CN110134018A - A kind of underwater multi-foot robot system polypody cooperative control method - Google Patents
A kind of underwater multi-foot robot system polypody cooperative control method Download PDFInfo
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Abstract
A kind of underwater multi-foot robot system polypody cooperative control method, belongs to underwater multi-foot robot Collaborative Control technical field.The present invention is to be influenced between different mechanical foots that there are communication delay in order to solve the problem of multi-foot robot by processor arithmetic speed and signal transmission path.Present invention introduces a kind of obstacle liapunov functions of logarithmic form, and the track following error of system to be made to meet the error limitation requirement of setting always；The communication topology required nothing more than between different mechanical foots is digraph, and only part follower can obtain the information of pilotage people, avoids bring communication burden known to the information overall situation；Input signal source, which is selected, as virtual pilotage people makes the change of pilotage people more flexible, meets requirement of the robot for kinematic dexterity.The cooperative motion that the present invention is suitable for underwater multi-foot robot controls.
Description
Technical field
The invention belongs to underwater multi-foot robot Collaborative Control technical fields.
Background technique
As an ocean big country, in recent years, China greatly develops marine economy, and the development and utilization in coastal waters seem more heavy
It wants.Wherein, the carrier that offshore drilling platform is utilized as marine resources development, the research in relation to offshore drilling platform safety by
Gradually deeply, the current check maintenance work of offshore drilling platform is extremely important, but due to harsh environments, causes manually to examine
Maintenance is repaired to be inconvenient.With the development of science and technology the R&D work of underwater robot is more paid attention to, multi-foot robot phase
The advantage of traditional idler wheel or caterpillar robot is gradually shown, the design of underwater multi-foot robot has become a heat
Point.The research of the control problem of the coordinated movement of various economic factors of polypody bio-robot has attracted the attention of more and more experts and scholar.
Underwater multi-foot robot it is presently used to theory be minimum energy it is assumed that i.e. by optimizing contour structures and control
Algorithm makes energy consumed by the movement of multi-foot robot reach minimum.Dynamics of multibody systems is multi-foot robot research and development
Most important theories basis, therefore, can use for reference grinding for the coordinated control of multi-body system for the control problem of underwater multi-foot robot
Study carefully achievement.Currently, what the research of multi-body system collaboration tracking problem was mostly used is mode that follower tracks pilotage people,
It only needs accurately to be planned that other follower utilize under the action of effective control algolithm to the motion profile of pilotage people
Tracking of the information realization of oneself or neighbours to pilotage people reaches frequently with this control mode in multi-foot robot system
Reduce energy consumption, the purpose of save the cost.It wherein, is virtually pilotage people by signal source, by each machine of underwater multi-foot robot
Tool regards one as enough has multivariant follower.
It is often higher for control accuracy requirement but in actual engineering project, especially in multi-foot robot system
In system, if error is too big, it may result in multi-foot robot and rollover even paralysis occur, cause the consequence that can not be retrieved.
It is therefore desirable to limit to output error, a good method of limitation control error is BLF (obstacle Li Yapu
Promise husband function) technology.Adaptive controller is constructed using asymmetrical time-varying BLF (obstacle liapunov function) at present, is answered
Guarantee output error in the range of setting with Lyapunov stability theory.But multi-foot robot mostly uses microcomputer
Calculation machine network is controlled, and is influenced by processor arithmetic speed and signal transmission path, is often resulted between different mechanical foots
Communication delay.
Summary of the invention
The invention aims to solve multi-foot robot to be influenced by processor arithmetic speed and signal transmission path, no
There are problems that communication delay between machinery foot, proposes a kind of underwater multi-foot robot system polypody cooperative control method.
A kind of underwater multi-foot robot system polypody cooperative control method of the present invention, the specific steps packet of this method
It includes:
Step 1: establishing the kinetic model of all mechanical foots of underwater multi-foot robot；Obtain underwater multi-foot robot control
System processed；
Step 2: the communication relations in underwater multi-foot robot system described in establishment step one between each machinery foot are oriented
Topology diagram；The root node of the directional topology figure is pilotage people, other each nodes are a mechanical foot, pilotage people
To control signal source, a mechanical foot is a follower；
Step 3: the neck obtained using directional topology figure described in distributed observer and step 2 to all nodes
Boat person's status information is estimated, the status information of pilotage people is obtained；
Step 4: carrying out error about using status information of the obstacle liapunov function to the pilotage people that step 3 obtains
Beam；Error variance is limited within the specified scope；
Step 5: using nerual network technique to the nonlinear uncertainty in underwater multi-foot robot system at
Reason；Unknown parameter is estimated in realization；
Step 6: the processing of nonlinear uncertainty described in the error compensation according to step 4 and step 5, is obtained
The adaptive control laws of underwater multi-foot robot control system are obtained, realizes and control is cooperateed with to the polypody of underwater multi-foot robot system
System.
