CN108050888B - A kind of explicit guidance method with no-fly zone constraint - Google Patents
A kind of explicit guidance method with no-fly zone constraint Download PDFInfo
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Abstract
A kind of explicit guidance method with no-fly zone constraint does not need that reference trajectory is stored in advance, acceleration instruction is the explicit expression of guided missile and target current state, no-fly zone characterising parameter different from the method for track reference trajectory.This method of guidance is made of virtual target guidance law and boundary constraint scheme.Target is first mapped to virtual target, then obtain virtual target and guided missile relative motion relation, last proportion of utilization guidance law by missile-operation control to virtual target, to get around no-fly zone.When guided missile hits virtual target, virtual target is overlapped with realistic objective, i.e., guided missile hits realistic objective.In some special circumstances, guided missile still is possible to then need to guarantee using boundary constraint scheme that no-fly zone constrains at this time because turning enters no-fly zone not in time.The acceleration instruction of boundary constraint scheme can smart missiles close to and along no-fly zone boundary flight.Using analytic solutions relevant to proportional guidance law to determine whether needing boundary constraint scheme.
Description
Technical field
The present invention relates to a kind of explicit guidance methods with no-fly zone constraint, belong to space technology, weapon technologies, guidance
Control field.
Background technique
In modern war, both sides at war generally can dispose air defence system in nucleus and forward position, to protect oneself
Square high pay-off target, and compress the skyborne scope of activities of enemy.The effective range of air defence missile is generally by the flight of target
Speed, the highly influence with RCS size.From the point of view of attacker, common penaid is improved the speed of one's own side's aircraft
Degree and mobility reduce flying height, reduce RCS, using bait and using saturation attack etc., but when target is in no-fly zone
When outer movement, optimal way is to bypass the no-fly zone being made of air defense missile system.
Proportional guidance is the Typical Representative of method of guidance, and acceleration instruction is proportional to sight angular rate of change and guided missile is opposite
In the speed of target.Since proportional guidance method is simple, effectively and is easily achieved, proportional guidance is widely used.Although with
Terminal velocity and trajectory tilt angle constraint can be constrained in some explicit guidance methods developed based on proportional guidance, but can not also
Processing has the case where no-fly zone constraint.Currently, considering that common method is when the constraint of no-fly zone: planning one first around prohibiting
Fly the trajectory in area, then controls this reference trajectory of guided missile tracking.Although the track constraint that the method is easily handled various complexity is asked
Topic, but need that reference trajectory is stored in advance, it is only applicable to strike fixation or low-speed motion target.
Summary of the invention
The purpose of the present invention is to solve the above problems, propose a kind of explicit guidance method with no-fly zone constraint.
Different from the method for track reference trajectory, this method of guidance does not need that reference trajectory is stored in advance, and acceleration instruction is guided missile
With the explicit expression of target current state, no-fly zone characterising parameter.This method of guidance by virtual target guidance law and boundary about
Beam scheme composition.The thinking of virtual target guidance law is: target is first mapped to virtual target, then obtain virtual target with
The relative motion relation of guided missile, last proportion of utilization guidance law by missile-operation control to virtual target, to get around no-fly zone.When
When guided missile hits virtual target, virtual target is overlapped with realistic objective, i.e., guided missile hits realistic objective.But some special
In the case of, guided missile still be possible to because turning not in time and enter no-fly zone, then need at this time using boundary constraint scheme come
Guarantee no-fly zone constraint.The acceleration instruction of boundary constraint scheme can smart missiles close to and along no-fly zone boundary flight.
It utilizes herein and proportional guidance law phase
Step 1: establishing kinematics and dynamics equation
Guided missile and the belligerent problem of target in the horizontal plane establish reference system o-xy, and M is guided missile mass center, and T is target matter
The heart, guided missile needs evade the point centered on E point, radius rERound no-fly zone, the position vector of central point E is XE=
[xE,yE]T, wherein xE,yERespectively component of the center position vector in reference axis x-, y-.Then there are following movement difference equations
Wherein, XM=[xM,yM]TFor missile position vector, xM,yMRespectively missile position vector is in reference axis x-, y-
Component,For missile velocity vector,Respectively missile velocity vector is in reference axis x-, y-
Component,For guided missile vector acceleration,Respectively guided missile vector acceleration is in reference axis x-, y-
On component；XT=[xT,yT]TFor target position vector, xT,yTRespectively point of the target position vector in reference axis x-, y-
Amount,For target velocity vector,Respectively component of the target velocity vector in reference axis x-, y-,For aimed acceleration vector,Respectively component of the aimed acceleration vector in reference axis x-, y-.
