CN108594845A - More AUV formation methods based on PREDICTIVE CONTROL under a kind of communication limitation - Google Patents
More AUV formation methods based on PREDICTIVE CONTROL under a kind of communication limitation Download PDFInfo
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- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
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- G05D1/10—Simultaneous control of position or course in three dimensions
Abstract
A kind of more AUV formation methods based on PREDICTIVE CONTROL under being limited the present invention relates to communication, the control strategy of invention logic-based communication designs predictive controller, suitable for there are under weak communication constraint, including when data-bag lost and communication delay, the formation control of more AUV.The invention mainly comprises：The design of the path following control device of single AUV, when communication condition ideal more AUV formation controls, there are the designs that logic-based when weak communication constraint communicates predictive controller.This method carries out a large amount of information exchange between not needing AUV during forming into columns, and the invention enables more AUV, and desired formation can be still formed and kept under weak communication constraint, and method is fairly simple, has a wide range of application.
Description
Technical field
The present invention relates to a kind of more AUV formation methods, and PREDICTIVE CONTROL is based on more particularly to a kind of communication limitation is lower
More AUV formation methods.
Background technology
AUV needs the information such as the position, course of other AUV, speed in being formed into columns when executing formation task.In water
Under the only effective communication mode be underwater sound communication, but the bandwidth of underwater sound communication it is narrow, distance shorter, quality nor spy
Not good, communication failure and time delay can all increase the unstability and uncontrollability of system, be unfavorable for the formation formed into columns and formation is protected
It holds.Formation control is divided into two sub-problems by the scholar having for this situation：In bottom, AUV is according to control law to virtual mesh
Mark movement realizing route tracking；In high level, by adjusting virtual target speed make between AUV move to it is consistent.Have
Scholar manually restrain by potential field method design formation control, and communication delay is solved by the requirement to communication during reduction formation,
The present invention establishes communication network using graph theory, is exchanged using communication network or shares relevant movable information to realize more AUV
Coordination control.
It is assumed that when more AUV in underwater sound communication distance range, consider that the communication condition between more AUV is weak communication,
The control strategy of logic-based communication designs predictive controller, and each AUV uses simple principle and a small amount of information in formation
It exchanges, reduces the traffic, the coordination between more AUV is realized by estimating the correlated state of AUV adjacent thereto, the method
Communications cost can be reduced, complicated subsurface communication environment is suitable for.
Invention content
For the above-mentioned prior art, providing one kind the technical problem to be solved by the present invention is to using for reference PREDICTIVE CONTROL thought makes
AUV can still form desired flight pattern under the conditions of communication constraint (including data-bag lost and communication delay), and can
More AUV formation methods based on PREDICTIVE CONTROL under a kind of communication limitation to keep the navigation of this formation.
In view of the above technical problems, more AUV formation methods based on PREDICTIVE CONTROL under a kind of communication limitation of the present invention, including
Following steps：
Step 1：Establish the horizontal surface model of each AUV；
Step 2：The speed of each AUV in forming into columns, position and bow are initialized to angle；
Step 3：The horizontal surface models of AUV based on step 1 introduce virtual reference point, design motivation path trace control
Device processed and kinematics path following control device, complete the path trace of single AUV；
Step 4：Judge to whether there is communication constraint between AUV, when communication constraint is not present between AUV, executes step
Five；When communication has constraint between AUV, step 6 is executed；
Step 5：Design coordination formation control device establishes communication topology relationship and coordination error between more AUV using graph theory
Model realizes flight pattern, executes step 8 by the total tune control to virtual reference point；
Step 6：The control strategy of logic-based communication, designs predictive controller, is carried out to the correlated state of other AUV
Estimation；
Step 7：Judge whether to realize and it is expected to form into columns, it is expected to form into columns when being formed, execute step 8；It is expected to compile when not formed
Team, return to step six continue to execute；
Step 8：This formation is kept to navigate by water to target point.
More AUV formation methods based on PREDICTIVE CONTROL under a kind of communication of the present invention limits further include：
The horizontal surface model of 1.AUV meets：
Wherein：mur=m-Yr, du=-Xuuu2-Xvvv2, dv=-Yvuv-
Yv|v|V | v |, dr=-Nvuv-Nv|v|v|v|-NrUr, IzFor permanent moment；X{.}、Y{.}And N{.}For hydrodynamic force coefficient；F and T is represented
The thrusts of AUV in the longitudinal direction and turn bow torque, u is the propulsion speed of AUV, and v is the lateral movement velocity of AUV, and r is represented
AUV's turns bow speed, and x represents the lateral positions AUV, and y represents AUV lengthwise positions, and ψ represents AUV bows to angle.
2. the speed of step 2 initialization each AUV in forming into columns, position and bow are to angle, specially：
N number of AUV in formation, it is pilotage people to carve specify wherein any one AUV at the beginning, remaining AUV is follower；
N number of AUV is engraved at the beginning floating to sea, and each AUV obtains the location information of itself by GPS；
Sonar set entrained by pilotage people's use to follower adjacent thereto send position, speed and the bow of itself to
Position, speed, bow are also sent to AUV adjacent thereto to angle between follower by angle information using entrained sonar set.
N number of AUV dives to same depth starts depth-keeping navigation, and pilotage people sends the position of itself, speed and bow to angle
To AUV adjacent thereto.
