CN101893441A - Unmanned aerial vehicle flight path optimization method based on deviation maximization and grey correlation analysis - Google Patents

Abstract

The invention discloses an unmanned aerial vehicle flight path optimization method based on deviation maximization and grey correlation analysis, belonging to the unmanned aerial vehicle flight path planning and uncertainty multiattribute decision making field. In the method, an unmanned aerial vehicle flight path scheme optimization decision-making target system is established according to different threats of the unmanned aerial vehicle, and an unmanned aerial vehicle flight path scheme optimization mathematical model is constructed by virtue of evaluation attributes. Concretely, according to a flight path planning scheme set, deviation maximization method is adopted to objectively weight all the evaluation attributes, grey correlation analytic method is adopted to solve the optimization model, grey correlation information existed among all the attributes are fully utilized, and finally an optimal flight path scheme is determined according to relevancy of decision layer. The method of the invention has strong objectivity, requires no expert advice to estimate and has strong feasibility.

Description

Unmanned aerial vehicle flight path optimization method based on deviation maximization and grey correlation analysis

Technical field

The present invention relates to a kind of flight path optimization method, relate in particular to a kind of unmanned aerial vehicle flight path Scheme Optimum Seeking Methods, belong to unmanned aerial vehicle flight path planning and uncertain multiple attribute decision making (MADM) field based on deviation maximization and grey correlation analysis.

Background technology

Unmanned plane (UAV) has obtained extensive studies and has obtained develop rapidly since the sixties in last century.Initial unmanned plane is as target drone, and along with the going deep into of research, it begins progressively to play the part of various air battle roles, pins down, fights as scouting, supervision, firepower strike, electronic interferences, deception and decrease assessment etc.Early stage unmanned plane all is the track flight that calculates in advance and configure according to mission planning center, ground, the real-time trajectory planning of unmanned plane is the basis of senior autonomous flight technology such as the unmanned plane cluster cooperates, the cluster tactics are planned again, cluster tactical goal reenacts, and is the most effective a kind of means that improve the unmanned plane survival probability.

Reasonably the trajectory planning scheme makes unmanned plane evade threat effectively, improves survival probability and Operational Effectiveness Rat.Unmanned plane is mainly considered 5 cost attribute when finishing a flight path scheme, be respectively that oil consumption cost, threat radar cost, missile threat cost, antiaircraft gun threat cost and atmosphere threaten cost.This problem belongs to for the multiple attribute decision making (MADM) problem, because attribute weight information is unknown fully, in the past generally all rule of thumb technique of estimation determine weight, therefore there is certain subjectivity and is difficult to adapt to the shortcoming that situation changes, in case situation has change, weight should constantly be adjusted according to situation, and expertise often is difficult in time judge.

In addition, consider that the killing range of guided missile, radar reaches constraints such as effectively detection, and have certain association between the threat constraint, play an important role to guiding guided missile specifically to attack as the radar Effect on Detecting.Therefore, the unmanned aerial vehicle flight path scheme optimization is the optimum decision system of multiple goal multiple constraint, and is an organic whole, the interrelated common system performance that influences of each attribute, and since influence degree be difficult to determine, so be a kind of grey information system.These grey informations are often comprising the degree of association between each attribute, thereby be information of overall importance with system's meaning, in design flight path scheme optimization decision process, should fully use these grey correlation information, and the relevant scientific paper of publishing is not at present all discussed the grey correlation information between each scheme, but directly be weighted summation, to determine the synthesized attribute value of each scheme, do the grey information that often can not reflect these attributes like this.

Summary of the invention

The present invention is directed to the deficiency that existing unmanned aerial vehicle flight path scheme optimization technology exists, and propose a kind ofly objectively to obtain each attribute weight and make full use of the method that flight path scheme internal relation is carried out the flight path scheme optimization.

The key step of the inventive method is as follows:

(1) sets up unmanned aerial vehicle flight path evaluate alternatives attribute data matrix, adopt the deviation maximization method that each evaluation attributes is carried out objective tax power;

(2) adopt gray relative analysis method that each evaluation attributes data of unmanned aerial vehicle flight path scheme are handled;

(3) weight with each evaluation attributes of obtaining in the step (1) is weighted, and obtains the degree of association of each unmanned aerial vehicle flight path program decisions layer, with each unmanned aerial vehicle flight path schemes ranking, finally determines the optimal trajectory scheme according to the degree of association.

