CN108151746B - Improved label real-time airway re-planning method based on multi-resolution situation mapping - Google Patents

Improved label real-time airway re-planning method based on multi-resolution situation mapping Download PDF

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CN108151746B
CN108151746B CN201711441037.8A CN201711441037A CN108151746B CN 108151746 B CN108151746 B CN 108151746B CN 201711441037 A CN201711441037 A CN 201711441037A CN 108151746 B CN108151746 B CN 108151746B
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李�杰
牛轶峰
尹栋
王祥科
贾圣德
相晓嘉
王菖
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National University of Defense Technology
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Abstract

The invention belongs to the technical field of unmanned aerial vehicle systems, and discloses an improved label real-time airway re-planning method based on a multi-resolution situation map. The situation mapping method is used for counting the average operation time of about 305 milliseconds under a low-power-consumption embedded computing platform. On the basis of drawing, an improved label setting method is provided for generating the lowest detection/damage risk route under multiple constraints of oil consumption, endurance and the like on line. The statistical average operation time is about 25 milliseconds under the low-power-consumption embedded computing platform, and the method has a good application prospect in an avionics system with limited computing resources.

Description

Improved label real-time airway re-planning method based on multi-resolution situation mapping
Technical Field
The invention is oriented to the technical field of unmanned aerial vehicle systems, and can also be applied to the field of other robots. Specifically, multi-resolution wavelet compression is adopted to build a global situation map on line, and an improved label setting method is adopted to carry out on-line real-time route re-planning.
Background
The improvement of the autonomous capability of an unmanned aerial vehicle (or a robot) is a continuously pursued target in the field of intelligent robots. At present, a widely used unmanned aerial vehicle system mostly makes a flight route thereof through a ground station operator or a ground station computer system, and uploads the flight route to an airplane for execution. Recently, the development of an autonomous system supporting technology enables an unmanned system to have basic autonomous obstacle avoidance and automatic planning capabilities. However, the technical level still needs to be continuously improved, and a system is required to automatically generate a flight route by automatically utilizing the information of the airborne sensor and the airborne computing unit, so that the task response capability in a dynamic environment is improved. The high-autonomous unmanned aerial vehicle system can utilize all airborne available information to autonomously plan a flight route, improve the environment response capability and reduce the burden of ground station operators. The system should avoid obstacles or threats in a specific time window and reach a specified target position to execute a task.
The flight route planning is used as the basic capability of the autonomous unmanned aerial vehicle flight management system, is not only the basic capability of the unmanned aerial vehicle system, but also the important standard for measuring the autonomous level of the unmanned aerial vehicle system. High-level unmanned aerial vehicle routing techniques require that the aircraft be able to make on-line, real-time routing based on global and ambient aircraft-perceived situations. The air route needs to consider a global task target and local obstacle avoidance and threat avoidance capacity, so that the detection probability or the killing probability of a threatened/target is reduced to the maximum extent, and the airplane can be guided to approach to a final target. Meanwhile, the calculation resources and the storage resources distributed to the autonomous system components by the airborne avionic system are limited, and how to dynamically generate the air routes in real time and efficiently under the constraint condition of calculation performance is the key for restricting the availability of the system. The large range of the global situation and the high precision of the local situation bring irrecoverable burden to storage and calculation, and the contradiction between the global situation and the local situation needs to be solved, which is also a key technology to be solved urgently in the field.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: under the condition of low computing resources and low storage resources of an airborne system of the unmanned aerial vehicle, the flight path with low risk, low oil consumption and other performances can be autonomously generated in real time.
Aiming at the problems in the prior art, the invention mainly comprises two parts:
firstly, adopting multi-resolution compression to build a situation map: by analyzing situation distribution characteristics and strength and weakness of a task area of an unmanned aerial vehicle (or other robots), multi-resolution division is carried out on the global situation according to a plurality of critical distances, high-resolution situation mapping is carried out on an area closer to the airplane, and the airplane can carry out finer flight control; areas further away from the aircraft are mapped with a lower resolution, and the aircraft can be steered more coarsely. The situation mapping method can ensure the global characteristics of subsequent route planning, overcomes the defect that the classic rolling time domain control idea cannot meet the convergence, and can ensure that the airplane can accurately avoid obstacles and avoid flight control. The situation mapping method can meet the airborne real-time application requirement, and the statistical average operation time is about 305 milliseconds under a low-power-consumption embedded computing platform.