3. step 3 detailed process is：
For the horizontal surface model that step 1 is established, design control law τa=[τu,τr]T, makeWherein Ud(t)=[ud,rd]T∈R2；
ue(t)=U (t)-Ud(t) representation speed tracking error, control law are：
Wherein, K1=diag { ku,krIt is positive definite matrix, MaFor quality and inertial matrix, CaFor Coriolis and centripetal matrix, Da
For damping and frictional force matrix, udAnd rdFor desired speed and angular speed, τuAnd τrFor power and torque；
The site error of path trace is defined asIts derivation can be obtained：
Whereinη1=[x, y]T, function S (v2) it is vector v2=[0, r]T∈R2Antisymmetric matrix,
S(v2) meet：
Using the distance of the current track points of AUV and reference point between the two as new error vector (ε-δ), ν1=[u, v]T, δ
It is a constant, it is known that U=Ud+ue, formula (3) can be written as：
Design UdControl law, udIt is speed corresponding with parameter ξ, the desired speed of target point isThere is following formula
It sets up：
I.e.:
Control law
Wherein, { 1,0.01 } P=diag, f are hyperbolic tangent function：F (x)=tanh (x), wherein K2=diag { kx,
kyIt is positively definite matrix.
4. step 5 is specially：
Multiple AUV situations ∑s:={ 1 ..., n }, with ξ=[ξ1,…,ξn]TIndicate the correlated state between AUV；
For the follower AUV in formation, it isDesign control law so thatIt sets up, simultaneously
Ensure to form into columns whole with desired speed udNavigation, that is, meet
Error is coordinated in definition：
ξe=G ξ (7)
Wherein, G=D-1(D-A), D is the Vertex Degree matrix of communication topology figure G, and A is adjacency matrix, works as DiiWhen=0,There is an isolated vertex,If ξeGradually level off to zero, so that it may to realize formation coordination,
It is assumed that the communication topology relationship between more AUV be to determine it is constant, in ξeIn i-th be：
To in (7) derivation and wushu (5) substitution (7), obtaining
udIt is the vector being made of the desired speed of each AUV, i.e.,
Each AUV is navigated by water in the desired path of the motion control of design rule (2) and (6) effect lower edge in then forming into columns, false
Determine Laplacian Matrix that G is a standard, describe the Communication topology between more AUV, it is assumed that the communication between adjacent AUV is
Continuously, decentralised control rule is：
uL=ud+kef(Gξ) (9)
Wherein, f (x)=tanh (x), keIt is a sufficiently large constant value.
5. step 6 is specially：
Formula (5) and formula (9) are updated in formula (8), obtaining state estimation equation is：
By the way that its actual value and estimated value were compared to determine to the time of adjacent AUV transmission information, if
Some specific time point tk, the difference between estimated value and actual value is more than some threshold value, i.e.,When,
AUVi will carry out information exchange with adjacent AUV, and each AUV can timely update its estimated value, following formula is made to set up
Then formation coordination control law (9) can become：
It is assumed that AUVi is in time tkWhen begin through communication topology to AUV adjacent thereto send oneself correlated state letter
Breath, the AUVj and AUVk beside it are in tk+τ1And tk+τ2Receive this information；
Estimator that the communication link between AUVj and AUVk is provided on AUVi is represented to ξiEstimated value, if when
Carve tk, AUVi will contain actual value ξiWith moment tkInformation be sent to AUVj, in moment tk+ τ AUVj receive the message, but
State estimation is not updated timely, an information is replied to AUVi and informs that " reception " has arrived information for it, realizes
Synchronism between AUVi, in tk+ 2 τ moment were updated its estimated value, at this point, the ξ on link ijiEvaluated error
Meet：
When time delay bounded, above formula is exactly bounded；
In tkWhen AUVi pass information to AUVj, AUVj is in tk+τijThe information is received, the AUVj meetings after receiving the information
The delay, τ being calculated at the momentijAUV i are passed to, and it is t=t that AUV i, which receive information at the time of point,k+τij+
τji, it is assumed that there is following formula establishment：
WhereinI.e.：
Assuming that AUVi is in moment tkInformation ξ is exchanged with AUVji, it is assumed that the maximum value of propagation delay time is τmaxIf in tk+
τmaxAUVi can receive AUVj and be transmitted back to the return information come before this time point, then in tk+τmaxMoment all AUV
Estimated state information update finish；
If being not received by return information before the deadline, it is meant that the information has been lost, need at this time will under
One data clapped send over, by the maximum time difference is selected as newest ξ between the two when information transmission and information updateiAnd τmax,
Error between actual value and estimated value meets：
Estimation between same link synchronizes, i.e.,：
If AUVj has received information, AUVi does not still receive return information, then only AUVj has carried out state letter
Breath update, then AUVi retransmits an information again, in spite of there are time delay control law (12) all continuously effectives.
Beneficial effects of the present invention：The present invention is based on the control strategies of logic communication to design predictive controller, suitable for depositing
The formation control of (including data-bag lost and communication delay) more AUV under weak communication constraint.
1. method is suitble to practical application.Due to the constraint of underwater environment, between AUV there is time delay in communication certainly, and communicate letter
Breath amount is smaller, and this method carries out a large amount of information exchange between not needing AUV during forming into columns.
2. having actual application value.AUV monomers often have a single function, and application can be restricted, and more AUV form into columns collaboration can
With the more efficient task that fulfils assignment.Formation work can be used for the maintenance etc. of offshore oilfield pipeline.
