CN109669475A - Multiple no-manned plane three-dimensional formation reconfiguration method based on artificial bee colony algorithm - Google Patents
Multiple no-manned plane three-dimensional formation reconfiguration method based on artificial bee colony algorithm Download PDFInfo
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Abstract
The invention discloses a kind of multiple no-manned plane three-dimensional formation reconfiguration methods based on artificial bee colony algorithm, belong to unmanned aerial vehicle (UAV) control technical field.The method initially sets up the motion model of unmanned plane, then provides the mathematical description of three-dimensional formation reconfiguration time optimal control；After carrying out piece-wise linearization control input, no-manned plane three-dimensional formation reconfiguration is carried out using ABC algorithm.Compared with the prior art, the present invention is most short by the time of ABC algorithm search to unmanned plane formation reconfiguration, realizes the rapidity of unmanned plane formation reconfiguration；ABC algorithm is global search method, can be to avoid local optimum is fallen into, so that the precision of unmanned plane formation reconfiguration rises.
Description
Technical field
The invention belongs to unmanned aerial vehicle (UAV) control technical fields, are related to a kind of reconstructing method that multiple no-manned plane collaboration is formed into columns, specifically
Ground is said, refers to one kind based on artificial bee colony algorithm (Artificial Bee Colony Algorithm, hereinafter referred to as ABC)
Multiple no-manned plane three-dimensional formation reconfiguration method.
Background technique
Unmanned plane (Unmanned Aerial Vehicle, UAV) is a kind of aircraft without driver on machine, can be with
It is operated by autonomous or remote control, can be consumptive or recuperability, lethal or non-lethal can be carried
Loading device.
Englishman successfully has developed first unmanned plane in the world within 1917, and unmanned plane have passed through unmanned target drone, pre- later
The development process of programming control scounting aeroplane, command remote control scounting aeroplane and complex controll multi-purpose unmanned aerial vehicle, but it is straight
Increasingly extensive application is just obtained to the 1980s, and important function has been played in local war several times.
With the rapid development of calculating, communication, material etc., the performance of unmanned plane is being promoted rapidly, the function having
It can enrich constantly.Due to unmanned plane have good concealment, vitality it is strong, it is cheap, do not fear that loss, landing be simple, operation
The features such as flexible, either military or be all widely used in civilian aspect unmanned plane.Afield, unmanned plane by with
To execute the monitoring work on various search works and battlefield；In agricultural, agriculture can with high-efficiency environment friendly be sprayed using unmanned plane
Medicine；When communication disruption, unmanned plane can be carried out rescue using most fast speed and as temporary base station.
Relative maturity, inspiration of the people by migration of birds propose the flight control technology of single rack unmanned plane at present
There is the unmanned plane of autonomous control ability to arrange according to specified three-dimensional formation and structure multi rack, and is formed into columns by design
Each task is completed in the stabilization that controller makes all unmanned planes that can not only keep rank in flight course, collaboration, and
And the real-time adjustment of troop can be carried out, here it is multiple no-manned planes to cooperate with formation flight (Coordinated Formation
Flight, CFF), such unmanned plane can complete more extensive, more complicated task.Multiple no-manned plane cooperates with formation flight, can
To pass through the success rate of the mutual cooperation raising task of formation member in formation flight, pass through the air formation of different function type
Flight improves efficiency.
For a unmanned plane fleet system, if to guarantee that system can be smoothly performed specified task, wherein
It is primary a little seek to guarantee the formation can normally safe flight, unmanned plane form into columns between there can be no collisions, conflict
The case where equal self-destructions, this is the premise for executing follow-up work.It is just necessary if keeping the safe flight of UAV Formation Flight
Optimal Collaborative Control is carried out to the position of fleet system unmanned plane, speed, direction etc., to realize the flight that unmanned plane is formed into columns
Control.