Secondly, multi-constraint minimum risk route optimization: on the basis of the first part of multi-resolution situation rasterization mapping, an improved label setting method is provided for generating the lowest detection/damage risk route under multiple constraints of oil consumption, time of flight and the like on line, the method avoids the defect that the planning problem analytic solution cannot be solved by a variational method, and the flight route is optimized by a discrete optimization approach. Under the condition that a plurality of radars are deployed by an opponent, a discrete optimization method is adopted to obtain a lowest risk route meeting various constraints such as oil consumption, endurance and the like. On the basis of multi-resolution situation mapping, a minimum risk route optimization problem with multiple constraints is described as a weight constraint shortest path problem, an improved label setting method is provided, the algorithm is tested through a series of standard example sets, the statistical average operation time is about 25 milliseconds under a low-power-consumption embedded computing platform, and the improved label setting method has a good application prospect in a avionic system with limited computing resources.
Drawings
FIG. 1 is a diagram of a fast lifting wavelet decomposition;
FIG. 2 is a multi-resolution situation map of an agent at a current location;
FIG. 3 is a multi-resolution cell division at different levels;
FIG. 4 is a recursive raster scan method for identifying individual cells;
FIG. 5 is a adjacency attribute for an individual cell;
FIG. 6 is a left search of adjacent individual cells;
FIG. 7 is a top left, top up search of adjacent individual cells;
FIG. 8 is a three-level multi-resolution cell adjacency diagram;
FIG. 9 is an unconstrained optimal trajectory for the case of two radars;
FIG. 10 is an optimal trajectory under length constraints for the case of two radars;
fig. 11 is a schematic diagram of an example network flow for solving the risk minimization problem.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
Step one, multi-resolution situation map building and lifting wavelet transformation;
in the present invention, a world environment is assumed
Figure BDA0001526675460000031
Including the space of obstacles
Figure BDA0001526675460000032
And an unobstructed configuration space F ═ W \ O. And performing multi-resolution decomposition on W by adopting wavelet transformation. By a basic elementary function phiJ,kAnd psiJ,kIs constructed by linear combination of
Figure BDA0001526675460000033
As follows
Figure BDA0001526675460000034
Wherein phi isJ,k(x)=2J/2φ(2Jx-k) and psij,k=2j/2ψ(2jx-k). The choice of J depends on a low resolution or a rough approximation of f.
Figure BDA0001526675460000035
Is wavelet function psij,k(x) To describe, function details that provide higher or finer resolution. In other words, when the function f is analyzed at the coarsest level (low resolution), only the most prominent features will appear. Adding finer levels (high resolution) means increasingPlus function f has more and more details. Thus (1) the resolution at different levels reveals the characteristics of f. Also ideally, both the scale function and the wavelet function have continuous support, i.e. they are non-zero only for a limited time interval. This allows the wavelet to capture local features of the function f.
Extending to two-dimensional cases, giving a function
Figure BDA0001526675460000036
Can obtain
Figure BDA0001526675460000037
Wherein, for the case of orthogonal wavelets, the approximation coefficients are given by
Figure BDA0001526675460000038
Detail coefficient of
Figure BDA0001526675460000039
Scale function
Figure BDA0001526675460000041
Wavelet function
Figure BDA0001526675460000042
The function is in [0,1 ]]Upper continuum, then, the scale function φ (x) and the wavelet function ψ (x) are 1/2 in lengthjInterval of (1)
Figure BDA0001526675460000043
And also continuous therein. Similarly, a two-dimensional scale function
Figure BDA0001526675460000048
And having rectangular cells
Figure BDA0001526675460000044
Wavelet function of
Figure BDA0001526675460000045
The same is true.
Fast lifting wavelet transform provides fast decomposition of functions at different resolution levels, twice the speed of classical wavelet transform. It builds the wavelet directly in the time domain, avoiding the fourier analysis process. In addition, the fast lifting wavelet transform integer arithmetic can greatly reduce the calculation cost. This makes the fast lifting wavelet transform particularly suitable for processing data in low power microcontrollers. The use of the fast lifting wavelet transform also has the property of allowing adjacent cells to be directly related by wavelet coefficients, thereby eliminating the need for quadtree decomposition.