The invention enables more AUV, and desired formation can be still formed and kept under weak communication constraint, and method is fairly simple, answers
It is wide with range.
Description of the drawings
Fig. 1 is the work flow diagram of the present invention；
Fig. 2 is more AUV formation flight path schematic diagrames；
Fig. 3 is navigator AUV speed and angular speed schematic diagram；
Fig. 4 is to follow AUV1 speed and angular speed schematic diagram；
Fig. 5 is to follow AUV2 speed and angular speed schematic diagram；
Fig. 6 is to follow AUV3 speed and angular speed schematic diagram；
Fig. 7 is to follow AUV4 speed and angular speed schematic diagram；
Fig. 8 is the site error schematic diagram of each AUV.
Specific implementation mode
The present invention is described further with case below in conjunction with the accompanying drawings.
Flow of the present invention as shown in Figure 1, when between more AUV communication condition be weak communication when, logic-based communication control strategy
Predictive controller is designed, is estimated by the correlated state to AUV, achievees the purpose that coordinate to form into columns, set in a program
Be communication delay it is 5s, follower just receives the information of pilotage people after 5s, and data-bag lost is the information in 5s around here
It being lost, the information that follower obtains is that discrete, designed predictive controller can be very good to estimate information,
It realizes flight pattern, is mainly illustrated with time delay situation.
Step 1：Establish the horizontal surface model of AUV：
Wherein：mur=m-Yr, du=-Xuuu2-Xvvv2, dv=-Yvuv-
Yv|v|V | v |, dr=-Nvuv-Nv|v|v|v|-Nrur。IzFor permanent moment；X{.}、Y{.}And N{.}For hydrodynamic force coefficient；F and T is represented
The thrusts of AUV in the longitudinal direction and turn bow torque, u is the propulsion speed of AUV, and v is the lateral movement velocity of AUV, and r is represented
AUV's turns bow speed, and x represents the lateral positions AUV, and y represents AUV lengthwise positions, and ψ represents AUV bows to angle.Wherein, m=
2234.5kg,Xvv=-128.4Kgm-1,Xuu
=-35.4Kgm-1,Yv|v|=-667Kgm-1,Yv=-346Kg, Yr=435Kg, Nr=-1427Kgm, Nv|v|=
443Kg,Nv=-686Kg, Iz=2000Nm2
Step 2：The design of piece controller
Present case is illustrated by taking 5 AUV as an example, it is assumed that and the controller of pilotage people and follower are the same, for
Kinetics equation (1) used, enables Ud(t)=[ud,rd]T∈R2, it is assumed that UdBe it is smooth, to the time can micro- and bounded, design
Control law τa=[τu,τr]T, make
ue(t)=U (t)-Ud(t) representation speed tracking error.Control law is
The AUV kinematics models established by front, kinematics path following control problem can be expressed as：Use continuous variable
ξ (t) ∈ R are expected path Γ (ξ) ∈ R2Parametrization, ud(ξ) ∈ R are desired speeds, when variable ξ is differential bounded, and it is expected
Path Γ (ξ) is continuous and derivable, AUV flight paths can be allowed to converge to expected path by designing suitable controller.
The site error of path trace can be defined as
Its derivation can be obtained
Whereinη1=[x, y]T, function S (v2) it is vector v2=[0, r]T∈R2Antisymmetric matrix.
Using the distance of the current track points of AUV and reference point between the two as new error vector (ε-δ), ν1=[u, v]T,
Know U=Ud+ue, formula (4) can be written as：
Design UdControl law, udIt is not the true velocity of AUV, is speed corresponding with parameter ξ, the expectation of target point
Speed isThere is following formula establishment：
I.e.:
Control law
Wherein, { 1,0.01 } P=diag, f are hyperbolic tangent function：F (x)=tanh (x),
Third walks：Under control law (2) and (7) effect, the path trace of monomer may be implemented, below for desired communication
Under the conditions of, it realizes and forms into columns, formation control device is designed, with ξ=[ξ1,…,ξn]TIndicate the correlated state between AUV.
For other AUV in formation, it isDesign control law so thatIt sets up, simultaneously
Ensure to form into columns whole with desired speed udNavigation, that is, meet
Error is coordinated in definition
ξe=G ξ (8)
Wherein, G=D-1(D-A)。If ξeGradually level off to zero, so that it may to realize association of forming into columns
It adjusts.It is assumed that the communication topology relationship between more AUV be to determine it is constant, in ξeIn i-th be
To in (8) derivation and wushu (6) substitution (8), obtaining
udIt is the vector being made of the desired speed of each AUV, i.e.,
Each AUV can restrain the desired path of (2) and (7) effect lower edge in the motion control of design and navigate in forming into columns in this way
Row, it is assumed that G is the Laplacian matrixes of a standard, the Communication topology between the more AUV of this matrix description, it is assumed that adjacent
Communication between AUV is continuous, and decentralised control rule is
uL=ud+kef(Gξ) (10)
Wherein, f (x)=tanh (x), ke=4000.
4th step：Design of Predictive.When communication condition is weak communication between more AUV, formation coordination that front is designed
Controller is no longer applicable in, and logic-based communication control strategy designs a kind of predictive controller at this time, and the collaboration between more AUV can lead to
It crosses and estimates the correlated state of AUV adjacent thereto to realize, the method can reduce communications cost, be suitable for the underwater logical of complexity
Believe environment, the coordination of formation is to realize that AUV needs to estimate it in formation by exchanging the collaboration state between certain two AUV
The collaboration state of its individual.