When multiple unmanned planes are when formation flight executes same task, in the way for going to task or in the task of execution
It needs according to oil consumption, landform, whether there is the situation etc. of barrier, war to carry out reconfiguration.Multiple-uav formation flight executes
When task, avoidance radar, electromagnetic interference, enemy plane and larger barrier are needed, converting suitable formation can be improved task completion
Rate, this relates to three-dimensional formation reconfiguration technology.The core of three-dimensional formation reconfiguration technology be exactly when encountering emergency case, it is how complete
At the reconstruct of multiple no-manned plane formation, so that formation remains unchanged or is optimal the completion that formation guarantees task.
Summary of the invention
The purpose of the present invention is to provide a kind of multiple no-manned plane three-dimensional formation reconfiguration method based on artificial bee colony algorithm, with
The problems such as solving the fast- time control of three-dimensional formation reconfiguration, shortest time and least energy comprehensively control in the prior art, with
And the central controlled optimization problem of the complication systems such as more formation reconfigurations, multi-machine collaborative.
The present invention provides a kind of multiple no-manned plane three-dimensional formation reconfiguration method based on ABC algorithm, and the method is initially set up
Then the motion model of unmanned plane carries out the mathematical description of three-dimensional formation reconfiguration time optimal control, design based on ABC algorithm
No-manned plane three-dimensional formation reconfiguration method, specific as follows:
The first step establishes the motion model of unmanned plane；
The state of flight of unmanned plane is sufficiently complex, it is difficult to it describes, especially when doing the movements such as steering speed change, and unmanned plane system
System is the system of a time-variant nonlinear, and mathematical model is difficult to determine.In order to determine the motion model of unmanned plane, to unmanned plane and
Environment does following setting:
Assuming that unmanned plane is rigid body, and symmetrical shape, uniform quality；
Unmanned plane mass conservation in flight course；
Acceleration of gravity does not change with height change in flight course；
Ignore the influence of the factors such as earth rotation, earth curvature.
In the above conditions, the motion model of unmanned plane can be described by the differential equation (1)~(6):
Formula gives the non-linear relation of state variable (v, γ, χ, x, y, z) and control input (F, n, φ), wherein v
For the speed of unmanned plane, γ is track inclination angle, and χ is flight path azimuthangle, and (x, y, z) indicates the unmanned plane in earth axes
Position, g are acceleration of gravity, and F is motor power, and D is air drag, and W is the weight of unmanned plane, and n is overload, and φ is pitching
Angle.
Second step, the mathematical description of three-dimensional formation reconfiguration time optimal control.
Assuming that the quantity of unmanned plane is N in unmanned plane formation, t=0 is the initial time of formation reconfiguration, and t=T is that formation is heavy
The end time of structure, the control input of unmanned plane are thrust F respectively, overload n and pitch angle φ, therefore the i-th frame in fleet system
Unmanned plane control input mathematic(al) representation beIndicate control
The dimensional space of input vector.The control input vector of fleet system isNobody
The state variable of machine is respectively speed v, track inclination angle γ, flight path azimuthangle χ and three-dimensional position (x, y, z), therefore is formed into columns
The mathematic(al) representation of the state variable of interior i-th frame unmanned plane is Indicate state variable
Dimensional space.Therefore, the state variable of fleet system is defined asThe equation of motion of fleet system
It can state are as follows:
X (t) indicates the state variable of fleet system t moment, and U (t) indicates the control input vector of fleet system t moment.
It is assumed that the continuous control formed into columns inputs U and formation original state X (0)=X0, then formula (8) can uniquely determine
T ∈ (0, T] any time form into columns state variable:
If X (t) is only uniquely determined by U given original state, it is also possible to and X (t | U) it indicates；
The time optimal control problem of fleet system can be stated are as follows: find a continuous control input vector U and end
End time T makes fleet system cost function J (U) minimum, namely:
Fleet system cost function J (U) can be stated are as follows:
J (U)=T (10)
Control the range of input vector are as follows:
UminAnd UmaxRespectively indicate the minimum value and maximum value of control input vector.