The inventive method has overcome the deficiency that existing unmanned aerial vehicle flight path scheme optimization technology exists, need not each attribute weight to be set by artificial experience, and considered the gray relation that exists between each scheme, improved the objectivity of unmanned aerial vehicle flight path scheme optimization greatly, avoid traditionally the deviser subjectivity and the randomness of type selecting by rule of thumb, all can adopt this method to carry out scheme optimization at unmanned plane two and three dimensions trajectory planning in addition.

Description of drawings

Fig. 1 is the schematic network structure of two-dimentional flight path node.

Fig. 2 is the schematic network structure of three-dimensional flight path node.

Fig. 3 is the unmanned plane two dimension flight path scheme synoptic diagram of embodiment.

Fig. 4 is the no-manned plane three-dimensional flight path scheme synoptic diagram of embodiment.

Embodiment

(1) the flight path space is described

(I) two-dimentional flight path space is described

Unmanned plane is at the general maintenance of cruising phase stable speed and height, and the enemy defence area is in smooth region, therefore can not consider to utilize the landform attribute to impend evades, and the flight path space can be reduced to the two-dimensional search space of a multiple goal multiple constraint, but still the survival probability and the fighting efficiency of need consideration unmanned plane, so be still comparatively special optimization problem.By the right angle grid dividing is carried out in the flight path space, search next adjacent node by present node,, form the flight path that connects start node and destination node until searching destination node, employing is based upon the oil consumption on the grid chart and threatens the cost model, sets up the flight path preferred version.Each node arrival adjacent node in the grid chart need be by the directed edge that connects adjacent node and have weight.The data structure of algorithm is to be the JiuGongTu at center with the present node, have 8 adjacent nodes, be illustrated in figure 1 as the adjacent node synoptic diagram of two-dimentional flight path node alpha, flight path is the knot vector that is made of a group node, the front and back node is neighbouring relations each other, and sizing grid needs according to the practical problems scale and threatens the some distribution situation rationally to be provided with, can not be excessive, and also can not be too small.

(II) three-dimensional flight path space is described

Divide by three-dimensional planning space being carried out the cube grid, three dimensions is divided into equal and opposite in direction, cube adjacent one another are, search pattern is from starting point, search next adjacent node, advance and reconnoiter, until searching destination node, the final flight path that connects start node and destination node that forms adopts the cost model and the optimized Algorithm that are based upon on the grid chart to find the solution optimal trajectory.Therefore, the data structure of algorithm is to be the three-dimensional structure diagram at center with the present node, have 26 adjacent nodes, be illustrated in figure 2 as the schematic network structure of three-dimensional trajectory planning node, next node must be from being to select 27 nodes constituting of center with this node, and wherein the sizing grid of X, Y, Z all directions is expressed as X respectively _Gird, Y _Gird, Z _GirdSizing grid needs according to the practical problems scale and threatens a some distribution situation rationally be provided with, and is provided with excessively, and then spatial resolution is low excessively; Be provided with too for a short time, then data space is excessive, causes calculated amount excessive.

(2) threaten model to determine

The evaluation attributes of unmanned aerial vehicle flight path planning mainly comprise the oil consumption cost and threaten cost, wherein threaten cost to comprise that threat radar cost, missile threat cost, antiaircraft gun threaten cost and atmosphere to threaten cost, the purpose of trajectory planning is exactly to make whole cost minimum, as the formula (1).And because there are constraints such as maximum operating range and damage effect distance in the model of radar, guided missile, antiaircraft gun and atmosphere, therefore, this problem belongs to multiple goal multiconstraint optimization problem.

Optim[W _R(s)，W _M(s)，W _A(s)，W _C(s)，W _O(s)]＝W _R(s ^*)，W _M(s ^*)，W _A(s ^*)，W _C(s ^*)，W _O(s ^*)](1)

In the formula (1): s is the unmanned aerial vehicle flight path scheme; s ^*Be the optimal trajectory programme; W _R(s) be the threat radar cost of flight path s; W _M(s) be the missile threat cost; W _A(s) threaten cost for antiaircraft gun; W _C(s) threaten cost for atmosphere; W _O(s) be the oil consumption cost.The oil consumption cost is the function of voyage, and other threatens the lethal radius attribute of the detectivity of cost model and unmanned plane and guided missile, antiaircraft gun etc. relevant.