Formula (6) and formula (10) are updated in formula (9), obtaining state estimation equation is：
By the way that its actual value and estimated value are compared to determine when to send information to adjacent AUV, if
In some specific time point tk, the difference between its estimated value and actual value is more than some threshold valueWhen,
AUV will carry out information exchange with adjacent AUV, and each AUV can timely update its estimated value, following formula is made to set up
Then formation coordination control law (10) can become：
It is assumed that AUV1, which begins through communication topology in time t=10s, sends the coordination shape of oneself to AUV adjacent thereto
State information, the AUV2 beside it, AUV3, AUV4, AUV5 receive this in t=15s, t=15s, t=20s, t=20s respectively
Information.If their four ξ that can timely update after receiving information1Estimated value, then the estimation applied
Module cannot keep synchronism again, but when communication network topology structure needs to carry out information update it has to be ensured that when
Between it is upper there is synchronism, so communication strategy needs to change.Being equipped with different numbers for each AUV, (its value is and its phase
The number of adjacent AUV) estimation module (being exactly that there are two estimators for meeting on a communication link), for solving to have time delay
When how to realize state estimation synchronize problem.
WithEstimator that the communication link between AUV1 and AUV2 is provided on AUV1 is represented to ξ1Estimated value.If
Moment t=10s, AUV1 will contain actual value ξ1Information be sent to AUV2, receive the message in moment t=15s AUV2,
But state estimation is not updated timely, only replys an information to AUV1 and informs that " reception " has arrived letter for it
Breath, may insure the synchronism between AUV1 in this way.Its estimated value is updated at the t=20s moment, at this point, in chain
ξ on road 121Evaluated error can write following formula：
When time delay bounded, above formula is exactly bounded.
Formation control strategy designed by front all assumes that the time delay between communication channel both ends is the same, but
In reality, it may appear that the both ends of same communication channel send and receive this different situation of the time used in information, in t=10s
When AUV1 pass information to AUV2, AUV2 receives the information in t=15s, and AUV2 can be counting at the moment after receiving the information
Obtained delay, τ21Pass to AUV1, and it is t=20s that AUV1, which receives information at the time of point, it is assumed that have following formula at
It is vertical：
|τ21-τ12|≤0.01
I.e.：
AUV1 will exchange information ξ in moment t=10s with AUV2i, the maximum value for setting propagation delay time is 5s, if in t=
AUV1 can receive AUV2 and be transmitted back to the return information come before this time point of 15s, it means that at the t=15s moment
The estimated state information of all AUV, which has all been updated over, to be finished.
If being not received by return information before the deadline, it is meant that the information has been lost, need at this time will under
One data clapped are (by the maximum time difference is selected as newest ξ between the two when information transmission and information update1And t=5s) be transmitted across
Come compared with the control strategy of front, the application condition between actual value and estimated value in this strategy is big, that is, have following formula at
It is vertical：
In addition, this ensures the estimation synchronizations between same link, i.e.,
If AUV2 has received information, but AUV1 does not still receive return information, this just illustrate only AUV2 into
State information updating is gone, this when, AUV1 can retransmit an information again.In spite of there are time delay control laws
(13) all continuously effective, if AUV is equipped with multiple estimation modules, it is assumed that there are two estimation modules by AUV2, can estimating by AUV1
Meter module obtains ξ1It is accurate estimate, this module can be applied to its value in control law, can similarly obtain, AUV3, AUV4,
AUV5, estimation module can also use ξ3, ξ4, ξ5Therefore there is following formula establishment：
Simulation result, in order to preferably examine the controller designed by last chapter effective, is imitated as shown in Fig. 2-Fig. 8
Track is divided into straight line and circle when true, it can be seen from the figure that AUV is when straight line is formed into columns and navigated by water, the initial position of each AUV is simultaneously
Irregularly, therefore in the starting stage, tracking error is bigger, but each follower can still track pilotage people, despite the presence of
Communication delay, formation can keep linear formation, and tracking error also levels off to zero.At 400m the navigation path of pilotage people from
When straight line becomes round, formation dynamic change that AUV is constituted, it can be seen that the tracking error of each AUV is larger when starting, warp
Navigation after a period of time, each AUV can track the flight path of pilotage people in formation, and fleet system is there are communication delay
In the case of, remaining to obtain good flight pattern, but because there are time delay, the tracking error of AUV does not converge to zero, but
A small constant is converged to, error is uniform ultimate bounded.
The specific embodiment of the invention further includes：
Include the following steps：
Step 1：Establish the horizontal surface model of each AUV；
Step 2：The speed of each AUV in forming into columns, position and bow are initialized to angle；
Step 3：The horizontal surface models of AUV based on step 1 introduce virtual reference point, design motivation path trace control
Device processed and kinematics path following control device, complete the path trace of single AUV；
Step 4：Judge to whether there is communication constraint between AUV, when communication constraint is not present between AUV, executes step
Five；When communication has constraint between AUV, step 6 is executed；
Step 5：Design coordination formation control device establishes communication topology relationship and coordination error between more AUV using graph theory
Model realizes flight pattern, executes step 8 by the total tune control to virtual reference point；
Step 6：Design coordination formation control device, the control strategy of logic-based communication, designs predictive controller, to AUV
Correlated state estimated；
Step 7：Judge whether to realize and it is expected to form into columns, it is expected to form into columns when being formed, execute step 8；It is expected to compile when not formed
Team, return to step six continue to execute；
Step 8：This formation is kept to navigate by water to target point.