In fast lifting wavelet decomposition, as shown in fig. 1. Splitting the original signal a in a first blocknTwo disjoint sample sets containing odd and even indexed samples. Since the odd and even subsets are locally related to each other, each signal is boosted (double and original boosting or prediction and update) by the opposite signal after passing through the respective operators P and U. Finally, the result is normalized to a constant kaAnd kdRespectively obtaining an approximation coefficient and a detail coefficientn-1And dn-1
Fast lifting wavelets have many advantages, such as faster computation speed (twice that of the usual discrete wavelet transform), in-situ computation of coefficients (saving memory), instantaneous inverse transform, broadening the generality of the irregularity problem, etc. In particular, the lifting scheme is suitable for many applications where the input data is integer samples.
Suppose W is [0,1 ]]×[0,1]Use of 2N×2NThe separation grid of (2). Resolution J of finest levelmaxBounded by N. The wavelet is more than or equal to J in resolution level JminDecomposition, as shown below
Figure BDA0001526675460000046
Then use a function
Figure BDA0001526675460000047
Representing the risk metric at (x, y), where M is a set of integer M different risk metric levels, defined as follows
Figure BDA0001526675460000051
Obstacle space O is defined as the risk metric value exceeding a certain threshold
Figure BDA0001526675460000052
Space (A) of
Figure BDA0001526675460000053
For x e F, consider rm (x) as the spatial proximity of the agent to the obstacle, or the probability x e O.
At different levels of resolution Jmin≤j≤JmaxConstruct an approximation of W, in the sense that j is used for all points inside
Figure BDA0001526675460000054
Wherein,
Figure BDA00015266754600000514
thereby meaning that a higher resolution is used for points close to the current position, and a different level of coarser resolution is used elsewhere depending on the distance from the current point. Thus, the further away from the current position, the coarser the representation of W, which is shown in fig. 2. J. the design is a squaremaxThe choice of (c) is determined by the requirement that all cells of the hierarchy can be resolved into free or obstacle cells. J. the design is a squareminAnd window span rjIs selected fromDetermined by the onboard computing resources.
The multi-resolution unit decomposition on W is as follows
Figure BDA0001526675460000055
Wherein,
Figure BDA0001526675460000056
is 1/2j×1/2jDimensional unit
Figure BDA0001526675460000057
The union of (a).
Decomposing C for multi-resolution unitdOne topology G ═ V, E is assigned. The nodes belonging to the set V represent CdUnit of
Figure BDA0001526675460000058
The edges in set E represent connectivity relationships between these nodes. The connectivity of graph G can be constructed directly from the wavelet coefficients. Equivalently, the adjacency list of G is computed directly from the wavelet coefficients obtained from the fast-lifting wavelet.
Because of the scale function of the two-dimensional wavelet
Figure BDA00015266754600000515
Sum wavelet function
Figure BDA0001526675460000059
Associated with the square cells, the corresponding approximation and non-zero detail coefficients encode the necessary information of the relevant cell geometry (size and position). The approximation coefficients are the average of the unit risk measures and the detail coefficients determine the size of each unit. More specifically, consider a case at j0Hierarchical unit
Figure BDA00015266754600000510
Dimension of
Figure BDA00015266754600000511
Is positioned as
Figure BDA00015266754600000516
If the cell is associated with a non-zero approximation coefficient
Figure BDA00015266754600000513
Associated while in range j0≤j≤JmaxCorresponding detail coefficient
Figure BDA00015266754600000512
Are all zero and the cell is said to be independent. Otherwise, the cell is marked as the parent cell and again at j0The +1 level is divided into four subunits. If a sub-unit cannot be further subdivided, it is classified as an independent unit. As shown in FIG. 3, the uppermost parent unit is at j0The +1 level is divided into three independent units, each with a non-zero approximation coefficient in quadrants I, II, and III. For quadrant IV, the cell is at j0The +2 level is further subdivided into four independent subunits.
Suppose that the risk metric function rm given the wavelet transform reaches JminAnd (4) hierarchy. The coarsest level of the unit dimension is set to Jmin. In fig. 4, the initial coarse grid is depicted on the left. The agent is located at x ═ x, y, and the high resolution is given by r. From coarse cells
Figure BDA0001526675460000061
Initially, cells of different resolution levels are distinguished by determining that the cells partially intersect or belong entirely to the set N (x, r). The unit being readily responsive to selection of a marker, e.g.
