CN108803331A - For the pre-determined characteristics control method of bilateral teleoperation system under asymmetric time-vary delay system - Google Patents
For the pre-determined characteristics control method of bilateral teleoperation system under asymmetric time-vary delay system Download PDFInfo
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Abstract
The invention discloses a kind of adaptive pre-determined characteristics control method for bilateral teleoperation system under asymmetric time-vary delay system, content includes：It assists intermediate variable that remote control system is split as two subsystems by introducing, and the system mode with time-vary delay system is disposed only in two subsystems；It is based on that the design of Backstepping method is adaptive should a pre-determined characteristics strategy for the first subsystem, ensures that the synchronous error of the first subsystem meets preset temporary steady-state behaviour while asymptotic convergence；For the second subsystem design pre-determined characteristics control strategy, and using multidimensional small gain theorem establish system performance parameter, controller parameter, the time delay derivative upper bound and system stability relationship.The present invention does not depend on the adaptive pre-determined characteristics control method of asymmetric time-vary delay system precise information by design, meet preset temporary steady-state behaviour while synchronous error asymptotic convergence between ensureing principal and subordinate robot, therefore there is higher application value in practice.
Description
Technical field
The present invention relates to the non-linear remote control system control technology fields of networking, more particularly to the non-of bilateral structure
Linear pre-determined characteristics control method of the remote control system under asymmetric time-vary delay system.
Background technology
The appearance of remote control system allows the mankind to complete complicated operation in the case where being difficult to close or hostile environment and appoints
Business, and huge economic and social value is created simultaneously.In recent years, remote control system successively in space and deep-sea detecting, again
It is able into the operation of the Nature disaster (such as earthquake rescue, volcanic eruption are rescued) and hazardous environment (such as nuclear accident scene)
Work(application enhances the operational capacity of the mankind to expand the scope of activities of the mankind to a certain extent.
With the fast development of computer networking technology, network is successfully introduced into remote operating control field by researcher,
The development of teleoperation is pushed to a new height while bringing new opportunity to the development of teleoperation.But
The problems such as existence and randomness for being network delay, has seriously affected the stability and operable of remote control system control
Property.Therefore, a large amount of researcher for the delay control method of networking remote control system largely divide in recent years
Analysis and research work, these are operated in document《Bilateral teleoperation:An history survey》And
Document《Passivity-based control for bilateral teleoperation:Atutorial》In carry out point
Analysis and summary.
However by existing remote control system control method the study found that existing remote operating control method only focuses on mostly
Whether can steady operation and the transient performance during ignoring system convergence in system.Therefore often companion in principal and subordinate's convergence process
With larger overshoot, and convergence rate is slower, and convergence precision is poor.A good control effect is mentioned in Classical control
It should make system while meet steady, accurate, fast performance requirement, and system should have smaller overshoot.It is under existing control method
Accuracy, rapidity and the overshoot of system can only in most cases pass through constantly regulate controller parameter, comparison system response
It is realized as a result, responding to selecting the system for best suiting practical application request.When external environment or actual demand vary slightly,
It need to carry out largely testing to redefine new parameter.Whether can be simultaneous in controller design according to practical application request
The steady-state behaviour and transient performance of Gu system, are the problem of researcher intend to solve always.
For the problem --- obtain the extensive pass of researcher for the pre-determined characteristics control problem of remote control system
Note, such as document《Adaptive neural networkbasedprescribedperformance control for
teleoperation system under input saturation》,《Adaptive neural network based
prescribedperformance control forteleoperation system under input saturation》
Deng.But assume that the communication delay between master and slave robot is Chang Shiyan in above-mentioned work.And delay of communication is often non-
How symmetrical time-vary delay system designs the pre-determined characteristics controlling party independent of time delay precise information under asymmetric time-vary delay system
Method, and ensure that it is this to meet scheduled temporary steady-state behaviour while synchronous error asymptotic convergence to the origin between principal and subordinate robot
Invent the main control technology problem intended to solve.
Invention content
Can only ensure system stable operation the purpose of the present invention is to solve remote control system under existing control technology and
The problem of ignoring system transient modelling performance provides a kind of pre-determined characteristics control for the bilateral teleoperation system under asymmetric time-vary delay system
Method processed has temporary, steady-state behaviour well while ensureing principal and subordinate's robot synchronous error asymptotic convergence.
In order to solve the above technical problems, present invention employs following control programs：
A kind of pre-determined characteristics control method for bilateral teleoperation system under asymmetric time-vary delay system, content include such as
Lower step：
S1. introduce auxiliary intermediate variable and remote control system be split as two subsystems --- the first subsystem and the second son
System, and the system mode with time-vary delay system is disposed only in the second subsystem；
S2. it is directed to the first subsystem and is based on the adaptive pre-determined characteristics strategy of Backstepping method design, ensure the first subsystem
The synchronous error of system meets preset temporary steady-state behaviour while asymptotic convergence；
S3. it is directed to the second subsystem and designs pre-determined characteristics control strategy, and systematicness is established using multidimensional small gain theorem
The relationship of energy parameter, controller parameter and the time delay derivative upper bound and system stability.