The horizontal surface model of AUV meets：
Wherein：mur=m-Yr, du=-Xuuu2-Xvvv2, dv=-
Yvuv-Yv|v|V | v |, dr=-Nvuv-Nv|v|v|v|-NrUr, IzFor permanent moment；M=2234.5kg, X{.}、Y{.}And N{.}For hydrodynamic(al)
Force coefficient；Xuu=-35.4Kg, Xvv=-128.4N
m2,Yv=-346Kg, Yv|v|=-667Kgm-1, Yr=435Kg, Nr=-1427Kgm, Nv|v|=443Kg, Nv=-686Kg,
Iz=2000Nm2, F and T represent the thrusts of AUV in the longitudinal direction and turn bow torque, and u is the propulsion speed of AUV, v AUV
Lateral movement velocity, what r represented AUV turns bow speed, and x represents the lateral positions AUV, and y represents AUV lengthwise positions, and ψ represents AUV
Bow is to angle.
The speed of step 2 initialization each AUV in forming into columns, position and bow are to angle, specially：
N number of AUV in formation, it is pilotage people to carve specify wherein any one AUV at the beginning, remaining AUV is follower；
N number of AUV is engraved at the beginning floating to sea, and each AUV obtains the location information of itself by GPS；
Pilotage people sends position, speed and the bow of itself to angle information by sonar set to follower adjacent thereto,
The position of itself and bow are sent to adjacent AUV by follower by sonar set to angle；
N number of AUV dives to same depth starts depth-keeping navigation, and the position of itself and bow are sent to therewith by pilotage people to angle
Adjacent AUV.
Step 3 detailed process is：Pilotage people's control law
For the horizontal surface model that step 1 is established, design control law τa=[τu,τr]T, makeWherein Ud(t)=[ud,rd]T∈R2；
ue(t)=U (t)-Ud(t) representation speed tracking error, control law are：
Wherein, K1=diag { ku,krIt is positive definite matrix, MaFor quality and inertial matrix, CaFor Coriolis and centripetal matrix, Da
For damping and frictional force matrix, udAnd rdFor desired speed and angular speed, τuAnd τrFor power and torque；
The site error of path trace is defined asIts derivation can be obtained：
Whereinη1=[x, y]T, function S (v2) it is vector v2=[0, r]T∈R2Antisymmetric matrix,
S(v2) meet：
Using the distance of the current track points of AUV and reference point between the two as new error vector (ε-δ), ν1=[u, v]T, δ
It is a constant, it is known that U=Ud+ue, formula (3) can be written as：
Design UdControl law, udIt is speed corresponding with parameter ξ, the desired speed of target point isThere is following formula
It sets up：
I.e.:
Control law
Wherein, { 1,0.01 } P=diag, f are hyperbolic tangent function：F (x)=tanh (x),
Step 5 is specially：
Multiple AUV situations ∑s:={ 1 ..., n }, with ξ=[ξ1,…,ξn]TIndicate the correlated state between AUV.
For the follower AUV in formation, it isDesign control law so thatIt sets up, simultaneously
Ensure to form into columns whole with desired speed udNavigation, that is, meet
Error is coordinated in definition：
ξe=G ξ (7)
Wherein, G=D-1(D-A), D is the Vertex Degree matrix of communication topology figure G, and A is adjacency matrix, works as DiiWhen=0,G can be obtained by algebraic graph theory knowledge, wherein have an isolated vertex),If ξeGradually approach
In zero, so that it may to realize formation coordination.It is assumed that the communication topology relationship between more AUV be to determine it is constant, in ξeIn i-th be
To in (7) derivation and wushu (5) substitution (7), obtaining
udIt is the vector being made of the desired speed of each AUV, i.e.,
Each AUV can restrain the desired path of (2) and (6) effect lower edge in the motion control of design and navigate in forming into columns in this way
Row, it is assumed that G is Laplce (Laplacian) matrix of a standard, the communication topology knot between the more AUV of this matrix description
Structure, it is assumed that the communication between adjacent AUV is continuous, and can must follow the control law of AUV to be
uL=ud+kef(Gξ) (9)
Wherein, f (x)=tanh (x), ke=4000.
Step 6 is specially：
Formula (5) and formula (9) are updated in formula (8), obtaining state estimation equation is：
By the way that its actual value and estimated value are compared to determine when to send information to adjacent AUV, if
In some specific time point tk, the difference between its estimated value and actual value is more than some threshold valueWhen,
AUVi will carry out information exchange with adjacent AUV, and each AUV can timely update its estimated value, following formula is made to set up
Then formation coordination control law (9) can become：
It is assumed that AUVi is in time tkWhen begin through communication topology to AUV adjacent thereto send oneself correlated state letter
Breath, the AUVj and AUVk beside it are in tk+τ1And tk+τ2Receive this information.
WithEstimator that the communication link between AUVj and AUVk is provided on AUVi is represented to ξiEstimated value.If when
Carve tk, AUVi will contain actual value ξiWith moment tkInformation be sent to AUVj, in moment tk+ τ AUVj receive the message, but
State estimation is not updated timely, only an information is replied to AUVi and informs that " reception " has arrived information for it,
It may insure the synchronism between AUVi in this way.In tk+ 2 τ moment were updated its estimated value, at this point, in link ij
Upper ξiEvaluated error can write following formula：
When time delay bounded, above formula is exactly bounded.
