CN106294280B - A kind of trajectory planning method - Google Patents
A kind of trajectory planning method Download PDFInfo
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- CN106294280B CN106294280B CN201610700477.XA CN201610700477A CN106294280B CN 106294280 B CN106294280 B CN 106294280B CN 201610700477 A CN201610700477 A CN 201610700477A CN 106294280 B CN106294280 B CN 106294280B
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/10—Simultaneous control of position or course in three dimensions
- G05D1/107—Simultaneous control of position or course in three dimensions specially adapted for missiles
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
Abstract
It is applied to the guided missile with deflecting ability, such as the defect of boost-glide missile, existing inadaptability for traditional trajectory planning method, the invention proposes a kind of trajectory planning methods.The intelligent factors of this method introducing people, ballistic characteristic is directly designed based on analytic curve, it is reverse to calculate control amount and constraint condition, and designer's wish and computer project process are organically combined by sketch interaction technique, the intuitive of trajectory planning process is significantly improved, the efficiency of boost-glide missile trajectory planning under Complex Constraints is improved.
Description
Technical field
The present invention relates to a kind of trajectory planning technical field more particularly to a kind of trajectory parameter is calculated by curved profile
Sketch interacts virtual Domain dynamic inverse trajectory planning method.
Background technique
As what missile defense systems was made the overall arrangement for closes on, competitively research has certain maneuverability at present for each military power
Guided missile to improve Penetration Ability of Missile to keeping guided missile striking capabilities.However this kind of guided missile mostly flies in endoatmosphere,
While meeting transmitting constraint with mission requirements, it is necessary to consider that energy, overload, hot-fluid, dynamic pressure etc. constrain, to considerably increase
Missile flight process complexity.How trajectory is planned, fighting efficiency is improved under the conditions of meeting Complex Constraints, is
The significant challenge that such missile operations application faces.
Conventional trajectory planning method is applied to exist when such missile trajectory is planned following difficult：(1) using control amount as bullet
Planning and designing variable in road changes guided missile stress by adjusting control amount, thus realize that trajectory is modified, it can not be according to task need
It asks and directly trajectory position feature is adjusted, cause trajectory planning process excessively complicated；(2) change it in guided missile stress
Afterwards, it generally requires and the flight characteristics for obtaining guided missile to be integrated by trajectory and constraint condition meets situation, due in trajectory planning
Integral operation needs a large amount of iterations, causes trajectory planning process efficiency lower；(3) change bullet indirectly by changing control amount
The mode in road is difficult to obtain the program results completely the same with target trajectory in practical applications, cause trajectory planning process without
Method reflects designer's wish comprehensively.
Dynamic inverse thought is applied to guidance field by Lu Ping [1], keeps guidance algorithm more succinct, is improved space flight and is flown
The machine ascent stage guides efficiency.Dynamic inversion from path due to that can obtain control amount, thus in robot path planning, fight
Machine and the fields such as unmanned aerial vehicle flight path planning and cruise missile trajectory planning attract attention, and obtain preliminary phased Achievements [2]-
[4].Since dynamic inverse thought needs to it requires the continuous differential of equation of locus to obtain the necessary informations such as speed, acceleration
System equation all-order derivative has specific meanings in the time domain, and does so the wish for being difficult to meet " track is adjustable ".In this regard,
Track optimizing problem is transformed into virtual Domain from time domain, then use dynamic inverse by introducing virtual route by Yakimenko [5], [6]
Method optimize track, propose virtual Domain dynamic inverse (Inverse Dynamics in the Virtual Domain,
IDVD) method.Virtual Domain path and time domain path are mapped by this method by pseudo-velocity.Virtual Domain dynamic inversion is first
First by virtual Domain parameter differential, the information such as virtual Domain speed, acceleration and overload are obtained, but these information do not have the time of time domain
Label.Next using pseudo-velocity by virtual Domain acceleration and overload etc. information correspond in time domain, and plus time domain when
Between label.The parametric solution equation of available parsing is done so, therefore calculating speed is very fast.Due to setting for virtual Domain track
Meter is by fitting of a polynomial, and virtual track does not ensure that global optimum, and then also not can guarantee the overall situation of time-domain traces
It is optimal.John A.Lukacs [7], Ian D.Cowling [8], George Boyarko etc. [9] are closed with Yakimenko respectively
Make, have studied virtual Domain dynamic inversion guide online in quadrotor drone trajectory planning and guidance, interceptor, aircraft friendship
The application of meeting etc..N Akhtar etc. [10] has studied virtual Domain dynamic inversion answering in aerodone real-time track planning simulation
With, the results showed that this method calculating speed is fast, and trajectory planning scheme is conducive to save fuel.Yan Liang etc. [3] is counted using switching political loyalty
Method improves virtual Domain dynamic inversion, operation efficiency is improved in the case where node total number is constant, but algorithm exists
In most cases, it may need to be integrated through successive ignition and determine node location, computational complexity is high.Zhang Yu etc. [2] will be empty
Near-field dynamic inversion is applied in the Trajectory Planning of unmanned fighter, and higher calculating speed and preferable receipts are obtained
Hold back characteristic.[11] such as Marco Ciarci à are based on virtual Domain dynamic inversion and propose a kind of nearly sorrow Guidance, and are applied to
Spacecraft Rendezvous is docked in ground experiment, demonstrates the validity of method by comparative experiments.Jacopo Ventura etc. [12]
It has studied quick optimum attitude track and generates problem, have evaluated the calculated performance of virtual Domain dynamic inversion under different situations.