The transposition of subscript " T " representation vector.In terms of guided missile angle, aimed acceleration vector aTIt can use filter to estimate to obtain, lead
Play vector acceleration aMBe it needs to be determined that control variable.Unit vector shown in Fig. 1 defined belowWith WithIt is vector respectivelyWithUnit vector, it is as follows
Wherein,WithIt is 2- norm.Respectively willWith90 degree are rotated clockwise, unit vector is obtained
Step 2: virtual target Guidance Law Design
Using guided missile mass center M as origin, non-inertial reference frame M-x is establishedMMyMM, xMMThe direction of axis and unit vectorIt is identical,
yMMThe direction of axis and unit vectorIt is identical.The existing translation of this coordinate system, and have rotation, since coordinate origin is located at guided missile matter
In the heart, translational velocity is missile velocity vector VM, translatory acceleration is guided missile vector acceleration aM, ωMAnd βMRespectively
Rotational angular velocity and angular acceleration are in a counterclockwise direction positive direction, and are calculated by following formula
Unit of account vector is described belowDerivativeAssuming that by tiny time section dt, unit vectorIt turns over
Angle d θ is to vectorThen have
D θ=ωMdt (11)
Then unit vectorDerivative be
Utilize Taylor Zhan Shiyou
Wherein, o [(d θ)2] and o [(d θ)3] it is the Pei Yanuo remainder that Taylor is unfolded, it is higher order indefinite small, substitutes into
Formula (13) has
Similarly it can be derived from
Then formula (10) can be further solved to
Notice unit vectorThen above formula can be reduced to
It can similarly obtain, unit vectorWithRotational angular velocity ωTWith angular acceleration βTIt is as follows
In order to get around no-fly zone, target centroid T is first mapped to virtual target point T by virtual target guidance lawm, then will lead
Bullet is guided to virtual target point TmFlight.Virtual target point TmSpecific location determined by following methods
1) it establishes using E point as the center of circle, ME is the great circle C of radius2；
2) great circle C2N point is met at the extended line of line segment ET, N point is mapped to non-inertial reference frame M-xMMyMMXMMAxis
Upper Nm, meet line segment MNmWithArc length it is equal.NmIn non-inertial reference frame M-xMMyMMCoordinate beIts
Middle η is vectorWithAngle, determined by following method；
3)TmPoint is in non-inertial reference frame M-xMMyMMIn coordinate be
NoteFor TmRelative to M-xMMyMMVelocity vector, thenAlong xMMThe component of axisFor
Along yMMThe component of axisFor
It is virtual target point TmRelative to non-inertial reference frame M-xMMyMMIn vector acceleration.Along xMMPoint of axis
AmountIt is as follows
Formula (9) and formula (21-23) are substituted into above formula, and arranged
Along yMMThe component of axisIt is as follows
Formula (9) and (22) are substituted into above formula to obtain
Virtual target guidance law a can be obtained by formula (28) and (30)M0, as follows
Wherein
In order to determine aM0, it is necessary to first determineIn non-inertial reference frame M-xMMyMMObserve virtual target point TmMovement,
Virtual target point T is guided here with proportional guidance lawmMove to M point.Obviously, as M and TmWhen coincidence, guided missile is also just ordered at this time
Middle target.It is obtained by proportional guidance law
Wherein, kPN>=3 be proportional guidance coefficient.By above formula in non-inertial reference frame M-xMMyMMMiddle expansion can obtain
Wherein,WithIt can be calculated respectively by formula (25) and (26).It is line segment MTmIn non-inertial ginseng
According to being M-xMMyMMIn turning rate, be counterclockwise positive, calculated by following formula
Formula (35) substitution formula (31-33) be can be obtained by into virtual target guidance law acceleration instruction aM0。
Step 3: boundary constraint conceptual design
In order to bypass no-fly zone, the target outside no-fly zone, virtual target guidance law a are hitM0Smart missiles will be to virtual mesh
Punctuate TmFlight.As guided missile mass center M and TmWhen coincidence, guided missile has also just hit target.But under a few special, guided missile
It is possible to touching no-fly zone, the following two kinds situation
Case 1: the initial velocity of guided missile is directed toward virtual target point, and under the action of virtual target guidance law, guided missile is gradually
No-fly zone is approached, is hit target before entering no-fly zone；
Case 2: the initial velocity of guided missile is directed toward no-fly district center E, at this point, leading under the action of virtual target guidance law
Bullet is first turned to virtual target point direction, but since turning Maneuver Acceleration is not big enough, is caused guided missile to enter no-fly zone and flown
Row.
Obviously, for be similar to Case 1 track, guided missile after hitting target just can enter no-fly zone the case where, be not necessarily to
Additional measures are taken, missile-target impact otherwise can be interfered, still, for the track for being similar to Case 2, guided missile is in hit mesh
The case where advancing into no-fly zone of mark needs to meet using boundary constraint scheme no-fly zone constraint.Boundary constraint side of the present invention
Case generates the acceleration instruction vector perpendicular to directional velocityIt can directing aircraft slowly close to no-fly zone, and along taboo
Fly area's boundary flight, without entering no-fly zone.
No-fly zone central point E is crossed to guided missile velocity vector VMMake vertical line, intersection point F.DefinitionIt is perpendicular to the list of speed
Bit vector, as follows
The unit vector of vectorAs follows
Then boundary constraint scheme vector acceleration of the present inventionIt can be denoted as
Wherein,It is vector accelerationModulus value.
The distance for defining guided missile to no-fly zone boundary is H, and round no-fly zone radius is rE, missile velocity vector and no-fly zone
The angle of tangential direction is σ, and specific computing rule is as follows
Wherein | | VM| | it is missile velocity vector VM2- norm.Then H is to the derivative of time
σ is to the derivative of time
Formula (9) and formula (39) are substituted into above formula to obtain
Due toPerpendicular to directional velocity, then | | VM| | it is steady state value.It is then made of formula (40), (42), (44) non-linear
System S1:
It is state variable for nonlinear control system S1, H and σ,It is control variable.The present invention imitates damping spring
System constructsControl law, i.e. boundary constraint scheme is as follows
Wherein, ωnSimilar to frequency of natural vibration, value size influences the speed that guided missile is approached to no-fly zone boundary,
It can be calculated by following formula
Wherein kωIt is constant.ξ is similar to damped coefficient, and meets
Wherein H0And σ0For the state of initial time.
Step 4: the coordinate scheme design between virtual target guidance and boundary constraint scheme
Coordinate scheme between virtual target guidance and boundary constraint scheme is required to meet: playing master in virtual target guidance law
Under the premise of acting on, boundary constraint scheme acts in due course, i.e., guarantees boundary constraint when necessary, and do not interfere and lead
Bullet is hit target.Here strategy of the invention is: by the belligerent process of simulation and prediction, if had alwaysThen
Boundary constraint scheme does not act on, if at a timeHaveThen boundary constraint scheme plays a role.