In tkWhen AUVi pass information to AUVj, AUVj is in tk+τijThe information is received, the AUVj meetings after receiving the information
The delay, τ being calculated at the momentijAUV i are passed to, and it is t=t that AUV i, which receive information at the time of point,k+τij+
τji, it is assumed that there is following formula establishment：
WhereinI.e.：
Assuming that AUVi is in moment tkInformation ξ is exchanged with AUVji, it is assumed that the maximum value of propagation delay time is τmaxIf in tk+
τmaxAUVi can receive AUVj and be transmitted back to the return information come before this time point, it means that in tk+τmaxMoment
The estimated state information of all AUV, which has all been updated over, to be finished.
If being not received by return information before the deadline, it is meant that the information has been lost, need at this time will under
One data clapped are (by the maximum time difference is selected as newest ξ between the two when information transmission and information updateiAnd τmax) be transmitted across
Come compared with the control strategy of front, the application condition between actual value and estimated value in this strategy is big, that is, have following formula at
It is vertical：
In addition, this ensures the estimation synchronizations between same link, i.e.,
If AUVj has received information, but AUVi does not still receive return information, this just illustrate only AUVj into
State information updating is gone, this when, AUVi can retransmit an information again.In spite of there are time delay control laws
(12) all continuously effective.
The specific embodiment of the invention further includes：
The speed of AUV in forming into columns, position and bow are initialized to angle；
Virtual reference point, design motivation ways for education diameter tracking control unit and kinematics path following control device are introduced, is realized single
The path trace of a AUV；
Design coordination formation control device describes the communication topology relationship between more AUV using graph theory, establishes and coordinate error mould
Type realizes flight pattern by the total tune control to virtual reference point.
When communication condition is weak communication between more AUV, predictive controller is designed, is estimated by the correlated state to AUV
Meter achievees the purpose that coordinate to form into columns.
N number of AUV in formation, carve at the beginning it is specified wherein any one as pilotage people, remaining is follower.
N number of AUV is engraved at the beginning floating to sea, and respective location information is obtained using entrained GPS；
Sonar set entrained by pilotage people's use to follower adjacent thereto send position, speed and the bow of itself to
Angle information also uses entrained sonar set by speed between follower, and bow is sent to AUV adjacent thereto to information such as angles.
N number of AUV dives to same depth starts depth-keeping navigation, and pilotage people can be by the speed of itself at this time, and bow is to letters such as angles
Breath is sent to AUV adjacent thereto.
For the AUV models established, design control law τa=[τu,τr]T, makeWherein Ud
(t)=[ud,rd]T∈R2。
ue(t)=U (t)-Ud(t) representation speed tracking error, control law are
Wherein, K1=diag { ku,krIt is positive definite matrix, MaFor quality and inertial matrix, CaFor Coriolis and centripetal matrix, Da
For damping and frictional force matrix, udAnd rdFor desired speed and angular speed, τuAnd τrFor power and torque.
The site error of path trace is defined asIts derivation can be obtained
Whereinη1=[x, y]T, function S (v2) it is vector v2=[0, r]T∈R2Antisymmetric matrix.
Using the distance of the current track points of AUV and reference point between the two as new error vector (ε-δ), ν1=[u, v]T,
Know U=Ud+ue, formula (2) can be written as：
Design UdControl law, udIt is not the true velocity of AUV, is speed corresponding with parameter ξ, the expectation of target point
Speed isThere is following formula establishment：
I.e.:
Control law
Wherein, { 1, δ } P=diag, f are hyperbolic tangent function：F (x)=tanh (x), wherein K2=diag { kx,kyBe
Positively definite matrix.
What the step of front discussed is the situation of single AUV, and multiple AUV situations ∑s are considered below:={ 1 ..., n }, uses ξ
=[ξ1,…,ξn]TIndicate the correlated state between AUV.
For other AUV in formation, it isDesign suitable control law so thatAt
It is vertical, while it is whole with desired speed u to ensure to form into columnsdNavigation, that is, meet
Error is coordinated in definition
ξe=G ξ (7)
Wherein, G=D-1(D-A).(G can be obtained by algebraic graph theory knowledge, and wherein D is the Vertex Degree matrix of communication topology figure G, A
For adjacency matrix, work as DiiWhen=0, haveThere is an isolated vertex).If ξeGradually approach
In zero, so that it may to realize formation coordination.It is assumed that the communication topology relationship between more AUV be to determine it is constant, in ξeIn i-th be
To in (7) derivation and wushu (5) substitution (7), obtaining
udIt is the vector being made of the desired speed of each AUV, i.e.,
Each AUV can restrain the desired path of (3) and (6) effect lower edge in the motion control of design and navigate in forming into columns in this way
Row, it is assumed that G is the Laplacian matrixes of a standard, the Communication topology between the more AUV of this matrix description, it is assumed that adjacent
Communication between AUV is continuous, and decentralised control rule is
uL=ud+kef(Gξ) (9)
Wherein, f (x)=tanh (x), keIt is a sufficiently large constant value.