Figure BDA0001526675460000064
To determine that the property is satisfied. If a cell needs to be subdivided into higher resolution cells, an inverse fast lifting wavelet transform is first performed on the current cell (local reconstruction) to recover at j0Four approximation coefficients and corresponding detail coefficients at level + 1. Then, the overlapping of each cell within the cell is checked using the raster scan method (zigzag search: I → II → III → IV). This process has been usedThe process is recursively repeated until the highest resolution level J is reachedmax. Figure 4 shows a recursive raster scan search. Once a cell is identified as independent, a node is assigned in graph G whose cost is an approximation coefficient representing the average risk metric in the cell. In addition, the detail coefficients associated with the current cell are all set to zero; this will provide the necessary connectivity information between the units.
After a cell is determined to be an independent cell, neighboring cells are searched to establish an adjacency with the current cell. Two units ciAnd cjIs contiguous if
Figure BDA0001526675460000062
i ≠ j, wherein
Figure BDA0001526675460000063
Presentation Unit ciThe boundary of (2). For the case of square cells, this implies that two cells are only contiguous along the following eight directions: left, top, right, bottom and four diagonal directions. Following a recursive grid search with cell identification, a neighbor search requires a connection to be established between two cells that are identified as independent cells. Reviewing the left-to-right, top-to-bottom (zig-zag progression) grid search process, as shown in fig. 4, the direction of the adjacency search is limited: left, top and top right of the current cell. By doing so, half of the links (eight connections) are given to connect with the current cell, and the remaining links proceed as a recursive raster scan to the next cell to connect with the current cell. In addition, since units with different dimensions are processed, a general method needs to be designed to find the adjacency relation between the units.
FIG. 5 shows the basic search directions of subunits within a parent unit. The dotted arrow points towards the outer search area, i.e. the neighboring cells may be beyond the cell, while the solid arrow points towards the inner search area belong to the cell. In each search, the hierarchy of implicitly assumed neighboring cells may vary from parent cell to Jmax(external connection), or from the current cell to Jmax(internal connection).
The subunit inherits the search area from the present unit, whose search direction ends with one of the solid arrows in fig. 5. Fig. 6 illustrates such inherited properties. In FIG. 6 the current cell is selected as
Figure BDA0001526675460000071
The unit being a parent unit
Figure BDA0001526675460000072
Also becomes the topmost end unit
Figure BDA0001526675460000073
A sub-unit of (1). Unit cell
Figure BDA0001526675460000074
At the uppermost notebook unit
Figure BDA0001526675460000075
In the fourth quadrant, pair
Figure BDA0001526675460000076
Search area of j0The +1 level inner search ends with the neighbor search attribute at left, top left and top search directions inherited to the cells
Figure BDA0001526675460000077
After determining the basic search direction, the neighbor search is optimized to find independent opposite cells that are adjacent to the current cell. Since the relative cell of the current cell may have different dimensions, the connection is established by examining the relative detail coefficients of the relative cell.
If the relative cell is not a separate cell, that is, if it is composed of finer cells, the adjacency search algorithm refines its search to a higher level. This refinement then forces a search for finer dimensions (hierarchies). The detail coefficients of the opposite cell are then examined to find the next finer cell adjacent to the current cell. For the
Figure BDA0001526675460000078
Upper left search direction, as shown in FIG. 7(a), the search process initially checks the upper left cell located at the current cell by the corresponding detail coefficient
Figure BDA0001526675460000079
If and unit
Figure BDA00015266754600000710
The associated detail coefficient takes a non-zero value and the cell is not a separate cell. Subsequently, the unit
Figure BDA00015266754600000711
Segmented, relative cell to current cell becomes independent neighbor cell search process at j0+2 level repetition. In fig. 7(a), since there is no other independent unit except for the shadow 1 in the upper left direction, a bidirectional connection is established between the current and opposite units.
Likewise, for the top search direction, two j0+3 levels and a j0The +2 level cell is considered independent and contiguous to the current cell. The bidirectional connection is correspondingly changed from the current unit
Figure BDA00015266754600000712
Are connected to these adjoining units. Fig. 7(b) depicts this situation. Finally, fig. 8 shows an example of a graph structure resulting from a multi-resolution cell decomposition associated with wavelet coefficients. Without loss of generality, the node is located at the center of each unit. The solid line indicates the connection relationship between the cells.