Summary of the invention
Traditional trajectory planning method is applied to the guided missile with deflecting ability, such as boost-glide missile, has maneuverability
Ballistic and cruise missiles etc. existing for inadaptability.If existing virtual Domain dynamic inversion is in theory of optimal control frame
Lower proposition solves trajectory planning problem using the method for processing two-point boundary value problem its purpose is to solve guidance problems,
It is generally possible to that the location parameter of beginning and end is adjusted, but human-computer interaction not can be carried out to procedure parameter such as flight path
Adjustment, therefore do not have the interaction ability of regulation and control to trajectory.
For disadvantages described above of the existing technology, the invention proposes a kind of trajectory planning methods.This method introduces people
Intelligent factors, ballistic characteristic is directly designed based on analytic curve, it is reverse to calculate control amount and constraint condition, and pass through sketch friendship
Mutual technology organically combines designer's wish and computer project process, significantly improves the intuitive of trajectory planning process, mentions
The efficiency of boost-glide missile trajectory planning under high Complex Constraints.
The technical solution adopted by the present invention is that：
A kind of trajectory planning method, includes the following steps：
S1. boost-glide missile motion model is established；
If ground level is a flat surface, missile flight yaw angle is zero, obtains boost-glide missile Three Degree Of Freedom dynamics meter
Calculate equation：
Wherein, x1、x2、x3Respectively indicate the position of boost-glide missile in east northeast three reference axis of coordinate system lower edge, v
For missile flight speed, γ is trajectory tilt angle, and ψ is trajectory deflection angle, and g is acceleration of gravity；
nx、ny、nzRespectively along the overload in three directions of reference axis under ballistic coordinate system：
Wherein, T is missile propulsive plant thrust, and α is the missile flight angle of attack, and D is missile flight resistance, and L is missile flight liter
Power, Z are missile flight lateral force, and m is the quality of boost-glide missile；
T, α and m is the function of time, is acquired by the formula after interpolation or fitting：
T=T (t) (3)
α=α (t) (4)
M=m (t) (5)
The resistance of guided missile, lift, lateral force are under speed system
Wherein ρ is atmospheric density, and S is characterized area, CD、CL、CZRespectively resistance coefficient, lift coefficient and lateral force system
Number, is obtained by the formula after interpolation or fitting：
CD=CD(α,v,-x3) (9)
CL=CL(α,v,-x3) (10)
CZ=CZ(α,v,-x3) (11)
S2. constraint condition models
(1) stationary point heat flow density
Stationary point heat flow density qwsIt is calculated using Kemp-Riddell formula：
In formula
ρο=1.225 (kg/m3)；
νc=7900 (m/s)；
RNStationary point radius of curvature (m)；
qwsStationary point heat flow density (kW/m2)；
hwWall surface enthalpy (kJ/kg)；
hsStationary point enthalpy (kJ/kg)；
qwsmaxMaximum stationary point heat flow density (kW/m2)；
ρ∞Carry out current density；
ν∞Speed of incoming flow；
(2) n is overloaded
nx≤nxmax
ny≤nymax (13)
nz≤nzmax
Wherein nxmax、nymax、nzmaxFor the boost-glide missile most serious offense that three directions can be born under ballistic coordinate system
It carries；
(3) dynamic pressure q
qmaxThe max-Q that can be born for boost-glide missile；
(4) control amount
When only considering that boost-glide missile indulges plane motion, taking missile flight angle of attack is control amount, is needed to its amplitude
It is constrained, it is as follows：
αmin≤α≤αmax (15)
αminFor the minimum angle of attack, αmaxFor the maximum angle of attack；
(5) initial conditions and end conswtraint
The initial position of boost-glide missile
WithFor given launch point coordinate；
S3. virtual Domain sketch rapid generation；
S3.1 boost-glide missile vertical ascent section sketch generation method
Taking launch point coordinate is origin, i.e. O (0,0,0), then can pass through control point V0(0,0,V0z) define on vertical
Section track is risen, wherein V0zFor control point V0Z-axis coordinate, O and V0The as control point of vertical ascent section trajectory；
Without loss of generality, if τ ∈ [a, a+1), when wherein a=0,1,2 ..., τ are independent variable, that is, virtual Domain of virtual Domain
Between, then virtual Domain track is in east northeast under coordinate system Oxyz：