Preferably, in step sl, remote control system is split as two subsystems by the introducing auxiliary intermediate variable
System --- the first subsystem and the second subsystem, and the system mode with time-vary delay system is disposed only in the second subsystem,
Specific implementation mode is as follows：
Non-linear bilateral teleoperation system is：
Wherein, subscript m represents main robot, and subscript behalf is from robot, Mm(qm),Ms(qs)∈Rn×nJust for system
Determine inertial matrix；For the vector of coriolis force and centrifugal force；Gm(qm),Gs(qs)∈RnFor
The gravity item of system；Fh∈RnAnd Fe∈RnThe torque that the torque and environment that respectively human operator applies apply；τm∈RnWith
τs∈RnThe control moment that device provides in order to control.
The main goal in research of the present invention is by designing new control algolithm, ensureing to apply as operator and external environment
When power is zero, master-slave synchronisation error qm-qs(t-Ts(t)), qs-qm(t-TmAnd the speed of master and slave robot (t))WithGradually
It is close to converge to zero, while within master-slave synchronisation error is in set and delimits always.Wherein Tm(t) indicate that main robot end is arrived
Time-vary delay system, and T are transmitted from the information of robotic ends(t) it is when transmitting time-varying to the information at main robot end from robotic end
Prolong.
For the above bilateral teleoperation system, it is defined as follows variable xi1=qi,I=m, s, then remote operating system
System equation (1) will be done by writing again：
Define new variableAnd then it is defined as follows variable ei1=
xi1-ψi1,Wherein ψi1It is defined as follows：
Wherein,Be specifically defined and will be provided in the content below.
Therefore based on auxiliary intermediate variable ψi1, ψi2, define ei2=xi2-ψi2, former remote control system (2) is split as follows
Two subsystems, wherein the concrete form of the first subsystem is as follows：
Wherein, Fmhe=Fh, Fshe=-Fe, i=m, s.And the second subsystem is formula (3).
Preferably, it in the step S2, is based on Backstepping method for the first subsystem and designs adaptive pre-determined characteristics
Strategy ensures that the synchronous error of the first subsystem meets preset temporary steady-state behaviour while asymptotic convergence.First, assuming that
ψi2AndIn the presence of and bounded on the basis of, adaptive precordainment is designed using the method for Backstepping for the first subsystem
It can control strategy.
For the following error converted variable η of the first subsystem definitioni：
Wherein, i=m, s, j=1,2 ..., n；
And then error transfer equationIt is designed as：
Wherein,It is time-varying variance for system performance equation,ConstantIt representsThe permitted maximum synchronous error when system is stablized,Rate of descent representThe minimum convergence speed of permission
Degree,Expression system allow maximum overshoot andMeet
To above-mentioned variable ηiDerivation can obtain：
Wherein,
According to rightWithDefinition can obtain as follows about equation property：
New auxiliary variable xi2Ideal trajectory be defined as xi2d, it is designed specifically to：
Wherein, ki1For normal number.
Based on error delta xi2=xi2-xi2d, can obtain：
In turn, as follows for the adaptive pre-determined characteristics controller design of the first subsystem：
Wherein, ki2Normal number is chosen for,For the regression matrix of system,For parameter adaptive tune
Section variable is used for approaching the vectorial θ being made of system uncertain parameteri。
Parameter adaptive adjusts rule and is designed as：
Wherein, ΛiFor diagonal positive definite constant matrices.
Choose Lyapunov equationsIts first derivative at any time is：
According to variable Δ xi2Definition, can obtain：
In turn, following Lyapunov equations are chosen：
(15) formula derivation can be obtained：
Wherein,
Based on controller (11) formula, can obtain：
Wherein,
It is final to choose following new Lyapunov equations：
Its first derivative is：
Based on inequalityIt can obtainAgain due to V >=0, it may thus be appreciated that variable ηi, Δ
xi2,Bounded, and variable ηi,Δxi2Same bounded.The variable η of boundediIllustrate that the first subsystem meets scheduled temporary stable state
Performance.Work asWhen existWhenWhenAnd then according to machine
The property of device people's model can obtainBounded,Bounded.Finally, according to Barbalat lemma can proper t → ∞ when ηi→ 0, ei→
0 i.e. qi-ψi1→0。
Preferably, in step s3, described to be directed to the second subsystem design pre-determined characteristics control strategy and small using multidimensional
Gain theorem establishes the relationship of system performance parameter, controller parameter and the time delay derivative upper bound and system stability.
To ensure master-slave synchronisation errorIt is asymptotic while meeting pre-determined characteristics to tend to zero, it need to further design
SuitablySo thatMeet scheduled temporary steady-state behaviour while asymptotic convergence.
