CN116382313A - AUH cooperative formation control method considering communication limitation - Google Patents
AUH cooperative formation control method considering communication limitation Download PDFInfo
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Abstract
The invention discloses an AUH cooperative formation control method considering communication limitation, which comprises the following steps: (1) Forming AUH (autonomous Underwater vehicle) into a multi-agent system with nonlinear uncertain dynamics and external time-varying disturbance, and constructing a dynamics model of the system; (2) Designing a finite time distributed observer based on a consistency principle, so that the follower estimates the position information of the navigator cooperatively; (3) In the controller, the formation configuration of the follower is designed to maintain the control rate, RBFNN is used for approximating dynamic lumped uncertainty, and an adaptive method is used for estimating the boundary of external disturbance, so that the precise tracking of the follower to the pilot is realized. The invention fully considers that the complexity of the underwater environment can limit the information exchange between AUH, so that the follower can cooperatively observe and acquire the state information of the navigator, and the tracking control can be more effectively carried out.
Description
Technical Field
The invention belongs to the field of underwater helicopter formation control, and particularly relates to an AUH cooperative formation control method considering communication limitation.
Background
With the improvement and progress of marine equipment systems, autonomous underwater vehicles AUVs are widely applied in the fields of marine monitoring, marine observation and the like due to the advantages of intellectualization, flexible maneuver and the like. A new AUV, called underwater helicopter (Autonomous underwater helicopter, AUH), has outstanding advantages in near observation, fixed-point hovering, etc. due to its special structure and propulsion, and is more suitable for the above tasks. Meanwhile, the multi-AUV formation has good cooperativity, robustness and fault tolerance when cooperatively working in a complex marine environment, so that the problem of cooperative control of the formation of underwater intelligent agents becomes one of research hotspots of scientific researchers.
The complexity of underwater multi-agent formation control comes from a number of aspects, including the fact that the AUH has complex unknown nonlinear dynamics, the underwater environment has unknown time-varying disturbances, and communication delays and failures exist inside the AUH formation. The existing researches propose effective solutions to the above problems, and radial basis function neural networks (Radial basis function neural network, RBFNN) are widely used for approximating dynamics uncertainty items of a system, and coping strategies of external disturbance include a disturbance observer, a state expansion observer and the like.
For example, chinese patent document publication No. CN113821028A discloses an underactuated AUV formation track tracking control method based on distributed model predictive control, which uses a radial basis function neural network to approach an uncertain partial system equation, and combines a minimum learning parameter method to reduce computational complexity.
The Chinese patent publication No. CN113009826A discloses an AUV preset performance track tracking control method based on novel error transformation, which adopts an improved performance function and a novel error transformation method, so that the AUV track tracking error can be converged in a specified time.
The scheme fully researches the use of various strategies to control the AUV to accurately track the reference track, however, the method generally assumes that all AUHs in the formation can acquire the state information of the navigator without limitation, and does not consider the limitation of the communication range of the underwater environment, and not all followers can receive the state information of the navigator. Meanwhile, the disturbance observer is used for processing external time-varying disturbance, so that the burden of the controller is increased, and the convergence speed of errors is limited.
Disclosure of Invention
The invention provides an AUH cooperative formation control method considering communication limitation, which fully considers the complexity of an underwater environment to limit information exchange among AUH, so that a follower can cooperatively observe and acquire state information of a pilot, and tracking control can be more effectively carried out.
An AUH cooperative formation control method considering communication limitation, comprising:
(1) Forming AUH (autonomous Underwater vehicle) into a multi-agent system with nonlinear uncertain dynamics and external time-varying disturbance, and constructing a dynamics model of the system;
(2) Designing a finite time distributed observer based on a consistency principle, so that the follower estimates the position information of the navigator cooperatively;
(3) In the controller, the formation configuration of the follower is designed to maintain the control rate, RBFNN is used for approximating dynamic lumped uncertainty, and an adaptive method is used for estimating the boundary of external disturbance, so that the precise tracking of the follower to the pilot is realized.
The invention fully considers the problem of limited communication among AUH, and provides a finite time distributed observer based on a consistency principle to cooperatively estimate the state information of a pilot. In addition, the cooperative radial basis function neural network RBFNN is used in the controller, the dynamics information is shared among the followers, and the approximation speed of the neural network to the dynamics uncertainty item is accelerated. Finally, the boundary of the external disturbance is estimated using an adaptive method and introduced into the controller in a specific way to compensate for the external disturbance.