The present invention has comprehensively considered between the mechanical foots of difference of multi-foot robot system that there are constant communication delay, polypody
Broad sense disturbed condition existing for Dynamic Models of Robot Manipulators, while the obstacle liapunov function for introducing a kind of logarithmic form makes
The error limitation that the track following error for the system of obtaining meets setting always requires；Require nothing more than the communication topology between different mechanical foots
For digraph, only part follower can obtain the information of pilotage people, avoid bring communication known to the information overall situation
Burden；Input signal source, which is selected, as virtual pilotage people makes the change of pilotage people more flexible, meets robot for movement
The requirement of flexibility.
Detailed description of the invention
Fig. 1 is the flow chart of underwater multi-foot robot system polypody cooperative control method of the present invention；
Fig. 2 is the mechanical sufficient schematic diagram of underwater multi-foot robot；
Fig. 3 is the communication topological diagram of the mechanical foot of underwater multi-foot robot；
Fig. 4 is the structural schematic diagram of mechanical foot；
Fig. 5 is the path curves figure that each mechanical podarthrum 1 tracks pilotage people joint 1；
Fig. 6 is the path curves figure that each mechanical podarthrum 2 tracks pilotage people joint 2；
Fig. 7 is the track following error curve diagram of each mechanical podarthrum 1 and pilotage people joint 1；
Fig. 8 is the track following error curve diagram of each mechanical podarthrum 2 and pilotage people joint 2；
Fig. 9 is the input control M curve figure at each mechanical podarthrum 1；
Figure 10 is the input control M curve figure at each mechanical podarthrum 2；
Figure 11 is auxiliary variable Z11With the graph of relation of time-varying error limitation；
Figure 12 is auxiliary variable Z12With the graph of relation of time-varying error limitation；
Figure 13 is auxiliary variable Z21With the graph of relation of time-varying error limitation；
Figure 14 is auxiliary variable Z22With the graph of relation of time-varying error limitation；
Figure 15 is auxiliary variable Z31With the graph of relation of time-varying error limitation；
Figure 16 is auxiliary variable Z32With the graph of relation of time-varying error limitation；
Figure 17 is auxiliary variable Z41With the graph of relation of time-varying error limitation；
Figure 18 is auxiliary variable Z42With the graph of relation of time-varying error limitation.
Specific embodiment
Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings and examples, how to apply to the present invention whereby
Technological means solves technical problem, and the realization process for reaching relevant art effect can fully understand and implement.This Shen
Please each feature in embodiment and embodiment, can be combined with each other under the premise of not colliding, be formed by technical solution
It is within the scope of the present invention.
Specific embodiment 1: illustrating present embodiment, a kind of underwater polypody machine described in present embodiment below with reference to Fig. 1
Device people's system polypody cooperative control method, the specific steps of this method include:
Step 1: establishing the kinetic model of all mechanical foots of underwater multi-foot robot；Obtain underwater multi-foot robot control
System processed；
Step 2: the communication relations in underwater multi-foot robot system described in establishment step one between each machinery foot are oriented
Topology diagram；The root node of the directional topology figure is pilotage people, other each nodes are a mechanical foot, pilotage people
To control signal source, a mechanical foot is a follower；
Step 3: the neck obtained using directional topology figure described in distributed observer and step 2 to all nodes
Boat person's status information is estimated, the status information of pilotage people is obtained；
Step 4: carrying out error about using status information of the obstacle liapunov function to the pilotage people that step 3 obtains
Beam；Error variance is limited within the specified scope；
Step 5: using nerual network technique to the nonlinear uncertainty in underwater multi-foot robot system at
Reason；Unknown parameter is estimated in realization；
Step 6: the place of nonlinear uncertainty described in the processing of the error compensation according to step 4 and step 5
Reason obtains the adaptive control laws of underwater multi-foot robot control system, realizes and assists to the polypody of underwater multi-foot robot system
With control.
Present embodiment proposes the observer for considering communication delay between different mechanical foots, in terms of the limitation of error,
The obstacle liapunov function for introducing a kind of logarithmic form devises a kind of distributed self-adaption using the method for Backstepping
Control algolithm is come near guaranteeing the machinery foot of multi-foot robot to the track following error convergence of pilotage people to 0.