The invention obtains a general method for optimally avoiding threatening route planning while satisfying the route distance (oil consumption) constraint, and particularly focuses on risks related to radar detection. Fig. 9 and 10 are the unconstrained optimal trajectory and the length constrained optimal trajectory, respectively, for the two radar cases. The curves in these figures correspond to a set of risk levels near the maximum in the radar field. The risk decreases when the aircraft leaves the radar and increases when the aircraft approaches.
To formulate a solution to optimize risk paths, there are the following assumptions:
(1) the horizontal airplane model, i.e., the position of the airplane, is considered to be on only one horizontal plane.
(2) Radar detection of an aircraft is independent of the heading and climb angle of the aircraft.
(3) The angle of rotation is independent of the track position.
(4) The admissible field of the aircraft trajectory is assumed to be one detection zone for all radar devices. That is, the aircraft is no further away from each radar device than the maximum detection range of the radar.
(5) The risk is quantified in terms of a risk index per unit length for any particular aircraft location. The simplified threat model assumes that the risk index r is proportional to the risk factor σ, and is reciprocal to the square of the aircraft position to radar position distance. The risk factor σ depends on the technical characteristics of the radar, such as maximum detection range, minimum detectable signal, transmission power of the antenna, antenna gain and wavelength of the radar energy. It can be assumed that all radar technology characteristics remain unchanged, so σ is assumed for the radar under such a risk factoriIs constant. Suppose that
Figure BDA0001526675460000081
Is the aircraft position (x, y) to the radar position (a)i,bi) Distance of (d), risk index r of trace point (x, y)iBy
Figure BDA0001526675460000082
It is given. Although in the present invention we consider the risk to be the inverse of the square of the distance, this assumption is not crucial to the application of the development method. For example, the risk index may be expressed as
Figure BDA0001526675460000083
Which corresponds to a radar detection model of the reflected signal from the aircraft. In this case, the risk factor σiA Radar Cross Section (RCS) of the aircraft is defined.
(6) N radar devices at each point of allowable deviation domainIs evaluated as the sum of the risks per radar, e.g.
Figure BDA0001526675460000084
(7) The aircraft speed is assumed to be constant, so the time increment dt is linearly related to the unit length ds: ds is V0dt。
(8) For any particular aircraft location (x, y), the risk per unit length ds is calculated as the product of a risk index and a unit length, e.g.
Figure BDA0001526675460000085
(9) Risk accumulation R along pathway P is represented by the expression R (P) ═ PjPrds presents.
Based on model assumptions 1-9, the optimization problem in path length constraints is set forth in the following manner. N represents the number of radars, (a)i,bi) Indicating a radar position, wherein
Figure BDA0001526675460000086
The departure and destination of the airplane are respectively A (x)1,y1) And B (x)2,y2). The path P from a to B is associated with a combined risk r (P) and a total length l (P). Best path P*The length constraint l (P). ltoreq.l should be minimized*. The optimization problem is presented in the following equation
Figure BDA0001526675460000087
Wherein R (P) and l (P) are defined by the following expressions
Figure BDA0001526675460000091
Figure BDA0001526675460000092
Step two, discrete optimization solution;
to solve (12-14), analytical and discrete optimization methods should be considered. Under the condition of considering any radar number, the discrete optimization method provided by the invention can solve the problem of reducing the generation problem of the optimal risk path to the weight value constraint shortest path of the grid undirected graph in the length constraint. The weight constraint shortest path problem of the grid undirected graph can be effectively solved through a network flow optimization algorithm. However, the computation time of these algorithms is exponential to the accuracy of the predetermined optimal trajectory. We assume that the allowable deviation domain of the aircraft trajectory is an undirected graph G ═ (V, a), where V ═ 1. The trajectory (x (), y ()) is approximated by a path P in the graph G, where the path P is approximated by a series of nodes<j0,j1,...,jp>Definitions, e.g. j0=A,jpB and for all values of k from 1 to p, satisfies<jk-1,jk>E.g. A. To configure (12-14) to the network optimization problem, we determine its risk and trajectory length using discrete approximations for equations (13) and (14), respectively.
