CN105912005B - Combine take over control method using the space non-cooperative target posture of tether thruster - Google Patents
Combine take over control method using the space non-cooperative target posture of tether thruster Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
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- B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
- B64G1/244—Spacecraft control systems
Abstract
Combining take over control method using the space non-cooperative target posture of tether thruster the invention discloses a kind of, control instruction and measured value of state error is generated by formula first to instruct, then the partial parameters of online real-time update controller recycle attitude-adaptive control law to generate pseudo- controlled quentity controlled variable:Control moment.It converts the assignment problem of controlled quentity controlled variable to robust optimization problem again, converts robust optimization problem to conic quadratic optimization problem, and solve using interior point method, obtain true controlled quentity controlled variable:Thrust and tension finally respectively drive 12 thrusters and tether tension, and the posture of noncooperative target is combined in realization takes over control.
Description
【Technical field】
The invention belongs to Spacecraft Attitude Control fields, are related to a kind of space non-cooperative target appearance using tether thruster
State combines take over control method.
【Background technology】
It refers to after forming a fixed connection with passive space vehicle using the operating mechanism of Servicing spacecraft, utilizing appearance to take over control
The rail control system of rail control system take over passive space vehicle, realizes its rail control system.It is in-orbit with the development of space technology
Service receives more and more attention.The satellite of failure, posture are caused in the stranded satellite of discarded track, posture rolling
It is directed toward mistake and causes satellite that can not work normally etc., take over if posture can be carried out to it using Servicing spacecraft, carried for it
Determine appearance etc. for auxiliary change rail, auxiliary and take over control, will have great economic benefit and social influence.The DEOS of German DLR
(Deutsche Orbital Servicing) project, SMART-OLEV (the SMART Orbital Life of European Space Agency
Extension Vehicle) project, FREND (the Front-end Robotics Enabling Near-term in the U.S.
Demonstration) project etc. is studied for problems and prepares to carry out in-orbit experiment.
But study at present it is mostly to take over control is to carry the rigid spaces robots such as mechanical arm using Servicing spacecraft to grab
Target is caught, the rail control system take over control targe spacecraft of Servicing spacecraft is then utilized.Robot of space rope system is one
The novel hard and soft interblock space robot system of kind has the advantages such as remote operating distance, safety, flexible, has obtained in recent years extensively
General concern.Due to needing to approach passive space vehicle at a distance, the operating mechanism of robot of space rope system has thruster.Therefore,
Passive space vehicle combine using thruster and tether and takes over control.Wang Dong sections et al. have carried out tether and have joined with thruster
Close the research for carrying out targeted attitude control.But target inertia is considered as it is known that and not considering control allocation, controlled quentity controlled variable
The problems such as constrained, and thinking the operating mechanism of robot of space rope system can utilize thruster to export any control moment.It is practical
On, for noncooperative target, the rotary inertia of target satellite is unknown, and thruster output torque is limited, and target satellite centroid position is not
Know that also result in thrust point, action direction unknown.These problems significantly increase using tether/thruster combine into
The difficulty of row target satellite posture take over control.For this problem, the present invention fully considers these unknown and constrained state amounts and control
Amount processed provides a kind of posture take over control method of noncooperative target star.
【Invention content】
It is an object of the invention to solve the posture take over control problem of space non-cooperative target star, providing a kind of utilize is
The space non-cooperative target posture of rope thruster combines take over control method.
In order to achieve the above objectives, the present invention is achieved by the following scheme:
Combine take over control method using the space non-cooperative target posture of tether thruster, includes the following steps:
1) space non-cooperative target star posture take over Controlling model is established;
2) the attitude-adaptive take over control law of noncooperative target star is designed;
3) the robust distribution of take over control moment.