WithSize need to be judged by the analytic solutions of proportional guidance law, below the present invention do not having
There is any lineization and carries out the derivation of proportional guidance analytic solutions under the premise of assuming.
In non-inertial reference frame M-xMMyMMIn, due in the case where proportional guidance law acts onPerpendicular toTherefore's
Size is constant.λ is virtual line of sightOpposite xMMThe angle of axis, is counterclockwise positive.ψ isOpposite xMMThe angle of axis,
Equally, it is counterclockwise positive.They are calculated by following formula respectively
In addition rememberRelative virtual sightAngle beIn Fig. 6, as λ-ψ < 0, enableWhen
When λ-ψ > 0, enableThenNote that not considering hereThe case where because this for than
It is singular point for example guidance law.It is abbreviated missile-target distanceWith relative velocity sizeThen have
It can be obtained by proportional guidance law
Formula (52) is updated to above formula to obtain
By
In addition, being had by kinematic relation
Formula (55) are removed into above formula, and are arranged
Above formula is integrated
Wherein, C1It is integral constant, can be obtained by original state
Wherein R0Missile-target distance when being initial,When being initialRelative virtual sightAngle, then have
Formula (53) integral can be obtained
Δ ψ=kPNΔλ (61)
Wherein, Δ ψ=ψ-ψ0, Δ λ=λ-λ0, ψ0And λ0It is initial time state.In addition by being previously with regard toDefinition have
WhereinIt is obtained by formula (61) and (62)
Due to the missile-target distance R of terminal juncturefIt is 0, then can be obtained by formula (60), terminal junctureRelative virtual sightAngleAlso it is 0, then has
Wherein λf, ψfFor the SOT state of termination, work as λ0-ψ0When < 0,Work as λ0-ψ0When > 0,
And haveDue to kPN>=3, then it can obtain range: λf∈ (- 1.5 π, 1.5 π),
ψf∈(-2.5π,2.5π).In addition, virtual target point T can be obtained by formula (60) and formula (63)mOpposite guided missile
The polar equation of mass center M motion profile
Wherein, λ is between λ0And λfBetween, it is independent variable.Conveniently, work as kPNWhen=2, as long as above-mentioned polar coordinates are converted
At rectangular co-ordinate, it is easy for proving that relevant path is one section of circular arc.
Being converted into rectangular co-ordinate analytic solutions just by the polar coordinates analytic solutions of aforementioned proportion guidance law can be used forThe judgement of size, to determine whether boundary constraint scheme plays a role.
Virtual target guidance law aM0EdgeComponent size be
Wherein, aM0It is calculated by formula (31),It is calculated by formula (38).Virtual target guidance law aM0And boundary constraint
Scheme guidance lawBetween coordinate scheme it is as follows:
If boundary constraint scheme plays a role,
Otherwise
aM=aM0 (70)
Wherein,It is calculated by formula (47).Under the action of above-mentioned coordinate scheme, if target is flown outside no-fly zone,
This Guidance Law can guarantee that guided missile does not enter no-fly zone；If target enters no-fly zone, due toVirtual target
Guidance law effect, therefore this Guidance Law has also taken into account the ability that strike enters no-fly zone target.
For some guided missiles, only perpendicular to the control force of directional velocity, and axial acceleration is unadjustable.At this point, only
Take aMPerpendicular to the component of speedIt is as follows as command acceleration
Step 5: the three dimensional form of Guidance Law of the present invention
Respectively in former two-dimensional coordinate system o-xy and M-xMMyMMOn the basis of, increase z- and z vertically upwardMMAxis is established
Three-dimensional coordinate system o-xyz and M-xMMyMMzMM, then the corresponding virtual target point T of targetmPosition vector beWhereinRespectively virtual target point TmComponent of the position vector on respective coordinates axis.
WhereinIt is along zMMThe unit vector of axis,It was the unit vector vertically upward of target point mass center T, η can
It is calculated by formula (24).Then three-dimensional space Guidance Law can be written as
Wherein
Wherein,It is calculated by formula (34), and the virtual target T in formula (34)mIn coordinate system M-xMMyMMzMM
In speedFor
Wherein
So far, the analytic solutions form that Guidance Law of the present invention is applied in three-dimensional space has been obtained.
The present invention has the advantages that
(1) it proposes novel no-fly zone bypassing method, by spatial alternation, the guidance problems constrained with no-fly zone is converted
For the guiding to virtual target in non-inertial reference frame, method is simple, effectively and is easily achieved；
(2) the boundary constraint scheme in the method for guidance can the boundary constraint of strict guarantee no-fly zone, to improve guided missile
It dashes forward anti-performance；
(3) it is different from traditional reference trajectory tracking, which does not need that reference trajectory is stored in advance, add
Speed command is the explicit expression of guided missile and target current state, no-fly zone characterising parameter, therefore missile-borne computer can be real-time
Calculating and more new command.
Detailed description of the invention
Fig. 1 is the belligerent schematic diagram containing no-fly zone in the horizontal plane.
Fig. 2 is non-inertial reference frame M-xMMyMMWith virtual target point Tm。
Fig. 3 is unit vectorDerivative solves auxiliary schematic diagram.
The case where Fig. 4 is touching no-fly zone.
Fig. 5 is instructed around no-fly zone Flight Acceleration.
Fig. 6 is virtual target in M-xMMyMMIn relative motion schematic diagram.
Fig. 7 is the ballistic trajectory curve of embodiment one.
Fig. 8 is the acceleration instruction curve of embodiment one.
Fig. 9 is the ballistic trajectory curve of embodiment two.
Figure 10 is the acceleration instruction curve of embodiment two.
Specific embodiment
Below in conjunction with drawings and examples, the present invention is described in further detail.
