CN116449703A - AUH formation cooperative control method under finite time frame - Google Patents
AUH formation cooperative control method under finite time frame Download PDFInfo
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Abstract
The invention discloses an AUH formation cooperative control method under a limited time frame, which comprises the following steps: (1) Constructing a dynamics model and a parameterized path of a navigator-AUH; (2) Introducing a parameterized path when designing the track tracking control rate of a navigator, estimating dynamics lumped uncertainty by using a limited-time state dilation observer, and ensuring that an observation error converges in limited time; (3) Introducing a finite time preset performance control method into the control rate of the follower; (4) Approximating the dynamic uncertainty using RBFNN in the control rate of the follower; (5) And (3) designing an experience-based formation configuration maintenance control rate, and realizing accurate tracking of a pilot by a follower to maintain the formation configuration. By utilizing the method and the device, the navigator can accurately track the parameterized path, meanwhile, the follower can accurately track the navigator to keep a formation configuration, and the control performance of the system is improved.
Description
Technical Field
The invention belongs to the field of underwater helicopter control, and particularly relates to an AUH formation cooperative control method under a limited time frame.
Background
In recent years, autonomous underwater vehicles (Autonomous underwater vehicle, AUV) have received extensive attention from researchers because of their outstanding advantages in the application fields of pipeline inspection, military defense, marine observation, and the like. A new AUV, known as an underwater helicopter (Autonomous underwater helicopter, AUH), is more suitable for the above-mentioned underwater work tasks due to its special structure. Meanwhile, in some special cases, a plurality of AUVs are required to track a given trajectory while maintaining a formation configuration, so the formation control problem of the AUVs becomes a research hotspot.
The complexity of AUV formation control comes from a number of aspects, including AUVs having complex unknown nonlinear dynamics, tracking errors being difficult to converge quickly due to the complexity of the underwater environment, etc. The prior researches put forward some effective solutions to the problems, radial basis function neural networks (Radial basis function neural network, RBFNN) are widely used for approximating the dynamics uncertainty term of a system, a state expansion observer is used for estimating the dynamics uncertainty term, and a preset performance control method is used for controlling an AUV so as to accelerate the convergence speed of errors 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 track tracking methods only consider the space dimension, but not the time dimension, and the movement speed of the AUV during path tracking is not controlled. Meanwhile, when the state expansion observer estimates the dynamic uncertainty, the convergence of the observation error in a limited time cannot be ensured, and the convergence speed of the tracking error can be accelerated but the convergence time cannot be set in advance by the preset performance control method used in the prior art. In addition, the existing research fully utilizes the global approximation capability of RBFNN, but omits the local learning of RBFNN.
Disclosure of Invention
The AUH formation cooperative control method under the finite time frame can realize that a pilot accurately tracks a parameterized path, and simultaneously realize that a follower accurately tracks the pilot to keep a formation configuration, so that the control performance of a system is improved.
An AUH formation cooperative control method under a finite time frame is characterized by comprising the following steps:
(1) Constructing a navigator-AUH dynamics model and a parameterized reference path;
(2) Introducing a parameterized path when designing the track tracking control rate of a navigator, estimating dynamics lumped uncertainty by using a limited-time state dilation observer, and ensuring that an observation error converges in limited time;
(3) Introducing a finite time preset performance control method into the control rate of the follower;
(4) Approximating the dynamic uncertainty using RBFNN in the control rate of the follower;
(5) And (3) designing an experience-based formation configuration maintenance control rate, and realizing accurate tracking of a pilot by a follower to maintain the formation configuration.
