CN104965519B - A kind of terminal guidance method with angle of fall constraint based on Bezier - Google Patents
A kind of terminal guidance method with angle of fall constraint based on Bezier Download PDFInfo
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Abstract
A kind of terminal guidance method with angle of fall constraint based on Bezier disclosed by the invention is related to a kind of band angle of fall constraint method of guidance based on Bezier for aircraft guidance, belongs to technical field of air vehicle guidance.The present invention includes the following steps：Step 1, aircraft particle dynamics kinematical equation is established；Step 2, it is based on Bezier and carries out kinematic trajectory planning；Step 3, angle of attack is solved based on the aerial vehicle trajectory that step 2 providesm, angle of heel μmIt guidances command, and Real-time Feedback is carried out to aircraft the present situation, realize that carrying out the track weight-normality based on Bezier model online draws, and inquires into the instruction of subsequent time acceleration, until completing whole guidance.The present invention adapts to the lower precision strike demand of a wide range of angle of fall constraint, and can also ensure that aircraft is finally completed strike task in the case where controlled quentity controlled variable is saturated, and has certain robustness to external interference and environmental uncertainty.
Description
Technical field
The present invention relates to a kind of band angle of fall constraint method of guidance more particularly to it is a kind of for aircraft guidance based on shellfish plug
The band angle of fall of your curve constrains method of guidance, belongs to technical field of air vehicle guidance.
Background technology
As the final tache that speed reentry aircrafts are hit over the ground, high-precision terminal guidance technology is related to that entire flight is appointed
The success or failure of business.In practical strike task, in order to obtain best damage effectiveness, terminal point constraint often has important meaning
Justice.In recent years, Planning thought has also been used among Design of Guidance Law.It can be met by carrying out geometric programming to flight path
The demand of terminal position and angle can directly obtain the control instruction of parsing by planning controlled quentity controlled variable, then integrate
To corresponding flight path.The design process of Guidance Law can be considerably simplified using planning technology.In addition, may be used also
Its dependent variable is introduced into performance indicator to use restraint, multiple constraint guidance is more in line with and requires.Aircraft planning strategy is improving
Play an important roll in terms of operational performance and survival ability.
Path planning has obtained the extensive concern of related scholar as a major class particularly important in planning strategy.Road
Diameter planning can be cooked up satisfied flight track for aircraft, improve flight in the case where agreeing with the different mission requirements of aircraft
Quality, to effectively improve the success rate that aircraft is hit over the ground.The one kind of Bezier as nurbs curve, because of its tool
There is stronger geometric flexibility, contains less moulding variable simultaneously, for aircraft, since the geometry of trajectory is in the nature
One smooth curve, and Bezier can almost characterize all smooth curves, therefore Bezier is in characterization trajectory
When there is preferable agreeing with property.
The basic conception of Bezier is introduced first below.Bezier is to utilize spatially one group of control
The curve of point definition, change in shape only rely upon control point number and position.N+1 control point can define N rank Beziers,
Its expression-form is as follows:
In formula：Pi(0≤i≤n) is referred to as i-th of control point coordinates of Bezier, is sequentially connected with PiIt can be somebody's turn to do
The characteristic polygon of Bezier, Bezier are uniquely determined by characteristic polygon.Bi,n(τ) is n times Bernstein bases
Function, expression-form are as follows:
Bezier has the property that：
Property 1：The starting point of Bezier, terminal are overlapped with the starting point of corresponding characteristic polygon, terminal.
Property 2：Tangential direction and characteristic polygon a line at Bezier beginning and end and the last item
The trend on side is consistent.
Property 3：Point on Bezier, which is all fallen within, is controlled by it point PiAmong the convex closure of composition.
Can be seen that Bezier has larger geometric flexibility by above-mentioned introduction, simple structure, design parameter is few,
Complicated trajectory shape, the angle of fall constraint of satisfaction -180deg~0deg can be characterized.Bezier is widely used in flying
Device gliding section and cruise section trajectory planning Bezier, for dive section since aerodynamic parameter variation is violent, flight environment of vehicle is complicated more
Become.Often more demanding to Guidance Law, proposition adapts to the lower precision strike demand of a wide range of angle of fall constraint, and can be full in controlled quentity controlled variable
Also ensure that aircraft is finally completed strike task in the case of, and certain to having to external interference and environmental uncertainty
The terminal guidance method of robustness is very important.