The present invention describes the topological structure between each mechanical foot of underwater multi-foot robot using digraph, mainly for
The motion conditions of the mechanical foot of the n item of underwater multi-foot robot are studied；Due to the mechanical foot of each of underwater multi-foot robot
Control signal can be individually received, there is the independence of movement, therefore individual individual can be regarded as.Underwater polypody
Robot system is considered as a multi-body system, it is contemplated that Euler-Lagrange equation is wide in nonlinear multibody system
General application, so being described with motion conditions of the Euler-Lagrange equation to the machinery foot of underwater multi-foot robot.By water
The mechanical foot of each of lower multi-foot robot regards the follower with p freedom degree as, and follower is indicated with 1 ..., n.
Since underwater multi-foot robot is for the more demanding of kinematic dexterity, it usually needs by increasing and arranging pilotage people to realize
Another plus flexible movement, so signal source is set as a virtual pilotage people by us, pilotage people is indicated with n+1.
It is indicated between 1 virtual pilotage people and the n item machinery foot of underwater multi-foot robot with digraph ζ=(υ, ε, A)
Communication relations, in digraph, υ={ 1,2 ..., n+1 } is the set on all vertex,Indicate the collection on all sides
It closes, A={ aij}∈R(n+1)×(n+1)The adjacency matrix of expression；In point set υ, υiIndicate i-th machinery of underwater multi-foot robot
Foot, side (υi,υj) ∈ ε indicates that the j-th strip machinery of underwater multi-foot robot can be to obtain the information of i-th mechanical foot.υiReferred to as
Father node, υjReferred to as child node, and υiAnd υjIt is two adjacent nodes.The path of digraph is a limited vertex sequence
Arrange υi1,...,υin, meet (υi,υj)∈ε.If in digraph other than a node (referred to as root node (root)), remaining
Each node one and only one father node, and there are root nodes to the path of remaining any node, then the digraph is referred to as
Directed tree (directed tree).The directed spanning tree (directed spanning tree) of digraph is oriented comprising this
Scheme the directed tree of all nodes.If there are the subgraphs that one is directed spanning tree for digraph, the digraph is claimed to have oriented
Spanning tree.Defining adjacency matrix A is a nonnegative matrix.And if only if (υi,υj) ∈ ε when, element aij=1, otherwise aij=0.
For all j=1 ..., n+1, there is a(n+1)j=0, define matrixWhereini∈
{ 1 ..., n }, j=1 ..., n+1.When digraph ζ includes that a directed spanning tree is set up,Denominator be not 0.
Specific embodiment 2: present embodiment is to a kind of underwater multi-foot robot system polypody described in embodiment one
Cooperative control method is described further, in present embodiment, all mechanical foots of underwater multi-foot robot described in step 1
Kinetic model method it is all the same, be illustrated by taking the kinetic model of i-th mechanical foot as an example, specifically:
Wherein, qiFor the articulation angle of i-th mechanical foot, i=1,2 ..., n }, n is positive integer,It is i-th
The articulation angular speed of mechanical foot,For the articulation angular acceleration of i-th mechanical foot, and qi,RpIt is p dimension
Real number column vector, τiIndicate that the control force of input i-th mechanical foot is refused, τi∈Rp, Mi(qi) indicate symmetric positive definite inertial matrix,
Mi(qi)∈Rp×p, Rp×pIt is the real number matrix of p row p column,Indicate the eccentric force of i-th mechanical foot,
gi(qi) indicate i-th mechanical sufficient gravity, gi(qi)∈Rp, ωiIndicate external disturbance, ωi∈Rp, the external disturbance includes
Environmental perturbation and external noise；Wherein, the inertial matrix M of symmetric positive definitei(qi), eccentric forceWith gravity gi(qi) it is not
Know parameter.
Specific embodiment 3: present embodiment is to a kind of underwater multi-foot robot system polypody described in embodiment two
Cooperative control method is described further, and in present embodiment, distributed observer and step 2 institute are utilized described in step 3
The directional topology figure stated estimates pilotage people's status information that all nodes obtain, and obtains the status information of pilotage people
Method particularly includes:
The kinetic model as described in formula (1) meets property:
Property 1: matrixIt is antisymmetric, then having: for
Property 2: there are two positive numbersWithBSo thatWherein IpIndicate the unit matrix of p × p.
Therefore, the generalized coordinates q of boat personn+1It is expressed as:
qn+1=Fv (3)
Wherein, v is the auxiliary State Variable of pilotage people, v ∈ Rm,For the derivative of v, S and F are constant real number matrix, S ∈
Rm×m, F ∈ Rn×m；
Distributed observer estimates pilotage people's status information:
Wherein, For matrixElement,For adjacency matrix, ηjIt is j-th of follower to pilotage people
Location information estimated value,J-th of follower is to the estimated value of the velocity information of pilotage people, j=1 ..., n+1, ηiTable
Show i-th of follower for the estimated value of v, ηi∈Rm,It is estimated value of the i follower to the velocity information of pilotage people, T table
Show that the communication delay between adjacent follower i and j, t are the time.