Wherein x (τ), y (τ), z (τ) are respectively east northeast ground coordinate of x-axis, y-axis and z-axis in coordinate system Oxyz；
Then obtain x (τ), y (τ), z (τ) virtual Domain first derivative and second dervative：
The turning of S3.2 boost-glide missile and gliding section sketch generation method
The sketch of boost-glide missile turning and gliding section can pass through C1Full curve, C2Full curve or C3It is continuous bent
Line generates；
S4. sketch interaction virtual Domain dynamic inverse trajectory parameter method for solving；
After obtaining a complete curve by S3, curve can be expressed as to contain only the function r (τ) an of independent variable,
Using virtual Domain time instant τ as independent variable, the value range of τ is [0, n], and wherein n is curve number of segment；
Assuming that having function f (), τ and t is respectively virtual Domain moment and time domain moment, τ and t have mathematical relationship：
It defines herein
λ (τ) is pseudo-velocity, and is arrangedIndicate f () derivation in time domain, i.e.,F ' () indicates f
() in virtual Domain derivation, i.e.,
Had according to (34), (35) two formulas：
And then have：
After determining virtual Domain curve r (τ), take N number of node that virtual Domain curve r (τ) is discrete in the value range of τ；If τ's
Value range is [0, τf], then the time interval between node in virtual Domain can be obtained by the following method
Each node corresponding virtual Domain moment is represented by
τj=τj-1+ Δ τ, j=2 ..., N (39)
Wherein N is even number；
Boost-glide missile using solid engines as power, when m- relationship between quality m (t), when m- thrust relationship T
(t) it is considered as known；Virtual Domain basic status x at present node is found out firsti、x′i、x″i(i=1,2,3), by r (τ) and its
Single order, second dervative obtain virtual Domain basic status, and result formats are as follows after arrangement：
Work as τj-1∈ [r (τ when 0,1)j-1)=r1(τj-1), work as τj-1R (τ when [1,2] ∈j-1)=r2(τj-1), wherein xi,j-1
Indicate virtual Domain basic status xiValue at node (j-1), i.e. xi(τj-1)；Same x 'i,(j-1)Indicate the basic shape of virtual Domain
Statex′iValue at node (j-1), x "i,(j-1)Indicate virtual Domain basic status x "iValue at node (j-1)；Wherein each section
The calculation method of quantity of state and control amount at point is as follows：
(1) trajectory tilt angle
(2) trajectory deflection angle
(3) trajectory tilt angle virtual Domain derivative γ 'j-1With trajectory deflection angle virtual Domain derivative ψ 'j-1
(4) direction y is overloaded
(5) direction z is overloaded
(6) atmospheric density
hj-1=-x3,j-1 (47)
ρj-1=fair(hj-1) (48)
Wherein fair(hj-1) it is atmospheric density function；
(7) lift
Indicate that lift coefficient is using the linear function of the angle of attack：
CL,j-1=l1αj-1+l2 (49)
So lift
Wherein S is missile signature area, it is assumed that this numerical value is constant in flight course；Wherein l1And l2For fitting coefficient；
(8) angle of attack
(9) resistance
Wherein
d1And d2For fitting coefficient；
(8) the virtual Domain derivative of speed
(9) speed at next node
vj=vj-1+g(nx,j-1-sinγj-1)/λj-1Δτ (56)
(10) node (j-1) arrives the flight time of node j
(11) the next node time domain moment
tj=tj-1+Δtj (58)
(12)Δt2Estimated value
(13)λ1Estimated value
In S3.2 of the present invention, the sketch of boost-glide missile turning and gliding section passes through C1The method that full curve generates is such as
Under：
Defining following 3 multinomials about t first is belt shape parameter lambdabAnd μbBlending functions three times：
Wherein 0≤λb,μb≤3；
Then 3 control vertex V in two dimension or three-dimensional space are giveni(i=0,1,2), curve r (t) is referred to as regulatable
Three cubed Bezier：
R (t)=X0(t)V0+X1(t)V1+X2(t)V2,t∈[0,1] (20)
Wherein Xi(t) (i=0,1,2) is the blending functions defined by formula (19)；
Alternatively, being write above formula (20) as matrix form and being：
In S3.2 of the present invention, the sketch of boost-glide missile turning and gliding section passes through C2The method that full curve generates is such as
Under：
Give one group of control point<V0,V1,…,Vn>, control tangent polygon is constituted with it, takes reconfigurable control point：
λ in formula (22)ciFor point of contact control parameter, and 0 < λci< 1；
So by reconfigurable control point b0,b1,…,b2nThe curve of composition is：
Wherein αcFor adjustment parameter, and 0≤αc≤π；B0(t),B1(t),B2(t),B3It (t) is C-B spline base function, respectively
It is defined as follows：
Wherein C=cos αc, S=sin αc；
Alternatively, by C2Continuous C-B spline curve is write as matrix form and is：
Wherein i=0,1 ..., 2n.