Figure BDA0001526675460000093
Figure BDA0001526675460000094
Wherein,
Figure BDA0001526675460000095
is an arc<jk-1,jk>The length of (a) of (b),
Figure BDA0001526675460000096
arc of representation<jk-1,jk>The risk index of (a). Suppose x (j)k) And y (j)k) Is node jkX and y coordinates of (2), arc length
Figure BDA0001526675460000097
Is defined by the following expression
Figure BDA0001526675460000098
The risk index is determined as
Figure BDA0001526675460000099
When in use
Figure BDA00015266754600000910
Approaching zero, the risk index has a limit
Figure BDA00015266754600000911
In the limit case where the temperature of the molten metal is too high,
Figure BDA00015266754600000912
e.g. jk-1→jkIs provided with
Figure BDA00015266754600000913
Formula (18) at point jkConsistent with the definition of risk index.
Fig. 11 illustrates an example network flow to solve the risk minimization problem. In the case of two radars, the polyline is a path in the area,<jk-1,jk>is an arc of this path. Two nodes jk-1And jkThe distance between them is the arc length
Figure BDA0001526675460000101
Figure BDA0001526675460000102
And
Figure BDA0001526675460000103
define radar 1 to node j respectivelyk-1And jkThe distance of (c).
Figure BDA0001526675460000104
The values R (P) and l (P) are rearranged
Figure BDA0001526675460000105
Figure BDA0001526675460000106
Thus, each arc<jk-1,jk>e.A and its length
Figure BDA0001526675460000107
And non-negative cost
Figure BDA0001526675460000108
The correlation is defined in (17) and (19), respectively. Taking into account the value
Figure BDA0001526675460000109
As the weights of the arcs, we denote the cost of path P by R (P), and l (P) denotes the total weight accumulated along path P. If the total weight l (P) is at most l, i.e., l (P) is less than l, then the path P is weighted.
Step three, solving the shortest path problem by improving a label setting method;
the weight constraint shortest path problem is expressed in the following way. It is desirable to find a feasible path P from point A to point B that minimizes the cost R (P)
Figure BDA00015266754600001010
Equation (22) is closely related to the time window shortest path problem and the resource constraint shortest path problem, and uses vectors of weights or resources instead of scalars. These problems are solved in a fleet generation method for time-windowed aircraft path problems and long-haul aircraft path problems. Algorithms for solving the weight constraint shortest path problem are divided into three major categories: a label setting algorithm based on a dynamic programming method, a scaling algorithm and an algorithm based on a Lagrange relaxation method. In the case of a positive weight, the label setting algorithm is most effective. The gradient optimization and cutting plane method is the core of the Lagrange relaxation algorithm, and is effective to solve the Lagrange dual problem of the weight constraint shortest path problem under the condition of one resource. The scaling algorithm uses two complete polynomial approximation schemes of cost-based scaling and rounding for the weight constrained shortest path problem. The first approach is a geometric binary search, while the second iteratively extends the path. To solve the weight constrained shortest path problem, we use an improved label setting method with preprocessing, defined by (22).

Claims (5)

1. An improved label real-time airway re-planning method based on a multi-resolution situation map is characterized by comprising two parts: firstly, adopting multi-resolution compression to build a situation map: performing multi-resolution division on the global situation by analyzing situation distribution characteristics and strength and weakness confrontation degree of the unmanned aerial vehicle task area and taking a plurality of critical distances as the basis; secondly, multi-constraint minimum risk route optimization: on the basis of drawing construction, an improved label setting method is provided for generating a path with the lowest detection/damage risk under the conditions of oil consumption and multi-constraint during navigation on line; under the condition that a plurality of radars are deployed by an opponent, obtaining a lowest risk route meeting various constraints such as oil consumption, endurance and the like by adopting a discrete optimization method; the constraint of the oil consumption is distance constraint, and the lowest risk route meeting the oil consumption constraint is obtained by adopting a discretization method:
Figure FDA0002638050060000011
Figure FDA0002638050060000012
wherein σiRepresents a risk factor, diRepresenting the distance of the drone position from the radar position,
Figure FDA0002638050060000013
is an arc<jk-1,jk>The length of (a) of (b),
Figure FDA0002638050060000014
arc of representation<jk-1,jk>For x (j)k) And y (j)k) Is node jkX and y coordinates of (2), arc length
Figure FDA0002638050060000015
Is defined by the following expression:
Figure FDA0002638050060000016
the risk index is determined as:
Figure FDA0002638050060000017
wherein,
Figure FDA0002638050060000018