In the present embodiment, the track of the dynamic virtual pilotage people of the machinery foot (follower) of underwater robot is by formula
(2) it is indicated with formula (3).In view of that, due to signal transmission path difference, can be made between the mechanical foot of the difference of underwater multi-foot robot
At the communication delay between different mechanical foots.The case where only some mechanical foot (follower) can obtain pilotage people's information
Under, devising distributed observer and neural network control algorithm ensures every mechanical foot to the track following of pilotage people
Error bounded.Simultaneously, it is contemplated that in multi-foot robot system, if error is too between actual motion track and expected trajectory
Greatly, it may result in multi-foot robot and rollover even paralysis occur, cause the consequence that can not be retrieved.Therefore we are to underwater polypody
Rotational angle at robotic podarthrum limits.
Because S and F are real number matrix, the value of element is unrelated with the quantity of state of time and pilotage people in real number matrix, works as institute
When some mechanical foots can obtain S and F information, it is meant that a part of machinery can be to obtain q by formula (3)n+1's
Value achievees the purpose that the information for obtaining pilotage people；A kind of common method be designed using the dynamic matrix of target object it is corresponding
Observer the state of pilotage people is believed using the status information of adjacent machine foot by distribution observer shown in formula (4)
Breath is estimated.If:Obtain the observation error η of observeri- v is bounded, is indicated are as follows:
Wherein:
U0It is less than
1 positive number, the positive number level off to 0, ReFor communication delay gain matrix, 1nThe n for for element being 1 is column vector,It is n-th
Follower to the evaluated error of pilotage people,It is neural operator, because S and F are real number matrix, A is
The adjacency matrix of cum rights, the value of element is unrelated with the quantity of state of time and pilotage people in real number matrix, utilizes the dynamic of target object
The corresponding observer of state matrix design.
Specific embodiment 4: present embodiment is to a kind of underwater multi-foot robot system polypody described in embodiment three
Cooperative control method is described further, the pilotage people obtained using obstacle liapunov function to step 2 described in step 4
Status information carry out error constraints；Error variance is limited within the specified scope method particularly includes:
Rotational angle at robotic podarthrum is limited, variable boundary when setting are as follows:kC (t)=[kc1(t),kc2(t),...,kcn(t)]TWithLimit the quantity of state q of the rotational angle of outputi
(t) region are as follows:
kci(t) andRespectively i-th mechanical sufficient t moment expected motion trajectory qriUpper and lower boundary,kcn(t) andRespectively n-th mechanical sufficient t moment expected motion trajectory qriUpper and lower boundary, qiIt (t) is t moment i-th mechanical foot
Articulation angle；R is real number matrix.
Specific embodiment 5: present embodiment is to a kind of underwater multi-foot robot system polypody described in embodiment four
Cooperative control method is described further, using nerual network technique to non-in underwater multi-foot robot system described in step 5
Linear uncertainty is handled, what unknown parameter was estimated in realization method particularly includes:
Utilize formula:
Realize the nonlinear uncertainty amount to i-th mechanical foot of multi-foot robot systemIt is mended
It repays, wherein WiIndicate ideal weighting matrix, Wi TIt is ideal weighting matrix WiTransposition, riIt is the virtual of i-th of mechanical foot
Controller,For riDerivative；It is activation primitive, △iIndicate approximate error；And △iIt is bounded, there are one
A positive number △MiSo that | | △i||≤△Mi；Obtain i-th mechanical foot of underwater multi-foot robotValuation:
Wherein,It is ideal weighting matrix WiEstimated value.
Specific embodiment 6: present embodiment is to a kind of underwater multi-foot robot system polypody described in embodiment four
Cooperative control method is described further, in present embodiment, at the error constraints according to step 4 described in step 6
The processing of nonlinear uncertainty described in reason and step 5, obtains the adaptive control laws of underwater multi-foot robot control system
Are as follows:
Wherein, α, β and μ are positive number, and α, β and μ are substantially equal to zero, K2iIt is the matrix of a symmetric positive definite, Z2i
For virtual track tracking error variable vector, Z2i TIt is vector Z2iTransposition,It is matrixTransposition, Z1iIt is follower couple
The track following error variance vector of pilotage people, intermediate variablekaiAnd kbiBe respectively with
The upper and lower boundary of track error variance；Wherein,
Influence of the present embodiment in view of control error to underwater multi-foot robot, has used a kind of obstacle Lee of time-varying
The quantity of state that Ya Punuofu function ensures to export meets the limitation requirement of the time-varying of setting.In view of underwater multi-foot robot system
Model uncertainty and unknown dynamic parameter problem, it is adaptive that the present invention using the method for Backstepping proposes a kind of distribution
Answer control method.This method is realized based on mathematics lemma 1 to 4；
Lemma 1: if there is continuous Lyapunov (Liapunov) function V (L, t), meetMeetWhereinU is positive number, obtains L (t)
It is bounded.