In S3.2 of the present invention, the sketch of boost-glide missile turning and gliding section passes through C3The method that full curve generates is such as
Under：
Give one group of control point<V0,V1,…,Vn>, controlling polygon is constituted with it, constructs side vector：
ai=Vi-Vi-1, i=1,2 ..., n (27)
The tangent vector of each apex of controlling polygon can then be calculated
It enables
And
Take reconfigurable control point
Wherein λiTo control to adjust parameter, and 0 < λi< 1；
Four B-spline curves so may make up by reconfigurable control point
Wherein
The beneficial effects of the present invention are：
(1) present invention is detached from theory of optimal control frame, directly designs ballistic characteristic based on complete analytic curve, inversely
Control amount and constraint condition are calculated, the location parameter of beginning and end can not only be adjusted, it more can be to procedure parameter such as
Flight path is adjusted.Compared with existing best technique, the present invention is not limited to solve the guidance problems of guided missile, in addition to this
The trajectory planning of guided missile can also be solved, ballistic design, realize the problems such as trajectory capability evaluation.
(2) wisdom of humanity is introduced into algorithm by the present invention by way of sketch trajectory, compared with prior art, is realized
The high efficiency interactive of people and computer is linked up, and the person that greatly facilitates trajectory planning realizes my wish using computer, reduce because
Computer understanding deviation leads to a possibility that retrying, and improves computational efficiency.
(3) prior art is to realize adjustment to trajectory by adjusting the control amount of missile flight, and adjustment process is complicated, straight
The property seen is poor, it is difficult to carry out the adjustment or planning of form complexity trajectory.The present invention realizes direct adjustment of the designer to trajectory, letter
Change that adjustment process, intuitive are strong, has been easy to carry out the adjustment or planning of form complexity trajectory.
(4) present invention obtains trajectory parameter using the continuous differential of curve of parsing, saves compared with currently used integration method
Gone integral element, verified by emulation experiment, when average computation of every trajectory a length of 0.013s, improve three compared with integration method
The order of magnitude.
Detailed description of the invention
Fig. 1 is realization process schematic of the invention；
Fig. 2 is flow chart of the invention；
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and specific embodiments.
A kind of trajectory planning method, includes the following steps：
S1. boost-glide missile motion model is established；
If ground level is a flat surface, missile flight yaw angle is zero, and boost-glide missile Three Degree Of Freedom dynamics can be obtained
Accounting equation：
Wherein, x1、x2、x3Respectively indicate the position of boost-glide missile in east northeast three reference axis of coordinate system lower edge, v
For missile flight speed, γ is trajectory tilt angle, and ψ is trajectory deflection angle, and g is acceleration of gravity, is uniformly taken as 9.8m/s in text2；
nx、ny、nzRespectively along the overload in three directions of reference axis under ballistic coordinate system：
Wherein, T is missile propulsive plant thrust, and α is the missile flight angle of attack, and D is missile flight resistance, and L is missile flight liter
Power, Z are missile flight lateral force, and m is the quality of boost-glide missile.
T, α and m is the function of time, and the general formula by after interpolation or fitting acquires：
T=T (t) (3)
α=α (t) (4)
M=m (t) (5)
The resistance of guided missile, lift, lateral force are under speed system (document [15] are shown in definition)
Wherein ρ is atmospheric density, and S is characterized area, CD、CL、CZRespectively resistance coefficient, lift coefficient and lateral force system
Number, they and angle of attack, flying speed V and flying height h (h=-x3) related, interpolation table is generally fabricated to after being tested,
It is obtained by the formula after interpolation or fitting：
CD=CD(α,v,-x3) (9)
CL=CL(α,v,-x3) (10)
CZ=CZ(α,v,-x3) (11)
S2. constraint condition models
(1) stationary point heat flow density
Because stationary point is that boost-glide missile heats more serious part, usually as trajectory planning it is important about
Beam condition.It is calculated in the present invention using Kemp-Riddell formula：
In formula
ρο=1.225 (kg/m3)；
νc=7900 (m/s)；
RNStationary point radius of curvature (m)；
qwsStationary point heat flow density (kW/m2)；
hwWall surface enthalpy (kJ/kg)；
hsStationary point enthalpy (kJ/kg)；
qwsmaxMaximum stationary point heat flow density (kW/m2)；
ρ∞Carry out current density；
ν∞Speed of incoming flow；
(2) n is overloaded
To destroy guided missile structure not in flight course, generally requires and overload is constrained.
nx≤nxmax
ny≤nymax (13)
nz≤nzmax
Wherein nxmax、nymax、nzmaxFor the boost-glide missile most serious offense that three directions can be born under ballistic coordinate system
It carries.
