CN108279699A - The spherical surface track formation tracking and controlling method of aircraft under a kind of space-time variable air flow fields - Google Patents
The spherical surface track formation tracking and controlling method of aircraft under a kind of space-time variable air flow fields Download PDFInfo
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/10—Simultaneous control of position or course in three dimensions
- G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
- G05D1/104—Simultaneous control of position or course in three dimensions specially adapted for aircraft involving a plurality of aircrafts, e.g. formation flying
Abstract
The present invention discloses a kind of spherical surface track formation tracking and controlling method of aircraft under space-time variable air flow fields, the dynamic of aircraft is the incomplete kinetics equation indicated in spherical coordinate system and known flow field is with time and spatial variations, and described method includes following steps：A) it is indicated with the vehicle dynamics equation under spherical coordinate system with Fu Laina formula；B) spherical surface tracking error, track tracking error and lateral formation error are calculated；C) desired yaw velocity, tilt angular speed and linear acceleration are designed so that ensure that aircraft does not move to the line of south poles while error reaches design requirement；D) design yaw angle and tilt angular acceleration make actual sideway and tilt angular speed reach desired value.Such method is simple and reliable, precision is higher, is adapted to the complex tasks such as the cooperation monitoring in arbitrary known space-time variable air flow fields.
Description
Technical field
The present invention relates to the present invention relates to a kind of spherical surface track formation tracing control sides of aircraft under space-time variable air flow fields
Method.
Background technology
In recent years, limited in order to effectively utilize with the development of the communication technology, network technology and sensor technology
A movable body realizes the information collection of Three dimensional Targets in all directions, it usually needs each autokinesis of movable body is on target spherical surface
Expectation track and keep certain formation, i.e. spherical surface track formation tracking control problem.U.S. ocean office once combined multiple
Country and scientific research institution have successively carried out Argo plans and underwater multi-robot cooperation marine monitoring project.NASA is early in 1993
It just announces in year to carry out the plan of exploring the Mars, the last time, which is announced, shows that the U.S. intends structure and is based on explorer satellite and Marsokhod vacant lot
The mars exploration system of one.It can be seen that spherical surface track formation control technology has in terms of three-dimensional spatial information acquisition, monitoring
There is important value.
Currently, most of spherical surface track formation control method all ignores the influence of External airflow field and the movement of aircraft is adopted
With simplest newton particle (Chen Yangyang, wangkai rotation, " geometric design method of the Spherical Ring around formation control ", the patent No.：
CN201510582120.1).However in practical applications, either in ocean the shoal of fish, micropopulation information collection, still too
Empty celestial body detecting, multiple movement bodies inevitably can all be influenced (such as ocean current, wind) by flow field in external environment.Actually
Flow field can not only make movable body deviate the expectation track of oneself but also can destroy desired formation between movable body, in turn result in and adopt
Collect the detrimental effects such as data precision decline.Nearly all collect currently for there is the design of the track formation tracing control of flow
In constant when two dimensional surface and flow field are (Chen Yangyang, a kind of " trailing formation of multirobot in Two-dimensional Steady wind speed field
Control method ", the patent No.：ZL201310318275.5), however either ocean current field or wind field are all with the time in reality
With spatial variations, it is clear that existing design method no longer adapts to, need to develop a kind of new control method solve space-time can
Thus the spherical surface track formation tracking control problem of unsteady flow aircraft off field, this case generate.
Invention content
The purpose of the present invention is to provide a kind of spherical surface track formation tracing control side of aircraft under space-time variable air flow fields
Method, it is simple and reliable, precision is higher, it is adapted to the complex tasks such as the cooperation monitoring in arbitrary known space-time variable air flow fields.
In order to achieve the above objectives, solution of the invention is：
The dynamic of the spherical surface track formation tracking and controlling method of aircraft under a kind of space-time variable air flow fields, aircraft is that ball is sat
The incomplete kinetics equation and known flow field indicated in mark system is with time and spatial variations, and the method includes such as
Lower step：
A) it is indicated with the vehicle dynamics equation under spherical coordinate system with Fu Laina formula；
B) spherical surface tracking error, track tracking error and lateral formation error are calculated；
C) desired yaw velocity, tilt angular speed and linear acceleration are designed so that error reaches design requirement
Ensure that aircraft does not move to the line of south poles simultaneously；
D) design yaw angle and tilt angular acceleration make actual sideway and tilt angular speed reach desired value.