Lemma 2:When E is symmetric positive definite matrix, there is inequality:Wherein λminIndicate the minimal eigenvalue of E, λmaxIndicate the maximum eigenvalue of E.
Lemma 3: equation Ψ (t) continuously differentiable for one, if Ψ (t) meet for|Ψ(t)|≤
Φ, wherein Φ is a positive number, for It is bounded.
Lemma 4: considering a positive number G ∈ R, if x ∈ R and | x | < | G |, following inequality are set up:
Consider underwater multi-foot robot system containing model uncertainty and external disturbance, under water multi-foot robot
There are in the case where constant communication delay between different machinery foots, there are 1), 2) He 3) set up；
1), external disturbance ωiIt is bounded, that is, there is a positive number γ, so that | | ωi||≤γ。
2), v andIt is all bounded, S and F is all known for all follower.
3), digraph ζ includes a directed spanning tree.
The expected motion trajectory q of i-th of mechanical foot is defined firstri:
qri=F ηi (7)
Track following error variance vector Z of the follower to pilotage people1iAre as follows:
Z1i=qi-qri (8)
Virtual track tracking error variable vector Z2iAre as follows:
Wherein riFor Virtual Controller；
Track following error variance vector Z of the follower to pilotage people1iWhen variable boundary are as follows:
kai(t)=qri(t)-kci(t) (10)
kaiAnd kbi(t) be tracking error variable t moment upper and lower boundary,For the phase of i-th of mechanical sufficient t moment
Hope the coboundary of motion profile,kciIt (t) is the lower boundary of the expected motion trajectory of i-th of t moment mechanical foot, qri(t) be t when
Carve the expected motion trajectory of i-th of mechanical foot；
Wherein, Lyapunov (Liapunov) function V1i(t):
Wherein, kaiIt (t) is t moment tracking error variable coboundary, kbiIt (t) is t moment tracking error variable lower boundary, h
(i) it defines:
To follower to the track following error variance vector Z of pilotage people1iIt is deformed, is enabled:
It can be obtained being substituted into (12) in formula (14):
V is obtained from formula (15)1i(t) exist | εi| it is positive definite and continuously differentiable when < 1；To V1i(t) derivation can obtain:
Tracking error variable coboundary kaiDerivative,For tracking error variable lower boundary kbiDerivative；
The Virtual Controller r of i-th of mechanical footiAre as follows:
Wherein,Are as follows:
Ensure?WithBounded, K are kept when being all 01=diag [k11,k12,...,k1i..., k1n] it is symmetric positive definite
Matrix, k1iFor gain matrix K1In i-th of non-zero element, formula (17) and (18) are substituted into (16), can be obtained:
Wherein, XiIs defined as:
And Xi∈ X, X=diag [X1,X2,....,Xi,....,Xn]；
Using distributed self-adaption control law, adaptive control laws are obtained:
Wherein, α, β and μ are positive number, and α, β and μ are substantially equal to zero, K2iIt is the matrix of a symmetric positive definite, Z2i
For virtual track tracking error variable vector, Z2i TIt is vector Z2iTransposition,It is matrixTransposition, Z1iIt is follower to neck
The track following error variance vector of boat person,kaiAnd kbiIt is tracking error variable respectively
Upper and lower boundary；Wherein,
Auxiliary variable Z under the action of distributed observer (5) and distributed self-adaption control law (21) and (22)1iFinally
Tracking error bounded between uniform bound and each mechanical foot and pilotage people.Meanwhile output state amount qi(t) meet the defeated of time-varying
Restrictive condition out, i.e.,
To 1), 2) He 3) proving: formula (9) has t derivation:
Formula (23) are substituted into and arranges and can obtain in (1):
Wherein,For the Z of virtual track tracking error variable vector2iDerivative；
Because of Mi(qi),gi(qi) all unknown, exist in the underwater multi-foot robot system that formula (1) indicates
Nonlinear uncertainty.In view of neural network has good approximation capability to unknown nonlinear function, it is usually used to handle
Uncertain problem in nonlinear system.
Therefore, using nerual network technique to the nonlinear uncertainty of underwater multi-foot robot systemInto
Row adaptive equalization, specific method:
Wherein WiIndicate ideal weighting matrix, φiFunction is activation primitive, △iExpression approaches difference, △iIt is bounded,
There is a positive number △MiSo that | | △i||≤△Mi, for i-th mechanical foot of underwater multi-foot robot,Estimated value write as:
Wherein,It is WiEstimation value matrix,For matrixTransposition,For activation primitive.