(3) dynamic pressure q
Dynamic pressure reflects the superiority and inferiority of boost-glide missile flight environment of vehicle to a certain extent, generally also as important constraint condition
It provides.
qmaxThe max-Q that can be born for boost-glide missile.
(4) control amount
When only considering that boost-glide missile indulges plane motion, generally taking missile flight angle of attack is control amount, is needed exist for
Its amplitude is constrained.
αmin≤α≤αmax (15)
αminFor the minimum angle of attack, αmaxFor the maximum angle of attack.
(5) initial conditions and end conswtraint
According to mission requirements, position, speed, speed inclination angle, angle of attack etc. can be constrained.In most cases, bullet
All this initial conditions of the initial position containing boost-glide missile in road planning problem.
WithFor given launch point coordinate.
In the constraint condition of above-mentioned (1) to (5), the value at inequality both ends, such as qwsmax、αminEtc. being guided missile parameter, by guided missile
Flying quality determine, guided missile sizing after, these parameters also determine therewith, can be considered known.
S3. virtual Domain sketch rapid generation；
(1) boost-glide missile vertical ascent section sketch generation method
Taking launch point coordinate is origin, i.e. O (0,0,0), then can pass through control point V0(0,0,V0z) define on vertical
Section track is risen, wherein V0zFor control point V0Z-axis coordinate, O and V0The as control point of vertical ascent section trajectory.Control point is control
The key node of a curved profile is made, curve shape can be adjusted by changing their position, thus song needed for building
Line.
Without loss of generality, if τ ∈ [a, a+1) (a=0,1,2 ...) be virtual Domain independent variable, i.e. virtual Domain time, that
In east northeast under coordinate system Oxyz, virtual Domain track is：
Wherein x (τ), y (τ), z (τ) are respectively east northeast ground coordinate of x-axis, y-axis and z-axis in coordinate system Oxyz.
Then obtain x (τ), y (τ), z (τ) virtual Domain first derivative and second dervative：
(2) boost-glide missile turning and gliding section sketch generation method
Necessary explanation is made to curve continuity first.A complete curve C (τ) is constituted equipped with m sections of polynomial curves, wherein
I-th polynomial curve is Ci(τ), i=1,2 ..., if m.For CiThe j rank of (τ) leads arrow, τiFor CiThe distal point of (τ)
Independent variable, ifEvery section of curve is all set up, then claims curve C (τ) in τiPlace is CkContinuously
's[23],[24]。
The sketch of turning and gliding section can pass through C1Full curve, C2Full curve or C3Full curve generates, and divides below
Their generation method is not introduced.
(a)C1Full curve sketch generation method
Bezier (B é zier) curve[25]It is intuitive with operation, the features such as smooth is connected, suitable for solving the bullet in the present invention
Road indicates problem.The regulatable cubic polynomial curve of one type described herein.
Defining 1 following 3 multinomials about t is belt shape parameter lambdabAnd μbBlending functions three times：
Wherein 0≤λb,μb≤3。
Define 3 control vertex V in 2 given two dimensions or three-dimensional spacei(i=0,1,2), curve r (t) is referred to as regulatable
Three cubed Bezier：
R (t)=X0(t)V0+X1(t)V1+X2(t)V2,t∈[0,1] (20)
Wherein Xi(t) (i=0,1,2) is the blending functions defined by formula (19).
Above formula (20) is rewritten into matrix form and is：
(b)C2Full curve sketch generation method
Give one group of control point<V0,V1,…,Vn>, control tangent polygon is constituted with it, takes reconfigurable control point[31][32]
λ in formula (22)ciFor point of contact control parameter[33], and 0 < λci< 1.
So by reconfigurable control point b0,b1,…,b2nThe curve of composition is：
Wherein αcFor adjustment parameter, and 0≤αc≤π。
B0(t),B1(t),B2(t),B3(t) it is C-B spline base function, is defined respectively as：
Here C=cos αc, S=sin αc。
It can also be by C2Continuous C-B spline curve is write as matrix form
Wherein i=0,1 ..., 2n.
