatedi,yi) Then the small grid corresponds to the probability Pgrid≈gridArea·f(xi,yi) The small grid area gridArea corresponds to the bottom area of the rectangular parallelepiped, f (x)i,yi) Is equivalent to the height of a cuboid, provided that the grids are sufficiently thin
The theoretical basis of the method is that
After binary series expansion, only low-order terms are considered, and high-order terms are ignored.
Let u1＝0,σ1 2＝1，μ2＝0,σ 2 21, rho 0 is standard two-dimensional normal distribution, and the density calculation formula is fs(x, y), the steps of calculation are as follows:
inputting: polygon region polygon of debris falling region, intersection polygon region D of debris falling region and edge region
(1) Solving the maximum and minimum values of the polygon in the input debris falling area on the X axis and the Y axis, establishing a minimum enclosing rectangle minRect with the lower left point of (X)min,ymin) The upper right point is (x)max,ymax）；
(2) By the center point of minRect
Establishing two-dimensional normal distribution, and taking X on X axisσTaking Y on sigma, Y axisσσ (generally take x)σ＝yσ＝6)。
(3) Establishing a conversion equation to the standard distribution, and converting the values on the plane into the standard two-dimensional normal distribution:
for the standard distribution, the last σ of the above equation is omitted since σ is 1. The above formula is such that xminCorrespond to
xmaxCorrespond to
yminCorrespond to
ymaxCorrespond to
The method can be converted to a standard two-dimensional normal distribution coordinate system for any point in the original polygon coordinate system.
(4) Dividing the minimum envelope rectangle minRect into N equal parts in X-axis and Y-axis directions, respectively, to obtain N × N squares
The area is dxdy; in the standard two-dimensional normal coordinate system,
(5) take the midpoint (x) of each squareci,yci) Converting the characteristic points of the square into a standard coordinate system: (x)ci_standard,yci_standard) If the midpoint (x)ci,yci) In the integration region D (not the debris fall region polygon, but the intersection region of the debris fall region and the avoidance region is the integration region D, as { k' in FIG. 72,b0,c0,k1}), calculate fs(xci_standard,yci_standard)dxstandarddystandardThe probability of the grid area;
(6) and superposing all the calculated grid probabilities, namely the probability of the integral area D.
3. Ballistic enclosure volumetric construction
The trajectory is composed of discrete passing points acquired during the flight of the projectile, and together with the uncertainty of each position, forms a spatial cylinder, as shown in fig. 8:
b is a cylinder formed by the trajectory and uncertainty thereof, and a certain section is selected from the following figures and is described as follows:
assuming that the projectile body passes through two points B _ pt1 and B _ pt2, and the uncertainty is R, a cylinder can be formed, the center of the cylinder is point O, which is the midpoint of the connecting line between B _ pt1 and B _ pt2, and according to the construction principle of bounding volume, the center of the cylinder bounding box is point O, and the three axial vectors are respectively denoted as bbox.axis1, bbox.axis2, bbox.axis, 3. In fact, since the directions of the bbox.axis1 and bbox.axis2 are not determined in the plane perpendicular to the axial direction as long as they are perpendicular to each other, as shown by the imaginary axis (left drawing) in fig. 9, for the sake of simplification of the calculation, the bbox.axis1 is specified to be located in the horizontal plane of the geocentric coordinate system (parallel to the XOY plane), that is, the Z coordinate is 0, as shown in fig. 9, and thus the three axial unit vectors can be obtained by making the inner product of the mutually perpendicular vectors 0
Note the book
The coordinates are respectively (x)1,y1,z1)，(x2,y2,z2)， (x3,y3,z3)
Because the B _ pt1 and B _ pt2 coordinates are known,
and then unitizing the materials:
because of the fact that
And
perpendicular, so there are:
Also known is z1When the axial vector is 0 and the unit vectors are all axial vectors, the following equation system can be obtained:
to obtain
And also
Then, the vector cross product formula is used to obtain
The 3 axial vectors are stored in a 3 x 3 array.