Based on nerual network technique, select distributed self-adaption control law formula (21) and (22), obstacle Liapunov letter
Number V2i；
Wherein, For matrixTransposition, Z1iFor follower to the track following error of pilotage people to
Amount, Z2iFor virtual track tracking error vector, Z2i TFor vector Z2iTransposition,ForMark.
To V2iDerivation, in conjunction with hemihedrism and distributed self-adaption control law:And power
It is worth estimation self-adaptive rule:K2iIt is the matrix of a symmetric positive definite, obtains:
Wherein, φiIt is activation primitive, Z2i TThe transposition of virtual track tracking error matrix, φiIt is activation primitive, △iIt is to estimate
Error is counted,It is to indicateIt isMark.Because of △iAnd ωiIt is bounded, therefore there are one
A positive numberSo that:It obtains simultaneously:
Wherein,It is | | △i+ωi| | coboundary, σ is positive number, and is substantially equal to 0；
In formula (29),It is a scalar, then equationIt sets up；
Had according to the Operation Nature of trace of a matrix:
Formula (19), (30) and (31), which are substituted into (29), to be obtained:
λmin(K2i) it is symmetric positive definite matrix K2iMinimum value, formula (32) write as:
Wherein:
It is MiMaximum value.
According to lemma 1-4, it is known that, V2iMeet full ultimately uniform boundary, integrating simultaneously to formula (33) two sides can obtain:
Enable κ1> 0, υ1> 0, obtains:
V2i(t) it is t moment obstacle liapunov function, ρ is the constant less than 1, from formula (28):
V1i≤V2i (38)
Then have:
Formula (13) and (14), which are substituted into (39), to be obtained:
From (7):
qi-qn+1=qi-Fηi+Fηi-qn+1=qi-Fηi+F(ηi-v) (41)
It can be obtained by formula (6), (40) and (41):
The mechanical foot of i-th of underwater multi-foot robot is bounded, upper boundary values such as formula to the tracking error of pilotage people
(42) shown in.
From formula (4), (8), (10), (11) and formula (40):
The output state amount q known to formula (43)i(t) meet the export-restriction condition of time-varying.
The invention has the characteristics that between the mechanical foot of the difference for having comprehensively considered multi-foot robot system, there are constant communications
Broad sense disturbed condition existing for delay, multi-foot robot kinetic model, while introducing a kind of BLF (obstacle Lee of logarithmic form
Ya Punuofu function) make the track following error of system meet always setting error limitation require；Require nothing more than different machinery
Communication topology between foot is general digraph, and only part follower can obtain the information of pilotage people, avoid
Bring communication burden known to the information overall situation；Input signal source is selected to make the change of pilotage people as virtual pilotage people in research
It is more flexible, meet requirement of the robot for kinematic dexterity.
Specific simulation example
The setting of simulation parameter first:
In order to verify the validity of distributed self-adaption collaboration tracing control rule proposed by the present invention.With the 8 underwater polypodies of foot
Emulation experiment is carried out for robot.Since the underwater multi-foot robot movement of 8 foots uses double 4 sufficient gaits, as shown in Fig. 2,
It can guarantee to remain to provide the support of four feet when the underwater multi-foot robot half walking leg of 8 foots is lifted away from ground in this way.Simultaneously as 8 foots
The structural symmetry of underwater multi-foot robot can grind one synkinematic 4 mechanical foot of the underwater multi-foot robot of 8 foots
Study carefully, is made of the mechanical foot (follower) of underwater multi-foot robot of the virtual pilotage people and 4 two-freedoms of 1 two-freedom
Oriented communication network is compiled wherein number 1-4 indicates four mechanical foots (follower) of the underwater multi-foot robot of 8 foot shown in FIG. 1
Numbers 5 indicate virtual pilotage peoples, and communication topological relation is as shown in Figure 3.
The kinetics equation of i-th mechanical foot of the underwater multi-foot robot of 8 foots can indicate are as follows:
In formula:
qi=[qi1,qi2]T (45)
Wherein qi1,qi2Respectively indicate the rotation angle of machinery two joints of foot of underwater multi-foot robot.