The present invention, which further improves, to be:
In the step 1), the specific method for establishing space non-cooperative target star posture take over Controlling model is:
With OTFor the barycenter of space non-cooperative target star, target satellite this system O is establishedTXTYTZT, with OGFor operating mechanism
Barycenter establishes operating mechanism this system OGXGYGZG, OCFor the tie point of tether and operating mechanism;To simplify modeling process, it is assumed that
Two each reference axis of coordinate system are mutually parallel, if operating mechanism barycenter OGIn target satellite this system OTXTYTZTUnder coordinate be XG
=[xG,yG,zG];
Four groups of operating mechanisms, totally 12 thrusters are in the installation of " ten " word;Wherein, the 1st group of operating mechanism (4) and the 2nd group of behaviour
Make the thruster that mechanism (5) includes 5 orthogonal installations, the 3rd group of operating mechanism (6) is respectively 1 with the 4th group of operating mechanism (7) to be pushed away
Power device;
If the thrust range of each thruster is [0 a] N, the then thrust that 12 thrusters are generated in operating mechanism this system
And it is in the position of action point of operating mechanism this system:
First group:
Second group:
Third group and the 4th group:
To simplify modeling process, it is assumed that its direction is constant and along the directions operating mechanism this system-x;Therefore, if tether is maximum
Pulling force is a5N, tether pulling force and position are expressed as under operating mechanism this system:
Tension | Position | Tension restriction | |
Tether | F13=[- F13x,0,0] | X5=[x5,y5,z5] | 0N≤F13x≤a5N |
Since operation object is noncooperative target, measuring device and executing agency are mounted on the behaviour of robot of space rope system
Make in mechanism, therefore, under operating mechanism this system, the attitude dynamic equations for establishing space non-cooperative target are:
Wherein, J is target satellite moment of inertia matrix, and ω is the angular speed of target satellite,×For multiplication cross operator, TdFor perturbed force
Square, T=Tc+TtTorque in order to control, TcThe control moment generated for thruster:
FiFor the corresponding thrust of i-th of thruster, i is the label of thruster, TtThe control moment generated for tether:
Tt=(XG+X5)×F13 (3)
Then control moment T abbreviations are:
Wherein, D measures allocation matrix in order to control, and F is the column vector of actuator composition;
It is using the target satellite attitude kinematics equations that Douglas Rodríguez parameter describes are corrected:
Wherein, σ is the attitude rectification Douglas Rodríguez parameter of target satellite, I3For 3 × 3 unit matrix;
If the expectation posture of noncooperative target star is σd, it is expected that angular speed is ωd, then target satellite attitude error dynamics/fortune
Moving equation is:
Wherein, σeFor attitude error, ωeExpression formula for angular speed error, the two is:
In formula (8),Indicate MRP multiplication.
In the step 2), the method for designing the attitude-adaptive take over control law of noncooperative target star is:
First, definition auxiliary error variance:S=ωe+ασe, α >=0, then
Wherein, L=- (ω) × J (ω)-[J+ α JG (σe)]ωd+Td+αJG(σe)ω;With | | | | indicate the Europe of vector
Norm is obtained in several, right | | L | | it analyzes:
Due toωdBounded;If external disturbance TdEuclid norm meet | | Td|
|≤cd0+cd1||ω||2, cd0And cd1It is unknown and non-negative constant, then:
||L||≤b0+b1||ω||+b2||ω||2 (10)
Wherein, b0、b1And b2It is unknown and non-negative constant;
Then, on this basis, attitude-adaptive control law is designed:
Wherein, k1And k2For the normal number of design, sgn () is sign function,WithIt is parameter b respectively0、b1With
b2Estimated value, online updating rule is:
c0、c1And c2For the normal number of design;
Finally, carrying out stability proves:
Selection:
Wherein,
To formula (13) both sides derivation, obtain:
It brings formula (9)~(12) into above formula, and abbreviation, obtains:
Therefore, under the control of control law formula (11) and parameter update law formula (12), systems compliant Asymptotic Stability.