The central point of the B-surrounding solid is the midpoint of a connecting line between B _ pt1 and B _ pt2, and the axial radiuses of the B-surrounding solid are corresponding to three axes respectively
R is obtained from the coordinate uncertainty (Δ x, Δ y, Δ z) at each point:
the surrounding solid with the smallest rocket trajectory can be obtained through the series of conversion.
4. Surrounding three-dimensional space for constructing flight-forbidden area
As in fig. 10, n boundary points (black dots) are read and converted to the geocentric coordinate system by the coordinate conversion formula:
the boundary points (black triangles) on the top surface are converted by the following equation:
thus, the data of the 2n coordinate points are stored into a 2n x 3 array, and then a covariance matrix is obtained by solving the mean value and the covariance:
the coordinates of the center point of the bounding box are the mean value of the coordinates of the 2n coordinate points:
the covariance is defined as:
the 3 × 3 covariance matrix is:
thus, three axial unit vectors C _ type vector 3 can be obtained according to an algorithm for solving the covariance matrix eigenvalue and the eigenvector, and then the three axial unit vectors C _ type vector 3 are stored in a 3 x 3 array A _ box.
Sequentially obtaining a 2n vector { (x) pointing from the bounding box center point to 2n pointsi-μx,yi-μy,zi-μz)|i∈[0,2n-1]H, sequentially projected for one of the axial vectors, assuming a first axis A _ box.axis [0 ]]: the projection values are:
Abox.axis[0][0]·(xi-μx)+Abox.axis[0][1]·(yi-μy)+Abox.axis[0][2]·(zi-μz)
and acquiring the maximum projection value as the axial radius in the axial direction, and acquiring the radius in three directions through the thought.
5. Mainly aiming at volume optimization of space flight-forbidden region
The prior algorithm mainly calculates the center of the box body by a method of directly calculating the mean value of the coordinates of the endpoints, and the method has small error when the points are uniformly distributed, but the situation that several endpoints are relatively close in the practical situation is considered, so the calculated center is biased to the relatively close points and is easy to cause larger error, as shown in the following figure:
in fig. 10, point a2 is the theoretical minimum bounding box center point, and point a1 is the calculated center point by the averaging method. As shown in fig. 10, the lower left point is more concentrated, if the method of obtaining the central point by averaging is adopted, the obtained central point a is close to the point locations with dense distribution, and on this basis, the maximum projection value in each direction is obtained to obtain the radius, as shown by the arrow pointing to the right end point of a1 in the figure and the dotted line of the projection thereof, the obtained radius is larger, and the thus obtained OBB bounding box is larger than the theoretical minimum value. In this case, it is easy to make it difficult to obtain a usable trajectory, and therefore, the optimization is performed here, and the result of the finding is shown in a smaller cube in fig. 10.
The basis of the solution is the covariance matrix, and a point must be determined here, that is, the eigenvector solved by the covariance matrix must be the direction of the theoretical minimum bounding box axis vector, which can be proved by the maximum variance theory and the minimum square error theory, and will not be described here again.
The principle is shown in the following diagram by a two-dimensional diagram:
the specific algorithm flow is as follows:
(1) the direction of the optimal radius (i.e., the axial radius) is determined by the covariance matrix, and coincides with the axial vector direction. Firstly, selecting a datum point (which can be selected randomly), wherein the origin of the geocentric coordinate system is taken as the datum point;
(2) and sequentially projecting the vector determined by each point and the origin of the no-fly zone on the three characteristic vectors to obtain the maximum value and the minimum value of the projection in each direction, and calculating the radius in the three directions by taking the difference between the maximum value and the minimum value. In the context of figure 11 of the drawings,
the point with the maximum direction projection is recorded as Amax1, the projection value is x1max, the point with the minimum direction projection is Amax2, the projection value is x1min, and the difference between the two is obtained
2 times the radius 2R1 of the direction.