It defines first
Wherein, i=m, s, j=1,2 ..., n；And then error transfer equationIt is designed as：
For vector system performance equationIn a number, j=1,2 ..., n；
ConstantIt representsThe permitted maximum synchronous error when system is stablized,Rate of descent representThe minimum convergence of permission
Speed,Expression system allow maximum overshoot andMeet
In turn, Δ ψ is definedi2=ψi2-ψi2d,To variableDerivation can obtain
Based on Δ ψi2DerivativeAndIt is defined as：
Wherein, λi1And λi2For the fixation normal number of selection；
In turn, it can obtain：
According to formula (21) and formula (23), further can be obtained：
Wherein,For quadratic equationRoot.Due to λi2, λi1,For positive number, then clearlyIt is similarly positive number.Seeking πi
When will useApparent basisπiIt can very simply seek；According to differ
Formula (24) can obtain the second subsystem with variableWith Δ ψi2(t) it is system mode, withIt is weak as system input
Input-to-state stability, and gain is πi；
The output of closed loop remote control system is：
It can be obtained according to result above, as t → ∞, Δ xi2,ηi,ei→0.Further basisIt can obtainSo, closed loop remote control system withTo input, with variable xi2It is lower full to export
Foot is weak to be input to output stable condition.And weak be input to exports stable and gain as (1+ υi)πi,
Based on the above analysis it is found that remote control system, which can be seen as one, is exported closing of forming by two inputs and two
Loop system, therefore have y1=xm2, y2=xs2,Have been proven that the closed loop remote control system meets
It is weak to be input to output stable condition.And the weak output constant gain matrix that is input to of system isIt is specifically defined as
On the other hand, according to about time delay it is assumed thatWithEstimation can obtain：
Therefore, connection matrix Γ:={ νji}
ν12=1+ Υs, ν21=1+ Υm (28)
According to the above analysis, can obtain closed-loop system gain matrix isWherein
According to small gain theorem, ifSo variableΔψi2,xi2Bounded.And as t → ∞,
ψi1→ 0,Δψi2→ 0, xi2→0.Therefore it can further obtainAndAlways it is in scheduled model
Within enclosing.Therefore it can obtain：
Can finally obtain | | xm1-xs1||→0,t→∞。
When operator, extraneous input power are zero, and controller parameter chooses so that inequality max ((1+ Υs)πmj) 1 Hes of <
max((1+Υm)πsj) < 1 is when setting up, then the synchronous error of the bilateral teleoperation system under asymmetric time-vary delay system is gradually
Meet preset temporary steady-state behaviour while nearly convergence.
Due to the adoption of the above technical scheme, the present invention has such advantageous effect compared with prior art：
The pre-determined characteristics control method of bilateral teleoperation system under the asymmetric time-vary delay system of consideration of the present invention, a side
Face, pre-determined characteristics control method proposed by the invention can be in time-vary delay system compared with existing most of remote operating control methods
Lower guarantee master-slave synchronisation error meets the requirements such as preset convergence rate, convergence precision and overshoot while asymptotic convergence；
On the other hand, compared with the existing pre-determined characteristics control method for remote operating, when considering asymmetric time-varying in the present invention
Prolong, therefore more meet real network application environment, and establishes pre-determined characteristics parameter, controller parameter and upper delay for the first time
Relationship, the foundation of On Delay-Dependent Stability condition not only reduce the conservative of system, and are controller parameter in practical application
And the selection of system performance parameter provides theoretical foundation.
The present invention does not depend on the adaptive pre-determined characteristics control method of asymmetric time-vary delay system precise information by design,
Meet preset temporary steady-state behaviour while synchronous error asymptotic convergence between guarantee principal and subordinate robot, therefore has in practice
Higher application value.
Description of the drawings
Fig. 1 is the structure diagram of bilateral teleoperation system under asymmetric time-vary delay system；
Fig. 2 is pre-determined characteristics control principle drawing；
The control principle drawing of remote control system under Fig. 3 present invention.
Specific implementation mode
Embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples.Following embodiment is used for
Illustrate the present invention, but cannot be used for limiting the scope of the invention.