Invention content
The terminal guidance side with angle of fall constraint that the technical problem to be solved in the present invention is to provide a kind of based on Bezier
Method adapts to the lower precision strike demand of a wide range of angle of fall constraint, and can also ensure that aircraft in the case where controlled quentity controlled variable is saturated
It is finally completed strike task, and there is certain robustness to external interference and environmental uncertainty.The a wide range of angle of fall is about
Beam refers to ranging from -180 ° to 0 ° of the angle of fall.
The purpose of the present invention is be achieved through the following technical solutions：
The present invention discloses a kind of terminal guidance method constrained with the angle of fall based on Bezier, includes the following steps：
Step 1, ignore earth rotation, establish aircraft particle dynamics kinematical equation：
Wherein：xm,ym,zmFor position coordinates of the aircraft under inertial system；Vm,γm,χmRespectively speed, trajectory tilt angle,
Trajectory deflection angle；G is acceleration of gravity；μmFor angle of heel；Lm, DmRespectively lift and resistance, wherein SrefFor the area of reference of aircraft；ρ is atmospheric density；CLm,CDmRespectively lift coefficient
And resistance coefficient, lift coefficient CLm, resistance coefficient CDmIt is about angle of attackmWith the function of Mach number Ma.
Step 2, it is based on Bezier and carries out kinematic trajectory planning.
Current location information determines aerial vehicle trajectory with directional velocity and terminal location with angle restriction, is directed to respectively vertical
To planar configuration Bezier track, the track need to be the Bezier of three ranks or more.It is preferred that three rank Bezier are bent
Line constructs Bezier track.
If given control point coordinates is followed successively by (xA,yA,zA), (pxA,pyA,pzA), (pxB,pyB,pzB), (xB,yB,zB),
It can obtain three rank bezier curve equations of aircraft coordinate：
Here for convenience of expression, by controlling polygon starting point (xA,yA,zA) and (xB,yB,zB) it is denoted as endpoint, (pxA,pyA,
pzA) and (pxB,pyB,pzB) still it is denoted as control point.
xm=axτ3+bxτ2+cxτ+dx (9)
ym=ayτ3+byτ2+cyτ+dy (10)
zm=azτ3+bzτ2+czτ+dz (11)
Wherein：τ ∈ [0,1] are intermediate variable, and the multinomial coefficient in formula (9)-(11) can be by following formula (12)-
(14) it determines：
Step 3, angle of attack is solved based on the aerial vehicle trajectory that step 2 providesm, angle of heel μmIt guidances command.
Step 3.1 solves angle of attack using inverse dynamicsm, angle of heel μmIt guidances command.
After determining aircraft movement locus by Bezier, guidanceed command using the solution of inverse dynamics theory, method
To acceleration ayWith longitudinal acceleration azIt is defined as：With following expression-form：
Wherein, ' represent to y derivations, γ 'm,χ′mWith following expression-form：
Can see in conjunction with above-mentioned inverse dynamics analysis, aircraft acceleration instruction not only with aircraft current flight shape
State is related, at the same also with the shape of flight path (range xmWith horizontal journey zmAbout height ymFirst derivative and second dervative) it is related,
Therefore above-mentioned guidance problems are substantially converted into trajectory planning problem.
Acquire aircraft acceleration ayWith azAfter instruction, aircraft angle of heel μmIt can be determined by following formula (18)：
Aircraft lift L can be inquired by formula (18) and aircraft acceleration definitionmWith lift coefficient CLm, and then counter push away
Go out Aircraft Angle of Attack αmInstruction.
Step 3.2, Real-time Feedback is carried out to aircraft the present situation, be iteratively repeated step 2 and step 3.1 realize online into
Track weight-normality of the row based on Bezier model is drawn, and the instruction of subsequent time acceleration is inquired into, until completing whole guidance.It is controlling
Ensure that aircraft realizes the precision strike met under impact angle constraint in the case of amount saturation, and not to external interference and environment
Certainty has certain robustness.
Easily there is saturation this case in acute variation and controlled quentity controlled variable for aircraft dive section environment, at this point, flight
Device will deviate from the flight path planned in advance, only simple to be difficult to ensure attack precision using tracking fixation locus.It will flight
Device current flight state introduces closed loop feedback, by Real-time Feedback, using current state as initial conditions, repeats step 2 and step
3.1 realize that carrying out the track weight-normality based on Bezier model online draws, and inquires into the instruction of subsequent time acceleration, it is dynamic to bring aircraft into
Power kinematics model obtains new state of flight, this process is repeated, when aircraft is due to external disturbance and controlled quentity controlled variable
Track weight-normality is got the full passing to draw, the Guidance Law can gradual correction of deviation, be finally completed whole guidance.