Threaten model to have constraints such as maximum operating range and damage effect distance, the present invention introduces constraint condition in the objective function by setting up the reasonable target cost function, threatens model to be defined as follows respectively at radar, guided missile, antiaircraft gun and atmosphere:

But radar to the detection probability approximate representation of unmanned plane is:

$P_R\left(d_R\right)=\left\{\begin{array}{cc}0& (d_R>d_{R\max })\\ 1/d_R^4& (d_{R\min }\&le;d_R\&le;d_{R\max })\\ 1& (d_R<d_{R\min })\end{array}\right.---\left(2\right)$

In the formula (2): P _R(d _R) expression threat radar probability; d _RDistance between expression unmanned plane and the radar; d _RmaxThe maximum radius of expression radar detection area, surpass this apart from the time, return signal is extremely faint, is submerged in the noise; d _RminThe effective radius of investigation of expression radar, in this scope, the probability that unmanned plane is detected is 1.The present invention supposes that antenna does 360 ° of scannings on the orientation, can form whole investigative ranges of radar, promptly radar detection azimuth coverage 0-360 °.P _R(d _R)=1 found the probability of expression unmanned plane is 1, then threatens cost can think infinity; P _R(d _R)=0, expression unmanned plane found probability is 0, then to be subjected to the threat radar cost be 0 to unmanned plane; Work as d _MIn the time of between the two, the found probability of unmanned plane is

But guided missile to the kill probability approximate representation of unmanned plane is:

$P_M\left(d_M\right)=\left\{\begin{array}{cc}0& (d_M>d_{M\max })\\ 1/d_M& (d_{R\min }\&le;d_M\&le;d_{M\max })\\ 1& (d_M<d_{M\min })\end{array}\right.---\left(3\right)$

In the formula (3): P _M(d _M) expression missile threat probability; d _MDistance between expression unmanned plane and the guided missile.P _M(d _M)=1 expression is worked as unmanned plane at guided missile effective kill radius d _MminWhen interior, the probability that unmanned plane is smashed is 1, and it threatens to infinitely great; P _M(d _M)=0 expression is worked as unmanned plane at the maximum lethal radius d of guided missile _MmaxWhen outer, the probability that unmanned plane is hit is 0, and then to be subjected to the missile threat cost be 0 to unmanned plane; Work as d _MIn the time of between the two, the probability that unmanned plane is hit is 1/d _M

But antiaircraft gun to the kill probability approximate representation of unmanned plane is:

$P_A\left(d_A\right)=\left\{\begin{array}{cc}0& (d_A>d_{A\max })\\ 1/d_A& (d_{A\min }\&le;d_A\&le;d_{A\max })\\ 1& (d_A<d_{A\min })\end{array}\right.---\left(4\right)$

In the formula (4): P _A(d _A) expression antiaircraft gun threat probabilities; d _ADistance between expression unmanned plane and the antiaircraft gun.P _A(d _A)=1 expression is worked as unmanned plane at antiaircraft gun effective kill radius d _AminWhen interior, the probability that unmanned plane is smashed is 1, and it threatens to infinitely great; P _A(d _A)=0 expression is worked as unmanned plane at the maximum lethal radius d of antiaircraft gun _AmaxWhen outer, the probability that unmanned plane is hit is 0, and then to be subjected to antiaircraft gun to threaten cost be 0 to unmanned plane; Work as d _AIn the time of between the two, the probability that unmanned plane is hit is 1/d _A

But atmosphere to the kill probability approximate representation of unmanned plane is:

$P_C\left(d_C\right)=\left\{\begin{array}{cc}0& (d_C>d_{C\max })\\ 1/d_C& (d_{C\min }\&le;d_C\&le;d_{C\max })\\ 1& (d_C<d_{C\min })\end{array}\right.---\left(5\right)$

In the formula (5): P _C(d _C) expression atmosphere threat probabilities; d _CDistance between expression unmanned plane and the atmosphere.P _C(d _C)=1 expression is worked as unmanned plane at atmosphere effective kill radius d _CminWhen interior, the probability that unmanned plane is smashed is 1, and it threatens to infinitely great; P _C(d _C)=0 expression is worked as unmanned plane at the maximum lethal radius d of atmosphere _CmaxWhen outer, the probability that unmanned plane is hit is 0, and then to be subjected to atmosphere to threaten cost be 0 to unmanned plane; Work as d _CIn the time of between the two, the probability that unmanned plane is hit is 1/d _C

After each attribute function of optimizing is determined, can calculate its each attribute cost respectively for given flight path scheme.