When communication condition is weak communication between more AUV, the formation coordination controller that front is designed no longer is applicable in, and is designed at this time
A kind of predictive controller, the collaboration between more AUV can realize by estimating the correlated state of AUV adjacent thereto, the method
Communications cost can be reduced, is suitable for complicated subsurface communication environment, the coordination of formation is by exchanging between certain two AUV
What collaboration state was realized, AUV needs to estimate the collaboration state of other individuals in formation.
Formula (6) and formula (10) are updated in formula (9), obtaining state estimation equation is：
By the way that its actual value and estimated value are compared to determine when to send information to adjacent AUV, if
In some specific time point tk, the difference between its estimated value and actual value is more than some threshold valueWhen,
AUVi will carry out information exchange with adjacent AUV, and each AUV can timely update its estimated value, following formula is made to set up
Then formation coordination control law (9) can become：
It is assumed that AUVi is in time tkWhen begin through communication topology to AUV adjacent thereto send oneself correlated state letter
Breath, the AUVj and AUVk beside it are in tk+τ1And tk+τ2Receive this information.WithRepresent the communication between AUVj and AUVk
Link is provided in the estimator on AUVi to ξiEstimated value.If moment tk, AUVi will contain actual value ξiWith moment tkInformation
It is sent to AUVj, in moment tk+ τ AUVj receive the message, are not updated timely to state estimation but, are only given
AUVi replys an information and informs that " reception " arrives information for it, may insure the synchronism between AUVi in this way.In tk+2τ
Moment is updated its estimated value, at this point, the ξ on link ijiEvaluated error can write following formula：
When time delay bounded, above formula is exactly bounded.
In tkWhen AUVi pass information to AUVj, AUVj is in tk+τijThe information is received, the AUVj meetings after receiving the information
The delay, τ being calculated at the momentijAUV i are passed to, and it is t=t that AUV i, which receive information at the time of point,k+τij+
τji, it is assumed that there is following formula establishment：
WhereinA very small positive value, the meaning be exactly we when carrying out state estimation there are one meetings very
Small evaluated error exists, i.e.,：
Assuming that AUVi is in moment tkInformation ξ is exchanged with AUVji, it is assumed that the maximum value of propagation delay time is τmaxIf in tk+
τmaxAUVi can receive AUVj and be transmitted back to the return information come before this time point, it means that in tk+τmaxMoment
The estimated state information of all AUV, which has all been updated over, to be finished.
If being not received by return information before the deadline, it is meant that the information has been lost, need at this time will under
One data clapped are (by the maximum time difference is selected as newest ξ between the two when information transmission and information updateiAnd τmax) be transmitted across
Come compared with the control strategy of front, the application condition between actual value and estimated value in this strategy is big, that is, have following formula at
It is vertical：
In addition, this ensures the estimation synchronizations between same link, i.e.,
If AUVj has received information, but AUVi does not still receive return information, this just illustrate only AUVj into
State information updating is gone, this when, AUVi can retransmit an information again.In spite of there are time delay control laws
(11) all continuously effective.
Claims (6)
1. a kind of more AUV formation methods based on PREDICTIVE CONTROL under communication limitation, which is characterized in that include the following steps：
Step 1：Establish the horizontal surface model of each AUV；
Step 2：The speed of each AUV in forming into columns, position and bow are initialized to angle；
Step 3：The horizontal surface models of AUV based on step 1 introduce virtual reference point, design motivation ways for education diameter tracking control unit
With kinematics path following control device, the path trace of single AUV is completed；
Step 4：Judge to whether there is communication constraint between AUV, when communication constraint is not present between AUV, executes step 5；When
When communication has constraint between AUV, step 6 is executed；
Step 5：Design coordination formation control device establishes communication topology relationship and coordination error mould between more AUV using graph theory
Type realizes flight pattern, executes step 8 by the total tune control to virtual reference point；
Step 6：The control strategy of logic-based communication, designs predictive controller, estimates the correlated state of other AUV；
Step 7：Judge whether to realize and it is expected to form into columns, it is expected to form into columns when being formed, execute step 8；It is expected to form into columns when not formed, return
Step 6 is returned to continue to execute；
Step 8：This formation is kept to navigate by water to target point.
2. more AUV formation methods based on PREDICTIVE CONTROL under a kind of communication limitation according to claim 1, feature exist
In：The horizontal surface model of AUV meets：
Wherein：mur=m-Yr, du=-Xuuu2-Xvvv2, dv=-Yvuv-Yv|v|v|
V |, dr=-Nvuv-Nv|v|v|v|-NrUr, IzFor permanent moment；X{.}、Y{.}And N{.}For hydrodynamic force coefficient；F and T represents AUV vertical
Upward thrust and turn bow torque, u is the propulsion speed of AUV, and v is the lateral movement velocity of AUV, and what r represented AUV turns bow
Speed, x represent the lateral positions AUV, and y represents AUV lengthwise positions, and ψ represents AUV bows to angle.
3. more AUV formation methods based on PREDICTIVE CONTROL under a kind of communication limitation according to claim 1, feature exist
In：The speed of step 2 initialization each AUV in forming into columns, position and bow are to angle, specially：
N number of AUV in formation, it is pilotage people to carve specify wherein any one AUV at the beginning, remaining AUV is follower；
N number of AUV is engraved at the beginning floating to sea, and each AUV obtains the location information of itself by GPS；
Sonar set entrained by pilotage people's use sends position, speed and the bow of itself to follower adjacent thereto to be believed to angle
It ceases, position, speed, bow is also sent to AUV adjacent thereto to angle using entrained sonar set between follower.