In step (1), the dynamics model of the navigator-AUH is expressed as:
in χ 0 ＝M -1 [-C(ν 0 )ν 0 -D(ν 0 )ν 0 -Δ(η 0 ,ν 0 )]Representing the lumped uncertainty; j (eta) 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 i ∈R 6 Representing a control input;representing displacement and heading bias angle in world coordinate system, wherein x is i ,y i ,z i Coordinate values representing the x-axis, y-axis and z-axis of AUH in the world coordinate system, respectively,/->θ i ,ψ i Respectively representing the roll angle, pitch angle and yaw angle of the AUH in a world coordinate system; v (v) i ＝[u i ,υ i ,w i ,p i ,q i ,r i ] T Represents the linear and angular velocities in a body coordinate system, where u i ,υ i ,w i Representing the speed of the AUH along the x, y and z axes, p, respectively, in a volumetric coordinate system i ,q i ,r i Respectively representing the rolling angular velocity, the pitch angle velocity and the yaw angular velocity of the AUH in a body coordinate system; m represents an inertial matrix containing additional mass; subscript i indicates the ith AUH agent,>wherein 0 represents a navigator-AUH, 1, 2..n represents a follower-AUH, respectively; />Representing eta 0 First derivative of time, +.>Representing v 0 The first derivative with respect to time.
In step (1), the parameterized reference path is expressed as:
wherein x is ro (σ),y r0 (σ),z ro (sigma) represents parameterized parameters, respectivelyReference coordinate values of the examination path in the x-axis, the y-axis and the z-axis of the world coordinate system;θ r0 (σ),ψ r0 (sigma) represents the reference roll, pitch and yaw angles, respectively, of the parameterized path in the world coordinate system; σ (t) is a parameter variable of the path.
In step (2), the finite time state dilation observer is designed to
In the formula, the function sig () is defined as sig α (m)＝sign(m)|m| α WhereinAs a sign function. m is the observer gain, β1 1 E (0, 1) is the adjustment parameter, < ->And->Respectively represent eta 0 、ν 0 And χ (x) 0 Estimated value of ∈10->And->Respectively indicate->And->First derivative of>Representing eta 0 Is calculated as +.>
The design process of the track tracking control rate of the navigator is as follows:
tracking error of the pilot is expressed as
z 1,0 ＝η 0 -η r,0 (σ)
Its derivative is calculated as
In the method, in the process of the invention,for ideal path parameter update rate, p is externally introduced path update control variable, satisfying the relation
Selecting v 0 Virtual control rate alpha as virtual control amount 0 Designed as
Wherein K is 1,0 Determining a gain diagonal matrix for positive;
update rate of path parameter control variablesDesigned as
Wherein k is p > 0 is the gain to be designed;
error variable z 2,0 Calculated as
z 2,0 ＝v 0 -α 0
Its first derivative is calculated as
The parameterized track tracking control rate of the navigator is designed as follows
Wherein K is 2,0 The gain diagonal matrix is determined for positive.
The step (3) is specifically as follows:
the reference tracking trace of the ith AUH is expressed as
In the method, in the process of the invention,a relative position vector for determining a formation configuration;
the tracking error is calculated as
e 1,i ＝η i -η r,i ＝[e 1,i1 ,...,e 1,i6 ] T
Under the performance preset control framework, the error conversion relation is described as
e 1,ij ＝h ij (t)G ij (z 1,ij )
Wherein G is ij As an error transfer function, z 1,ij To convert errors
h ij (t) is a finite time performance function, limiting error convergence in finite timeThe finite time performance function is designed as
Wherein T is 2,i For a preset time, h ij (0) > 1 and h ij (++) v0 is a design parameter for limiting overshoot and steady state error, respectively;
conversion error z 1,ij Calculated as
The step (4) is specifically as follows:
derivative of conversion errorCalculated as
Wherein z is 1,i ＝[z 1,i1 ,...,z 1,i6 ] T ，Φ i ＝diag[c i1 ,...,c i6 ]，Ξ i ＝diag[g i1 ,...,g i6 ]Wherein c ij And g ij The definition is as follows
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
Let F i (γ i )＝M -1 [C(v i )v i +D(v i )ν i +Δ(η i ,ν i )]＝f i1 (γ i ),...,f i6 (γ i )] T Approximation of the dynamic set total uncertainty term using RBFNN;
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->
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.