The present invention is a kind of explicit guidance's method with no-fly zone constraint, this method of guidance is mainly used for strike no-fly
The target of high-speed motion near area.Different from the method for track reference trajectory, this Guidance Law method does not need that reference is stored in advance
Trajectory, acceleration instruction are the explicit expressions of guided missile and target current state, no-fly zone characterising parameter, therefore missile-borne meter
Calculation machine can calculate in real time and more new command.This method of guidance consists of two parts: virtual target guidance law and boundary constraint side
Case.In order to get around no-fly zone, virtual target guidance law is that target is first mapped to virtual target, then proportion of utilization guiding side
Method is by missile-operation control to virtual target.When guided missile reaches virtual target, virtual target is overlapped with realistic objective, at this time guided missile
Just it hits target.But in some special circumstances, guided missile still is possible to advance into no-fly zone hitting target, at this time then
Boundary constraint scheme is needed to guarantee that no-fly zone constrains.Boundary constraint side is judged here with the analytic solutions of proportional guidance law
Whether case acts on.Whole process including the following steps:
Step 1: establishing kinematics and dynamics equation
Fig. 1 illustrates guided missile and the belligerent problem of target in the horizontal plane, and M is guided missile mass center, and T is target centroid, guided missile
Need to evade the point centered on E point, radius rERound no-fly zone, the position vector of central point E is XE=[xE,yE]T,
Middle xE,yERespectively component of the center position vector in reference axis x-, y-.In reference system o-xy, there is following movement side
Journey group
Wherein, XM=[xM,yM]TFor missile position vector, xM,yMRespectively missile position vector is in reference axis x-, y-
Component,For missile velocity vector,Respectively missile velocity vector is in reference axis x-, y-
Component,For guided missile vector acceleration,Respectively guided missile vector acceleration is in reference axis x-, y-
On component；XT=[xT,yT]TFor target position vector, xT,yTRespectively point of the target position vector in reference axis x-, y-
Amount,For target velocity vector,Respectively component of the target velocity vector in reference axis x-, y-,For aimed acceleration vector,Respectively component of the aimed acceleration vector in reference axis x-, y-.On
Mark the transposition of " T " representation vector.In terms of guided missile angle, aimed acceleration vector aTIt can use filter to estimate to obtain, guided missile
Vector acceleration aMBe it needs to be determined that control variable.Unit vector shown in Fig. 1 defined belowWith
WithIt is vector respectivelyWithUnit vector, it is as follows
Wherein,WithIt is 2- norm.Respectively willWith90 degree are rotated clockwise, unit vector is obtained
Step 2: virtual target Guidance Law Design
Fig. 2 is non-inertial reference frame M-xMMyMM, coordinate origin is located at guided missile mass center M, xMMIt is single in the direction of axis and Fig. 1
Bit vectorIt is identical, yMMUnit vector in the direction of axis and Fig. 1It is identical.The existing translation of this coordinate system, and have rotation, due to
Coordinate origin is located on guided missile mass center, and translational velocity is missile velocity vector VM, translatory acceleration be guided missile acceleration to
Measure aM, ωMAnd βMRespectively rotational angular velocity and angular acceleration are in a counterclockwise direction positive direction, and are calculated by following formula
Unit of account vector is described belowDerivativeIn Fig. 3, by tiny time section dt, unit vectorTurn
Over-angle d θ is to vectorThen have
D θ=ωMdt (93)
Then unit vectorDerivative be
Utilize Taylor Zhan Shiyou
Wherein, o [(d θ)2] and o [(d θ)3] it is the Pei Yanuo remainder that Taylor is unfolded, it is higher order indefinite small, substitutes into
Formula (95) has
Similarly it can be derived from
Then formula (92) can be further solved to
Notice unit vectorThen above formula can be reduced to
It can similarly obtain, unit vectorWithRotational angular velocity ωTWith angular acceleration βTIt is as follows
In Fig. 2, in order to get around no-fly zone, target centroid T is first mapped to virtual target point T by virtual target guidance lawm,
Then by missile-operation control to virtual target point TmFlight.Virtual target point TmSpecific location determined by following methods
1) it establishes using E point as the center of circle, ME is the great circle C of radius2；
2) great circle C2N point is met at the extended line of line segment ET, N point is mapped to non-inertial reference frame M-xMMyMMXMMAxis
Upper Nm, meet line segment MNmWithArc length it is equal.NmIn non-inertial reference frame M-xMMyMMCoordinate beIts
Middle η is vectorWithAngle, determined by following method；
3)TmPoint is in non-inertial reference frame M-xMMyMMIn coordinate be
NoteFor TmRelative to M-xMMyMMVelocity vector, thenAlong xMMThe component of axisFor
Along yMMThe component of axisFor
It is virtual target point TmRelative to non-inertial reference frame M-xMMyMMIn vector acceleration.Along xMMPoint of axis
AmountIt is as follows
Formula (91) and formula (103-105) are substituted into above formula, and arranged
Along yMMThe component of axisIt is as follows
Formula (91) and (104) are substituted into above formula to obtain
Virtual target guidance law a can be obtained by formula (110) and (112)M0, as follows
Wherein
In order to determine aM0, it is necessary to first determineIn non-inertial reference frame M-xMMyMMObserve virtual target point TmMovement,
Virtual target point T is guided here with proportional guidance lawmMove to M point.Obviously, as M and TmWhen coincidence, guided missile is also just ordered at this time
Middle target.It is obtained by proportional guidance law
Wherein, kPN>=3 be proportional guidance coefficient.By above formula in non-inertial reference frame M-xMMyMMMiddle expansion can obtain
Wherein,WithIt can be calculated respectively by formula (107) and (108).It is line segment MTmNon-inertial
Reference system M-xMMyMMIn turning rate, be counterclockwise positive, calculated by following formula
Formula (117) substitution formula (113-115) be can be obtained by into virtual target guidance law acceleration instruction aM0。
Step 3: boundary constraint conceptual design
In order to bypass no-fly zone, the target outside no-fly zone, virtual target guidance law a are hitM0Smart missiles will be to virtual mesh
Punctuate TmFlight.As guided missile mass center M and TmWhen coincidence, guided missile has also just hit target.But under a few special, guided missile
It is possible to touching no-fly zone.Fig. 4 illustrates the special circumstances of two touching no-fly zones, wherein and M point is guided missile centroid position,
T is fixed target centroid position, and E point is no-fly zone central point, and no-fly zone boundary is represented by the dotted line.