The free terminal of fleet system constrains g1(U) are as follows:
In formula: m ∈ { 1 ..., N } defines m frame unmanned plane as the center unmanned plane formed into columns, [xm(T),ym(T),zm
(T)] the moment position center unmanned plane terminal T is indicated；For the terminal T moment form into columns in the i-th frame unmanned plane relative to
The desired relative coordinate values of center unmanned plane that number is m, [xi(T),yi(T),zi(T)]TFor the terminal T moment form into columns in the i-th frame
The position of unmanned plane；
Defining distance between any two framves unmanned plane is di,j(ζi(t),ζj(t)) (wherein, i, j ∈ { 1 ..., N }), table
Up to formula are as follows:
Unmanned plane bumps against in order to prevent, form into columns in any two frame distance d between nobodyi,j(ζi(t),ζj(t)) it has to be larger than
Anticollision distance Dsafe:
In order to ensure in forming into columns can normal real-time communication, the real-time update posture of operation, distance between any two framves unmanned plane
di,j(ζi(t),ζj(t)) it is necessarily less than communication and ensures distance Dcomm:
To sum up, the mathematical description of the time optimal control problem of fleet system are as follows: meeting constraint condition (7) (11) (12)
(14) it under the constraint condition of (15), finds a continuous control input U and terminal time T and (9) (10) two formula is set up.
Third step, piece-wise linearization control input U.
Artificial bee colony algorithm is a kind of global optimization method for imitating honeybee behavior and proposing, is one of swarm intelligence thought
Concrete application.Artificial bee colony algorithm has the characteristics that global search, parameter be less, fast convergence rate, and is not by objective function
No is linear limitation, is suitble to solve three-dimensional formation reconfiguration optimal control problem.However the control of each unmanned plane is defeated in forming into columns
Entering is continuous quantity, and ABC algorithm can not solve continuous control input.Therefore, the control of each unmanned plane in forming into columns first
System input carries out piece-wise linearization processing, controls input with approximate piece-wise linearization and replaces continuous control input, then adopts
It is scanned for ABC algorithm, finds out piece-wise linearization control input.
Control the piece-wise linearization of input: the action time T for controlling input is divided into npA time subregion, each time
Subregion is Δ tp, for the i-th frame unmanned plane in forming into columns, define a ε * npTie up constant set
Then in time T, the continuous control of the i-th frame unmanned plane
Input action u processediFollowing formula can approximatively be stated as using piecewise function:
In above formula,Indicate the i-th frame unmanned aerial vehicle (UAV) control variable in j-th of time subregion Δ tpLinear approximation, χj(t)
It is given by:
The piece-wise linearization constant coefficient collection that definition is formed into columns is combined into Ω={ Ω1,…,ΩN, the approximation control of fleet system is defeated
Enter collection to be combined into
Approximation parameters: after approximate processing, finding optimum control input set U and T makes cost function J for control input
(U) minimum problem is approximatively equivalent to find optimal constant parameter set omega and Δ tp；Therefore, the optimal control of three-dimensional formation reconfiguration
The cost function of system approximate can state are as follows:
Control allows constraint approximate can state are as follows:
Wherein, (umin)iDominant vector minimum value after indicating piece-wise linearization, (umax)iControl after indicating piece-wise linearization
Vector maximization processed.
Free terminal constraint approximate can be stated are as follows:
The statement of fleet system state equation approximation are as follows:
Other constraint condition expression formulas are constant；
After piece-wise linearization control input U, that is, ABC algorithm can be used and solve three-dimensional formation reconfiguration optimal control problem；
The control of formation is inputted into constant set omega={ Ω1,…,ΩNAnd each time subregion Δ tpCombination, wherein
For the input of the i-th frame unmanned aerial vehicle (UAV) control
Six dimensional spaces, as long as these parameters have been determined, so that it may solve formation control input；In this way, no-manned plane three-dimensional formation reconfiguration
It is actually converted into N × npThe problem for keeping cost function optimal is found in × τ+1 dimension；When definition three-dimensional formation reconfiguration is optimal
Between the extension cost function that controls are as follows:
In formula, σijWith σ 'ijThe respectively punishment constant coefficient of anticollision distance restraint and communication guarantee distance restraint；σ*For
The punishment constant coefficient of end conswtraint (20)；For the free terminal constraint expression form of (20) formula left end, i.e. terminal T moment
Square of each unmanned plane position and center unmanned plane location error and the error of the desired relative position of center unmanned plane in forming into columns
With.