The step (5) comprises the following steps:
input of RBFNNRegression of subvector S as periodic signal p (x) Is continuously active, the exact approximation of the dynamics uncertainty term f (x) is made by +.>Realization of
In the method, in the process of the invention,for empirical values obtained by learning
Wherein T is i ＝inf{z 1,0 (t)≤ι 1 ,e 1,i (t)≤l 2 -indicating the moment when the auss formation enters the steady-state phase of the reference trajectory of the tracking cycle;
the formation configuration maintenance control rate based on experience is designed as
Compared with the prior art, the invention has the following beneficial effects:
1. according to the invention, by introducing the parameterized path in the track tracking control method of the navigator, the independent control of the tracking speed is realized while the accurate tracking of the reference path is ensured, and furthermore, the finite-time state dilation observer is used for estimating the lumped uncertainty and ensuring that the observation error converges in finite time.
2. The control of the follower according to the invention is realized in the pilot-follower formation framework, so that the follower tracking speed control will be realized by a fixed formation configuration. Meanwhile, RBFNN is used for approaching dynamic uncertainty in the control rate of the follower, and a finite time preset performance control method is introduced into the control rate to ensure that errors are converged at fixed time. In addition, when AUHs tracks a periodic reference trajectory, the dynamics uncertainty will be learned using a deterministic learning method, and the learned empirical values will be used to build an empirical-based co-formation controller.
Drawings
FIG. 1 is a flow chart of an AUH formation cooperative control method under a finite time frame;
fig. 2 is a schematic diagram of an AUH communication topology according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a parameterized path method for controlling path tracking speed according to an embodiment of the present invention;
FIG. 4a is a graph of a heave tracking error under the influence of an adaptive-based control algorithm according to an embodiment of the invention;
FIG. 4b illustrates a cross-over tracking error under the influence of an adaptive-based control algorithm in accordance with an embodiment of the present invention;
FIG. 4c illustrates yaw tracking error under the influence 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. 6a is a graph of heave tracking error under the influence of an empirically based control algorithm according to an embodiment of the invention;
FIG. 6b is a graph of the cross-over tracking error under the influence of an empirically based control algorithm in an embodiment of the present invention;
FIG. 6c illustrates yaw angle tracking error under the influence of an empirically based control algorithm in 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 invention relates to a multi-agent system with nonlinear uncertain dynamics, which consists of N+1 underwater helicopters (AUH), wherein the dynamics model of the system is expressed as
Wherein the subscript i represents the ith agent,wherein 0 represents a navigator-AUH, 1, 2. />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 i ∈R 6 Representing a control input.
Definition mapIn (1) the->Represents the vertex set,representing the set of adjacent edges, vertex b i Neighbor set (The neighbor set of node b) i ) 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->Furthermore, if->Definition->Is undirected graph, otherwise->Is a directed graph. In the directed graph, if 9b is present 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 view, 9b 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.
The communication topology between AUH teams is described by graph theory, pilot-AUH is denoted 0, follower-AUH is denoted 1. Communication topology between followers is represented by undirected graphDescription. 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。
f(x)＝W *T S(x)+ε
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 requirementsWherein (1)>For unknown small constants, S (x) =s 1 (x),...,s q (x)] T ∈R q 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.
Consider being limited to a certain bounded set Ω x The continuous periodic signal x (t) in (a) then being uniformly distributed for the center and being able to cover the area Ω x Is a radial basis neural network W T S (x) corresponding to the regression sub-vector S p (x) Is continuously active (Persistently exciting).
For regression sub-vector S p (x) The continuously activated local RBFNN has the following conclusion that
(1) Weight estimation of local RNFBBWill converge to an optimal value +.>Is within a small neighborhood of (a).
(2) The exact approximation of the unknown nonlinear function f (x) can be determined byRealizing the method.
In the method, in the process of the invention,for empirical values obtained by learning ε E To use error of empirical approximation
The present invention satisfies the following three assumptions:
assume one: undirected graphIs communicated.