(3) based on the weight calculation of deviation maximization

Form trajectory planning scheme collection by n flight path scheme, each scheme is the property set that is made of m evaluation attributes, and n can get 50 among the present invention, and m gets threat cost and the oil consumption cost that 5,5 evaluation attributes are respectively radar, guided missile, antiaircraft gun, atmosphere.

If u _jRepresent j attribute, x _IjThe u that represents i scheme _jProperty value, the m of i scheme attribute availability vector x then _iBe expressed as:

x _i＝(x _i1，x _i2，…x _ij…，x _im)i＝1，2，…，n j＝1，2，…，m (6)

Then can use following matrix representation for m attribute of all n scheme:

$X_{n\&times;m}=\left[\begin{array}{c}{x}_1\\ x_2\\ ...\\ x_n\end{array}\right]=\left[\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1m}\\ x_{21}& x_{22}& ...& x_{2m}\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ x_{n1}& x_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">n</figure-callout>}2}& ...& x_{\mathrm{nm}}\end{array}\right]---\left(7\right)$

For the ease of carrying out, not directly use initial attribute data X based on the deviation maximization weight analysis _{N * m}, can cause the big attribute weight of property value big like this, the attribute weight that property value is little is little, and should be at first to X _{N * m}Carry out the dimensionless standardization processing, disposal route is as follows:

The flight path plan attribute is cost attribute among the present invention, is the attribute of cost type, therefore, wishes that overall cost is the smaller the better, so adopt following standardization formula:

$r_{\mathrm{ij}}=\frac{-x_{\mathrm{ij}}+\max (x_{1j},x_{2j},...,x_{\mathrm{nj}})}{\max (x_{1j},x_{2j},...,x_{\mathrm{nj}})-\min (x_{1j},x_{2j},...,x_{\mathrm{nj}})},i=\mathrm{1,2},...,n,j=\mathrm{1,2},...,m---\left(8\right)$

Formula (7) through after the standardization processing is:

$R_{n\&times;m}=\left[\begin{array}{cccc}{r}_{11}& r_{12}& ...& r_{1m}\\ r_{21}& {\mathrm{<figure-callout\; id="22"\; label="r"\; filenames="HSA00000156717500012.png"\; state="\{\{state\}\}">r</figure-callout>}}_{22}& ...& r_{2m}\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ r_{n1}& {\mathrm{<figure-callout\; id="2"\; label="r\; n"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">r</figure-callout>}}_n& ...& r_{\mathrm{nm}}\end{array}\right]---\left(9\right)$

In the multiattribute multifactorial evaluation, if all schemes are at attribute u _jUnder property value difference more little, then think this attribute to program decisions with the ordering role more little; Otherwise, act on big more.Therefore, the big more attribute of scheme attribute value deviation should be given big more weight.For attribute u _j, use V _Ij(ω) representation scheme x _iTo the deviation between other all schemes, then definable:

$V_{\mathrm{ij}}\left(\mathrm{\&omega;}\right)=V_{\mathrm{ij}}\left(\mathrm{\&omega;}\right)=\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}|r_{\mathrm{ij}}{\mathrm{\&omega;}}_j-r_{\mathrm{kj}}{\mathrm{\&omega;}}_j|,i=\mathrm{1,2},...,n,j=\mathrm{1,2},...,m---\left(10\right)$

Order:

$V_j\left(\mathrm{\&omega;}\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_{\mathrm{ij}}\left(\mathrm{\&omega;}\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}|r_{\mathrm{ij}}-r_{\mathrm{kj}}|{\mathrm{\&omega;}}_j,j=\mathrm{1,2},...,m---\left(11\right)$

V then _j(ω) expression is to attribute u _j, total deviation of all schemes and other scheme.The selection of weighing vector ω should make the total deviation maximum of all properties to all schemes.For this reason, structure objective function:

$\max V\left(\mathrm{\&omega;}\right)=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{V}_j\left(\mathrm{\&omega;}\right)=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}|r_{\mathrm{ij}}-r_{\mathrm{kj}}|{\mathrm{\&omega;}}_j---\left(12\right)$

Then finding the solution weighing vector ω is equivalent to and finds the solution following optimal model:

$\left\{\begin{array}{c}\max V\left(\mathrm{\&omega;}\right)=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}|r_{\mathrm{ij}}-r_{\mathrm{kj}}|{\mathrm{\&omega;}}_j\\ s.t.\mathrm{\&omega;}\&GreaterEqual;0,j=\mathrm{1,2},...,m,\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">j</figure-callout>}}^2=1\end{array}\right.---\left(13\right)$

Separate this Optimization Model, make Lagrange (Lagrange) function:

$L(\mathrm{\&omega;},\mathrm{\&zeta;})=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}|r_{\mathrm{ij}}-r_{\mathrm{kj}}|{\mathrm{\&omega;}}_j+\frac{1}{2}\mathrm{\&zeta;}(\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_j^2-1)---\left(14\right)$

Ask its partial derivative, and order:

$\left\{\begin{array}{c}\frac{\&PartialD;L}{\&PartialD;{\mathrm{\&omega;}}_j}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}|r_{\mathrm{ij}}-r_{\mathrm{kj}}|+\mathrm{\&zeta;}{\mathrm{\&omega;}}_j=0\\ \frac{\&PartialD;L}{\&PartialD;\mathrm{\&zeta;}}=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_j^2-1=0\end{array}\right.---\left(15\right)$

Try to achieve optimum solution:

${\mathrm{\&omega;}}_j^{*}=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}|r_{\mathrm{ij}}-r_{\mathrm{kj}}|}{\sqrt{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left[\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}\right|r_{\mathrm{ij}}-r_{\mathrm{kj}}\left|\right]}^2}},j=\mathrm{1,2},...,m$

It is carried out normalized, satisfies normalization constraint condition:

${\mathrm{\&omega;}}_j=\frac{{\mathrm{\&omega;}}_j^{*}}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_j^{*}},j=\mathrm{1,2},...,m$

Obtain thus:

${\mathrm{\&omega;}}_j=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}|r_{\mathrm{ij}}-r_{\mathrm{kj}}|}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left[\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}\right|r_{\mathrm{ij}}-r_{\mathrm{kj}}\left|\right]}^2}---\left(16\right)$

(4) grey correlation analysis of unmanned aerial vehicle flight path scheme collection

As mentioned above, unmanned aerial vehicle flight path programme collection is formed the scheme collection of gray system by n scheme, and the vector that each scheme is made up of m attribute is so gray system can be used matrix X _{N * m}Expression is R after the process standardization processing _{N * m}Because n scheme of unmanned aerial vehicle flight path programme collection preferably has a relativity that relatively goes up, in the gray system preferably for the evaluation attributes of the m in this system, so select a desirable reference scheme earlier, be designated as:

${\mathrm{<figure-callout\; id="0"\; label="F"\; filenames="HSA00000156717500022.png"\; state="\{\{state\}\}">F</figure-callout>}}^0={[{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">f</figure-callout>}}_1^0,{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">f</figure-callout>}}_2^0,...,{\mathrm{<figure-callout\; id="0"\; label="f\; j"\; filenames="HSA00000156717500022.png"\; state="\{\{state\}\}">f</figure-callout>}}_j^{},...,f_m^0]}^T---\left(17\right)$

In the formula (17):

J=1,2 ..., m, i.e. F ⁰In m evaluation attributes are the maximal values of participating in corresponding evaluation attributes in preferred all n schemes, with its ideal scheme as standard.As the reference sequence, n scheme distinguished sequence as a comparison ideal scheme.Data relationship between reference sequences and the comparative sequences is pressed close to degree, weighs with the size of correlation coefficient usually.Note ξ _{I, j}Be i comparative sequences and F ⁰The grey incidence coefficient of j attribute in the reference sequences is calculated by formula (18).

${\mathrm{\&xi;}}_{i,j}=\frac{\underset{j}{\min }\underset{i}{\min }|f_j^0-r_{i,j}|+\mathrm{\&rho;}\underset{j}{\max }\underset{i}{\max }|f_j^0-r_{i,j}|}{|f_j^0-r_{i,j}|+\mathrm{\&rho;}\underset{j}{\max }\underset{i}{\max }|f_j^0-r_{i,j}|},i=\mathrm{1,2},...,n,j=\mathrm{1,2},...,m---\left(18\right)$

In the formula, ρ ∈ [0,1] generally gets ρ=0.5, and the grey incidence coefficient matrix that obtains unmanned aerial vehicle flight path programme collection gray system thus is:

${\mathrm{\&Xi;}}_{m\&times;n}=\left[\begin{array}{cccc}{\mathrm{\&xi;}}_{11}& {\mathrm{\&xi;}}_{12}& ...& {\mathrm{\&xi;}}_{1m}\\ {\mathrm{\&xi;}}_{21}& {\mathrm{\&xi;}}_{22}& ...& {\mathrm{\&xi;}}_{2m}\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">n</figure-callout>}1}& {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">n</figure-callout>}2}& ...& {\mathrm{\&xi;}}_{\mathrm{nm}}\end{array}\right]---\left(19\right)$

(5) method for solving of flight path optimization model

The solution procedure of unmanned aerial vehicle flight path programme optimization model is: at first, under the prerequisite that satisfies constraint conditions such as radar, guided missile, antiaircraft gun and atmosphere, draw feasible unmanned aerial vehicle flight path scheme collection; Then, according to decision objective system and optimization model, utilization deviation maximization method is asked the weight of each attribute, promptly obtains the weight of radar, guided missile, antiaircraft gun, atmosphere threat cost and oil consumption cost, is expressed as δ respectively _O, δ _R, δ _A, δ _MAnd δ _C, then, the scheme collection made a strategic decision and estimate, and finally determine the unmanned aerial vehicle flight path scheme of integrate-cost minimum based on gray relative analysis method.Wherein, gray relative analysis method is used to carry out each attribute data processing.In the concrete flight path Scheme Choice, appraisement system comprises oil consumption, radar, guided missile, antiaircraft gun and 5 attributes of atmosphere cost, establishes total n bar flight path, and promptly n flight path scheme is expressed as s respectively ₁, s ₂S _iS _n, i bar flight path s wherein _iAttribute form and can use vector x _iExpression:

x _i＝(W _Ri，W _Mi，W _Ai，W _Ci，W _Oi) ^T (20)

N bar flight path constitutes alternatives collection X (x ₁, x ₂..., x _n).Behind each attribute quantification, can determine with reference to property set, be to constitute with reference to property set by the best attributes value of choosing each unmanned aerial vehicle flight path programme.Described a kind of with reference to unmanned aerial vehicle flight path design proposal, i.e. ideal scheme with reference to property set.So can further try to achieve the grey incidence coefficient matrix Ξ of n scheme relative reference design proposal.

$\mathrm{\&Xi;}=\left[\begin{array}{ccccc}{\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">R</figure-callout>}1}& {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">M</figure-callout>}1}& {\mathrm{\&xi;}}_{A1}& {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">C</figure-callout>}1}& {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="1"\; label="O"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">O</figure-callout>}1}\\ {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">R</figure-callout>}2}& {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">M</figure-callout>}2}& {\mathrm{\&xi;}}_{A2}& {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">C</figure-callout>}2}& {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="2"\; label="O"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">O</figure-callout>}2}\\ ...& ...& ...& ...& ...\\ {\mathrm{\&xi;}}_{\mathrm{Rn}}& {\mathrm{\&xi;}}_{\mathrm{Mn}}& {\mathrm{\&xi;}}_{\mathrm{An}}& {\mathrm{\&xi;}}_{\mathrm{Cn}}& {\mathrm{\&xi;}}_{\mathrm{On}}\end{array}\right]---\left(21\right)$

ξ in the formula (20) is the grey incidence coefficient of unmanned aerial vehicle flight path evaluate alternatives attribute with respect to the reference property set.

In addition, each attribute weight according to the deviation maximization method is obtained is weighted, and obtains the degree of association vector R of the decision-making level of each scheme, and computing formula is as follows:

$R=\left[\begin{array}{ccccc}{\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">R</figure-callout>}1}& {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">M</figure-callout>}1}& {\mathrm{\&xi;}}_{A1}& {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">C</figure-callout>}1}& {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="1"\; label="O"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">O</figure-callout>}1}\\ {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">R</figure-callout>}2}& {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">M</figure-callout>}2}& {\mathrm{\&xi;}}_{A2}& {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">C</figure-callout>}2}& {\mathrm{\&xi;}}_{\mathrm{<figure-callout\; id="2"\; label="O"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">O</figure-callout>}2}\\ ...& ...& ...& ...& ...\\ {\mathrm{\&xi;}}_{\mathrm{Rn}}& {\mathrm{\&xi;}}_{\mathrm{Mn}}& {\mathrm{\&xi;}}_{\mathrm{An}}& {\mathrm{\&xi;}}_{\mathrm{Cn}}& {\mathrm{\&xi;}}_{\mathrm{On}}\end{array}\right]{({\mathrm{\&delta;}}_R,{\mathrm{\&delta;}}_M,{\mathrm{\&delta;}}_A,{\mathrm{\&delta;}}_C,{\mathrm{\&delta;}}_O)}^T={({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">r</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000156717500011.png"\; state="\{\{state\}\}">r</figure-callout>}}_2,...,r_n)}^T---\left(22\right)$