4th step, the no-manned plane three-dimensional formation reconfiguration design based on ABC algorithm.
Based on described above, so that it may solve no-manned plane three-dimensional formation reconfiguration problem with ABC algorithm；Any given initial shape
State, the relative status at designated terminal moment are based on ABC algorithm proposed by the present invention, can find optimum control input, drive each nothing
It is man-machine to reach specified flight pattern, the specific steps are as follows:
Step 4.1: the parameter of setting ABC algorithm: bee colony population quantity Np, maximum cycle TpWith threshold value limit.Just
The original state of beginningization unmanned plane initializes SNA nectar source (is equal to the quantity N for employing beep/ 2, i.e. the control input of unmanned plane
Vector).Feasible solution x is randomly generatedijFormula it is as follows:
xij=xmin,j+rand(0,1)*(xmax,j-xmin,j) (23)
In formula, i ∈ { 1 ..., SN, j ∈ { 1 ..., D }, D are the numbers of Optimal Parameters, i.e. what the control of unmanned plane inputted
DimensionRand (0,1) indicates to generate a random number (real number) in (0,1)；xmax,jAnd xmin,jRespectively indicate feasible solution
Maximum value and minimum value.
Step 4.2: calculating the cost function in nectar source and retain position and the cost function in optimal nectar source, is i.e. formula (22)；
Step 4.3: employing bee to carry out neighborhood search according to the position of the food source in memory, find better nectar source.Honey
The formula of source neighborhood search is as follows:
Wherein, vijIndicate the jth dimension word in the neighborhood nectar source in i-th of nectar source, xkjIndicate k-th of the nectar source randomly selected
Jth dimension word；i,k∈{1,…,SN, k is to be randomly generated and k ≠ i,Random number between [- 1,1].Nectar source neighbour
Domain position brings cost function into, finds out the value of cost function, is compared by greedy algorithm, if nectar source neighborhood position cost letter
Number is greater than nectar source cost function, then updating nectar source position is nectar source neighborhood position, otherwise keeps nectar source original position；
Step 4.4: observation bee employs observation bee to adopt according to the nectar source information for employing bee to share by the way of roulette
Honey, nectar source are observed the probability P of bee selectioniFormula is as follows:
In formula, fit (xi) be i-th of feasible solution fitness value, the abundant degree in corresponding nectar source.Nectar source is abundanter, quilt
Observe the probability P of bee selectioniIt is bigger.
Step 4.5: ABC algorithm falls into local optimum in order to prevent, if employing bee searching times in the neighborhood of nectar source big
When given threshold value limit, the quality for improving solution is still failed to, then bee is employed to be converted into investigation bee, it is new to carry out random search
Nectar source.
Step 4.6: step (4.2)~(4.5) repeat, until meeting termination condition.
The present invention has the advantages that
(1) ABC algorithm can realize the real-time of unmanned plane formation reconfiguration with fast convergence；
(2) ABC algorithm is global search method, can be to avoid local optimum is fallen into, so that the essence of unmanned plane formation reconfiguration
Degree rises；
(3) most short by the time of ABC algorithm search to unmanned plane formation reconfiguration, realize the quick of unmanned plane formation reconfiguration
Property.
Detailed description of the invention
The relationship of Fig. 1 objective function and the number of iterations.
Fig. 2 three-dimensional formation reconfiguration motion profile figure.
Fig. 3 three-dimensional formation reconfiguration horizontal plane running track figure.
Fig. 4 three-dimensional formation process unmanned plane distance change curve.
Fig. 5 three-dimensional formation reconfiguration height change curve.
Fig. 6 three-dimensional formation reconfiguration process unmanned plane thrust variation curve.
Fig. 7 three-dimensional formation reconfiguration process unmanned plane overloads change curve.
Fig. 8 three-dimensional formation reconfiguration process unmanned plane pitch angle change curve.