In step (1), the kinetic model of the system is as follows:
wherein the subscript i denotes the ith intelligenceThe energy body of the energy-saving device,
wherein 0 represents a pilot of the AUH formation, 1,2,..n represents a follower of the AUH formation; />
Representing displacement and heading deflection angle v in world coordinate system i ＝[u i ,υ i ,w i ,p i ,q i ,r i ] T Represents the linear and angular velocities in the body coordinate system, M represents an inertial matrix containing additional mass, J (η i ) Representing a coordinate transformation matrix between the world and volume coordinate systems, C (v i ) Representing a matrix of coriolis and centripetal forces with uncertainty, D (v i ) Represents a hydrodynamic damping matrix with uncertainty, delta (eta i ,v i ) Representing the unmodeled dynamics of the system τ d,i Representing external time-varying disturbance, τ i ∈R 6 Representing a control input.
Communication topology between followers is represented by undirected graph
Description of the communication topology of the entire AUH formation by means of a directed graph +.>
The communication between the pilot and the follower is established in one direction, and the information transmission can only be initiated by the pilot.
In step (2), the designed finite time distributed observer is as follows:
in the method, in the process of the invention,
representing the i-th follower pair η obtained by the distributed observer 0 Is>
Represents the jth follower pair eta 0 Beta, observed value of (2) 2 E (0, 1) is the parameter, k 1 ＞0,/>
Gain for observer; a, a ij For the adjacency coefficient between followers, if the ith follower can obtain the information of j followers, a ij =1, otherwise, a ij ＝0；c i C, if the ith follower can obtain information of the navigator for the adjacency coefficient between the follower and the navigator i =1, otherwise, c i ＝0。
In the step (3), the formation configuration maintenance control rate of the follower is designed as follows
Wherein K is 2,i For gain diagonal matrix, z 1,i Z is the tracking error 2,i As a variable of the error it is possible to provide,
for virtual control rate alpha i Is a first order time derivative of τ i Maintaining control rate for formation configuration of follower, +.>
Is->
Is used for the estimation of the (c),
is a disturbance compensation term, wherein τ c,ij Designed as
Wherein s > 0 is a design parameter,
is->
Is designed to have an update rate of
Wherein, gamma d > 0 is a design parameter.
Tracking error z 1,i Expressed as:
in the method, in the process of the invention,
for the reference tracking track of the ith AUH, the formula is:
in the method, in the process of the invention,
for observations obtained by distributed observers, +.>
To determine the relative position vector of the formation configuration.
Virtual control rate alpha i Expressed as:
in the method, in the process of the invention,
is->
Is a first order time derivative of (a).
Error variable z 2,i The definition is as follows:
z 2,i ＝ν i -α i
in the formula, v i As virtual control variable, error variable z 2,i The derivative of (2) is calculated as:
wherein τ M,i ＝M -1 τ d,i Representing a disturbance term, assuming that the external time-varying disturbance is bounded, the disturbance term is not known to be an upper bound
Namely satisfy the relation
In the method, in the process of the invention,
is an unknown constant vector;
in step (3), approximating the dynamic lumped uncertainty using RBFNN in the control rate comprises:
let F i (γ i )＝M -1 [C(ν i )ν i +D(ν i )ν i +Δ(η i ,ν i )]＝[f i1 (γ i ),...,f i6 (γ i )] T For the total uncertainty of the dynamic set, RBFNN is used to approximate the total uncertainty
The update rate of RBFNN weight coefficient is designed as
Wherein, lambda 1,ij > 0 is the gain matrix to be designed, k W,ij Is a normal number, - Λ 1,ij S j (γ i )z 2,ij In order to adapt the term(s),
is a collaborative term.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention fully considers the complexity of the underwater environment and possibly limits the information exchange between AUH, and provides a distributed observer based on a consistency principle, so that the follower can cooperatively observe and acquire the state information of the navigator.