Advantageous effect
1, the present invention carries out trajectory planning using Bezier, enormously simplifies calculation amount, has stronger engineering can
Operability.Bezier has larger geometric flexibility, and simple structure, design parameter is few, can characterize complicated track
Shape can cover -180 ° to 0 ° of a wide range of angle of fall and require, realize and hit requirement to the full angle of fall of target.
2, the present invention have stronger robustness to external disturbance and uncertainty, and can successfully manage guidance during
Controlled quentity controlled variable saturated phenomenon.
Description of the drawings
Fig. 1 (a) is the Bezier Parameters design that last angle is constrained to acute angle；
Fig. 1 (b) is the Bezier Parameters design that last angle is constrained to obtuse angle；
Fig. 1 (c) is the Bezier Parameters design that last angle is constrained to right angle；
Fig. 2 is a kind of terminal guidance method flow chart with angle of fall constraint based on Bezier of the present invention；
Fig. 3 is the geometric locus of two Beziers splicing；
Fig. 4 is parameter selection schematic diagram in Bezier splicing strategy；
Fig. 5 (a) is the flight path curve under different angle of fall constraints for two-dimensional case；
Fig. 5 (b) is the trajectory tilt angle change curve under different angle of fall constraints for two-dimensional case；
Fig. 5 (c) is the speed change curves under different angle of fall constraints for two-dimensional case；
Fig. 5 (d) is the angle of attack variation curve under different angle of fall constraints for two-dimensional case；
Fig. 6 (a) is the flight path curve under different initial angles for two-dimensional case；
Fig. 6 (b) is the trajectory tilt angle change curve under different initial angles for two-dimensional case；
Fig. 6 (c) is the angle of attack variation curve under different initial angles for two-dimensional case；
Fig. 7 (a) is the flight path curve under the constraint of (- 160 °~-180 °) of the big angle of fall for two-dimensional case；
Fig. 7 (b) is the trajectory tilt angle change curve under the constraint of (- 160 °~-180 °) of the big angle of fall for two-dimensional case；
Fig. 7 (c) is the angle of attack variation curve under the constraint of (- 160 °~-180 °) of the big angle of fall for two-dimensional case；
Fig. 8 (a) is in three dimensions for the flight path curve under the constraint of the different angle of falls；
Fig. 8 (b) is in three dimensions for the trajectory tilt angle change curve under the constraint of the different angle of falls；
Fig. 8 (c) is in three dimensions for the trajectory deflection angle change curve under the constraint of the different angle of falls；
Fig. 8 (d) is in three dimensions for the angle of attack variation curve under the constraint of the different angle of falls；
Fig. 8 (e) is in three dimensions for the angle of heel change curve under the constraint of the different angle of falls；
Fig. 9 (a) is the flight path curve under different initial situations in three dimensions；
Fig. 9 (b) is the trajectory tilt angle change curve under different initial situations in three dimensions；
Fig. 9 (c) is the trajectory deflection angle change curve under different initial situations in three dimensions；
Fig. 9 (d) is the angle of attack variation curve under different initial situations in three dimensions；
Fig. 9 (e) is the angle of heel change curve under different initial situations in three dimensions.
Specific implementation mode
In order to better illustrate objects and advantages of the present invention, technical solution is done further with example below in conjunction with the accompanying drawings
It is described in detail.
Embodiment 1：The present embodiment is directed to two-dimensional space, provides the angle of fall in fore-and-aft plane and constrains in -150 °~0 ° range
Interior guidance example.
Step 1, ignore earth rotation, establish the aircraft particle dynamics kinematical equation such as formula in two-dimensional space
(19) shown in-(22).
Step 2, it is based on Bezier and carries out kinematic trajectory planning.
Current location information determines aerial vehicle trajectory with directional velocity and terminal location with angle restriction, is directed to respectively vertical
To planar configuration Bezier track, the track need to be the Bezier of three ranks or more.It is preferred that three rank Bezier are bent
Line constructs Bezier track.
If given control point coordinates is followed successively by (xA,yA), (pxA,pyA), (pxB,pyB), (xB,yB), wherein for convenience of table
Show, by controlling polygon starting point (xA,yA) and (xB,yB) it is denoted as endpoint, (pxA,pyA) and (pxB,pyB) still it is denoted as control point.
Aircraft range xm, height ymConcrete form such as formula (9)-(10) shown in, polynomial parameters are by formula (12)-
(13) it determines.
In the construction process of Bezier, for the selection of reduced parameter, new variables Bezier parameter is defined.Under
Face provides Bezier and the choosing method of parameter in xoy planes.