According to the grey relational grade vector R=(r of decision-making level ₁, r ₂..., r _n) ^TSize each scheme is carried out quality ordering, determine best unmanned aerial vehicle flight path scheme s ^*And corresponding attribute x ^*

(6) trajectory planning example emulation

Satisfy on the basis of above-mentioned 5 constraint conditions in assurance,, determine that respectively 50 unmanned planes two dimensions and three-dimensional flight path are as alternatives by determining the random search algorithm in zone; Unmanned plane two dimension flight path scheme as shown in Figure 3, no-manned plane three-dimensional flight path scheme as shown in Figure 4, square is the flight path starting point among the figure, pentagram is the flight path node, filled circles is an impact point, and rhombus is the threat radar point, and following triangle is that antiaircraft gun threatens point, sexangle is that atmosphere threatens point, and empty circles is the missile threat point.According to track plot, calculate the initial attribute data of every flight path, comprise that respectively radar, guided missile, antiaircraft gun, atmosphere threaten cost and oil consumption cost; Then,, adopt each attribute weight of obtaining based on the deviation maximization method, adopt gray relative analysis method to obtain the grey incidence coefficient of flight path evaluate alternatives attribute with respect to the reference property set according to above step; At last, be weighted summation, obtain the degree of association of the decision-making level of each scheme, sort, and finally determine the optimal trajectory scheme according to the degree of association.

Claims (4)

1. the unmanned aerial vehicle flight path optimization method based on deviation maximization and grey correlation analysis is characterized in that comprising the steps:

(1) sets up unmanned aerial vehicle flight path evaluate alternatives attribute data matrix, adopt the deviation maximization method that each evaluation attributes is carried out objective tax power;

(2) adopt gray relative analysis method that each evaluation attributes data of unmanned aerial vehicle flight path scheme are handled;

(3) weight with each evaluation attributes of obtaining in the step (1) is weighted, and obtains the degree of association of each unmanned aerial vehicle flight path program decisions layer, with each unmanned aerial vehicle flight path schemes ranking, finally determines the optimal trajectory scheme according to the degree of association.

2. the unmanned aerial vehicle flight path optimization method based on deviation maximization and grey correlation analysis according to claim 1 is characterized in that: the theing contents are as follows of described step (1):

At first determine trajectory planning scheme collection by n unmanned aerial vehicle flight path scheme, m evaluation attributes according to each flight path scheme are set up the evaluation attributes data matrix, and carry out the dimensionless standardization processing, calculate each flight path scheme then with respect to the deviation between other each flight path schemes, and calculate total deviation, obtain the weight of each evaluation attributes at last, and carry out normalized, wherein n, m are the natural number greater than 1.

3. the unmanned aerial vehicle flight path optimization method based on deviation maximization and grey correlation analysis according to claim 1 is characterized in that: the theing contents are as follows of described step (2):

With the evaluation attributes data matrix set up in the step (1) as the gray system matrix, and carry out the dimensionless standardization processing, in n unmanned aerial vehicle flight path scheme, choose the maximal value of each evaluation attributes then, composition standard ideal scheme, with this ideal scheme as the reference sequence, n unmanned aerial vehicle flight path scheme distinguished sequence as a comparison, calculate the grey incidence coefficient of evaluation attributes between reference sequences and each comparative sequences, be that data relationship between reference sequences and each comparative sequences is pressed close to degree, obtain the grey incidence coefficient matrix of trajectory planning scheme collection gray system thus, wherein n is the natural number greater than 1.

4. the unmanned aerial vehicle flight path optimization method based on deviation maximization and grey correlation analysis according to claim 2, it is characterized in that: the number m of described evaluation attributes gets 5,5 evaluation attributes and is respectively oil consumption cost, threat radar cost, missile threat cost, antiaircraft gun threat cost and atmosphere threat cost.

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