One embodiment of the present of invention：The pre-determined characteristics controlling party of bilateral teleoperation system under a kind of asymmetric time-vary delay system
Method, content include the following steps：
S1. introduce auxiliary intermediate variable and remote control system be split as two subsystems --- the first subsystem and the second son
System, and the system mode with time-vary delay system is disposed only in the second subsystem；Its specific implementation mode is as follows：
Consider the bilateral teleoperation system that is made of master and slave robot, main robot and from passing through net between robot
The connected row information transmission of going forward side by side of network, and under normal circumstances often there are asymmetric and time-varying characteristics in network inducement delay.For
Bilateral teleoperation system under asymmetric time-vary delay system designs pre-determined characteristics control method, tends to rely on principal and subordinate robot position
Set the derivative of error, however the time-vary delay system derivative information in the site error derivative between principal and subordinate robot in practical applications
In practice it is difficult to accurately measure, thus for asymmetric time-vary delay system presence brought to pre-determined characteristics control design case it is huge
Challenge；
Non-linear bilateral teleoperation system is：
Wherein, subscript m represents main robot, and subscript behalf is from robot, Mm(qm),Ms(qs)∈Rn×nJust for system
Determine inertial matrix；For the vector of coriolis force and centrifugal force；Gm(qm),Gs(qs)∈RnFor
The gravity item of system；Fh∈RnAnd Fe∈RnThe torque that the torque and environment that respectively human operator applies apply；τm∈RnWith
τs∈RnThe control moment that device provides in order to control；
For the above bilateral teleoperation system model, it is defined as follows auxiliary intermediate variable：xi1=qi,
So remote control system equation (31) will be done by writing again：
The main goal in research of the present invention is by designing new control algolithm, ensureing to apply as operator and external environment
When power is zero, master-slave synchronisation error qm-qs(t-Ts(t)), qs-qm(t-TmAnd the speed of master and slave robot (t))WithGradually
It is close to converge to zero, while within master-slave synchronisation error is in set and delimits always；Wherein Tm(t) indicate that main robot end is arrived
Time-vary delay system, and T are transmitted from the information of robotic ends(t) it is when transmitting time-varying to the information at main robot end from robotic end
Prolong；
For information transmission time-vary delay system Ti(t) meet following assumed condition：
1) there are equationsSo thatAnd for all t
> 0 exists | Ti(t)|≤T*(t)；
2) equation Ti(t) there are t-T as t →+∞ for satisfactioni(t)→+∞；
3) there are constant Υi>=0 so that for allt2> t1So that inequality | Ti(t2)-Ti(t1)|
≤Υi|t2-t1| it sets up.
It can be simply interpreted as above with respect to the hypothesis of time-vary delay system, there are a function T* (t), can be time-varying function
It is alternatively fixed value, when it is time-varying function, pace of change is less than or equal to itself.Same above-mentioned hypothesis illustrate it is main,
Exist from the communication time-vary delay system derivative between robot, and meets
To realize the above control targe and the control method of design being avoided to depend on the asymmetric time-vary delay system derivative upper bound,
Here new variable is definedAnd then it is defined as follows error variance ei1=xi1-
ψi1,Wherein ψi1It is defined as follows：
Wherein,Be specifically defined and will be provided in the content below；
Therefore based on auxiliary intermediate variable ψi1, ψi2, and then define ei2=xi2-ψi2, former remote control system formula (32) is split
It is divided into following two subsystems, wherein the concrete form of the first subsystem is as follows：
Wherein, Fmhe=Fh, Fshe=-Fe, i=m, s；
The concrete form of second subsystem is formula (33).
S2. it is directed to the first subsystem and is based on the adaptive pre-determined characteristics strategy of Backstepping method design, ensure the first subsystem
The synchronous error of system meets preset temporary steady-state behaviour while asymptotic convergence.Its specific implementation mode is as follows：
The simple main thought for providing pre-determined characteristics control.
For General System synchronous error e=[e1,e2,…,en]T, pre-determined characteristics refers to the aleatory variable in synchronous error
ej, strictly within the boundary in some predefined, which is formed by the equation to successively decrease at any time by j=1,2 ..., n.Tool
Body, which is represented by, works as ej(0) >=0 whenAnd work as ej(0) when < 0Specifically such as Fig. 2 institutes
Show, whereinFor smooth, bounded, the positive time-varying variance of strictly decreasing,Pre-determined characteristics equation.Constant
ρj(∞) represents ejPermitted maximum synchronous error, ρ when system is stablizedjRate of descent represent ejThe minimum convergence speed of permission
Degree,Expression system allow maximum overshoot andMeetIf not allowing overshoot presence that can pass through
Enable δj=0 realizes.It can be seen that different system performances can be met by defining suitable pre-determined characteristics equation
Demand.
To promote synchronous error ejAlways within the scope of being in predetermined, it is defined as follows error transfer equationWherein,For smooth strictly increasing equation, and meet following condition, works as ej(0) >=0 when,Work as ej(0) when < 0, R ():(-1,δj)→(-∞,+∞)；Define η=[η1,
η2,…,ηn]T, can obtain its derivative isWherein
AndClearly due to error transfer equationPossessed above-mentioned property, error
The pre-determined characteristics of e can be by makingTrack bounded realize.
First, assuming that ψi2AndIn the presence of and bounded on the basis of, for the first subsystem using Backstepping
Method designs pre-determined characteristics control strategy；
For the following error converted variable η of the first subsystem definitioni
Wherein, i=m, s, j=1,2 ..., n；
And then error transfer equation Rij() is designed as：
Wherein,For system performance equation,ConstantIt representsThe permitted maximum synchronous error when system is stablized,Rate of descent representThe minimum convergence rate of permission,Expression system allow maximum overshoot andMeet
To above-mentioned variable ηiDerivation can obtain：
Wherein,
According to rightWithDefinition can obtain as follows about equation property：
New auxiliary variable xi2Ideal trajectory be defined as xi2d, it is designed specifically to：
Wherein, ki1For fixed normal number.