1)-90°<γf<0°
0≤k1≤k2≤1 (24)
When realizing tracking strike task, if desired trajectory inclination value is smaller, as shown in Fig. 1 (a), control point abscissa is equal
Positioned at closed interval [xA,xB] on, inequality ensures the flatness and accessibility of curve in formula.
2)-150°<γf<-90°
With the variation of strike task, for dealing task head-on blows, larger impingement angle constraint is realized in collision moment,
The Parameters design provided in this up-to-date style (23)-(24) is no longer applicable in, using following parameter selection method, such as schemes (1) b
It is shown：
Wherein：(pxi,pyi) be tangent line at Bezier starting point tangent line and End of Curve intersecting point coordinate.
After Bezier parameter determines, corresponding control point coordinates can be obtained：
When the desired angle of fall is -90 °, when continuing using above method construction Bezier parameter, formula (26)-formula (28) acquires
Control point coordinates will appear unusual, by deformation, Fig. 1 (b) is deformed into Fig. 1 (c) at this time, corresponding control point can be obtained and sit
Mark is as follows：
It is noted here that the Bezier parametric configuration method that formula (25) provides is for -90 °<γf<0 ° of partial picture
It is equally applicable, but as desired trajectory tilt angle γfMeet condition with angle of sight λ | γf|<| λ | when, at Bezier endpoint
Tangent line can not intersect, and formula (25) will be unable to be applicable in.
Step 3, angle of attack is solved based on the aerial vehicle trajectory that step 2 providesmIt guidances command.
Step 3.1 solves angle of attack using inverse dynamicsmIt guidances command.
Since aircraft dive section flying height is generally monotone decreasing, rule of thumb, t is replaced using heightgo, as certainly
Variable build model can Simplified analysis, be more in line with engineering practice simultaneously, reduce by tgoEstimate the error introduced.It will flight
Device particle power is expressed as with kinematical equation with height ymFor the equation of independent variable：
In formula:' represent to ymDerivation, ayLongitudinal acceleration is represented, they have following expression-form：
By formula (33) can its acceleration expression formula be as follows with reverse：
That is acceleration instruction can be by instant position, speed, angle and γ 'mExpression obtains, and is managed using inverse dynamics
By γ ' can then be obtained by continuing derivation to formula (31)mExpression formula：
γ′m=-sin2γmx″ (36)
Convolution (35)-(36), aircraft guidance instruction are closely related with aerial vehicle trajectory, therefore by above-mentioned guidance problems
It is converted into trajectory planning problem, can solve to obtain aircraft acceleration instruction a in conjunction with formula (18)y, and then counter can inquire into
Obtain Aircraft Angle of Attack αm.In formula (31)-(33) ' indicate to height ymDerivation, and Bezier expression formula is represented as intermediate change
The function for measuring τ, arrangement is changed using compound function derivation law：
Step 3.2, Real-time Feedback is carried out to aircraft the present situation, be iteratively repeated step 2 and step 3.1 realize online into
Track weight-normality of the row based on Bezier model is drawn, and the instruction of subsequent time acceleration is inquired into, until completing whole guidance.It is controlling
Ensure that aircraft realizes the precision strike met under impact angle constraint in the case of amount saturation, and not to external interference and environment
Certainty has certain robustness.
Easily there is saturation this case in acute variation and controlled quentity controlled variable for aircraft dive section environment, at this point, flight
Device will deviate from the flight path planned in advance, only simple to be difficult to ensure attack precision using tracking fixation locus.It will flight
Device current flight state introduces closed loop feedback, by Real-time Feedback, using current state as initial conditions, repeats step 2 and step
3.1 realize that carrying out the track weight-normality based on Bezier model online draws, and inquires into the instruction of subsequent time acceleration, it is dynamic to bring aircraft into
Power kinematics model obtains new state of flight, this process is repeated, when aircraft is due to external disturbance and controlled quentity controlled variable
Track weight-normality is got the full passing to draw, the Guidance Law can gradual correction of deviation, be finally completed whole guidance.
The present embodiment provides the guidance example that the angle of fall in fore-and-aft plane constrains within the scope of -150 °~0 °.It provides first
It is expected that the angle of fall is 0 ° for strike static target point, -30 °, -90 ° and-150 ° of simulation scenarios, trajectory tilt angle initial value is -3 °.
Fig. 5 gives simulation result, can see by the aerial vehicle trajectory and trajectory tilt angle change curve that provide, one kind of the present embodiment
The terminal guidance method with angle of fall constraint based on Bezier can be realized in the case where meeting the angle of fall constraint in a wide range of to mesh
Target precision strike.Simultaneously at the strike moment, aircraft has higher speed, improves damage effectiveness.It is provided by Fig. 5 (d)
Angle of attack variation curve find out, when there is larger turning trend in flight path, the angle of attack instruct αmThere is apparent fluctuation,
This also causes aircraft speed to have significantly to decay.