Suppose two: adjacent weight matrix for navigator
Assume three: parameterized trajectory η r,0 And its derivativeIs periodic and bounded. At the same time (I)>Andis bounded.
The method comprises the steps of realizing the core content in two steps, firstly, designing the track tracking control rate of a pilot, realizing the precise tracking of a parameterized path of the pilot, and simultaneously ensuring that the tracking speed can be independently designed. Secondly, the pilot tracking control rate of the follower is designed, the precise tracking of the pilot by the follower is realized to keep the formation configuration, and on the basis, the knowledge obtained in the self-adaption process is used for constructing the formation control rate based on experience so as to improve the control performance.
Specifically, as shown in fig. 1, an AUH formation cooperative control method under a limited time frame includes the following steps:
and 1, constructing a dynamic model and a parameterized path of the navigator-AUH.
The dynamics model of the navigator-AUH can be expressed as
In χ 0 ＝M -1 [-C(v 0 )v 0 -D(v 0 )v 0 -Δ(η 0 ,v 0 )]Representing the lumped uncertainty.
The parameterized path of the navigator-AUH trace is denoted as
Where σ (t) is a parameter variable of the path.
And 2, designing the track tracking control rate of the navigator, and estimating the dynamics lumped uncertainty by using a limited-time state expansion observer.
The limited time state dilation observer is designed as
Where m is the observer gain, beta 1 E (0, 1) is the adjustment parameter,and->Respectively represent eta 0 、ν 0 And χ (x) 0 Is used for the estimation of the estimated value of (a).
Tracking error of the pilot is expressed as
z 1,0 ＝η 0 -η r,0 (σ)
Its derivative is calculated as
In the method, in the process of the invention,for ideal path parameter update rate, p is externally introduced path update control variable, satisfying the relation
Selecting v 0 Virtual control rate alpha as virtual control amount 0 Designed as
Wherein K is 1,0 The gain diagonal matrix is determined for positive.
Update rate of path parameter control variablesDesigned as
Wherein k is p And > 0 is the gain to be designed.
Error variable z 2,0 Calculated as
z 2,0 ＝v 0 -α 0
Its first derivative is calculated as
The parameterized track tracking control rate of the navigator is designed as follows
Wherein K is 2,0 The gain diagonal matrix is determined for positive.
And step 3, introducing a finite time preset performance control method into the control rate of the follower.
The reference trace of the ith AUH is shown as
In the method, in the process of the invention,to determine the relative position vector of the formation configuration.
The tracking error can be calculated as
e 1,i ＝η i -η r,i ＝[e 1,i1 ,...,e 1,i6 ] T
Under the performance preset control framework, the error conversion relationship can be described as
e 1,ij ＝h ij (t)G ij (z 1,ij )
Wherein G is ij As an error transfer function, z 1,ij To convert errors
h ij (t) is a finite time performance function, the constraint error converges in a finite time, in this patent the finite time performance function is designed as
Wherein T is 2,i For a preset time, h ij (0) > 1 and h ij (≡) > 0 as design parameter for limiting overshoot and steady state errors.
Conversion error z 1,ij Calculated as
And 4, approximating the dynamic uncertainty by using RBFNN in the control rate of the follower.
Derivative of conversion errorCalculated as
Wherein z is 1,i ＝[z 1,i1 ,...,z 1,i6 ] T ，Φ i ＝diag[c i1 ,...,c i6 ]，Ξ i ＝diag[g i1 ,...,g i6 ]Wherein c ij And g ij The definition is as follows
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
Let F i (γ i )＝M -1 [C(v i )v i +D(v i )ν i +Δ(η i ,ν i )]＝[f i1 (γ i ),...,f i6 (γ i )] T Approximation of the dynamic set total uncertainty term using RBFNN;
in the method, in the process of the invention,
in the method, in the process of the invention,is->Estimated value of ∈10->
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.
And 5, designing an experience-based formation configuration maintenance control rate.