Figure label and symbol description are as follows:
" o " --- indicate the initial position of unmanned plane
" x " --- indicate the final position of unmanned plane
J --- objective function
Cycles --- the number of iterations
T --- the time
F --- thrust
N --- overload
φ --- pitch angle
D --- the distance of any two framves unmanned plane
Specific embodiment
With reference to the accompanying drawing and example, the following further describes the technical solution of the present invention.
It is assumed that unmanned plane form into columns in unmanned plane quantity N=5, it is specified that terminal juncture form into columns in each unmanned plane opposite position
It sets, the parameter of ABC algorithm is set, with the multiple no-manned plane three-dimensional formation reconfiguration side proposed by the present invention based on artificial bee colony algorithm
Method, continuous iteration can find one group of solution under the requirement for meeting unmanned plane flight pattern, guarantee that the time of reconstruct is most short, specifically
Steps are as follows: step 1: the parameter of setting ABC algorithm: bee colony population quantity Np=600, maximum cycle Tp=600 and threshold value
Limit=10000.Initialize SNA nectar source (is equal to the quantity N for employing beep/ 2, SN=300).The public affairs of feasible solution are randomly generated
Formula is as follows:
xij=xmin,j+rand(0,1)*(xmax,j-xmin,j) (26)
In formula, xijIt is D dimension feasible solution, D is the number of Optimal Parameters, i ∈ { 1 ..., SN, j ∈ { 1 ..., D }；xmax,jWith
xmin,jRespectively indicate the maximum value and minimum value of feasible solution.
Step 2: calculating the cost function in nectar source and retain position and the cost function in optimal nectar source；
Step 3: employing bee to carry out neighborhood search according to the position of the food source in memory, find better nectar source.Nectar source
The formula of neighborhood search is as follows:
Wherein, i, k ∈ { 1 ..., SN, k is to be randomly generated and k ≠ i,Random number between [- 1,1].Nectar source neighbour
Domain position vijIt brings cost function into, finds out the value of cost function, be compared by greedy algorithm, if nectar source neighborhood position cost
Function is greater than nectar source cost function, then updating nectar source position is nectar source neighborhood position, otherwise keeps nectar source original position；
Step 4: observation bee employs observation bee gathering honey according to the nectar source information for employing bee to share by the way of roulette,
Formula is as follows:
In formula, fit (xi) it is i-th of fitness value solved, the abundant degree in corresponding nectar source.Nectar source is abundanter, is observed
The probability of bee selection is bigger；
Step 5: ABC algorithm falls into local optimum in order to prevent, if bee searching times in the neighborhood of nectar source is employed to be greater than
When given threshold value limit, the quality for improving solution is still failed to, then bee is employed to be converted into investigation bee, carries out the new honey of random search
Source.
Step 6: step 2~5 repeat, until meeting termination condition.
The specified reconstruct formation of this example is " > ", and Fig. 1-to Fig. 8 gives the simulation result with method proposed by the present invention.
Fig. 1 is the objective function iteration diagram of PSO, GA, HPSOGA and ABC algorithm search optimal solution respectively, it can be seen that
Whether convergence rate or search precision will be far better than other 3 kinds of algorithms for ABC algorithm.Fig. 2 gives no-manned plane three-dimensional
The motion profile figure of formation reconfiguration, it can be seen that unmanned plane substantially flies along shortest path.Fig. 3 gives unmanned plane level
The motion profile in face, it can be seen that horizontal plane meets preset ' < ' formation.Fig. 4 gives between unmanned plane apart from change curve, can
Meet safe distance and communication distance requirement to see.Fig. 5 gives the height change curve of unmanned plane.Fig. 6 gives three-dimensional
The change curve of variable thrust is controlled during formation reconfiguration.Fig. 7 controls variable overload during giving three-dimensional formation reconfiguration
Change curve.Fig. 8 gives the change curve of control variable pitch angle during three-dimensional formation reconfiguration.
The embodiments described herein is to help reader and understands the principle of the present invention, it should be understood that protection of the invention
Range is not limited to such specific embodiments and embodiments.For those skilled in the art, the present invention can have respectively
Kind change and variation.All within the spirits and principles of the present invention, for example, using other formations such as "-" type as formation reconfiguration
Formation etc., any modification, equivalent replacement, improvement and so on should be included within scope of the presently claimed invention.