Fig. 6 gives guides effect with larger initial deviation.Initial trajectory inclination angle is respectively selected as
25 °, 10 °, -10 ° and -25 °.Desired trajectory angle set is -60 °.Even if it can be seen from simulation result there are it is larger just
Beginning deviation, aircraft can under a kind of terminal guidance method guiding with angle of fall constraint based on Bezier of the present embodiment
Realize the zero-miss guidance under being constrained with the angle of fall.It can see by angle of attack variation curve, control occur at mission phase initial stage
A kind of terminal guidance method with angle of fall constraint based on Bezier of amount saturation, the present embodiment still is able to ensure aircraft court
To the trend of target, it is finally and successfully completed strike task.
Embodiment 2：The present embodiment is directed to two-dimensional space, provides the angle of fall in fore-and-aft plane and constrains in -180 °~-150 ° models
Interior guidance example is enclosed, a kind of constraining with the angle of fall based on Bezier of under big angle of fall the present embodiment is verified with this
The validity of terminal guidance method.
Step 1 is the same as embodiment 1.
Step 2, it is based on Bezier and carries out kinematic trajectory planning.
Aircraft range xm, height ymConcrete form such as formula (9)-(10) shown in, polynomial parameters are by formula (12)-
(13) it determines.
When aircraft needs deal target head-on blows with larger angle (- 150 °~-180 °), provided using upper section
Guidance will appear larger miss distance.By the geometric properties of three rank Beziers it is found that flight path initial stage very
In long a distance, the variation of trajectory tilt angle is smaller, until close to just occurring larger motor-driven turning when target, curve two at this time
There is larger fluctuating change in order derivative, that is, overloads demand and increase, controlled quentity controlled variable saturation easily occur.Once being saturated, shorter
Distance in, even if use track weight-normality draw can not ensure that aircraft can be it is expected angle of fall precision strike target.
The flexibility of curve planning can be greatly improved using two section of three rank Bezier splicing.But with curve quantity
Increase, the calculation amount of parameter regulation also accordingly increases, when carrying out trajectory planning designs using the Beziers of two sections of splicings
When, need the parameter adjusted to increase to 7, including the Bezier parameter k of first segment curve11,k12, first segment curve
Terminal (xmid,ymid), slope KmidAnd the Bezier parameter k of second segment curve21,k22.Fig. 3 gives two sections of Beziers
Geometric locus in the case of splicing.
In order to ensure being smoothly connected for two Beziers, it is desirable that curve single order leads even second order and leads continuous parameters, bent
Line is in intermediate point (xmid,ymid) at meet single order and lead continuous parameters condition, i.e.,This
When first segment it is consistent in middle point tangential direction with second segment Bezier.
Intermediate point (x is given belowmid,ymid) determination method.
When using the strategy of two sections of Beziers splicing, intermediate point (xmid,ymid) coordinate and the slope of curve
Kmid, as tuning parameter it needs to be determined that, it is however generally that, the selection of intermediate point will meet two conditions：Condition 1 is to minimize
The length of first segment track, condition 2 is as possible so that whole-process control amount is smaller.For intermediate selection without unique optimal
Solution, therefore during selection, principle is adjusted to reduced parameter.
Strike task under being constrained below for the big angle of fall, provides Bezier intermediate point (xmid,ymid) and slope
KmidA kind of building method：
1. determining intermediate point (x firstmid,ymid) coordinate.It chooses mode as shown in Figure 4, chooses for convenience, enables intermediate
Point is located at target point on same ordinate, and abscissa selection range is in the 40%~60% of total flying height.
2. determining the slope of curve K of middle pointmid.Corresponding corner cut is chosen in 25%~30% range of the desired angle of fall.
Incorporation engineering practical experience, selects y heremid=y0- 50% △ y Kmid=γ0- tan (30% △ γ).
In formula：△ y=y0-yB, △ γ=γ0-γf。
When Bezier angle at the end constraint satisfaction section (- 90 °, 0 °] when, Bezier parametric configuration method is such as public
Formula (23), shown in formula (28).
When Bezier angle at the end constraint satisfaction section [- 180 °, -90 °) when, Bezier parametric configuration method is such as
Shown in formula (25)-(28).
Step 3 is the same as embodiment 1.