In the step 3), the specific method of the robust distribution of take over control moment is:
Since control moment is realized jointly by thrust and tether tension, and thrust with tension be it is strictly limited, then:
If a=[a1 a1 a2 a3 a3 a1 a1 a2 a3 a3 a4 a4 a5], 0 is 13 × 1 null matrix;Formula (15) indicates
For:0≤F≤a;
The control moment T that step 2) calculates is assigned to using robust distribution method and really controls execution amount, i.e., 12
In the thrust and tether tension of thruster, the specific method is as follows:
3-1) with fuel consumption at least for object function, it converts control assignment problem to robust optimization problem below.
Object function:Min ([1 11111111111 0] F)=min (WTF);
Constraint:T=DF, 0≤F≤a;
It enablesConvert equality constraint to inequality constraints;
Constraint:HF >=N, 0≤F≤a;
Using robust optimum theory, optimization problem is rewritten as:
Wherein, hiFor the i-th row comprising probabilistic matrix H, and in uncertain collection ΞiMiddle value;Uncertain collection ΞiIt can
With ellipsoid uncertainty description, i.e.,:
Indicate the nominal value by each row for measuring or recognizing, ΘiFor with Uncertainty distribution it is relevant it is symmetrical just
Fixed or positive semidefinite matrix, uiFor with uncertain relevant column vector, ρ is the upper bound of probabilistic Euclid norm;
The feature for 3-2) utilizing ellipsoid uncertainty, using formula (17) abbreviation formula (16), and utilizes
min(xTΘui)=- ρ | | Θ x | |
Convert robust optimization problem to conic quadratic optimization problem:
Finally, above-mentioned cone optimization problem is solved using interior point method.
Compared with prior art, the invention has the advantages that:
The present invention carries out posture connection using the tether thruster based on robot of space rope system to space non-cooperative target star
Splice grafting pipe control method can make full use of tether tension, save the chemical propellant consumption during taking over control.At home and abroad
Tether is combined with thruster in the research controlled targeted attitude, is considered as target inertia it is known that and not considering controlled quentity controlled variable point
Match, the problems such as controlled quentity controlled variable is constrained so that its use scope is substantially reduced with reliability.Using Adaptive Attitude control and torque
Robust distribution method, fully considered that the inertia of noncooperative target is unknown, barycenter is unknown, operating mechanism arrests a little spies such as unknown
Property and constrained state amount and controlled quentity controlled variable so that system can obtain unknown parameter in real time online, and avoid constrained state amount
And influence of the controlled quentity controlled variable to system, greatly improve its practical use scope and reliability.
【Description of the drawings】
Fig. 1 is that space rope system robot target arrests schematic diagram;
Fig. 2 is the distribution map of thruster;
Fig. 3 is to combine take over control flow chart using the space non-cooperative target posture of tether/thruster.
Wherein, 1- space non-cooperative targets star;The operating mechanism of robot of 2- space ropes system;Robot of 3- space ropes system
Tether;The 1st group of operating mechanism of 4-;The 2nd group of operating mechanism of 5-;The 3rd group of operating mechanism of 6-;The 4th group of operating mechanism of 7-.
【Specific implementation mode】
The present invention is described in further detail below in conjunction with the accompanying drawings:
Referring to Fig. 1-Fig. 3, the present invention combines take over control method using the space non-cooperative target posture of tether thruster,
Include the following steps:
Step 1:Establish space non-cooperative target star posture take over Controlling model
As shown in Figure 1,1 is space non-cooperative target star, 2 be the operating mechanism of robot of space rope system, and 3 be space rope system
The tether of robot.OTFor the barycenter of space non-cooperative target star, OTXTYTZTFor target satellite this system, OGFor the matter of operating mechanism
The heart, OGXGYGZGFor operating mechanism this system, OCFor the tie point of tether and operating mechanism.To simplify modeling process, it is assumed that two
Each reference axis of coordinate system is mutually parallel.If operating mechanism barycenter OGIn target satellite this system OTXTYTZTUnder coordinate be XG=
[xG,yG,zG]。
As shown in Fig. 2, the 1st group of operating mechanism 4, the 2nd group of operating mechanism 5, the 3rd group of operating mechanism 6 and the 4th group of operating mechanism
7 totally ten two thrusters, and installed in " ten " word.1st group of operating mechanism 4 includes five orthogonal installations with the 2nd group of operating mechanism 5
Thruster, the 3rd group of operating mechanism 6 and the 4th group of operating mechanism 7 are respectively a thruster.