Wherein: Ξi1=Ji1+mi2li1 2,Ξi2=0.25mi2li2 2+Ji2,Ξi3=0.5mi2li1li2,Ξi4=(0.5mi1+mi2)
li1,
Ξi5=0.5mi2li2, g=9.8m/s2Indicate acceleration of gravity.As shown in figure 4, mi1And mi2Respectively indicate mechanical foot
The quality of two connecting rods of 2 junction of joint, li1And li2Respectively indicate the sufficient each connecting rod of machinery of underwater multi-foot robot
Length.Ji1And Ji2Indicate the rotary inertia of joint.Wherein the design parameter of mechanical foot is as shown in table 1:
Table 1: the design parameter of mechanical foot
The limitation setting of time-varying output is as follows:
k c(t)=[1.8+15e-0.8t,1.8+15e-0.5t,1.8+15e-0.5t,1.8+15e-0.3t]T (51)
Wherein tracking error Z1iThe table boundary value of tracking error be shown as:
kai(t)=qri(t)-k ci(t) (52)
Known to:
-kai(t)<Z1i(t)<kbi(t) (54)
The angle initialization of the machinery foot of underwater multi-foot robot is as follows:
q11(0)=π/5, q12(0)=- π/3, q21(0)=2 π/5, q22(0)=- π/6, q31(0)=3 π/5,
q32(0)=π/6, q41(0)=4 π/5, q42(0)=π/3,
For i-th of follower (i=1 ..., 4), the activation equation of nerve network system can be write as:
φi(z)=[φi1(z),...,φi6(z)]T (55)
Select Gauss equation as activation primitive, form are as follows:
Wherein,Assuming that all follower use the same activation equation.cijIt indicates uniformly to divide
Cloth is in [- 5,5]4×[-0.5,0.5]4On acceptance region center, σijIt indicates the width of Gauss equation, defines σij=2, weighting
MatrixInitial value be set as
The target trajectory of virtual pilotage people:
Wherein, q51_amp=π/6,q51_bias=pi/2, q52_amp=2 π/3,q52_bias
The π of=0, ω=0.1.
The quantity of state q of virtual pilotage people5It indicates are as follows:
q5=Fv (60)
Wherein:
The π of ω=0.1 (62)
In view of the underwater needs of multi-foot robot in practical projects of 8 foots, it usually needs by adaptive control laws τi's
Amplitude is plus a boundary limitation, to reach better control effect, we are using following limitation equation to τiIt shakes
The limitation of width:
Wherein, τimaxIt is a positive number, selects τimax=50.
We select the time of communication delay for T=0.2s in this control algolithm.To the simulation result of control algolithm
Analysis: in the control algolithm of design, selection of control parameter k1i=10, K2i=20I2, γ=1, v=10, I2For unit square
Battle array.The result of emulation is as shown in Fig. 5~18.
Fig. 5 and Fig. 6 indicates the quantity of state situation of change of virtual pilotage people and each mechanical foot, therefrom it can be seen that each machinery
Foot can effectively track pilotage people after about 5s.It can see two joints of each mechanical foot from Fig. 7 and Fig. 8
For the track following error Z of pilotage people1iAnd Z2iIt is all converged in the zonule near 0 after about 3s, and the Z after stablizing1i
Fluctuating range do not exceed 0.1, Z2iFluctuating range be no more than 0.05.Fig. 8 and Fig. 9 shows the control law that each machinery inputs enough
It is continuous and fluctuating range is no more than each mechanical foot of the display of 10, Figure 10~18 and all meets me to the track following error of pilotage people
The time-varying export-restriction restrictive condition that sets.The simulation process effectively illustrates effectiveness of the invention.
Although embodiment of the present invention is as above, the content is only to facilitate understanding the present invention and using
Embodiment, be not intended to limit the invention.Any those skilled in the art to which this invention pertains are not departing from this hair
Under the premise of the bright spirit and scope, any modification and change can be made in the implementing form and in details, but this
The scope of patent protection of invention, still should be subject to the scope of the claims as defined in the appended claims.
Claims (6)
1. a kind of polypody cooperative control method of underwater multi-foot robot system, which is characterized in that the specific steps packet of this method
It includes:
Step 1: establishing the kinetic model of all mechanical foots of underwater multi-foot robot；Obtain underwater multi-foot robot control system
System；
Step 2: the oriented topology of communication relations in underwater multi-foot robot system described in establishment step one between each machinery foot
Structure chart；The root node of the directional topology figure is pilotage people, other each nodes are a mechanical foot, and pilotage people is control
Signal source processed, a mechanical foot is a follower；
Step 3: the pilotage people obtained using directional topology figure described in distributed observer and step 2 to all nodes
Status information is estimated, the status information of pilotage people is obtained；
Step 4: carrying out error constraints using status information of the obstacle liapunov function to the pilotage people that step 3 obtains；
Error variance is limited within the specified scope；
Step 5: being handled using nerual network technique the nonlinear uncertainty in underwater multi-foot robot system；It is real
Now unknown parameter is estimated；
Step 6: the processing of nonlinear uncertainty described in the error constraints according to step 4 and step 5, obtains water
The adaptive control laws of lower multi-foot robot control system realize the polypody Collaborative Control to underwater multi-foot robot system.