Claims (3)
1. the multiple no-manned plane three-dimensional formation reconfiguration method based on artificial bee colony algorithm, it is characterised in that: the method includes as follows
Step,
The first step establishes the motion model of unmanned plane；
Second step, the mathematical description of three-dimensional formation reconfiguration time optimal control；
Assuming that the quantity of unmanned plane is N in unmanned plane formation, t=0 is the initial time of formation reconfiguration, and t=T is formation reconfiguration
End time, unmanned plane control input is respectively thrust F, overload n and pitch angle φ, therefore in fleet system the i-th frame nobody
Machine control input mathematic(al) representation beThe control of fleet system input to
Amount isThe state variable of unmanned plane is respectively speed v, track inclination angle γ, boat
Mark azimuth χ and three-dimensional position (x, y, z), therefore the mathematic(al) representation of the state variable for interior i-th frame unmanned plane of forming into columns is ζi
=[vi,γi,χi,xi,yi,zi]；Therefore, the state variable of fleet system is defined asThe fortune of fleet system
Dynamic equation statement are as follows:
X (t) indicates the state variable of fleet system t moment, and U (t) indicates the control input vector of fleet system t moment；
It is assumed that the continuous control formed into columns inputs U and formation original state X (0)=X0, then formula (8) uniquely determine t ∈ (0, T]
The state variable that any time forms into columns:
If X (t) is only uniquely determined by U given original state, indicated with X (t | U)；
The time optimal control problem of fleet system is stated are as follows: finding a continuous control input vector U and terminal time T makes
It is minimum to obtain fleet system cost function J (U), namely:
Fleet system cost function J (U) statement are as follows:
J (U)=T (10)
Control the range of input vector are as follows:
UminAnd UmaxRespectively indicate the minimum value and maximum value of control input vector；
The free terminal of fleet system constrains g1(U) are as follows:
In formula: m ∈ { 1 ..., N } defines m frame unmanned plane as the center unmanned plane formed into columns, [xm(T),ym(T),zm(T)] table
Show the center moment position unmanned plane terminal T；For the terminal T moment form into columns in the i-th frame unmanned plane be relative to number
The desired relative coordinate values of center unmanned plane of m, [xi(T),yi(T),zi(T)]TFor the terminal T moment form into columns in the i-th frame unmanned plane
Position；
Defining distance between any two framves unmanned plane is di,j(ζi(t),ζj(t)) (wherein, i, j ∈ { 1 ..., N }), expression formula
Are as follows:
Any two frame distance d between nobody in forming into columnsi,j(ζi(t),ζj(t)) anticollision distance D is had to be larger thansafe:
Distance d between any two framves unmanned planei,j(ζi(t),ζj(t)) it is necessarily less than communication and ensures distance Dcomm:
To sum up, the mathematical description of the time optimal control problem of fleet system are as follows: meeting constraint condition (7) (11) (12) (14)
(15) it under constraint condition, finds a continuous control input U and terminal time T and (9) (10) two formula is set up；
Third step, piece-wise linearization control input U；
Control the piece-wise linearization of input: the action time T for controlling input is divided into npA time subregion, each time subregion are Δ
tp, for the i-th frame unmanned plane in forming into columns, define a τ * npTie up constant set
Then in time T, the continuous control input action u of the i-th frame unmanned planeiFollowing formula is approximatively stated as using piecewise function:
In above formula,Indicate the i-th frame unmanned aerial vehicle (UAV) control variable in j-th of time subregion Δ tpLinear approximation, χj(t) under
Formula is given:
The piece-wise linearization constant coefficient collection that definition is formed into columns is combined into Ω={ Ω1,…,ΩN, the approximation control input set of fleet system
It is combined into
Approximation parameters: after approximate processing, finding optimum control input set U and T makes cost function J (U) for control input
Minimum problem is approximatively equivalent to find optimal constant parameter set omega and Δ tp；Therefore, three-dimensional formation reconfiguration optimum control
Cost function approximate can state are as follows:
Control allows constraint approximate can state are as follows:
Wherein, (umin)iDominant vector minimum value after indicating piece-wise linearization, (umax)iIndicate piece-wise linearization after control to
Measure maximum value；
Free terminal constraint approximate can be stated are as follows:
The statement of fleet system state equation approximation are as follows:
Other constraint condition expression formulas are constant；
After piece-wise linearization control input U, three-dimensional formation reconfiguration optimal control problem is solved using ABC algorithm；
Define the extension cost function of three-dimensional formation reconfiguration time optimal control are as follows:
In formula, σijWith σ 'ijThe respectively punishment constant coefficient of anticollision distance restraint and communication guarantee distance restraint；σ*For terminal
Constrain the punishment constant coefficient of (20)；
4th step, the no-manned plane three-dimensional formation reconfiguration design based on ABC algorithm.