Case 1: the initial velocity of guided missile is directed toward virtual target point, and under the action of virtual target guidance law, guided missile is gradually
No-fly zone is approached, is hit target before entering no-fly zone；
Case 2: the initial velocity of guided missile is directed toward no-fly district center E, at this point, leading under the action of virtual target guidance law
Bullet is first turned to virtual target point direction, but since turning Maneuver Acceleration is not big enough, is caused guided missile to enter no-fly zone and flown
Row.
Obviously, for be similar to Case 1 track, guided missile after hitting target just can enter no-fly zone the case where, be not necessarily to
Additional measures are taken, missile-target impact otherwise can be interfered, still, for the track for being similar to Case 2, guided missile is in hit mesh
The case where advancing into no-fly zone of mark needs to meet using boundary constraint scheme no-fly zone constraint.Boundary constraint side of the present invention
Case generates the acceleration instruction vector perpendicular to directional velocityIt can directing aircraft slowly close to no-fly zone, and along taboo
Fly area's boundary flight, without entering no-fly zone.
In Fig. 5, F is no-fly zone central point E to missile velocity vector VMIntersection point.DefinitionIt is perpendicular to the list of speed
Bit vector, as follows
The unit vector of vectorAs follows
Then boundary constraint scheme vector acceleration of the present inventionIt can be denoted as
Wherein,It is vector accelerationModulus value.
The distance for defining guided missile to no-fly zone boundary is H, and round no-fly zone radius is rE, missile velocity vector and no-fly zone
The angle of tangential direction is σ, and specific computing rule is as follows
Wherein | | VM| | it is missile velocity vector VM2- norm.Then H is to the derivative of time
σ is to the derivative of time
Formula (91) and formula (121) are substituted into above formula to obtain
Due toPerpendicular to directional velocity, then | | VM| | it is steady state value.It is then made of formula (122), (124), (126) non-
Linear system S1:
It is state variable for nonlinear control system S1, H and σ,It is control variable.The present invention imitates damping spring
System constructsControl law, i.e. boundary constraint scheme is as follows
Wherein, ωnSimilar to frequency of natural vibration, value size influences the speed that guided missile is approached to no-fly zone boundary,
It can be calculated by following formula
Wherein kωIt is constant.ξ is similar to damped coefficient, and meets
Wherein H0And σ0For the state of initial time.
Step 4: the coordinate scheme design between virtual target guidance and boundary constraint scheme
Coordinate scheme between virtual target guidance and boundary constraint scheme is required to meet: playing master in virtual target guidance law
Under the premise of acting on, boundary constraint scheme acts in due course, i.e., guarantees boundary constraint when necessary, and do not interfere and lead
Bullet is hit target.Here strategy of the invention is: by the belligerent process of simulation and prediction, if had alwaysThen
Boundary constraint scheme does not act on, if at a timeHaveThen boundary constraint scheme plays a role.
WithSize need to be judged by the analytic solutions of proportional guidance law, below the present invention do not having
There is any lineization and carries out the derivation of proportional guidance analytic solutions under the premise of assuming.
In Fig. 6, in non-inertial reference frame M-xMMyMMIn, due in the case where proportional guidance law acts onPerpendicular toThereforeSize it is constant.λ is virtual line of sightOpposite xMMThe angle of axis, is counterclockwise positive.ψ isOpposite xMMAxis
Angle is equally counterclockwise positive.They are calculated by following formula respectively
In addition rememberRelative virtual sightAngle beIn Fig. 6, as λ-ψ < 0, enableWhen
When λ-ψ > 0, enableThenNote that not considering hereThe case where because this for than
It is singular point for example guidance law.It is abbreviated missile-target distanceWith relative velocity sizeThen have
It can be obtained by proportional guidance law
Formula (134) is updated to above formula to obtain
By
In addition, being had by kinematic relation
Formula (137) are removed into above formula, and are arranged
Above formula is integrated
Wherein, C1It is integral constant, can be obtained by original state
Wherein R0Missile-target distance when being initial,When being initialRelative virtual sightAngle, then have
Formula (135) integral can be obtained
Δ ψ=kPNΔλ (143)
Wherein, Δ ψ=ψ-ψ0, Δ λ=λ-λ0, ψ0And λ0It is initial time state.In addition by being previously with regard toDefinition have
WhereinIt is obtained by formula (143) and (144)
Due to the missile-target distance R of terminal juncturefIt is 0, then can be obtained by formula (142), terminal junctureRelative virtual sightAngleAlso it is 0, then has
Wherein λf, ψfFor the SOT state of termination, work as λ0-ψ0When < 0,Work as λ0-ψ0When > 0,And haveDue to kPN>=3, then it can obtain range: λf∈ (- 1.5 π, 1.5 π), ψf∈(-2.5
π,2.5π).In addition, virtual target point T can be obtained by formula (142) and formula (145)mOpposite guided missile mass center M motion profile
Polar equation
Wherein, λ is between λ0And λfBetween, it is independent variable.Conveniently, work as kPNWhen=2, as long as above-mentioned polar coordinates are converted
At rectangular co-ordinate, it is easy for proving that relevant path is one section of circular arc.