N number of AUV dives to same depth starts depth-keeping navigation, pilotage people by the position of itself, speed and bow to angle be sent to
Adjacent AUV.
4. more AUV formation methods based on PREDICTIVE CONTROL under a kind of communication limitation according to claim 1, feature exist
In：Step 3 detailed process is：
For the horizontal surface model that step 1 is established, design control law τa=[τu,τr]T, makeIts
Middle Ud(t)=[ud,rd]T∈R2；
ue(t)=U (t)-Ud(t) representation speed tracking error, control law are：
Wherein, K1=diag { ku,krIt is positive definite matrix, MaFor quality and inertial matrix, CaFor Coriolis and centripetal matrix, DaFor resistance
Buddhist nun and frictional force matrix, udAnd rdFor desired speed and angular speed, τuAnd τrFor power and torque；
The site error of path trace is defined asIts derivation can be obtained：
Whereinη1=[x, y]T, function S (v2) it is vector v2=[0, r]T∈R2Antisymmetric matrix, S (v2)
Meet：
Using the distance of the current track points of AUV and reference point between the two as new error vector (ε-δ), ν1=[u, v]T, δ is one
Constant, it is known that U=Ud+ue, formula (3) can be written as：
Design UdControl law, udIt is speed corresponding with parameter ξ, the desired speed of target point isHave following formula at
It is vertical：
I.e.:
Control lawWherein, P=
Diag { 1,0.01 }, f are hyperbolic tangent function：F (x)=tanh (x), wherein K2=diag { kx,kyIt is positively definite matrix.
5. more AUV formation methods based on PREDICTIVE CONTROL under a kind of communication limitation according to claim 1, feature exist
In：Step 5 is specially：
Multiple AUV situations ∑s:={ 1 ..., n }, with ξ=[ξ1,…,ξn]TIndicate the correlated state between AUV；
For the follower AUV in formation, it isDesign control law so thatIt sets up, ensures simultaneously
It forms into columns whole with desired speed udNavigation, that is, meet
Error is coordinated in definition：
ξe=G ξ (7)
Wherein, G=D-1(D-A), D is the Vertex Degree matrix of communication topology figure G, and A is adjacency matrix, works as DiiWhen=0,
There is an isolated vertex,If ξeGradually level off to zero, so that it may to realize formation coordination, it is assumed that more
Communication topology relationship between AUV be to determine it is constant, in ξeIn i-th be：
To in (7) derivation and wushu (5) substitution (7), obtaining
udIt is the vector being made of the desired speed of each AUV, i.e.,
Each AUV is in the desired path navigation of the motion control of design rule (2) and (6) effect lower edge in then forming into columns, it is assumed that G is
The Laplacian Matrix of one standard describes Communication topology between more AUV, it is assumed that the communication between adjacent AUV is continuous
, decentralised control rule is：
uL=ud+kef(Gξ) (9)
Wherein, f (x)=tanh (x), keIt is a sufficiently large constant value.
6. more AUV formation methods based on PREDICTIVE CONTROL under a kind of communication limitation according to claim 1, feature exist
In：Step 6 is specially：
Formula (5) and formula (9) are updated in formula (8), obtaining state estimation equation is：
By the way that its actual value and estimated value are compared to determine to the time of adjacent AUV transmission information, if a certain
A specific time point tk, the difference between estimated value and actual value is more than some threshold value, i.e.,When, AUVi is just
Information exchange can be carried out with adjacent AUV, each AUV can timely update its estimated value, following formula is made to set up
Then formation coordination control law (9) can become：
It is assumed that AUVi is in time tkWhen begin through communication topology and send the correlated state information of oneself to AUV adjacent thereto,
AUV beside itjWith AUVk in tk+τ1And tk+τ2Receive this information；
Estimator that the communication link between AUVj and AUVk is provided on AUVi is represented to ξiEstimated value, if moment tk,
AUVi will contain actual value ξiWith moment tkInformation be sent to AUVj, in moment tk+ τ AUVj receive the message, no pair
State estimation is timely updated, and is replied an information to AUVi and is informed that " reception " has arrived information, realization and AUVi for it
Between synchronism, in tk+ 2 τ moment were updated its estimated value, at this point, the ξ on link ijiEvaluated error meet：
When time delay bounded, above formula is exactly bounded；
In tkWhen AUV i pass information to AUV j, AUV j are in tk+τijThe information is received, AUVj can be after receiving the information
The delay, τ being calculated at the momentijAUV i are passed to, and it is t=t that AUV i, which receive information at the time of point,k+τij+τji,
It suppose there is following formula establishment：
WhereinI.e.：
Assuming that AUVi is in moment tkInformation ξ is exchanged with AUVji, it is assumed that the maximum value of propagation delay time is τmaxIf in tk+τmax
AUVi can receive AUVj and be transmitted back to the return information come before this time point, then in tk+τmaxMoment all AUV's
Estimated state information update finishes；
If being not received by return information before the deadline, it is meant that the information has been lost, and is needed at this time by next bat
Data send over, information is sent and the maximum time difference is selected as newest ξ between the two when information updateiAnd τmax, really
Error between value and estimated value meets：
Estimation between same link synchronizes, i.e.,：
If AUVj has received information, AUVi does not still receive return information, then only AUVj has carried out status information more
Newly, then AUVi retransmits an information again, in spite of there are time delay control law (12) all continuously effectives.
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