If the thrust range of each thruster is [0 a] N, then, what 12 thrusters were generated in operating mechanism this system
Thrust and in the position of action point of operating mechanism this system it is:
First group:
Second group:
Third group and the 4th group
Since the tether of robot of space rope system is up to hundreds of meters, and in take over control, target satellite attitude motion causes
Tether direction change it is smaller, for simplify modeling process, it will be assumed that its direction is constant and along the directions operating mechanism this system-x.Cause
This, if tether maximum pull is a5N, tether pulling force and position are represented by under operating mechanism this system:
Tension | Position | Tension restriction | |
Tether | F13=[- F13x,0,0] | X5=[x5,y5,z5] | 0N≤F13x≤a5N |
Since operation object is noncooperative target, so the measuring devices such as gyro, the executing agencies such as thruster/tether are pacified
On operating mechanism loaded on robot of space rope system, therefore, under operating mechanism this system, space non-cooperative target is established
Attitude dynamic equations are:
Wherein, J is target satellite moment of inertia matrix, and ω is the angular speed of target satellite,×For multiplication cross operator, TdFor perturbed force
Square, T=Tc+TtTorque in order to control.TcThe control moment generated for thruster
TtThe control moment generated for tether
Tt=(XG+X5)×F13 (3)
Then control moment T can abbreviation be:
Wherein, D measures allocation matrix in order to control, and F is the column vector of actuator composition.
It is using the target satellite attitude kinematics equations that Douglas Rodríguez parameter describes are corrected:
Wherein, σ is the attitude rectification Douglas Rodríguez parameter of target satellite, I3For 3 × 3 unit matrix.
If the expectation posture of noncooperative target star is σd, it is expected that angular speed is ωd, then, and target satellite attitude error dynamics/
Kinematical equation is:
Wherein, σeFor attitude error, ωeExpression formula for angular speed error, the two is:
In formula,Indicate MRP multiplication.
Step 2:Design the attitude-adaptive take over control law of noncooperative target star
Since moment of thrust and tether Tension Moment constitute redundancy control system, and each thrust and tether tension are constrained
Amount, directly with thrust and tension in order to control measure design controller it is sufficiently complex, therefore, using posture take over control law and control divide
The method separately designed with rule.
In the design of posture take over control law, since the rotary inertia of noncooperative target is unknown, need design adaptive
Posture take over control law.
First, definition auxiliary error variance:S=ωe+ασe.Then
Wherein, L=- (ω) × J (ω)-[J+ α JG (σe)]ωd+Td+αJG(σe)ω.With | | | | indicate the Europe of vector
In several norm, below it is right | | L | | analyze.
Due toωdBounded.If external disturbance TdEuclid norm meet | | Td|
|≤cd0+cd1||ω||2, cd0And cd1It is unknown and non-negative constant.Then:
||L||≤b0+b1||ω||+b2||ω||2 (10)
Wherein, b0、b1And b2It is unknown and non-negative constant.
Then, on this basis, attitude-adaptive control law is designed:
Wherein, k1, k2For the normal number of design, sgn () is sign function,WithIt is parameter b respectively0、b1With
b2Estimated value, online updating rule is:
c0, c1And c2For the normal number of design.
Finally, carrying out stability proves:
Selection:
Wherein,
To formula (13) both sides derivation, obtain:
It brings formula (9)~(12) into above formula, and abbreviation, obtains:
Therefore, under the control of control law formula (11) and parameter update law formula (12), systems compliant Asymptotic Stability.
Step 3:The robust of take over control moment distributes
Since control moment is realized jointly by thrust and tether tension, and thrust is strictly limited with tension.