Being converted into rectangular co-ordinate analytic solutions just by the polar coordinates analytic solutions of aforementioned proportion guidance law can be used forThe judgement of size, to determine whether boundary constraint scheme plays a role.
Virtual target guidance law aM0EdgeComponent size be
Wherein, aM0It is calculated by formula (113),It is calculated by formula (120).Virtual target guidance law aM0About with boundary
Beam scheme guidance lawBetween coordinate scheme it is as follows:
If boundary constraint scheme plays a role,
Otherwise
aM=aM0 (152)
Wherein,It is calculated by formula (129).Under the action of above-mentioned coordinate scheme, if target flies outside no-fly zone
Row, this Guidance Law can guarantee that guided missile does not enter no-fly zone；If target enters no-fly zone, due toVirtually
The effect of target guiding rule, therefore this Guidance Law has also taken into account the ability that strike enters no-fly zone target.
For some guided missiles, only perpendicular to the control force of directional velocity, and axial acceleration is unadjustable.At this point, only
Take aMPerpendicular to the component of speedIt is as follows as command acceleration
Step 5: the three dimensional form of Guidance Law of the present invention
Respectively in former two-dimensional coordinate system o-xy and M-xMMyMMOn the basis of, increase z- and z vertically upwardMMAxis is established
Three-dimensional coordinate system o-xyz and M-xMMyMMzMM, then the corresponding virtual target point T of targetmPosition vector beWhereinRespectively virtual target point TmComponent of the position vector on respective coordinates axis.
WhereinIt is along zMMThe unit vector of axis,It was the unit vector vertically upward of target point mass center T, η can
It is calculated by formula (106).Then three-dimensional space Guidance Law can be written as
Wherein
Wherein,It is calculated by formula (116), and the virtual target T in formula (116)mIn coordinate system M-
xMMyMMzMMIn speedFor
Wherein
So far, the analytic solutions form that Guidance Law of the present invention is applied in three-dimensional space has been obtained.
Specific embodiment
Embodiment one
The present embodiment requires guided missile strict guarantee no-fly zone boundary constraint while hitting target.It is no-fly in the present embodiment
The center in area is E (0,0), radius rEFor the border circular areas of 20km.Table 1 lists the guided missile and target of the present embodiment emulation
Parameter setting in initial position, speed parameter and boundary constraint scheme.
Table 1
Target is done snakelike motor-driven in subsequent motion, and Maneuver Acceleration is as follows perpendicular to directional velocity
Wherein, d0=23km,It can be calculated by formula (88),It is perpendicular to target velocity VTUnit vector.
Fig. 7 is then ballistic trajectory curve, and Fig. 8 is acceleration instruction curve, whereinFor the axial acceleration of guided missile,
For normal acceleration.It can be seen from the figure that the boundary constraint that process guided missile does not break no-fly zone is entirely intercepted, along smooth
Trajectory target.Wherein only whithin a period of time close to no-fly zone boundary flight, and at this time since BCHS scheme acts on,Curve is upward.
Embodiment two
The present embodiment verifying Guidance Law evades effect to no-fly zone in three dimensions.In the present embodiment, no-fly zone is
It is the center of circle, radius r with E (0,0)EFor the infinite height cylindrical body of 20km.Table 2 lists the guided missile and mesh of the present embodiment emulation
Parameter setting in target initial position, speed parameter and boundary constraint scheme.
Table 2
Target subsequent motion is the horizontal circular movement in 5km height.Fig. 9 be guided missile and target motion profile and its
Track projection on cylindrical surface.Figure 10 is the accelerating curve of guided missile, wherein aM|x,aM|y,aM|zRespectively acceleration in x-,
Component on y-, z- axis.As can be seen that Guidance Law of the present invention can control guided missile along smooth, stable trajectory target, together
When the boundary constraint of strict guarantee no-fly zone.
Claims (1)
1. a kind of explicit guidance method with no-fly zone constraint, which is characterized in that include the following steps:
Step 1: establishing kinematics and dynamics equation
Guided missile and the belligerent problem of target in the horizontal plane establish reference system o-xy, and M is guided missile mass center, and T is target centroid, is led
Bullet needs evade the point centered on E point, radius rERound no-fly zone, the position vector of central point E is XE=[xE,yE]T,
Middle xE,yERespectively component of the center position vector in reference axis x-, y-；Then there are following movement difference equations
Wherein, XM=[xM,yM]TFor missile position vector, xM,yMRespectively point of the missile position vector in reference axis x-, y-
Amount,For missile velocity vector,Respectively point of the missile velocity vector in reference axis x-, y-
Amount,For guided missile vector acceleration,Respectively guided missile vector acceleration is in reference axis x-, y-
Component；XT=[xT,yT]TFor target position vector, xT,yTRespectively component of the target position vector in reference axis x-, y-,For target velocity vector,Respectively component of the target velocity vector in reference axis x-, y-,For aimed acceleration vector,Respectively component of the aimed acceleration vector in reference axis x-, y-；
The transposition of subscript " T " representation vector；In terms of guided missile angle, aimed acceleration vector aTEstimate to obtain using filter, guided missile adds
Velocity vector aMBe it needs to be determined that control variable；Define unit vectorWithWithIt is vector respectivelyWithUnit vector, it is as follows
Wherein,WithIt is 2- norm；Respectively willWith90 degree are rotated clockwise, unit vector is obtained
Step 2: virtual target Guidance Law Design
Using guided missile mass center M as origin, non-inertial reference frame M-x is establishedMMyMM, xMMThe direction of axis and unit vectorIt is identical, yMMAxis