Above-mentioned steps a) includes the following steps：
A1 aircraft kinematical equation and flow field velocity in spherical coordinate system) are synthesized, aircraft in Fu Laina equations is calculated and closes
At the corresponding yaw angle of speed；
A2 the corresponding main method direction of aircraft aggregate velocity in Fu Laina equations) is calculated by yaw angle；
A3) by the corresponding yaw angle of aggregate velocity and main method direction, the corresponding pitch angle of calculating aircraft aggregate velocity and
Unit speed direction；
A4 the secondary method direction all vertical with aggregate velocity direction and main method direction) is calculated；
A5 it) by the corresponding main method direction of aggregate velocity, calculating aircraft speed and flow field velocity, calculates aggregate velocity and throws
Shadow to track size in the planes；
A6 rail) is projected to by the corresponding main method direction of aggregate velocity, unit speed direction, secondary method direction and aggregate velocity
Road size in the planes obtain the aircraft Fu Laina equations under spherical coordinate system.
Above-mentioned steps b) includes the following steps：
B1 its distance to the centre of sphere) is calculated by aircraft current location, and then calculates spherical surface tracking error；
B2 angle of latitude) is calculated by aircraft current location, and then calculates track and tracks latitude angle error；
B3) calculate track planar aircraft resultant motion direction and track butt to orbit angle error；
B4 the rail level angle of aggregate velocity and interplanar where track) is determined by the corresponding pitch angle of aircraft aggregate velocity
Error；
B5 longitude angle) is calculated by aircraft current location, further according to the lateral volume of longitude angle calculating for the neighbours that communication obtains
Team's error and in-orbit speed.
Above-mentioned steps c) includes the following steps：
C1) by spherical surface tracking error, track tracking latitude angle error and rail level angular error design spherical tracing control
Rule so that spherical surface tracking error is reduced to the design requirement of satisfaction；
C2) by spherical surface tracking error, track tracking latitude angle error, orbit angle error, rail level angular error and volume
Team's tolerance design track tracing control rule so that track tracking error is reduced to the design requirement of satisfaction, while ensureing aircraft
The line of south poles is not moved to；
C3) by orbit angle error, lateral formation error and in-orbit speed designs transverse direction formation control rule so that form into columns
Error is reduced to the design requirement of satisfaction；
C4) by spherical surface tracing control rule, track tracing control rule and lateral formation control Lv Lianlie, aircraft is solved
Desired yaw velocity, tilt angular speed and linear acceleration.
Above-mentioned steps d) includes the following steps：
D1) the yaw-rate error between the true yaw velocity of calculating aircraft and desired yaw velocity, design
Sideway angular acceleration makes yaw-rate error be reduced to the design requirement of satisfaction；
D2) calculating aircraft really tilts the angle of heel velocity error between angular speed and desired tilt angular speed, design
Tilt angular acceleration makes angle of heel velocity error be reduced to the design requirement of satisfaction；
D3) the control input of aircraft is sent in slave computer by host computer, movement control is completed by servo-drive system
System.
After adopting the above scheme, the present invention is simple and reliable, and precision is higher, the association being applicable in arbitrary known space-time variable air flow fields
It monitors.
Description of the drawings
Fig. 1 is the aircraft under Fu Laina formula indicate；
Fig. 2 is the tracking of spherical surface track and lateral formation schematic diagram；
Fig. 3 is the flow chart of the present invention.
Parameter declaration in attached drawing：o：The origin of spherical coordinate system；x：The x-axis of spherical coordinate system；y：The y-axis of spherical coordinate system；z：Ball
The z-axis of coordinate system；vi：The speed of three-dimensional motion body；Three-dimensional motion body speed unit direction vector；f(pi,t)：Known space-time
The flow velocity in flow field；xi：The unit direction vector of aggregate velocity；yi：The main method direction vector of unit；zi：Unit time method direction vector；Project to the speed of the three-dimensional motion body of plane；W:Spin matrixvi：I-th of aircraft；vj：J-th winged
Row device；vk：K-th of aircraft；ψi：The corresponding longitude angle of i-th of position of aircraft；ψj：The corresponding warp of j-th of position of aircraft
Spend angle；ψk：The corresponding longitude angle of k-th of position of aircraft；φi：The corresponding angle of latitude of i-th of position of aircraft；δi：I-th winged
The corresponding orbit angle error of row device；Ti：I-th of aircraft it is expected the unit tangent vector of track；R：Diagonal matrix diag (1,1,
0)；λi：The range error of quantization；ρi：The radius of object ball；γei：The corresponding rail level angular error of i-th of aircraft.