(3) When the maximum and minimum projection values are obtained, the coordinates of the corresponding points of the no-fly zone are stored, the coordinates of the central point are set as x, y and z, the projection values of the vector determined by each maximum and minimum point and the central point in three directions are all radius values in the direction, so that a three-dimensional linear equation set of the central point is obtained, and then the equation is solved, as shown in fig. 12:
in which
For example, the center point a2 has coordinates of x, y, z,
the boundary points corresponding to the maximum value and the minimum value projected in the direction are Amax2 and Amax1 respectively, and the two points and the vector formed by A2 are positioned in
The projections of the directions are equal, that is, r1 ═ r2, so that a first equation about the coordinates (x, y, z) of a2 can be obtained, and equations in the other two directions can be obtained by the same method, and the system of equations in the three-element equation and the one-time equation can be solved.
After the surrounding solid of the rocket trajectory and the flight forbidding area is obtained, whether intersection exists can be judged according to the separation axis theorem (which is already stated in the background and is not described any more).
Although exemplary embodiments of the present invention have been described for illustrative purposes, those skilled in the art will appreciate that various modifications, additions, substitutions and the like can be made in form and detail without departing from the scope and spirit of the invention as disclosed in the accompanying claims, all of which are intended to fall within the scope of the claims, and that various steps in the various sections and methods of the claimed product can be combined together in any combination. Therefore, the description of the embodiments disclosed in the present invention is not intended to limit the scope of the present invention, but to describe the present invention. Accordingly, the scope of the present invention is not limited by the above embodiments, but is defined by the claims or their equivalents.
Claims (3)
1. An aircraft trajectory planning safety assessment method is characterized in that: the method comprises the following steps:
(1) selecting a first point of a polygon in the debris falling area as a tangent point to make a tangent plane;
(2) projecting the debris falling area and the non-falling area to the tangent plane;
(3) determining the intersection point of the debris falling area and the forbidden falling area by using a correlation algorithm of plane geometry;
(4) combining the debris falling area according to certain logic, wherein the forbidden falling area and the intersection point form an intersection area, namely a dangerous area;
(5) establishing an external rectangle for the polygon of the debris falling area and establishing a two-dimensional normal distribution law by taking the rectangular area as a reference;
(6) dividing the rectangular area into NxN small blocks to be recorded as unit areas, and calculating and storing corresponding probability of each unit area according to coordinates;
(7) calculating the number of unit areas contained in the debris falling area, summing the number of the unit areas and recording the sum as P1, calculating the number of the unit areas contained in the intersection area and summing the number as P2, wherein P2/P1 is the intersection probability of the debris falling area and the non-falling area;
(8) sequentially selecting two adjacent points on the trajectory as datum points, and solving a separation axis;
(9) the two points are connected by one axis, namely an axis, and the other axis is parallel to a certain plane of the geocentric coordinate system and is vertical to the axis;
(10) solving a third axis according to the definition that the separating shafts are mutually vertical;
(11) acquiring the radius of the surrounding solid according to the uncertainty of the ballistic trajectory;
(12) a construction and optimization process of a no-fly zone surrounding three-dimensional space;
(12.1) selecting a geocentric coordinate origin or a certain vertex of the polyhedron as a reference point;
(12.2) projecting each vertex of the polyhedron in three axial vector directions, and storing a projection value;
(12.3) screening the minimum and maximum projection values in each direction and making a difference, wherein the difference is the minimum surrounding solid radius;
(12.4) based on the radius, establishing projection equations of the vector determined by each maximum minimum point and the central point in three directions, and solving the equations;
storing coordinates of points of the no-fly zone corresponding to the maximum and minimum projection values when the maximum and minimum projection values are obtained, setting coordinates of a central point as x, y and z, wherein projection values of vectors determined by each maximum and minimum value point and the central point in three directions are radius values in the direction, so that a three-dimensional linear equation set of the central point is obtained and an equation is solved;
(13) and judging whether an intersection exists according to the separation axis theorem after the surrounding solid of the aircraft trajectory and the flight forbidden region is obtained.
2. The method of claim 1, wherein: and (4) performing ray method, straddle experiment or rapid exclusion experiment on the plane geometry related algorithm in the step (3).
3. The method of claim 1, wherein: n in the step (6) is more than or equal to 100.
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