Direction and unit vectorIt is identical；The existing translation of this coordinate system, and have rotation, since coordinate origin is located on guided missile mass center,
Its translational velocity is missile velocity vector VM, translatory acceleration is guided missile vector acceleration aM, ωMAnd βMRespectively angle of rotation
Speed and angular acceleration are in a counterclockwise direction positive direction, and are calculated by following formula
Unit of account vector is described belowDerivativeAssuming that by tiny time section dt, unit vectorTurn over angle d
θ is to vectorThen have
D θ=ωMdt (11)
Then unit vectorDerivative be
Utilize Taylor Zhan Shiyou
Wherein, o [(d θ)2] and o [(d θ)3] it is the Pei Yanuo remainder that Taylor is unfolded, it is higher order indefinite small, substitutes into formula
(13) have
Similarly push away
Then formula (10) is further solved to
Notice unit vectorThen above formula is reduced to
It similarly obtains, unit vectorWithRotational angular velocity ωTWith angular acceleration βTIt is as follows
In order to get around no-fly zone, target centroid T is first mapped to virtual target point T by virtual target guidance lawm, then guided missile is led
Guide virtual target point T intomFlight；Virtual target point TmSpecific location determined by following methods
2.1) it establishes using E point as the center of circle, ME is the great circle C of radius2；
2.2) great circle C2N point is met at the extended line of line segment ET, N point is mapped to non-inertial reference frame M-xMMyMMXMMOn axis
Nm, meet line segment MNmWithArc length it is equal；NmIn non-inertial reference frame M-xMMyMMCoordinate beWherein η
For vectorWithAngle, determined by following method；
2.3)TmPoint is in non-inertial reference frame M-xMMyMMIn coordinate be
NoteFor TmRelative to M-xMMyMMVelocity vector, thenAlong xMMThe component of axisFor
Along yMMThe component of axisFor
It is virtual target point TmRelative to non-inertial reference frame M-xMMyMMIn vector acceleration；Along xMMThe component of axisIt is as follows
Formula (9) and formula (21-23) are substituted into above formula, and arranged
Along yMMThe component of axisIt is as follows
Formula (9) and formula (22) are substituted into above formula to obtain
Virtual target guidance law a is obtained by formula (28) and formula (30)M0, as follows
Wherein
In order to determine aM0, it is necessary to first determineIn non-inertial reference frame M-xMMyMMObserve virtual target point TmMovement, here
Proportion of utilization guidance law guides virtual target point TmMove to M point；Obviously, as M and TmWhen coincidence, guided missile also just hits mesh at this time
Mark；It is obtained by proportional guidance law
Wherein, kPN>=3 be proportional guidance coefficient；By above formula in non-inertial reference frame M-xMMyMMMiddle expansion, obtains
Wherein,WithIt is calculated respectively by formula (25) and (26)；It is line segment MTmIn non-inertial reference frame M-
xMMyMMIn turning rate, be counterclockwise positive, calculated by following formula
Formula (35) substitution formula (31-33) is obtained into virtual target guidance law acceleration instruction aM0；
Step 3: boundary constraint conceptual design
In order to bypass no-fly zone, the target outside no-fly zone, virtual target guidance law a are hitM0Smart missiles will be to virtual target point
TmFlight；As guided missile mass center M and TmWhen coincidence, guided missile has also just hit target；But in a few cases, guided missile remains to touch
No-fly zone, the following two kinds situation:
3.1: the initial velocity of guided missile is directed toward virtual target point, and under the action of virtual target guidance law, guided missile gradually approaches taboo
Fly area, is hit target before entering no-fly zone；
3.2: the initial velocity of guided missile is directed toward no-fly district center E, at this point, under the action of virtual target guidance law, guided missile first to
The turning of virtual target point direction, but since turning Maneuver Acceleration is not big enough, guided missile is caused to enter no-fly zone flight；
Obviously, for be similar to situation 3.1 track, guided missile after hitting target just can enter no-fly zone the case where, without adopting
Additional measures are taken, missile-target impact otherwise can be interfered, still, for the track for being similar to situation 3.2, guided missile is being hit target
The case where advancing into no-fly zone, need to meet using boundary constraint scheme no-fly zone constraint；Boundary constraint scheme, which generates, hangs down
Directly in the acceleration instruction vector of directional velocityIts energy directing aircraft flies slowly close to no-fly zone along no-fly zone boundary
Row, without entering no-fly zone；
No-fly zone central point E is crossed to guided missile velocity vector VMMake vertical line, intersection point F；DefinitionBe perpendicular to the unit of speed to
Amount, as follows
The unit vector of vectorAs follows
Then boundary constraint scheme vector accelerationIt is denoted as
Wherein,It is vector accelerationModulus value；
The distance for defining guided missile to no-fly zone boundary is H, and round no-fly zone radius is rE, missile velocity vector and no-fly zone tangent line
The angle in direction is σ, and specific computing rule is as follows
Wherein | | VM| | it is missile velocity vector VM2- norm；Then H is to the derivative of time
σ is to the derivative of time
Formula (9) and formula (39) are substituted into above formula to obtain
Due toPerpendicular to directional velocity, then | | VM| | it is steady state value；Then it is made of formula (40), formula (42) and formula (44)
Nonlinear system S1:
It is state variable for nonlinear control system S1, H and σ,It is control variable；Damping spring system is imitated, is constructedControl law, i.e. boundary constraint scheme is as follows
Wherein, ωnSimilar to frequency of natural vibration, value size influences the speed that guided missile is approached to no-fly zone boundary, by as follows
Formula calculates
Wherein kωIt is constant；ξ is similar to damped coefficient, and meets