denotes x (j)k) And x (j)k-1) The included angle between the radar and the position connecting line of the radar,
Figure FDA0002638050060000019
represents node jk-1The distance to the radar location is determined,
Figure FDA00026380500600000110
represents node jkDistance to radar location;
the step of adopting multi-resolution compression to perform situation mapping comprises the following steps:
in the world environment W ═ 0,1]×[0,1]Wherein
Figure FDA00026380500600000111
including the space of obstacles
Figure FDA00026380500600000112
And barrier-free configuration space F ═ W \ O, using 2N×2NThe finest level of resolution JmaxTaking N as boundary, wavelet is more than or equal to J in resolution level JminDecomposition, as follows:
Figure FDA0002638050060000021
wherein N represents the boundary corresponding to the finest resolution, J represents the resolution level of the grid, JminRepresenting the minimum resolution level of the grid, f (x, y) representing the function of wavelet decomposition in a separate grid, k, l representing the position information of level cells in the wavelet function, aJ,k,lRepresenting the approximation coefficient, phiJ,k,l(x, y) represents a scale function of a two-dimensional wavelet,
Figure FDA0002638050060000022
the detail coefficients are shown in the form of,
Figure FDA0002638050060000023
a wavelet function representing a two-dimensional wavelet;
the function of the risk metric at (x, y) is expressed as rm:
Figure FDA0002638050060000024
where M is a set of different risk metric levels of integer M, defined as follows:
Figure FDA0002638050060000025
obstacle space O is defined as the measure of risk exceeding a certain threshold
Figure FDA0002638050060000026
The space of (a):
Figure FDA0002638050060000027
for x e F, rm (x) as the spatial proximity of the drone to the obstacle, or the probability x e;
at different levels of resolution Jmin≤j≤JmaxConstructing an approximation of W, j for all points inside, yields:
Figure FDA0002638050060000028
wherein, N (x)0,rj) Representing an approximate set of W, x0Indicates the current position, rjThe span of the window is represented by,
Figure FDA0002638050060000029
representing the window span corresponding to the maximum resolution, rJminRepresenting a window span corresponding to the minimum resolution;
Figure FDA00026380500600000210
higher resolution is used for points close to the current position, the farther away from the current position, the coarser the representation of W, JmaxIs determined by the requirement that all elements of this hierarchy can be resolved into free or obstacle elements; j. the design is a squareminAnd window span rjIs determined by on-board computing resources;
the multi-resolution unit decomposition on W is as follows:
Figure FDA00026380500600000211
wherein,
Figure FDA00026380500600000212
is 1/2j×1/2jDimensional unit
Figure FDA00026380500600000213
The union of (a) and (b),
Figure FDA00026380500600000214
is that
Figure FDA00026380500600000215
Dimensional unit
Figure FDA00026380500600000216
The union of (a) and (b),
Figure FDA00026380500600000217
is that
Figure FDA00026380500600000218
Dimensional unit
Figure FDA00026380500600000219
A union of (1);
decomposing C for multi-resolution unitdAnd assigning a topological graph G-V, E to obtain a situation graph.
2. The improved label real-time airway re-planning method based on multi-resolution situation mapping of claim 1, wherein: the multi-resolution division of the global situation refers to high-resolution situation mapping of an area close to the airplane, the airplane can conduct finer flight control, low-resolution situation mapping of an area far away from the airplane is conducted, and the airplane can conduct coarser direction guiding.
3. The improved label real-time airway re-planning method based on multi-resolution situation mapping of claim 2, wherein: the method for performing multi-resolution division on the global situation reduces the calculation cost by utilizing a fast lifting wavelet transformation method for establishing wavelets in a time domain, realizes fast decomposition on different levels of resolution, allows adjacent cells to directly pass through a structure represented by wavelet coefficients, and does not need to use quadtree decomposition.
4. The improved label real-time airway re-planning method based on multi-resolution situation mapping of claim 3, wherein: on the basis of multi-resolution situation mapping, a dynamic programming method-based improved label setting method is adopted, and the problem of route optimization under the condition of multiple constraints is solved.
5. The improved label real-time airway re-planning method based on multi-resolution situation mapping of claim 1, wherein: under the condition of meeting various constraints of oil consumption, time of flight and the like, a flight path with the lowest detected/killed risk is optimized and calculated by adopting a discrete optimization method, and the problem that a plurality of radar conditions are deployed by an opponent is solved.
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