2. The invention takes into account external time-varying disturbances when designing the control rate. The boundaries of the disturbance are estimated using an adaptive method and the estimation is applied to the control rate in a specific way to compensate for the external disturbance. In addition, the proposed strategy will achieve a more accurate approximation than a method that approximates the disturbance using a neural network.
3. In the invention, a synergistic item is introduced into RBFNN
Each AUH can be shared to its neighbors AUH in a coordinated manner based on the consistency principle by an adaptive method to estimate the dynamic uncertainty. Therefore, RBFNN added with the cooperative item has better generalization capability and is more suitable for formation control problems.
Drawings
Fig. 1 is a flowchart of an AUH cooperative formation control method considering communication limitation in the present invention;
fig. 2 is a schematic diagram of an AUH communication topology in the present invention;
FIG. 3 is an observation of a finite time distributed observer according to an embodiment of the present invention;
FIG. 4 is a graph showing tracking error under the action of an adaptive-based control algorithm in an embodiment of the present invention;
FIG. 5 is a graph of radial basis function neural network approximation error in an embodiment of the present invention;
FIG. 6 is a schematic diagram of a control input of an AUH system according to an embodiment of the present invention;
fig. 7 is a schematic diagram of path tracking for AUH formation in an embodiment of the present invention.
Detailed Description
The invention will be described in further detail with reference to the drawings and examples, it being noted that the examples described below are intended to facilitate the understanding of the invention and are not intended to limit the invention in any way.
The method is realized in two steps, firstly, the problem of limited communication distance of the underwater environment is fully considered, and a limited time distributed observer based on a consistency principle is designed to cooperatively observe the position information of a pilot. Secondly, the formation configuration of the follower is designed to maintain the control rate, the precise tracking of the follower to the navigator is realized, and the controller is built under an adaptive control framework.
The subject of the invention is a multi-agent system consisting of n+1 AUHs with non-linear uncertain dynamics and external time-varying disturbance, the dynamics model of which is expressed as
Wherein the subscript i represents the ith agent,
wherein 0 represents a navigator-AUH, 1, 2..n represents a follower +.>
Representing displacement and heading deflection angle in world coordinate system, v i ＝[u i ,υ i ,w i ,p i ,q i ,r i ] T Represents the linear and angular velocities in the body coordinate system, M represents an inertial matrix containing additional mass, J (η i ) Representing a coordinate transformation matrix between the world and volume coordinate systems, C (v i ) Representing a matrix of coriolis and centripetal forces with uncertainty, D (v i ) Represents a hydrodynamic damping matrix with uncertainty, delta (eta i ,ν i ) Representing the unmodeled dynamics of the system τ d,i Representing external time-varying disturbance, τ i ∈R 6 Representing a control input.
The communication topology between AUH teams is depicted graphically, pilot-AUH is denoted 0, follower-AUH is denoted 1.
Definition map
In (1) the->
Representing vertex set, ++>
Representing the set of adjacent edges, vertex b i Neighbor set (The neighbor set of node b) i ) Is defined as
Representing a weighted abutment matrix (the weighted adjacency matrix of->
) If (b) i ,b k ) Epsilon, then a ik > 0, otherwise a ik =0. Laplacian matrix (The Laplacian matrix)/(Laplacian matrix)>
Defined as->
l ik ＝-a ik . Furthermore, if->
Definition of
Is undirected graph, otherwise->
Is a directed graph. In the directed graph, if there is (b) 1 ,b 2 ),...,(b k-1 ,b k ) Edge sequences in the form of a sequence of edges, then called vertices b 1 To vertex b k Is directed along with vertex b k For vertex b 1 Is reachable (reachable). In the undirected graph, (b) 1 ,b 2 ),...,(b k-1 ,b k ) The edge sequence representation in form is represented by vertex b 1 To vertex b k In addition, if there is one undirected path between each vertex pair, the undirected graph is connected. In the directed graph, one directed edge is denoted as (b i ,b k ) Epsilon, b where i Called parent vertex，b k Called child vertices. A directed tree is a directed graph in which each node has only one parent node, only one node called the root node has no parent node, and other nodes are reachable to the root node. The directed graph is defined to include a directed spanning tree if and only if at least one node in the directed graph can reach every other node.