If a=[a1 a1 a2 a3 a3 a1 a1 a2 a3 a3 a4 a4 a5], 0 is 13 × 1 null matrix.Above formula can indicate
For:0≤F≤a.
In addition, due to operating mechanism barycenter OGCoordinate under target satellite this system is uncertain, leads to thrust and tether
Coordinate of the point of force application under target satellite this system is uncertain, and therefore, this step is calculated step 2 using robust distribution method
Control moment T be assigned to true control execution amount:In the thrust and tether tension of 12 thrusters.
First, with fuel consumption at least for object function, control assignment problem is converted to robust optimization problem below.
Object function:Min ([1 11111111111 0] F)=min (WTF);
Constraint:T=DF, 0≤F≤a.
It enablesConvert equality constraint to inequality constraints,
Constraint:HF >=N, 0≤F≤a.
Using robust optimum theory, optimization problem is rewritten as:
Wherein, hiFor the i-th row comprising probabilistic matrix H, and in uncertain collection ΞiMiddle value.Uncertain collection ΞiIt can
With ellipsoid uncertainty description, i.e.,:
Indicate the nominal value by each row for measuring or recognizing, ΘiFor with the relevant symmetric positive definite of Uncertainty distribution
Or positive semidefinite matrix, uiFor with uncertain relevant column vector, ρ is the upper bound of probabilistic Euclid norm.
Then, it using the feature of ellipsoid uncertainty, using formula (17) abbreviation formula (16), and utilizes
min(xTΘui)=- ρ | | Θ x | |
Convert robust optimization problem to conic quadratic optimization problem.
Finally, above-mentioned cone optimization problem is solved using interior point method.
Interior point method detailed step refers to:DAVID G,LUENBERGER,YINYU YE.Linear and Nonlinear
Programming[M].Third edition.Berlin:Springer Verlag,2008:111–140.
The above content is merely illustrative of the invention's technical idea, and protection scope of the present invention cannot be limited with this, every to press
According to technological thought proposed by the present invention, any change done on the basis of technical solution each falls within claims of the present invention
Protection domain within.
Claims (1)
1. the space non-cooperative target posture using tether thruster combines take over control method, which is characterized in that including following
Step:
1) space non-cooperative target posture take over Controlling model is established, specific method is:
With OTFor the barycenter of space non-cooperative target, target this system O is establishedTXTYTZT, with OGFor the barycenter of operating mechanism, establish
Operating mechanism this system OGXGYGZG, OCFor the tie point of tether and operating mechanism;To simplify modeling process, it is assumed that two coordinate systems
Each reference axis is mutually parallel, if operating mechanism barycenter OGIn target this system OTXTYTZTUnder coordinate be XG=[xG,yG,zG];
Four groups of operating mechanisms, totally 12 thrusters are in the installation of " ten " word;Wherein, the 1st group of operating mechanism (4) and the 2nd group of operation machine
Structure (5) includes the thruster of 5 orthogonal installations, and the 3rd group of operating mechanism (6) is respectively 1 thruster with the 4th group of operating mechanism (7);
Thrust that then 12 thrusters are generated in operating mechanism this system and in the position of action point of operating mechanism this system it is:
First group:
Second group:
Third group and the 4th group:
To simplify modeling process, it is assumed that its direction is constant and along the directions operating mechanism this system-x;Therefore, if tether maximum pull
For a5N, tether pulling force and position are expressed as under operating mechanism this system:
Since operation object is noncooperative target, measuring device and executing agency are mounted on the operation machine of robot of space rope system
On structure, therefore, under operating mechanism this system, the attitude dynamic equations for establishing space non-cooperative target are:
Wherein, J is target rotational inertia matrix, and ω is the angular speed of target, × it is multiplication cross operator, TdFor disturbance torque, T=Tc+