Numerical simulation is carried out to the strike situation in two dimensional surface, it is -3 ° to choose initial trajectory inclination angle.Simulation result is as schemed
Shown in 7.Red-label point in wherein Fig. 7 (a) indicates the splice point of two Beziers, it can be seen that due to Bezier song
The geometric properties of line, the splice point are the necessary point in air route.The Guidance, which can be realized, it can be seen from simulation result is falling greatly
Aircraft guiding under the constraint of angle, and reach higher precision, wherein trajectory tilt angle error is not more than 0.8 °, allows model in error
In enclosing.In end of flight, overload instruction is not saturated.
It notices a kind of terminal guidance method constrained with the angle of fall based on Bezier using the present embodiment, is connecting
The tracks Dian Chu only meet the condition of continuity, and are unsatisfactory for smoothness condition, i.e. Second Order Continuous condition, due to being wrapped in controlled quentity controlled variable expression-form
The second dervative x " of the curve containing aerial vehicle trajectory, z ", this brief acceleration, which instructs, saltus step, but general saltus step width occurs in junction
Degree is smaller, can obtain preferably smoothly, not influencing control system tracking effect by the way that second-order lag link is added.
Embodiment 3：
The present embodiment provides the guidance example in three dimensions, verifies a kind of band based on Bezier of the present embodiment
Guidance effect of the terminal guidance method of angle of fall constraint in three dimensions.
Step 1, ignore earth rotation, establish shown in aircraft particle dynamics kinematical equation such as formula (3)-(8).
Step 2, it is based on Bezier and carries out kinematic trajectory planning.
The present invention aerial vehicle trajectory is drawn using Bezier carry out being planned to realize to the position of aircraft end with
Angle restriction.It is preferred that three rank Beziers construction Bezier track.If given control point coordinates is followed successively by (xA,yA,
zA), (pxA,pyA,pzA), (pxB,pyB,pzB), (xB,yB,zB), wherein for convenience of indicating, by controlling polygon starting point (xA,yA,
zA) and (xB,yB,zB) it is denoted as endpoint, (pxA,pyA,pzA) and (pxB,pyB,pzB) still it is denoted as control point.
Aircraft range xm, height ym, horizontal journey zmConcrete form such as formula (9)-(11) shown in, polynomial parameters are by public affairs
Formula (12)-(14) determine.
In the construction process of Bezier, for the selection of reduced parameter, Bezier parameter selection method is shown in implementation
Example 1.
After Bezier parameter determines, corresponding control point coordinates can be obtained：
Step 3, angle of attack is solved based on the aerial vehicle trajectory that step 2 providesm, angle of heel μmIt guidances command.
Step 3.1 solves angle of attack using inverse dynamicsm, angle of heel μmIt guidances command.
Since aircraft dive section flying height is generally monotone decreasing, rule of thumb, t is replaced using heightgo, as certainly
Variable build model can Simplified analysis, be more in line with engineering practice simultaneously, reduce by tgoEstimate the error introduced.It will flight
Device particle power is expressed as with kinematical equation with height ymFor the equation of independent variable：
In formula:' represent to ymDerivation, ay,azLongitudinal acceleration with normal direction is represented, they have following expression-form：
By formula (45)-(47) can its acceleration expression formula be as follows with reverse：
That is acceleration instruction can be by instant position, speed, angle and γ 'm,χ′mExpression obtains, and utilizes inverse dynamics
Theory, γ ' can then be obtained by continuing derivation to formula (42)-(43)m,χ′mExpression formula：
In conjunction with formula (50), formula (18) counter can inquire into obtain Aircraft Angle of Attack αmWith angle of heel μmInstruction.
In formula (42)-(46) ' indicate to height ymDerivation, and Bezier expression formula is represented as intermediate variable τ's
Function is changed arrangement using compound function derivation law：
Step 3.2, Real-time Feedback is carried out to aircraft the present situation, be iteratively repeated step 2 and step 3.1 realize online into
Track weight-normality of the row based on Bezier model is drawn, and the instruction of subsequent time acceleration is inquired into, until completing whole guidance.It is controlling
Ensure that aircraft realizes the precision strike met under impact angle constraint in the case of amount saturation, and not to external interference and environment
Certainty has certain robustness.
First in the case of given primary condition, the guiding result under the constraint of the different expectation angle of falls is given；Then
By simulating, verifying under same end conswtraint, a kind of terminal guidance with angle of fall constraint based on Bezier of the present embodiment
Method is in the guidance performance with larger initial deviation.
Fig. 8 (a)-Fig. 8 (e) gives in three dimensions for the simulation result under the constraint of the different angle of falls, Fig. 8 (a)-Fig. 8
(e) flight path curve, trajectory tilt angle γ is set forthmChange curve, trajectory deflection angle χmChange curve, angle of attackmVariation is bent
Line, angle of heel μmChange curve.