Communication topology between followers is represented by undirected graph
Description. The communication topology of the entire AUHs formation can be represented by a directed graph +.>
Build up, wherein->
The communication between the pilot and the follower is unidirectional, which means that the information transfer can only be initiated by the pilot. />
Defined as a weighted adjacency matrix for the pilot, wherein the subscript +.>
c i > 0 means that the ith follower is connected to the navigator, otherwise c i ＝0。
In the present invention RBFNN will be used to approximate the unknown nonlinear function f (x): R m →R。
In the method, in the process of the invention,
for the optimal weight coefficient vector, epsilon is an inherent approximation error, and meets the following requirements
Wherein (1)>
Is unknown small constant, ++>
Is a basis function vector, wherein q is the number of nodes of the neural network, s i (x) Is a gaussian activation function.
Wherein mu is i And σ represents the center and base width of the ith node, respectively.
In the present invention, regarding the finite time convergence theorem, the expression of one system is as follows
For the system represented by equation (4), if there is a continuous positive definite function V (x) satisfying
Wherein k is greater than 0,0 < m is less than 1, x is E R n If x is not equal to 0, the system will converge to 0 for a finite time T, which is calculated as
The necessary assumptions of the invention are as follows:
assume one: undirected graph
Is communicated.
Suppose two: adjacent weight matrix for navigator
Assume three: trajectory eta of virtual navigator 0 And its derivative
It is a matter of course that it is not possible to provide a solution,
suppose four: external time-varying disturbance τ d,i Is bounded.
As shown in fig. 1, an AUH cooperative formation control method considering communication limitation includes:
step one: the AUH is formed into a multi-agent system with nonlinear uncertain dynamics and external time-varying disturbance, and a dynamics model of the system is constructed.
Step two: a finite time distributed observer based on a consistency principle is designed, so that the follower estimates the position information of the navigator cooperatively.
It can be known from the assumption two that not all the followers can receive the information of the navigator, i.e. some followers cannot obtain the state information of the navigator.
In the method, in the process of the invention,
represents the ith follower pair eta 0 Estimate of beta 2 E (0, 1) is the parameter, k 1 ＞0,/>
Is the observer gain.
Assume that 1 holds true and
on the premise of limitation, the estimation error of the observer corresponding to the formula (5) converges in a limited time.
The proving process of this step is as follows:
the estimation error and the error vector are respectively expressed as
Selecting Lyapunov function as
By definition
Rewritable as (6)
According to the assumption 1 that the data of the first cell,
from this, it can be seen that
Deriving (7) to obtain
In the method, in the process of the invention,
from the Helde inequality
Further deriving and obtaining
Obtained by reusing the Helde inequality
From (9), (11) and (12)
By combining inequality (8), it is possible to obtain
Thus, the error is estimated
Will be at a finite time T 1 Inner convergence, where T 1 Calculated as
The syndrome is known.
Step three: in the controller, the formation configuration of the follower is designed to maintain the control rate, RBFNN is used for approximating dynamic lumped uncertainty, and an adaptive method is used for estimating the boundary of external disturbance, so that the precise tracking of the follower to the pilot is realized.
The reference trace of the ith AUH is shown as
In the method, in the process of the invention,
for observations obtained by distributed observers, +.>
To determine the relative position vector of the formation configuration.
The tracking error can be calculated as
According to the formulas (1) and (17), the derivative thereof is calculated as
Selecting v i As a virtual control variable, the virtual control rate alpha i Designed as
Defining an error variable z 2,i ＝ν i -α i Its derivative is calculated as
In the method, in the process of the invention,
representing disturbance term, according to assumption four, disturbance term unknown upper bound +.>
Namely satisfy the relation
In the method, in the process of the invention,
is an unknown constant vector.
Let F i (γ i )＝M -1 [C(ν i )ν i +D(ν i )ν i +Δ(η i ,ν i )]＝[f i1 (γ i ),...,f i6 (γ i )] T For the dynamic set total uncertainty term, RBFNN is used to approximate it.
In the method, in the process of the invention,
control rate τ is maintained by formation configuration of follower i Designed as
In the method, in the process of the invention,
is->
Estimated value of ∈10->
τ c,i ＝[τ c,i1 ,...,τ c,i6 [ T Is a disturbance compensation term, wherein τ c,ij Designed as
Wherein s > 0 is a design parameter,
is->
Is designed to have an update rate of
Wherein, gamma d > 0 is a design parameter.