TtTorque in order to control, TcThe control moment generated for thruster:
FiFor the corresponding thrust of i-th of thruster, i is the label of thruster, TtThe control moment generated for tether:
Tt=(XG+X5)×F13 (3)
Then control moment T abbreviations are:
Wherein, D measures allocation matrix in order to control, and F is the column vector of actuator composition;
It is using the targeted attitude kinematical equation that Douglas Rodríguez parameter describes is corrected:
Wherein, σ is the attitude rectification Douglas Rodríguez parameter of target, I3For 3 × 3 unit matrix;
If the expectation posture of noncooperative target is σd, it is expected that angular speed is ωd, then targeted attitude error dynamics/kinematical equation
For:
Wherein, σeFor attitude error, ωeExpression formula for angular speed error, the two is:
In formula (8),Indicate MRP multiplication;
2) the attitude-adaptive take over control law of noncooperative target is designed, specific method is:
First, definition auxiliary error variance:S=ωe+ασe, α >=0, then
Wherein, L=- (ω)×J(ω)-[J+αJG(σe)]ωd+Td+αJG(σe)ω;With | | | | indicate the Euclid of vector
Norm is right | | L | | it analyzes:
Due toωdBounded;If external disturbance TdEuclid norm meet | | Td||≤
cd0+cd1||ω||2, cd0And cd1It is unknown and non-negative constant, then:
||L||≤b0+b1||ω||+b2||ω||2 (10)
Wherein, b0、b1And b2It is unknown and non-negative constant;
Then, on this basis, attitude-adaptive control law is designed:
Wherein, k1And k2For the normal number of design, sgn () is sign function,WithIt is parameter b respectively0、b1And b2's
Estimated value, online updating rule are:
c0、c1And c2For the normal number of design;
Finally, carrying out stability proves:
Selection:
Wherein,
To formula (13) both sides derivation, obtain:
It brings formula (9)~(12) into above formula, and abbreviation, obtains:
Therefore, under the control of control law formula (11) and parameter update law formula (12), systems compliant Asymptotic Stability;
3) the robust distribution of take over control moment, specific method are:
Since control moment is realized jointly by thrust and tether tension, and thrust with tension be it is strictly limited, then:
If a=[a1 a1 a2 a3 a3 a1 a1 a2 a3 a3 a4 a4 a5], 0 is 13 × 1 null matrix;Formula (15) is expressed as:0
≤F≤a;
The control moment T that step 2) calculates is assigned to true control execution amount, i.e. 12 thrusts using robust distribution method
In the thrust and tether tension of device, the specific method is as follows:
3-1) with fuel consumption at least for object function, it converts control assignment problem to robust optimization problem below;
Object function:Min ([1 11111111111 0] F)=min (WTF);
Constraint:T=DF, 0≤F≤a;
It enablesConvert equality constraint to inequality constraints;
Constraint:HF >=N, 0≤F≤a;
Using robust optimum theory, optimization problem is rewritten as:
Wherein, hiFor the i-th row comprising probabilistic matrix H, and in uncertain collection ΞiMiddle value;Uncertain collection ΞiIt can be with ellipse
Ball uncertainty description, i.e.,:
Indicate the nominal value by each row for measuring or recognizing, ΘiFor with the relevant symmetric positive definite of Uncertainty distribution or partly
Positive definite matrix, uiFor with uncertain relevant column vector, ρ is the upper bound of probabilistic Euclid norm;
The feature for 3-2) utilizing ellipsoid uncertainty, using formula (17) abbreviation formula (16), and utilizes
min(xTΘui)=- ρ | | Θ x | |
Convert robust optimization problem to optimization problem:
Finally, above-mentioned optimization problem is solved using interior point method.
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CN107187617B (en) * | 2017-04-27 | 2019-06-21 | 西北工业大学 | A kind of multiple-unit Torque distribution method for spacecraft adapter tube control |
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CN107797449B (en) * | 2017-09-27 | 2021-02-26 | 西北工业大学深圳研究院 | Method for taking over control of space non-cooperative target under condition of incomplete information |
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