Based on error delta xi2=xi2-xi2d, can obtain：
In turn, as follows for the adaptive pre-determined characteristics controller design of the first subsystem：
Wherein, ki2Normal number is chosen for,For the regression matrix of system,For parameter adaptive tune
Variable is saved, for approaching the vectorial θ being made of system uncertain parameteri；
Parameter adaptive adjusts rule and is designed as：
Wherein, ΛiFor diagonal positive definite constant matrices.
Assuming that ψi2AndIn the presence of and bounded on the basis of, choose Lyapunov equationsIts with
The first derivative of time is：
According to variable Δ xi2Definition, can obtain：
In turn, following new Lyapunov equations are chosen：
Above formula derivation can be obtained：
Wherein,
Based on designed adaptive pre-determined characteristics controller (41), can obtain：
Wherein,
It is final to choose following new Lyapunov equations：
Its first derivative is：
Based on inequalityIt can obtainAgain due to V >=0, it may thus be appreciated that variable ηi, Δ
xi2,Bounded, and variable ηi,Δxi2Same bounded；The variable η of boundediIllustrate that the first subsystem meets scheduled temporary stable state
Performance.Work asWhen existWhenWhen,And then according to machine
The property of people's model can obtainBounded,Bounded；Finally, according to Barbalat lemma can proper t → ∞ when ηi→ 0, ei→0
That is qi-ψi1→0。
S3. it is directed to the second subsystem and designs pre-determined characteristics control strategy, and systematicness is established using multidimensional small gain theorem
Can parameter, controller parameter, the time delay derivative upper bound and system stability relationship；Its specific implementation mode is as follows：
It defines first
Wherein, i=m, s, j=1,2 ..., n；And then error transfer equationIt is designed as：
For vectorFor a number in system performance equation, j=1,2 ..., n.
ConstantIt representsThe permitted maximum when system is stablized
Synchronous error,Rate of descent representThe minimum convergence rate of permission,Expression system allow maximum overshoot andMeetTo variableDerivation can obtain：
Wherein,
In turn, Δ ψ is definedi2=ψi2-ψi2d,It can obtain：
Based on Δ ψi2DerivativeAndIt is defined as：
Wherein, λi1And λi2For the fixation normal number of selection；
In turn, it can obtain：
Before providing further derive, following several definition are provided first：
Define 1：One continuity equationIf belonging to K class equations i.e. its strictly increasing of α ∈ K and meeting α (0)
=0.Equation α ∈ K belong to K∞If class equation α (s) → ∞ works as s → ∞.
DefinitionO is zero equation i.e. O (s) ≡ 0 for all s > 0.
EquationFor KL class equations, if β (, t) for first parameter, whenFor K classes
Equation, and β (s, t) is decremented to zero as t → ∞ for all fixed s >=0.
Define 2：EquationFor popularization (generalized) if K class functions, that is, GK class equations
And it is continuous, and for arbitrary r1> r2Meet：
It is worth noting that general K class equations are GK equations.EquationFor popularization
(generalized) KL equations (GKL), if for arbitrary fixed t >=0, equation β (s, t) is GK equations, and for arbitrary
Fixed s >=0 is decremented to zero as t → T, T < ∞.In general T is referred to as the stabilization time of GKL equation β ().
For following affine nonlinear multiinput-multioutput system：
Wherein,ForFor j ∈ Nq:=(1 ..., q), f
(), gi(), i ∈ Np, hj(), j ∈ NqFor the locally Lipschitz function equation with corresponding dimension, f (0)=0 and h (0)
=0.For arbitrary initial conditions x (t0), arbitrarily input u1(t),…,up(t) in [t0,t1) consistent intrinsic bounded, it is corresponding
X (t) is solved in [t0,t1] exist in section.
Define 3：For system (55), if there is equation β ∈ K∞, constantFor i ∈ Nq,j∈Np, exist and appoint
Anticipating, unanimously intrinsic bounded inputs u to LeibnizjFor all j ∈ NpSo that such as lower inequality：
(1) uniform bound：Have：
(2) asymptotic convergence gain：
It sets up, then system (55) is weak input-to-state stability, and in above-mentioned definitionIt is referred to as weak input
To in stable condition gain.
It is worth noting that for system (55), weak input-to-state stability again means that weak be input to exports stabilization,
It refers to that there are equation β ∈ K∞WithFor i ∈ Nq, j ∈ Np,t≥t0So that such as lower inequality：
It sets up, whereinIt is referred to as weak being input to output constant gain.