To allow the control point at curve negotiating endpoint to enable initial two control points and the ending control point end Liang Ge
It is overlapped[34]。
(c)C3Continuous sketch generation method
Give one group of control point<V0,V1,…,Vn>, controlling polygon is constituted with it[35],[36].Construct side vector
ai=Vi-Vi-1, i=1,2 ..., n (27)
The tangent vector of each apex of controlling polygon can then be calculated
It enables
And
Take reconfigurable control point
Wherein λiTo control to adjust parameter, and 0 < λi< 1.
Four B-spline curves so may make up by reconfigurable control point
Wherein
S4. sketch interaction virtual Domain dynamic inverse trajectory parameter method for solving；
After obtaining a complete curve by S3, curve can be expressed as to contain only the function r (τ) an of independent variable,
Using virtual Domain time instant τ as independent variable, the value range of τ is [0, n], (n is curve number of segment), at the time of it is not in time domain.r
(τ) cannot describe pair of each dotted state and moment in time domain on track although being able to reflect the shape of missile flight track
It should be related to.Establish the corresponding relationship of each dotted state and moment in time domain on track in advance below according to the method introduced before.
Assuming that having function f (), τ and t is respectively virtual Domain moment and time domain moment, τ and t have mathematical relationship：
Here it defines
λ (τ) is pseudo-velocity, since virtual Domain moment and time domain moment are about calculate node (hereinafter referred node)
Monotonically increasing function, therefore λ (τ) > 0, i.e. λ (τ) have orthotropicity.And arrangeIndicate f () derivation in time domain, i.e.,F ' () expression f () is in virtual Domain derivation, i.e.,Hereinafter the derivative of any order of other functions is with such
It pushes away.Had according to (34), (35) two formulas：
Further have：
After determining virtual Domain curve r (τ), for convenience of numerical value calculating, general way be to continuous function carry out it is discrete, this
In be to take N number of node by curve discrete in the value range of τ.Interstitial content can self-defining, but should be noted interstitial content increase
When calculation amount also increase with it.Taking N in the present invention for convenience of motors in boost phase penetration segmentation is even number.If the value range of τ is [0, τf], then
The time interval between node in virtual Domain can be obtained by the following method
Each node corresponding virtual Domain moment is represented by
τj=τj-1+ Δ τ, j=2 ..., N (39)
Wherein N is even number.
Boost-glide missile using solid engines as power, when m- relationship between quality m (t), when m- thrust relationship T
(t) it is considered as known.Virtual Domain basic status x at present node is found out firsti、x′i、x″i(i=1,2,3).By r (τ) and its
Single order, second dervative obtain virtual Domain basic status, and result formats are as follows after arrangement：
Work as τj-1∈ [r (τ when 0,1)j-1)=r1(τj-1), work as τj-1R (τ when [1,2] ∈j-1)=r2(τj-1).Wherein x1,j-1
Indicate x1Value at node (j-1), i.e. x1(τj-1), remaining is identical similar to subscript literary style meaning, herein before it will not obscure
It puts with this notation.Additionally need explanation, the corresponding time domain moment t of present node (j-1)j-1, a computationally node
(j-2) each quantity of state and when control amount (this tittle is referred to as node variable by the present invention) provide, specific method is described below.
(1) trajectory tilt angle
(2) trajectory deflection angle
(3) trajectory tilt angle virtual Domain derivative γ 'j-1With trajectory deflection angle virtual Domain derivative ψ 'j-1
Since this step is relatively complicated, to be more clear formula, γ, x are omittediSubscript (j-1).
(4) direction y is overloaded
(5) direction z is overloaded
(6) atmospheric density
Use the bright luxuriant atmospheric parameter model of poplar[38]Obtain atmospheric density ρj-1。
hj-1=-x3,j-1 (47)
ρj-1=fair(hj-1) (48)
Wherein fair(hj-1) it is atmospheric density function, it is known that it highly can directly seek atmospheric density.
(7) lift
Indicate that lift coefficient is using the linear function of the angle of attack herein：
CL,j-1=l1αj-1+l2 (49)
So lift
Wherein S is missile signature area, it is assumed that this numerical value is constant in flight course.Wherein l1And l2For fitting coefficient.
(8) angle of attack
(9) resistance
Wherein
d1And d2For fitting coefficient.
(8) the virtual Domain derivative of speed
(9) speed at next node
vj=vj-1+g(nx,j-1-sinγj-1)/λj-1Δτ (56)
Wherein Δ τ has passed through (38) formula and has provided.
(10) node (j-1) arrives the flight time of node j
(11) the next node time domain moment
tj=tj-1+Δtj (58)
(12)Δt2Estimated value
(13)λ1Estimated value
When practical calculating, λ1It can beNeighbouring value.