Specific implementation mode
Below with reference to attached drawing, technical scheme of the present invention is described in detail.
The present invention provides a kind of spherical surface track formation tracking and controlling method of aircraft under space-time variable air flow fields, particularly suitable
The incomplete space vehicle dynamic and known flow field indicated in spherical coordinate system is with time and spatial variations.Enable spherical coordinates
Be that the origin of s={ o, x, y, z } is located at the centre of sphere of target spherical surface, z-axis vertically with spherical surface circular orbit where plane.Certainly right
In the centre of sphere of target spherical surface is not in the plane out of plumb and z-axis where the origin of spherical coordinate system and spherical surface circular orbit the case where,
We can be realized by the translation and rotation of coordinate system.In spherical coordinate system, it is known that space-time variable air flow fields with about position
Set piWith the Second Order Continuous differentiable functions flow velocity f (p of time ti, t) and=[fx(pi,t),fy(pi,t),fz(pi,t)]TIt indicates, wherein
fx(pi,t)、fy(pi, t) and fz(pi, t) and the intensity of flow velocity in the x, y and z directions is indicated respectively.In known space-time variable air flow fields
Under effect, the kinetics equation of the incomplete aircraft of i-th of aircraft is as follows：
Wherein,For position coordinates, viFor linear velocity, xvi=[cos αicosθi,cosαisinθi,
sinαi]TFor directional velocity, αiAnd θiAngle of heel and yaw angle are indicated respectively,WithRespectively tilt angular speed and yaw angle
Speed,WithLinear acceleration is indicated respectively, tilts angular acceleration and sideway angular acceleration.
It is expected that the target spherical surface k of tracking can be expressed as in spherical coordinate system：
Wherein, ρ is the radius of target spherical surface.Since the every bit on the circular orbit in spherical coordinate system on spherical surface corresponds to phase
Same angle of latitude, uses angle of latitude hereTo indicate desired track.It laterally forms into columns and uses Adjacent aircraft position pair
The opposite longitude angle answered indicates.It keeps it is expected that lateral formation refers between each movable body：
Wherein, ψi∈ (- π, π) is the corresponding longitude angle of i-th of position of aircraft,For its desired formation longitude, ψj
∈ (- π, π) is the corresponding longitude angle of j-th of position of aircraft,For its corresponding desired formation longitude.
In the present invention, laterally form into columns be by two-way communication obtain neighbours longitude angle and desired formation longitude come
It realizes.Here two-dimensional plot is usedIt describes, whereinFor set of node,For directed edge
Set.If there is a line connecting nodeWithShow that aircraft i and k can exchange information, their adjacent nodes each other
(i.e. neighbours).The adjacent node collection of i-th of aircraft sharesIt indicates.When all there is one between any two node in figure
Path, then figure is connection.Here two nodesWithBetween path refer to by different nodesThe side andThe figure of composition.Adjacency matrix A=[a of figureij] a can be defined asij>0 and if only if (vi,
vj) ∈ ε when, other aij=0.When design, we once provide aircraft group's information interaction relationship, later each
I-th of aircraft of a momentAll it is constant, and corresponding two-dimensional plot is connection.