According to formula (51) and formula (53), further can be obtained：
Wherein,For quadratic equationRoot.Due to λi2, λi1,For positive number, then clearlyIt is similarly positive number.Seeking πi
When will useApparent basisπiIt can very simply seek；According to differ
Formula (59) can obtain the second subsystem with variableWith Δ ψi2For system mode, withIt is weak be input to for system input
It is in stable condition, and gain is πi；
The output of closed loop remote control system is：
It can be obtained according to result above, as t → ∞, Δ xi2,ηi,ei→0.Further basisIt can obtainSo, closed loop remote control system withTo input, with variable xi2For output
Under meet it is weak be input to output stable condition, and it is weak be input to output stablize and gain be (1+ υi)πi,
Based on the above analysis it is found that closed loop remote control system can be seen as one is made of two inputs and two outputs
Closed-loop system, therefore have y1=xm2, y2=xs2,The closed loop remote control system meets weak be input to
Stable condition is exported, and the weak output constant gain matrix that is input to of system isIt is specifically defined as
On the other hand, according to about time delay it is assumed thatWithEstimation can obtain：
Therefore, connection matrix Γ:={ νji}
ν12=1+ Υs, ν21=1+ Υm (64)
According to the above analysis, can obtain closed-loop system gain matrix isWherein：
According to small gain theorem, ifSo variableΔψi2,xi2Bounded, and as t → ∞,
ψi1→ 0,Δψi2→ 0, xi2→0；Therefore it can further obtainAndAlways it is in scheduled model
Within enclosing；Therefore it can obtain：
Can finally obtain | | xm1-xs1||→0,t→∞；
Therefore when operator, extraneous input torque are zero, and controller parameter chooses so that inequality max ((1+ Υs)
πmj) < 1 and max ((1+ Υm)πsj) < 1 is when setting up, then the synchronization of the bilateral teleoperation system under asymmetric time-vary delay system
Error meets preset temporary steady-state behaviour while asymptotic convergence.
The present invention considers the adaptive pre-determined characteristics control method of bilateral teleoperation system under asymmetric time-vary delay system, compares
Mainly there is the advantages of three aspects in the existing control method for remote control system：First, with general P+d, PD+d and
Direct force feedback method is compared, convergence rate faster, convergence precision higher, and have better transient performance；Secondly, with it is existing
Some is compared for the pre-determined characteristics control method of remote control system, and designed pre-determined characteristics control method can protect in the invention
The synchronous error for demonstrate,proving the remote control system under asymmetric time-vary delay system meets preset net synchronization capability while asymptotic convergence, and
Controller is easier to realize in practice in the design independent of asymmetric time-vary delay system information；Finally, in the invention
Controller parameter especially controller parameter is established for the first time, and the relationship of pre-determined characteristics equation parameter and the time-vary delay system upper bound is dropping
While the conservative of low system so that it is more convenient to the selection of controller parameter in practice, therefore practicability is stronger.
The embodiment of the present invention provides for the sake of example and description, and is not exhaustively or by this to send out
It is bright to be limited to disclosed form.Many modifications and variations are obvious for the ordinary skill in the art.Choosing
It is and to make those skilled in the art to more preferably illustrate the principle of the present invention and practical application to select and describe embodiment
It will be appreciated that various embodiments with various modifications of the present invention to design suitable for special-purpose.
Claims (4)
1. a kind of pre-determined characteristics control method for bilateral teleoperation system under asymmetric time-vary delay system, it is characterised in that：Institute
The method content of stating includes the following steps：
S1. introduce auxiliary intermediate variable and remote control system be split as two subsystems --- the first subsystem and the second subsystem
System, and the system mode with time-vary delay system is disposed only in the second subsystem；
S2. it is directed to the first subsystem and is based on the adaptive pre-determined characteristics strategy of Backstepping method design, ensure the first subsystem
Synchronous error meets preset temporary steady-state behaviour while asymptotic convergence；
S3. it is directed to the second subsystem and designs pre-determined characteristics control strategy, and establish system performance using multidimensional small gain theorem and join
The relationship of number, controller parameter and the time delay derivative upper bound and system stability.