2. a kind of polypody cooperative control method of underwater multi-foot robot system according to claim 1, which is characterized in that
The method of the kinetic model of all mechanical foots of underwater multi-foot robot described in step 1 is all the same, with i-th mechanical foot
Kinetic model for be illustrated, specifically:
Wherein, qiFor the articulation angle of i-th mechanical foot, i=1,2 ..., n }, n is positive integer,For i-th machinery
The articulation angular speed of foot,For the articulation angular acceleration of i-th mechanical foot, andRpIt is p dimension real number column
Vector, τiIndicate that the control force of input i-th mechanical foot is refused, τi∈Rp, Mi(qi) indicate symmetric positive definite inertial matrix, Mi(qi)
∈Rp×p, Rp×pIt is the real number matrix of p row p column,Indicate the eccentric force of i-th mechanical foot,gi(qi)
Indicate the gravity of i-th mechanical foot, gi(qi)∈Rp, ωiIndicate external disturbance, ωi∈Rp, the external disturbance includes that environment is disturbed
Dynamic and external noise；Wherein, the inertial matrix M of symmetric positive definitei(qi), eccentric forceWith gravity gi(qi) it is unknown parameter.
3. a kind of polypody cooperative control method of underwater multi-foot robot system according to claim 1 or 2, feature exist
In the neck obtained using directional topology figure described in distributed observer and step 2 to all nodes described in step 3
Boat person's status information is estimated, the status information of pilotage people is obtained method particularly includes:
Pass through formula:
qn+1=Fv (3)
Obtain the generalized coordinates q of pilotage peoplen+1, wherein v is the auxiliary State Variable of pilotage people, v ∈ Rm,For the derivative of v, S and
F is constant real number matrix, S ∈ Rm×m, F ∈ Rn×m；
Distributed observer estimates pilotage people's status information:
Wherein, For matrixElement,For adjacency matrix, ηjIt is j-th of follower to the position of pilotage people
The estimated value of confidence breath,J-th of follower is to the estimated value of the velocity information of pilotage people, j=1 ..., n+1, ηiIndicate i-th
Estimated value of a follower for v, ηi∈Rm,It is estimated value of i-th of follower to the velocity information of pilotage people, T indicates phase
Communication delay between adjacent follower i and j, t are the time.
4. a kind of polypody cooperative control method of underwater multi-foot robot system according to claim 3, which is characterized in that
Error constraints are carried out using status information of the obstacle liapunov function to the pilotage people that step 2 obtains described in step 4；It will
Error variance limits within the specified scope method particularly includes:
Rotational angle at robotic podarthrum is limited, variable boundary when setting are as follows:kC (t)=[kc1(t),kc2
(t),...,kcn(t)]TWithLimit the quantity of state q of the rotational angle of outputi(t)
Region are as follows:
kci(t) andRespectively i-th mechanical sufficient t moment expected motion trajectory qriUpper and lower boundary,kcn(t) and
Respectively n-th mechanical sufficient t moment expected motion trajectory qriUpper and lower boundary, qiIt (t) is the joint of t moment i-th mechanical foot
Rotational angle；R is real number matrix.
5. a kind of polypody cooperative control method of underwater multi-foot robot system according to claim 4, which is characterized in that
The nonlinear uncertainty in underwater multi-foot robot system is handled using nerual network technique described in step 5, is realized
Unknown parameter is estimated method particularly includes:
Utilize formula:
Realize the nonlinear uncertainty amount to i-th mechanical foot of multi-foot robot systemIt compensates,
In, WiIndicate ideal weighting matrix, Wi TIt is ideal weighting matrix WiTransposition, riIt is the virtual controlling of i-th of mechanical foot
Device,For riDerivative；It is activation primitive, △iIndicate approximate error；And △iIt is bounded, there are a positive numbers
△MiSo that | | △i||≤△Mi；Obtain i-th mechanical foot of underwater multi-foot robotEstimated value:
Wherein,It is ideal weighting matrix WiEstimated value,For matrixTransposition,For activation primitive.
6. a kind of polypody cooperative control method of underwater multi-foot robot system according to claim 5, which is characterized in that
The processing of nonlinear uncertainty described in the processing of the error constraints according to step 4 described in step 6 and step 5, is obtained
Obtain the adaptive control laws of underwater multi-foot robot control system specifically:
Wherein, α, β and μ are positive number, and α, β and μ are substantially equal to zero, K2iIt is the matrix of a symmetric positive definite, Z2iFor void
Quasi- track following error variance vector, Z2i TIt is vector Z2iTransposition, Z1iIt is that follower becomes the track following error of pilotage people
Measure vector, intermediate variablekaiAnd kbiIt is the upper and lower boundary of tracking error variable respectively；
Wherein,
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