The update rate of RBFNN weight coefficient is designed as
Wherein, lambda 1,ij > 0 is the gain matrix to be designed, k W,ij Is a normal number, - Λ 1,ij S j (γ i )z 2,ij In order to adapt the term(s),
is a collaborative term.
For the follower in the AUHs formation system, the dynamics model is (1), the control rate is designed to be (23), the adaptive update rate is designed to be (25) and (26), and the following conclusion is established: the follower can maintain an ideal formation configuration with the pilot and the state variables in the system are all ultimately consistent and bounded.
The proving process of the steps is as follows:
designed as Lyapunov function
In the method, in the process of the invention,
combining formulas (18), (20), (23), (25) and (26), the derivatives thereof can be calculated as
Wherein k is W,j ＝diag[k W,ij ,...,k W,Nj ]＞0，
According to hypothesis one->
Is a semi-positive definite matrix, thus +.>
Analysis shows that
Properties of the combination hyperbolic tangent function>
It can be seen that
From the Young's inequality
The combination of (28), (29) and (30) is known
In the method, in the process of the invention,
from equation (31), it can be deduced
Therefore, the following relationship holds
In the method, in the process of the invention,
represents a tight set of a size that can be defined by K 1,i 、K 2,i 、Λ 1,ij And gamma d And (5) adjusting.
It follows that by properly selecting the above parameters, z 1,i 、z 2,i And
are all ultimately consistent and bounded. Alpha is according to formula (19) and hypothesis two i And->
Is bounded. Further, since the kinetic uncertainty is bounded, +.>
And->
Is bounded.
The syndrome is known.
The embodiment of the invention carries out simulation experiments on an AUHs formation system consisting of 4 AUHs and one virtual pilot to verify the effectiveness of the proposed formation control rate.
The formation configuration vector is
The unmodeled kinetics is delta (eta i ,v i )＝[Δ 1 ,...,Δ 6 ] T Wherein->
The description of the communication topology of the AUH formation is shown in fig. 2, and the virtual pilot movement path and the initial state of the AUH are shown in table 1.
TABLE 1 tracking Path and AUH initial State
The parameter value design of the control rate is shown in table 2.
Table 2 parameter values of observer and control rate
The radial basis function neural network with 21 nodes is used for approximating the dynamics uncertainty term, the nodes are uniformly distributed in the interval [ -1,1], and the basis width is designed to be 2.
Simulation results as shown in fig. 3-7, fig. 3 illustrates the observation of the pilot state information by the finite time distributed observer based on the consistency principle, and the validity of the distributed observer is verified. Fig. 4 shows that the tracking error of the AUH in the formation is finally consistent and bounded under the action of a control algorithm, fig. 5 shows the approximation error of the neural network to the dynamics uncertainty term, and the effectiveness of the radial basis function neural network cooperative approximation is verified. Fig. 6 shows the control inputs under the control algorithm, verifying the feasibility of the algorithm. Fig. 7 shows that the AUH formation can effectively track the reference path, verifying the validity of the control algorithm.
The foregoing embodiments have described in detail the technical solution and the advantages of the present invention, it should be understood that the foregoing embodiments are merely illustrative of the present invention and are not intended to limit the invention, and any modifications, additions and equivalents made within the scope of the principles of the present invention should be included in the scope of the invention.
Claims (9)
1. An AUH cooperative formation control method considering communication limitation, comprising:
(1) Forming AUH (autonomous Underwater vehicle) into a multi-agent system with nonlinear uncertain dynamics and external time-varying disturbance, and constructing a dynamics model of the system;
(2) Designing a finite time distributed observer based on a consistency principle, so that the follower estimates the position information of the navigator cooperatively;
(3) In the controller, the formation configuration of the follower is designed to maintain the control rate, RBFNN is used for approximating dynamic lumped uncertainty, and an adaptive method is used for estimating the boundary of external disturbance, so that the precise tracking of the follower to the pilot is realized.