Fig. 3 is the design flow diagram of the present invention, is made of step P1-P4, each step is described below：
1) step P1
The present invention is a kind of spherical surface track formation tracing control design of aircraft under space-time variable air flow fields, it is known that space-time can
The original movement velocity of incomplete aircraft and direction can be changed by becoming flow field, therefore consider that aircraft closes under spherical coordinate system
Speed after；By needing to complete lateral formation in designing, the speed of plane needs where aircraft aggregate velocity projects to track
It provides；In order to realize spherical surface track, the main method direction vertical with aircraft aggregate velocity direction and time method direction are also required to table
Show；The Fu Laina equations of aircraft under space-time variable air flow fields are constructed in aggregate velocity direction, main method direction and secondary method direction, such as scheme
Shown in 1.Specific steps are as follows：
The first step：Synthesize aircraft speed in spherical coordinate systemWith flow field velocity fi(pi, t), it calculates in Fu Laina equations
The corresponding yaw angle β of aircraft aggregate velocityi：
Second step：By yaw angle βi, calculate the corresponding main method direction y of aircraft aggregate velocity in Fu Laina equationsi：
yi=[- sin βi,cosβi,0]T；
Third walks：According to yaw angle βiWith main method direction yi, the corresponding pitch angle γ of calculating aircraft aggregate velocityiAnd list
Bit rate direction xi：
xi=[cos γicosβi,cosγisinβi,sinγi]T,
Wherein,
4th step：Calculating and xiAnd y2iVertical secondary method direction zi：
zi=[- sin γicosβi,-sinγisinβi,cosγi]T；
5th step：By the corresponding main method direction y of aggregate velocityi, aircraft speed viAnd flow field velocity f (pi, t), it calculates
Aggregate velocity project to track size in the planes
Wherein, (1,1,0) R=diag；
6th step：By xi、yi、ziWithObtain the aircraft Fu Laina equations under spherical coordinate system：
Wherein,
2) step P2
Fig. 2 reflects spherical surface tracking error, track tracking error and lateral formation error.Step P2 is exactly according to flight
The neighbor information that device Fu Laina equations and communication obtain is formed into columns to calculate spherical surface tracking error, track tracking error and transverse direction
Error.Specific steps are as follows：
The first step：By aircraft current location piIt calculates it and arrives the distance of the centre of sphere, and then calculate the ball between desired distance ρ
Face tracking error λi：
Second step：By aircraft current location piCalculate angle of latitude φi：
And then it calculates and desired angle of latitude φi *Between track tracking latitude angle error φei：
φei=φi-φi *；
Third walks：Calculate track institute planar aircraft resultant motion direction yiWith track butt to TiBetween track angle
Spend error deltai：
Wherein, Ti=[sin ψi,-cosψi,0]T；
4th step：By the corresponding pitch angle γ of aircraft aggregate velocityiDetermine aggregate velocity and interplanar where track
Rail level angular error γei：
γei=γi-0；
5th step：By aircraft current location piCalculate longitude angle ψi：
Further according to the longitude angle ψ for the neighbours that communication obtainsjCalculate lateral formation errorAnd in-orbit speed ηi：
3) step P3
Step P3 tracks latitude angle error, lateral formation error and in-orbit speed according to spherical surface tracking error, track, if
Count desired yaw velocity, tilt angular speed and linear acceleration so that error ensures flight while reaching design requirement
Device does not move to the line of south poles.Design follows these steps to realize：
The first step：By spherical surface tracking error λi, track tracking latitude angle error φeiAnd rail level angular error γei, design
Spherical surface tracing control is restrained
Wherein, control gain k1>0,
Second step：By spherical surface tracking error λi, track tracking latitude angle error φei, orbit angle error deltai, rail level angle
Error γei, lateral formation errorAnd in-orbit speed ηi, designed path tracing control rule
Wherein, control gain k0,k2>0,
Third walks：By orbit angle error deltai, lateral formation errorAnd in-orbit speed ηi, design lateral formation control
Rule
Wherein, control gain k3>0, ηm=2max | f (pi, t) |, desired in-orbit speed η*<ηm,
4th step：It is restrained by spherical surface tracing controlTrack tracing control is restrained
And lateral formation control ruleConnection row solve winged
The desired yaw velocity of row deviceTilt angular speedAnd linear acceleration
Wherein,
4) step P4
Step P4 designs aircraft yaw angle according to the error really between desired yaw velocity, tilt angular speed
Acceleration and tilt acceleration make error be reduced to the requirement for meeting design.Design follows these steps to realize：
The first step：The true yaw velocity of calculating aircraftWith desired yaw velocityBetween yaw velocity
Error
And then design sideway angular acceleration
Wherein, control gain k4>0；
Second step：Calculating aircraft really tilts angular speedWith desired tilt angular speedBetween tilt angular speed
Error
And then design tilt angular acceleration
Wherein, control gain k5>0；
Third walks：The control of aircraft is inputted by host computerWithIt is sent in slave computer, passes through servo system
It unites to complete motion control.
Above example is merely illustrative of the invention's technical idea, and protection scope of the present invention cannot be limited with this, every
According to technological thought proposed by the present invention, any change done on the basis of technical solution each falls within the scope of the present invention
Within.