2. a kind of pre-determined characteristics control for bilateral teleoperation system under asymmetric time-vary delay system according to claim 1
Method, it is characterised in that：In step sl, remote control system is split as two subsystems by the introducing auxiliary intermediate variable
System --- the first subsystem and the second subsystem, and the system mode with time-vary delay system is disposed only in the second subsystem；Its
Specific implementation mode is as follows：
Consider the bilateral teleoperation system that is made of master and slave robot, main robot with from passing through network phase between robot
Connect row information transmission of going forward side by side, and under normal circumstances often there are asymmetric and time-varying characteristics in network inducement delay.For non-right
Claim the bilateral teleoperation system under time-vary delay system to design pre-determined characteristics control method, tends to rely on principal and subordinate robot location mistake
The derivative of difference, however the time-vary delay system derivative information in the site error derivative between principal and subordinate robot is in reality in practical applications
It is difficult accurately to measure, therefore huge choose is brought to pre-determined characteristics control design case for the presence of asymmetric time-vary delay system in border
War；
Non-linear bilateral teleoperation system is：
Wherein, subscript m represents main robot, and subscript behalf is from robot, Mm(qm),Ms(qs)∈Rn×nIt is used for the positive definite of system
Property matrix；For the vector of coriolis force and centrifugal force；Gm(qm),Gs(qs)∈RnFor system
Gravity item；Fh∈RnAnd Fe∈RnThe torque that the torque and environment that respectively human operator applies apply；τm∈RnAnd τs∈Rn
The control moment that device provides in order to control；
For the above bilateral teleoperation system model, it is defined as follows auxiliary intermediate variable：xi1=qi,I=m, s, then
Remote control system equation (1) will be done by writing again：
Define new variableWherein Tm(t) indicate main robot end to slave
The information transmission time-vary delay system at device people end, and Ts(t) it is to transmit time-vary delay system from robotic end to the information at main robot end；Into
And it is defined as follows error variance ei1=xi1-ψi1,Wherein ψi1It is defined as follows：
Wherein,Be specifically defined and will be provided in the content below；
Therefore based on auxiliary intermediate variable ψi1, ψi2, and then define ei2=xi2-ψi2, former remote control system formula (2) be split as
Lower two subsystems, wherein the concrete form of the first subsystem is as follows：
Wherein, Fmhe=Fh, Fshe=-Fe, i=m, s；
The concrete form of second subsystem is formula (3).
3. a kind of pre-determined characteristics control for bilateral teleoperation system under asymmetric time-vary delay system according to claim 1
Method, it is characterised in that：In step s 2, first subsystem that is directed to is based on the adaptive precordainment of Backstepping method design
Can be tactful, ensure that the synchronous error of the first subsystem meets preset temporary steady-state behaviour while asymptotic convergence, it is specific real
It is as follows to apply mode：
For the following error converted variable η of the first subsystem definitioni
Wherein, i=m, s, j=1,2 ..., n；
And then error transfer equationIt is designed as：
Wherein,It is time-varying variance for system performance equation,ConstantIt representsPermitted maximum synchronous error, time-varying variance when system is stablizedRate of descent representAllow most
Small convergence rate,Expression system allow maximum overshoot andMeet
To above-mentioned variable ηiDerivation can obtain：
Wherein,
According to rightWithDefinition can obtain as follows about equation property：
New auxiliary variable xi2Ideal trajectory be defined as xi2d, it is designed specifically to：
Wherein, ki1For normal number；
Based on error delta xi2=xi2-xi2d, can obtain：
In turn, as follows for the adaptive pre-determined characteristics controller design of the first subsystem：
Wherein, ki2Normal number is chosen for,It is used for approaching being made of system uncertain parameter for parameter adaptive regulated variable
Vectorial θi；
Parameter adaptive adjusts rule and is designed as：
Wherein, ΛiFor diagonal positive definite constant matrices；
Assuming that ψi2AndIn the presence of and bounded on the basis of, choose Lyapunov equationsIt is at any time
First derivative is：
According to variable Δ xi2Definition, can obtain：
In turn, following new Lyapunov equations are chosen：
Above formula derivation can be obtained：
Wherein,
Based on designed adaptive pre-determined characteristics controller (11), can obtain：
Wherein,
It is final to choose following new Lyapunov equations：
Its first derivative is：
Based on inequalityIt can obtainAgain due to V >=0, it may thus be appreciated that variable ηi, Δ xi2,
Bounded, and variable ηi,Δxi2Same bounded.The variable η of boundediIllustrate that the first subsystem meets scheduled temporary steady-state behaviour,
Work asWhen existWhenWhen,And then according to robot model
Property can obtainBounded,Bounded；Finally, according to Barbalat lemma can proper t → ∞ when ηi→ 0, ei→ 0 i.e. qi-ψi1
→0。
4. a kind of pre-determined characteristics control for bilateral teleoperation system under asymmetric time-vary delay system according to claim 1
Method, it is characterised in that：In step s3, described to be directed to the second subsystem design pre-determined characteristics control strategy, and utilize multidimensional