Wherein H0And σ0For the state of initial time；
Step 4: the coordinate scheme design between virtual target guidance and boundary constraint scheme
Coordinate scheme between virtual target guidance and boundary constraint scheme is required to meet: being worked in virtual target guidance law
Under the premise of, boundary constraint scheme acts in due course, i.e., guarantees boundary constraint when necessary, and guided missile is not interfered to hit mesh
Mark；Strategy is: by the belligerent process of simulation and prediction, if had alwaysThen boundary constraint scheme does not act on, such as
Fruit is at a timeHaveThen boundary constraint scheme plays a role；
WithSize need to be judged by the analytic solutions of proportional guidance law, below in no any line
With the derivation for carrying out proportional guidance analytic solutions under the premise of hypothesis；
In non-inertial reference frame M-xMMyMMIn, due in the case where proportional guidance law acts onPerpendicular toThereforeSize
It is constant；λ is virtual line of sightOpposite xMMThe angle of axis, is counterclockwise positive；ψ isOpposite xMMThe angle of axis, equally,
Counterclockwise it is positive；They are calculated by following formula respectively
In addition rememberRelative virtual sightAngle beAs λ-ψ < 0, enableAs λ-ψ > 0,
It enablesThenNote that not considering hereThe case where because this for proportional guidance law and
Speech, is singular point；It is abbreviated missile-target distanceWith relative velocity sizeThen have
It is obtained by proportional guidance law
Formula (52) is updated to above formula to obtain
By
In addition, being had by kinematic relation
Formula (55) are removed into above formula, and are arranged
Above formula is integrated
Wherein, C1It is integral constant, is obtained by original state
Wherein R0Missile-target distance when being initial,When being initialRelative virtual sightAngle, then have
Formula (53) integral is obtained
Δ ψ=kPNΔλ (61)
Wherein, Δ ψ=ψ-ψ0, Δ λ=λ-λ0, ψ0And λ0It is initial time state；In addition by being previously with regard toDefinition have
WhereinIt is obtained by formula (61) and (62)
Due to the missile-target distance R of terminal juncturefIt is 0, then is obtained by formula (60), terminal junctureRelative virtual sight
AngleAlso it is 0, then has
Wherein λf, ψfFor the SOT state of termination, work as λ0-ψ0When < 0,Work as λ0-ψ0When > 0,
And haveDue to kPN>=3, then range be: λf∈ (- 1.5 π, 1.5 π), ψf∈(-2.5π,2.5π)；In addition, by
Formula (60) and formula (63) obtain virtual target point TmThe polar equation of opposite guided missile mass center M motion profile
Wherein, λ is between λ0And λfBetween, it is independent variable；Work as kPNWhen=2, as long as above-mentioned polar coordinates are converted into rectangular co-ordinate,
It is easy to prove that relevant path is one section of circular arc；
Rectangular co-ordinate analytic solutions are converted by the polar coordinates analytic solutions of aforementioned proportion guidance law to be used forSize
Judgement, to determine whether boundary constraint scheme plays a role；
Virtual target guidance law aM0EdgeComponent size be
Wherein, aM0It is calculated by formula (31),It is calculated by formula (38)；Virtual target guidance law aM0It is led with boundary constraint scheme
Draw ruleBetween coordinate scheme it is as follows:
If boundary constraint scheme plays a role,
Otherwise
aM=aM0 (70)
Wherein,It is calculated by formula (47)；Under the action of above-mentioned coordinate scheme, if target is flown outside no-fly zone, this system
Leading rule can guarantee that guided missile does not enter no-fly zone；If target enters no-fly zone, due toVirtual target guiding
Rule effect, therefore this Guidance Law has also taken into account the ability that strike enters no-fly zone target；
For some guided missiles, only perpendicular to the control force of directional velocity, and axial acceleration is unadjustable；As long as at this point, taking aM
Perpendicular to the component of speedIt is as follows as command acceleration
Step 5: the three dimensional form of Guidance Law
Respectively in former two-dimensional coordinate system o-xy and M-xMMyMMOn the basis of, increase z- and z vertically upwardMMAxis is established three-dimensional
Space coordinates o-xyz and M-xMMyMMzMM, then the corresponding virtual target point T of targetmPosition vector be
WhereinRespectively virtual target point TmComponent of the position vector on respective coordinates axis；
WhereinIt is along zMMThe unit vector of axis,It was the unit vector vertically upward of target point mass center T, η is by formula
(24) it is calculated；Then three-dimensional space Guidance Law is written as
Wherein
Wherein,It is calculated by formula (34), and the virtual target T in formula (34)mIn coordinate system M-xMMyMMzMMIn speed
DegreeFor
Wherein
So far, the analytic solutions form that Guidance Law is applied in three-dimensional space has been obtained.
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| EP0807876A1 (en) * | 1996-05-13 | 1997-11-19 | Aerospatiale Societe Nationale Industrielle | Missile steering device |
| CN103090728A (en) * | 2013-01-07 | 2013-05-08 | 北京理工大学 | Tail angle restraining guidance method based on sliding mode control |
| CN106020231A (en) * | 2016-05-30 | 2016-10-12 | 中国人民解放军国防科学技术大学 | Hypersonic air vehicle reentry trajectory optimization method based on reentry point parameter |
| CN107065928A (en) * | 2017-05-04 | 2017-08-18 | 广西大学 | A kind of control method in unmanned plane during flying region |
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| EP0807876A1 (en) * | 1996-05-13 | 1997-11-19 | Aerospatiale Societe Nationale Industrielle | Missile steering device |
| CN103090728A (en) * | 2013-01-07 | 2013-05-08 | 北京理工大学 | Tail angle restraining guidance method based on sliding mode control |
| CN106020231A (en) * | 2016-05-30 | 2016-10-12 | 中国人民解放军国防科学技术大学 | Hypersonic air vehicle reentry trajectory optimization method based on reentry point parameter |
| CN107065928A (en) * | 2017-05-04 | 2017-08-18 | 广西大学 | A kind of control method in unmanned plane during flying region |
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