Claims (5)
1. the spherical surface track formation tracking and controlling method of aircraft under a kind of space-time variable air flow fields, it is characterised in that：Aircraft
Dynamic be the incomplete kinetics equation indicated in spherical coordinate system and known flow field be with time and spatial variations, it is described
Method includes the following steps：
A) it is indicated with the vehicle dynamics equation under spherical coordinate system with Fu Laina formula；
B) spherical surface tracking error, track tracking error and lateral formation error are calculated；
C) desired yaw velocity, tilt angular speed and linear acceleration are designed so that while error reaches design requirement
Ensure that aircraft does not move to the line of south poles；
D) design yaw angle and tilt angular acceleration make actual sideway and tilt angular speed reach desired value.
2. the spherical surface track formation tracking and controlling method of aircraft under a kind of space-time variable air flow fields as described in claim 1,
It is characterized in that the step a) includes the following steps：
A1 aircraft kinematical equation and flow field velocity in spherical coordinate system) are synthesized, aircraft synthesis speed in Fu Laina equations is calculated
Spend corresponding yaw angle；
A2 the corresponding main method direction of aircraft aggregate velocity in Fu Laina equations) is calculated by yaw angle；
A3) by the corresponding yaw angle of aggregate velocity and main method direction, the corresponding pitch angle of calculating aircraft aggregate velocity and unit
Directional velocity；
A4 the secondary method direction all vertical with aggregate velocity direction and main method direction) is calculated；
A5 it) by the corresponding main method direction of aggregate velocity, calculating aircraft speed and flow field velocity, calculates aggregate velocity and projects to
Track size in the planes；
A6 track institute) is projected to by the corresponding main method direction of aggregate velocity, unit speed direction, secondary method direction and aggregate velocity
Size in the planes obtains the aircraft Fu Laina equations under spherical coordinate system.
3. the spherical surface track formation tracking and controlling method of aircraft under a kind of space-time variable air flow fields as described in claim 1,
It is characterized in that the step b) includes the following steps：
B1 its distance to the centre of sphere) is calculated by aircraft current location, and then calculates spherical surface tracking error；
B2 angle of latitude) is calculated by aircraft current location, and then calculates track and tracks latitude angle error；
B3) calculate track planar aircraft resultant motion direction and track butt to orbit angle error；
B4) determine that aggregate velocity and the rail level angle of interplanar where track are missed by the corresponding pitch angle of aircraft aggregate velocity
Difference；
B5 longitude angle) is calculated by aircraft current location, calculates laterally to form into columns further according to the longitude angle for communicating obtained neighbours and miss
Poor and in-orbit speed.
4. the spherical surface track formation tracking and controlling method of aircraft under a kind of space-time variable air flow fields as described in claim 1,
It is characterized in that the step c) includes the following steps：
C1 it) is restrained, is made by spherical surface tracking error, track tracking latitude angle error and rail level angular error design spherical tracing control
Obtain the design requirement that spherical surface tracking error is reduced to satisfaction；
C2) by spherical surface tracking error, track tracking latitude angle error, orbit angle error, rail level angular error and mistake of forming into columns
Poor designed path tracing control rule so that track tracking error is reduced to the design requirement of satisfaction, while ensureing that aircraft is not transported
Move the line of south poles；
C3) by orbit angle error, lateral formation error and in-orbit speed designs transverse direction formation control rule so that formation error
It is reduced to the design requirement of satisfaction；
C4) by spherical surface tracing control rule, track tracing control rule and lateral formation control Lv Lianlie, aircraft expectation is solved
Yaw velocity, tilt angular speed and linear acceleration.
5. the spherical surface track formation tracking and controlling method of aircraft under a kind of space-time variable air flow fields as described in claim 1,
It is characterized in that the step d) includes the following steps：
D1) the yaw-rate error between the true yaw velocity of calculating aircraft and desired yaw velocity designs sideway
Angular acceleration makes yaw-rate error be reduced to the design requirement of satisfaction；
D2) calculating aircraft really tilts the angle of heel velocity error between angular speed and desired tilt angular speed, design tilt
Angular acceleration makes angle of heel velocity error be reduced to the design requirement of satisfaction；
D3) the control input of aircraft is sent in slave computer by host computer, motion control is completed by servo-drive system.
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