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Claims (1)
1. a kind of trajectory planning method, which is characterized in that include the following steps：
S1. boost-glide missile motion model is established；
If ground level is a flat surface, missile flight yaw angle is zero, obtains boost-glide missile Three Degree Of Freedom dynamics calculation side
Journey：
Wherein, x1、x2、x3The position of boost-glide missile in east northeast three reference axis of coordinate system lower edge is respectively indicated, v is to lead
Flying speed is played, γ is trajectory tilt angle, and ψ is trajectory deflection angle, and g is acceleration of gravity；
nx、ny、nzRespectively along the overload in three directions of reference axis under ballistic coordinate system：
Wherein, T is missile propulsive plant thrust, and α is the missile flight angle of attack, and D is missile flight resistance, and L is missile flight lift, Z
For missile flight lateral force, m is the quality of boost-glide missile；
T, α and m is the function of time, is acquired by the formula after interpolation or fitting：
T=T (t) (3)
α=α (t) (4)
M=m (t) (5)
The resistance of guided missile, lift, lateral force are under speed system
Wherein ρ is atmospheric density, and S is characterized area, CD、CL、CZRespectively resistance coefficient, lift coefficient and sideway force coefficient lead to
Formula after crossing interpolation or fitting obtains：
CD=CD(α,v,-x3) (9)
CL=CL(α,v,-x3) (10)
CZ=CZ(α,v,-x3) (11)
S2. constraint condition models
(1) stationary point heat flow density
Stationary point heat flow density qwsIt is calculated using Kemp-Riddell formula：
In formula
ρο=1.225kg/m3；
νc=7900m/s；
RNStationary point radius of curvature, unit：m；
qwsStationary point heat flow density, unit kW/m2；
hwWall surface enthalpy, unit kJ/kg；
hsStationary point enthalpy, unit kJ/kg；
qwsmaxMaximum stationary point heat flow density, unit kW/m2；
ρ∞Carry out current density；
ν∞Speed of incoming flow；
(2) n is overloaded
Wherein nxmax、nymax、nzmaxFor the boost-glide missile maximum overload that three directions can be born under ballistic coordinate system；
(3) dynamic pressure q
qmaxThe max-Q that can be born for boost-glide missile；
(4) control amount
When only considering that boost-glide missile indulges plane motion, taking missile flight angle of attack is control amount, needs to carry out its amplitude
Constraint, it is as follows：
αmin≤α≤αmax (15)
αminFor the minimum angle of attack, αmaxFor the maximum angle of attack；
(5) initial conditions and end conswtraint
The initial position of boost-glide missile
WithFor given launch point coordinate；
S3. virtual Domain sketch rapid generation；
S3.1 boost-glide missile vertical ascent section sketch generation method
Taking launch point coordinate is origin, i.e. O (0,0,0), then can pass through control point V0(0,0,V0z) define vertical ascent section
Track, wherein V0zFor control point V0Z-axis coordinate, O and V0The as control point of vertical ascent section trajectory；
Without loss of generality, if τ ∈ [a, a+1), wherein a=0,1,2 ..., τ are independent variable, that is, virtual Domain time of virtual Domain, that
In east northeast under coordinate system Oxyz, virtual Domain track is：
Wherein x (τ), y (τ), z (τ) are respectively east northeast ground coordinate of x-axis, y-axis and z-axis in coordinate system Oxyz；
Then obtain x (τ), y (τ), z (τ) virtual Domain first derivative and second dervative：
The turning of S3.2 boost-glide missile and gliding section sketch generation method
The sketch of boost-glide missile turning and gliding section can pass through C1Full curve, C2Full curve or C3Full curve is raw
At；
Wherein, the sketch of boost-glide missile turning and gliding section passes through C1The method that full curve generates is as follows：
Defining following 3 multinomials about t first is belt shape parameter lambdabAnd μbBlending functions three times：
Wherein 0≤λb,μb≤3；
Then 3 control vertex V in two dimension or three-dimensional space are giveni, i=0,1,2, curve r (t) is referred to as regulatable to join three times
Number curve：
R (t)=X0(t)V0+X1(t)V1+X2(t)V2,t∈[0,1] (20)
Wherein Xi(t), i=0,1,2 is the blending functions defined by formula (19)；
Alternatively, being write above formula (20) as matrix form and being：
The sketch of boost-glide missile turning and gliding section passes through C2The method that full curve generates is as follows：
Give one group of control point<V0,V1,…,Vn>, control tangent polygon is constituted with it, takes reconfigurable control point：
λ in formula (22)ciFor point of contact control parameter, and 0 < λci< 1；