Fig. 8 (a)-Fig. 8 (e) gives in three dimensions for the simulation result under the constraint of different initial angles, Fig. 9 (a)-
Flight path curve, trajectory tilt angle γ is set forth in Fig. 9 (e)mChange curve, trajectory deflection angle χmChange curve, angle of attackmVariation
Curve, angle of heel μmChange curve.
By Fig. 8 (a)-Fig. 8 (e), the simulation result of Fig. 9 (a)-Fig. 9 (e) can be seen that even if with larger initial
When angular deviation, a kind of terminal guidance method with angle of fall constraint based on Bezier of the present embodiment is for three dimensions
Still there is good guiding performance in the case of strike, while can realize in the case where ensureing smaller miss distance and fall on a large scale
Strike task under the constraint of angle, trajectory tilt angle and the trajectory deflection angle Error Absolute Value of collision moment are no more than 0.8 °, permit in error
Perhaps in range.The angle of attack and angle of heel instruction are smooth, are easy to rudder surface control system tracking.
In conclusion a kind of terminal guidance method with angle of fall constraint based on Bezier disclosed by the invention, multiple
It can be realized in two dimensional surface and three dimensions in the case of heterocycle border and controlled quentity controlled variable saturation and the object tape angle of fall is fixed about to ground
Precision strike under beam has very high engineering application value.
The scope of the present invention is not only limited to three embodiments that the present invention provides, and embodiment is used to explain the present invention,
All and change or modification of the invention under the conditions of same principle and design is within protection domain disclosed by the invention.
Claims (6)
1. a kind of terminal guidance method with angle of fall constraint based on Bezier, it is characterised in that：Include the following steps,
Step 1, ignore earth rotation, establish aircraft particle dynamics kinematical equation,
Wherein, xm,ym,zmFor position coordinates of the aircraft under inertial system；Vm,γm,χmRespectively speed, trajectory tilt angle, trajectory
Drift angle；G is acceleration of gravity；μmFor angle of heel；Lm, DmRespectively lift and resistance, wherein SrefFor the area of reference of aircraft；ρ is atmospheric density；CLm,CDmRespectively lift coefficient and resistance coefficient rise
Force coefficient CLm, resistance coefficient CDmIt is about angle of attackmWith the function of Mach number Ma；
Step 2, it is based on Bezier and carries out kinematic trajectory planning；
Aerial vehicle trajectory is determined with angle restriction, construct Bezier by current location information and directional velocity and terminal location
Curvilinear path, the Bezier track need to be the Bezier of three ranks or more；
If given control point coordinates is followed successively by (xA,yA,zA), (pxA,pyA,pzA), (pxB,pyB,pzB), (xB,yB,zB), it can be with
Obtain three rank bezier curve equations of aircraft coordinate：
For convenience of expression, by controlling polygon starting point (xA,yA,zA) and (xB,yB,zB) it is denoted as endpoint, (pxA,pyA,pzA) and
(pxB,pyB,pzB) still it is denoted as control point；
xm=axτ3+bxτ2+cxτ+dx (7)
ym=ayτ3+byτ2+cyτ+dy (8)
zm=azτ3+bzτ2+czτ+dz (9)
Wherein：τ ∈ [0,1] are intermediate variable, and the multinomial coefficient in formula (7)-(9) is determined by following formula (10)-(12)：
Step 3, angle of attack is solved based on the aerial vehicle trajectory that step 2 providesm, angle of heel μmIt guidances command, and current to aircraft
Situation carries out Real-time Feedback, realizes that carrying out the track weight-normality based on Bezier model online draws, and inquires into subsequent time acceleration and refers to
It enables, until completing whole guidance.