Small gain theorem establish system performance parameter, controller parameter, the time delay derivative upper bound and system stability relationship；It is specific real
It is as follows to apply mode：
It defines firstIts
In, i=m, s, j=1,2 ..., n；And then error transfer equationIt is designed as：
For vectorFor a number in system performance equation, j=1,2 ..., n；
ConstantIt representsIt is permitted maximum synchronous when system is stablized
Error,Rate of descent representThe minimum convergence rate of permission,Expression system allow maximum overshoot andMeetTo variableDerivation can obtain：
Wherein,
In turn, Δ ψ is definedi2=ψi2-ψi2d,It can obtain：
Based on Δ ψi2DerivativeAnd
It is defined as：
Wherein, λi1And λi2For the fixation normal number of selection；
In turn, it can obtain：
According to formula (21) and formula (23), further can be obtained：
Wherein,For quadratic equationRoot.Due to λi2, λi1,For positive number, then clearlyIt is similarly positive number.Seeking πi
When will useApparent basisπiIt can very simply seek；According to inequality
(25), the second subsystem can be obtained with variableWith Δ ψi2For system mode, withIt is weak to be input to shape for system input
State is stablized, and gain is πi；
The output of closed loop remote control system is：
It can be obtained according to result above, as t → ∞, Δ xi2,ηi,ei→0.Further basisIt can obtainSo, closed loop remote control system withTo input, with variable xi2It is weak to meet under output
It is input to output stable condition, and weak be input to exports stable and gain as (1+ υi)πi,
Based on the above analysis it is found that closed loop remote control system, which can be seen as one, is exported closing of forming by two inputs and two
Loop system, therefore have y1=xm2, y2=xs2,The closed loop remote control system, which meets, weak is input to output
Stable condition, and the weak output constant gain matrix that is input to of system isIt is specifically defined as
On the other hand, according to about time delay it is assumed thatWithEstimation can obtain：
Therefore, connection matrix Γ:={ νji}
ν12=1+ Υs, ν21=1+ Υm (29)
According to the above analysis, can obtain closed-loop system gain matrix isWherein：
According to small gain theorem, ifSo variableΔψi2,xi2Bounded, and as t → ∞, ψi1→
0,Δψi2→ 0, xi2→0；Therefore it can further obtainAndAlways be in scheduled range with
It is interior；Therefore it can obtain：
Can finally obtain | | xm1-xs1||→0,t→∞；
Therefore when operator, extraneous input torque are zero, and controller parameter chooses so that inequality max ((1+ Υs)πmj)
< 1 and max ((1+ Υm)πsj) < 1 is when setting up, then the synchronous error of the bilateral teleoperation system under asymmetric time-vary delay system
Meet preset temporary steady-state behaviour while asymptotic convergence.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109677634A (en) * | 2018-11-27 | 2019-04-26 | 北京空间技术研制试验中心 | Manned exploration's lunar surface remote control system framework |
| CN110361960A (en) * | 2019-06-26 | 2019-10-22 | 南京理工大学 | For the synchronisation control means of the bilateral teleoperation system based on time lag probability distribution |
| CN110794678A (en) * | 2019-11-05 | 2020-02-14 | 燕山大学 | Four-channel teleoperation force feedback control method under hysteresis nonlinearity limitation |
| CN113043280A (en) * | 2021-04-21 | 2021-06-29 | 南京邮电大学 | Control method for processing teleoperation system under DOS attack |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105319972A (en) * | 2015-11-27 | 2016-02-10 | 燕山大学 | Remote operating robot fixed time control method based on rapid terminal sliding mode |
| CN106647281A (en) * | 2017-01-18 | 2017-05-10 | 燕山大学 | Method for compensating finite interference time of remote operation system based on terminal slide model |
| CN107255922A (en) * | 2017-05-27 | 2017-10-17 | 燕山大学 | A kind of fast turn of speed method of estimation of remote control system based on adaptive double-deck sliding formwork |
-
2018
- 2018-06-20 CN CN201810637856.8A patent/CN108803331A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105319972A (en) * | 2015-11-27 | 2016-02-10 | 燕山大学 | Remote operating robot fixed time control method based on rapid terminal sliding mode |
| CN106647281A (en) * | 2017-01-18 | 2017-05-10 | 燕山大学 | Method for compensating finite interference time of remote operation system based on terminal slide model |
| CN107255922A (en) * | 2017-05-27 | 2017-10-17 | 燕山大学 | A kind of fast turn of speed method of estimation of remote control system based on adaptive double-deck sliding formwork |
Non-Patent Citations (1)
| Title |
|---|
| 杨亚娜: "网络诱导时延下遥操作系统的暂稳态性能约束控制研究", 《中国博士学位论文全文数据库 信息科技辑》 * |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109677634A (en) * | 2018-11-27 | 2019-04-26 | 北京空间技术研制试验中心 | Manned exploration's lunar surface remote control system framework |
| CN110361960A (en) * | 2019-06-26 | 2019-10-22 | 南京理工大学 | For the synchronisation control means of the bilateral teleoperation system based on time lag probability distribution |
| CN110361960B (en) * | 2019-06-26 | 2022-07-19 | 南京理工大学 | Synchronous control method for bilateral teleoperation system based on time-lag probability distribution |
| CN110794678A (en) * | 2019-11-05 | 2020-02-14 | 燕山大学 | Four-channel teleoperation force feedback control method under hysteresis nonlinearity limitation |
| CN110794678B (en) * | 2019-11-05 | 2021-07-30 | 燕山大学 | Four-channel teleoperation force feedback control method under hysteresis nonlinearity limitation |
| CN113043280A (en) * | 2021-04-21 | 2021-06-29 | 南京邮电大学 | Control method for processing teleoperation system under DOS attack |
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