So by reconfigurable control point b0,b1,…,b2nThe curve of composition is：
Wherein αcFor adjustment parameter, and 0≤αc≤π；B0(t),B1(t),B2(t),B3(t) it is C-B spline base function, defines respectively
It is as follows：
Wherein C=cos αc, S=sin αc；
Alternatively, by C2Continuous C-B spline curve is write as matrix form and is：
Wherein i=0,1 ..., 2n；
The sketch of boost-glide missile turning and gliding section passes through C3The method that full curve generates is as follows：
Give one group of control point<V0,V1,…,Vn>, controlling polygon is constituted with it, constructs side vector：
ai=Vi-Vi-1, i=1,2 ..., n (27)
The tangent vector of each apex of controlling polygon can then be calculated
It enables
And
Take reconfigurable control point
Wherein λiTo control to adjust parameter, and 0 < λi< 1；
Four B-spline curves so may make up by reconfigurable control point
Wherein
S4. sketch interaction virtual Domain dynamic inverse trajectory parameter method for solving；
After obtaining a complete curve by S3, curve can be expressed as to contain only the function r (τ) an of independent variable, with void
Near-field time instant τ is independent variable, and the value range of τ is [0, n], and wherein n is curve number of segment；
Assuming that having function f (), τ and t is respectively virtual Domain moment and time domain moment, τ and t have mathematical relationship：
It defines herein
λ (τ) is pseudo-velocity, and is arrangedIndicate f () derivation in time domain, i.e.,F ' () indicates that f () exists
Virtual Domain derivation, i.e.,
Had according to (34), (35) two formulas：
And then have：
After determining virtual Domain curve r (τ), take N number of node that virtual Domain curve r (τ) is discrete in the value range of τ；If the value of τ
Range is [0, τf], then the time interval between node in virtual Domain can be obtained by the following method
Each node corresponding virtual Domain moment is represented by
τj=τj-1+ Δ τ, j=2 ..., N (39)
Wherein N is even number；
Boost-glide missile is used as power using solid engines, when m- relationship between quality m (t), when m- thrust relationship T (t) regard
It is known；Virtual Domain basic status x at present node is found out firsti、x′i、x″i, wherein i=1,2,3, by r (τ) and one
Rank, second dervative obtain virtual Domain basic status, and result formats are as follows after arrangement：
Work as τj-1∈ [r (τ when 0,1)j-1)=r1(τj-1), work as τj-1R (τ when [1,2] ∈j-1)=r2(τj-1), wherein xi,j-1Indicate empty
Near-field basic status xiValue at node j-1, i.e. xi(τj-1)；Same x 'i,(j-1)Indicate virtual Domain basic status x 'iIt is saving
Value at point j-1, x "i,(j-1)Indicate virtual Domain basic status x "iValue at node j-1；Wherein the quantity of state at each node and
The calculation method of control amount is as follows：
(1) trajectory tilt angle
(2) trajectory deflection angle
(3) trajectory tilt angle virtual Domain derivative γ 'j-1With trajectory deflection angle virtual Domain derivative ψ 'j-1
(4) direction y is overloaded
(5) direction z is overloaded
(6) atmospheric density
hj-1=-x3,j-1 (47)
ρj-1=fair(hj-1) (48)
Wherein fair(hj-1) it is atmospheric density function；
(7) lift
Indicate that lift coefficient is using the linear function of the angle of attack：
CL,j-1=l1αj-1+l2 (49)
So lift
Wherein S is missile signature area, it is assumed that this numerical value is constant in flight course；Wherein l1And l2For fitting coefficient；
(8) angle of attack
(9) resistance
Wherein
d1And d2For fitting coefficient；
(8) the virtual Domain derivative of speed
(9) speed at next node
vj=vj-1+g(nx,j-1-sinγj-1)/λj-1Δτ (56)
(10) flight time of the node j-1 to node j
(11) the next node time domain moment
tj=tj-1+Δtj (58)
(12)Δt2Estimated value
(13)λ1Estimated value
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| CN107621198B (en) * | 2017-08-28 | 2019-04-12 | 北京航空航天大学 | A kind of multistep decision trajectory planning method around more no-fly zones |
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| CN108153328B (en) * | 2017-12-18 | 2020-04-14 | 北京理工大学 | Multi-missile collaborative track planning method based on segmented Bezier curve |
| CN109101035B (en) * | 2018-09-13 | 2021-06-11 | 西北工业大学 | Method for controlling vertical plane trajectory of UUV in high-altitude gliding |
| CN111462182B (en) * | 2020-03-31 | 2021-08-06 | 南京航空航天大学 | Trajectory missile three-dimensional trajectory estimation method based on infrared early warning image |
| CN112214834B (en) * | 2020-09-11 | 2024-02-06 | 北京空间飞行器总体设计部 | Axisymmetric aircraft pneumatic database establishment method |
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