2. a kind of terminal guidance method with angle of fall constraint based on Bezier as described in claim 1, it is characterised in that：
Step 3 implementation method includes step 3.1,3.2,
Step 3.1 solves angle of attack using inverse dynamicsm, angle of heel μmIt guidances command；
After determining aircraft movement locus by Bezier, guidanceed command using the solution of inverse dynamics theory, normal direction adds
Speed ayWith longitudinal acceleration azIt is defined as：With following expression-form：
Wherein, ' represent to ymDerivation, γ 'm,χ′mWith following expression-form：
In conjunction with above-mentioned inverse dynamics analysis, aircraft acceleration instruction is not only related to aircraft current flight state, simultaneously
Also related to the shape of flight path, i.e., with range xmWith horizontal journey zmAbout height ymFirst derivative is related to second dervative, therefore
Above-mentioned guidance problems are substantially converted into trajectory planning problem；
Acquire aircraft acceleration ayWith azAfter instruction, aircraft angle of heel μmIt is determined by following formula (16)：
Aircraft lift L can be inquired by formula (16) and aircraft acceleration definitionmWith lift coefficient CLm, and then it is counter release it is winged
Row device angle of attackmInstruction；
Step 3.2, Real-time Feedback is carried out to aircraft the present situation, is iteratively repeated step 2 and step 3.1 realizes online progress base
It is drawn in the track weight-normality of Bezier model, inquires into the instruction of subsequent time acceleration, until whole guidance is completed, it is full in controlled quentity controlled variable
Ensure that aircraft realizes the precision strike met under impact angle constraint in the case of, and uncertain to external interference and environment
Property have certain robustness.
3. a kind of terminal guidance method with angle of fall constraint based on Bezier as claimed in claim 1 or 2, feature exist
In：The Bezier has the property that,
Property 1：The starting point of Bezier, terminal are overlapped with the starting point of corresponding characteristic polygon, terminal；
Property 2：Tangential direction and characteristic polygon a line and the last item side at Bezier beginning and end
Trend is consistent；
Property 3：Point on Bezier, which is all fallen within, is controlled by it point PiAmong the convex closure of composition.
4. a kind of terminal guidance method with angle of fall constraint based on Bezier as claimed in claim 3, it is characterised in that：
It, need to be to being made using the end with angle of fall constraint of Bezier splicing in order to adapt to the guidance requirement within the scope of -180 °~-150 °
Guiding method includes the following steps：
Step 1 is the same as step 1 in claim 1；
Step 2, it is based on Bezier and carries out kinematic trajectory planning；
Aircraft range xm, height ymConcrete form such as formula (7)-(8) shown in, polynomial parameters are true by formula (10)-(11)
It is fixed；
The flexibility of curve planning can be improved using two section of three rank Bezier splicing；But with the increase of curve quantity, ginseng
The calculation amount that number is adjusted also accordingly increases, and when carrying out trajectory planning using the Beziers of two sections of splicings, needs to adjust
Parameter increases to 7, including the Bezier parameter k of first segment curve11,k12, the terminal (x of first segment curvemid,ymid),
Slope KmidAnd the Bezier parameter k of second segment curve21,k22；
In order to ensure being smoothly connected for two Beziers, it is desirable that curve single order leads even second order and leads continuous parameters, and curve exists
Intermediate point (xmid,ymid) at meet single order and lead continuous parameters condition, i.e.,At this time
One section consistent in middle point tangential direction with second segment Bezier；
Provide intermediate point (xmid,ymid) determination method；Intermediate point (xmid,ymid) coordinate and slope of curve Kmid, as tune
Try parameter it needs to be determined that, the selection of intermediate point will meet two conditions：Condition 1 is to minimize the length of first segment track, item
Part 2 is as possible so that whole-process control amount is smaller；
Step 3 is the same as step 3 in claim 1.
5. a kind of terminal guidance method with angle of fall constraint based on Bezier as claimed in claim 4, it is characterised in that：
Strike task under being constrained for the big angle of fall, provides Bezier intermediate point (xmid,ymid) and slope KmidOne kind
Building method,
1. determining intermediate point (x firstmid,ymid) coordinate；In order to facilitate selection, intermediate point is enabled to be located at same ordinate with target point
On, abscissa selection range is in the 40%~60% of total flying height；
2. determining the slope of curve K of middle pointmid；Corresponding corner cut is chosen in 25%~30% range of the desired angle of fall；
Incorporation engineering practical experience selects ymid=y0- 50% Δ y, y0For aircraft Initial Flight Level, Kmid=γ0-tan
(30% Δ γ)；
In formula：Δ y=y0-yB, Δ γ=γ0-γf；
When Bezier angle at the end constraint satisfaction section (- 90 °, 0 °] when, Bezier parametric configuration method such as formula
(17), shown in formula (22)；
When Bezier angle at the end constraint satisfaction section [- 180 °, -90 °) when, Bezier parametric configuration method such as formula
(19) shown in-(22)；
0≤k1≤k2≤1 (18)
6. a kind of terminal guidance method with angle of fall constraint based on Bezier as described in claim 1, it is characterised in that：
Bezier described in step 2 is that three rank Beziers construct Bezier track.
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| CN113834385B (en) * | 2021-09-08 | 2023-02-21 | 中国人民解放军91776部队 | Two-dimensional cooperative guidance method for control time of initial track angle freedom |
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