2. The AUH co-formation control method considering communication limitation according to claim 1, wherein in step (1), a dynamics model of the system is as follows:
wherein the subscript i represents the ith agent,
wherein 0 represents a pilot of the AUH formation, 1,2,..n represents a follower of the AUH formation; />
Representing displacement and heading deflection angle v in world coordinate system i ＝[u i ,υ i ,w i ,p i ,q i ,r i ] T Represents the linear and angular velocities in the body coordinate system, M represents an inertial matrix containing additional mass, J (η i ) Representing a coordinate transformation matrix between the world and volume coordinate systems, C (v i ) Representing a matrix of coriolis and centripetal forces with uncertainty, D (v i ) Represents a hydrodynamic damping matrix with uncertainty, delta (eta i ,ν i ) Representing the unmodeled dynamics of the system τ d,i Representing external time-varying disturbance, τ i ∈R 6 Representing a control input.
3. The AUH cooperative formation control method considering communication limitation according to claim 2, wherein the communication topology between followers is composed of undirected graph
Description of the communication topology of the entire AUH formation by means of a directed graph +.>
The communication between the pilot and the follower is established in one direction, and the information transmission can only be initiated by the pilot.
4. The AUH co-formation control method considering communication limitation according to claim 2, wherein in step (2), the finite time distributed observer is designed as follows:
in the method, in the process of the invention,
representing the i-th follower pair η obtained by the distributed observer 0 Is>
Represents the jth follower pair eta 0 Beta, observed value of (2) 2 E (0, 1) is the parameter, k 1 ＞0,/>
Gain for observer; a, a ij For the adjacency coefficient between followers, if the ith follower can obtain the information of j followers, a ij =1, otherwise, a ij ＝0；c i C, if the ith follower can obtain information of the navigator for the adjacency coefficient between the follower and the navigator i =1, otherwise, c i ＝0。
5. The AUH cooperative formation control method considering communication limitation according to claim 4, wherein in step (3), the formation configuration maintenance control rate of the follower is designed as
Wherein K is 2,i For gain diagonal matrix, z 1,i Z is the tracking error 2,i As a variable of the error it is possible to provide,
for virtual control rate alpha i Is a first order time derivative of τ i Maintaining control rate for formation configuration of follower, +.>
Is W i *T Is used for the estimation of the (c),
τ c,i ＝[τ c,i1 ,...,τ c,i6 ] T is a disturbance compensation term, wherein τ c,ij Designed as
Wherein s > 0 is a design parameter,
is->
Is designed to have an update rate of
Wherein, gamma d > 0 is a design parameter.
6. The AUH co-formation control method considering communication limitation according to claim 5, wherein the tracking error z 1,i Expressed as:
in the method, in the process of the invention,
for the reference tracking track of the ith AUH, the formula is:
in the method, in the process of the invention,
for observations obtained by distributed observers, +.>
To determine the relative position vector of the formation configuration.
7. The AUH cooperative formation control method considering communication limitation according to claim 6, wherein the virtual control rate α i Expressed as:
in the method, in the process of the invention,
is->
Is a first order time derivative of (a).
8. The AUH co-formation control method considering communication limitation according to claim 7, wherein the error variable z 2,i The definition is as follows:
z 2,i ＝ν i -α i
in v i As virtual control variable, error variable z 2,i The derivative of (2) is calculated as:
wherein τ M,i ＝M -1 τ d,i Representing a disturbance term, assuming that the external time-varying disturbance is bounded, the disturbance term is not known to be an upper bound
Namely satisfy the relation
In the method, in the process of the invention,
is an unknown constant vector.
9. The AUH co-formation control method considering communication limitation according to claim 8, wherein in step (3), approximating the dynamic lumped uncertainty using RBFNN in the control rate comprises:
let F i (Υ i )＝M -1 [C(ν i )ν i +D(ν i )v i +Δ(η i ,ν i )]＝[f i1 (γ i ),...,f i6 (γ i )] T For the total uncertainty of the dynamic set, RBFNN is used to approximate the total uncertainty
In the method, in the process of the invention,
the update rate of RBFNN weight coefficient is designed as
Wherein, lambda 1,ij > 0 is the gain matrix to be designed, k W,ij Is a normal number, - Λ 1,ij S j (γ i )z 2,ij In order to adapt the term(s),
is a collaborative term.
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| CN118295427B (en) * | 2024-06-04 | 2024-08-20 | 西北工业大学深圳研究院 | Underwater distributed state observation formation control method based on time sequence prediction |
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