2. the multiple no-manned plane three-dimensional formation reconfiguration method according to claim 1 based on artificial bee colony algorithm, feature exist
In: unmanned plane motion model described in the first step is as follows,
Following setting is done to unmanned plane and environment:
Assuming that unmanned plane is rigid body, and symmetrical shape, uniform quality；
Unmanned plane mass conservation in flight course；
Acceleration of gravity does not change with height change in flight course；
Ignore the influence of earth rotation, earth curvature factor；
In the above conditions, the motion model of unmanned plane is described by the differential equation (1)~(6):
Formula gives state variable v, γ, χ, x, y, z and control input F, and the non-linear relation of n, φ, wherein v is unmanned plane
Speed, γ is track inclination angle, and χ is flight path azimuthangle, and (x, y, z) indicates the position of the unmanned plane in earth axes, and g is
Acceleration of gravity, F are motor power, and D is air drag, and W is the weight of unmanned plane, and n is overload, and φ is pitch angle.
3. the multiple no-manned plane three-dimensional formation reconfiguration method according to claim 1 based on artificial bee colony algorithm, feature exist
In: specific step is as follows for the ABC algorithm:
Step 4.1: the parameter of setting ABC algorithm: bee colony population quantity Np, maximum cycle TpWith threshold value limit；Initialization
SNA nectar source is equal to the quantity N for employing beep/ 2, feasible solution x is randomly generatedijFormula it is as follows:
xij=xmin,j+rand(0,1)*(xmax,j-xmin,j) (23)
In formula, i ∈ { 1 ..., SN, j ∈ { 1 ..., D }, D are the numbers of Optimal Parameters, i.e. the dimension of the control input of unmanned plane；
Rand (0,1) indicates to generate a random number in (0,1)；xmax,jAnd xmin,jRespectively indicate the maximum value and most of feasible solution
Small value；
Step 4.2: calculating the cost function in nectar source and retain position and the cost function in optimal nectar source, is i.e. formula (22)；
Step 4.3: employing bee to carry out neighborhood search according to the position of the food source in memory, find better nectar source；Nectar source is adjacent
The formula of domain search is as follows:
Wherein, vijIndicate the jth dimension word in the neighborhood nectar source in i-th of nectar source, xkjIndicate the jth in k-th of the nectar source randomly selected
Dimension word；i,k∈{1,…,SN, k is to be randomly generated and k ≠ i,Random number between [- 1,1]；Nectar source neighborhood position
It brings cost function into, finds out the value of cost function, be compared by greedy algorithm, if nectar source neighborhood position cost function is greater than
Nectar source cost function, then updating nectar source position is nectar source neighborhood position, otherwise keeps nectar source original position；
Step 4.4: observation bee employs observation bee gathering honey, honey according to the nectar source information for employing bee to share by the way of roulette
Source is observed the probability P of bee selectioniFormula is as follows:
In formula, fit (xi) be i-th of feasible solution fitness value；
Step 4.5: if employ bee in the neighborhood of nectar source searching times be greater than given threshold value limit when, still fail to improve solution
Quality, then employ bee to be converted into investigation bee, carry out the new nectar source of random search；
Step 4.6: step (4.2)~(4.5) repeat, until meeting termination condition.
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