Input of RBFNNRegression of subvector S as periodic signal p (x) Is continuously active, the exact approximation of the dynamics uncertainty term f (x) is made by +.>Realization of
In the method, in the process of the invention,for empirical values obtained by learning
Wherein T is i ＝inf{z 1,0 (t)≤ι 1 ,e 1,i (t)＜ι 2 -indicating the moment when the auss formation enters the steady-state phase of the reference trajectory of the tracking cycle;
the formation configuration maintenance control rate based on experience is designed as
In order to verify the effectiveness of the present invention, a simulation experiment was performed with an auss formation system consisting of 5 aus.
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 parameterized paths and initial states of the AUH are shown in table 1.
TABLE 1 parameterized Path and AUH initial State
/>
1. Simulation experiment for controlling path tracking speed
A numerical simulation experiment was performed to verify the effectiveness of parameterized path tracking control rate on pilot path tracking speed control.
The control gain is designed to be K 1,0 ＝diag[0.5,0.5,0.5,0.5,0.5,0.5]，K 2,0 ＝diag[5,5,5,5,5,5]，k p =10. The parameters of the finite time state extended state observer are designed to be m=2, β 1 =0.8. The parameterized path is given in table 1, the ideal path parameter update rate is initially set to 1, and after 15 seconds the step changes to 2.
The simulation results are shown in FIG. 3, where (a) in FIG. 3 shows the control rateUnder the action of (a) the update rate of the path parametersRapidly converge to the desired value +.>In FIG. 3 (b), it is shown that the tracking speed of the navigator can be determined by specifying +.>And (3) independent design.
2. Formation control simulation experiment based on self-adaptive method
AUHs formation simulation control targets are specified as follows
(1) The steady state error of the path tracking does not exceed 0.02.
(2) The steady state error of the tracking speed is controlled within 0.1.
(3) The maximum convergence time of the whole system is not more than 20s.
To achieve the above objective, the parameter value designs of the observer and the control rate are 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.
Firstly, verifying the effectiveness of a formation control algorithm based on an adaptive method, wherein simulation results are shown in fig. 4 and 5, fig. 4 a-4 c show that tracking errors of a pilot and a follower are limited in time convergence under the action of the control algorithm, fig. 5 shows the approximation error of a dynamics uncertain term, and verifies the effectiveness of RBFNN approximation.
3. Formation control simulation experiment based on experience
Under the control of an empirical formation control algorithm, the tracking error of the AUH formation is shown in fig. 6 a-6 c, the path tracking of the AUH is shown in fig. 7, the tracking error can be converged in a limited time by the graph, the AUH formation can effectively track a parameterized path, and the effectiveness of the control algorithm is verified.
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 (8)
1. An AUH formation cooperative control method under a finite time frame is characterized by comprising the following steps:
(1) Constructing a navigator-AUH dynamics model and a parameterized reference path;
(2) Introducing a parameterized path when designing the track tracking control rate of a navigator, estimating dynamics lumped uncertainty by using a limited-time state dilation observer, and ensuring that an observation error converges in limited time;
(3) Introducing a finite time preset performance control method into the control rate of the follower;
(4) Approximating the dynamic uncertainty using RBFNN in the control rate of the follower;
(5) And (3) designing an experience-based formation configuration maintenance control rate, and realizing accurate tracking of a pilot by a follower to maintain the formation configuration.
2. The method of cooperative control of AUH formation in a finite time frame according to claim 1, wherein in step (1), the dynamics model of pilot-AUH is expressed as:
in χ 0 ＝M -1 [-C(v 0 )v 0 -D(v 0 )v 0 -Δ(η 0 ，v 0 )]Representing the lumped uncertainty; j (eta) 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 i ∈R 6 Representing a control input;representing displacement and heading bias angle in world coordinate system, wherein x is i ，y i ，z i Coordinate values representing the x-axis, y-axis and z-axis of AUH in the world coordinate system, respectively,/->θ i ，ψ i Respectively representing the roll angle, pitch angle and yaw angle of the AUH in a 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 a body coordinate system, where u i ，υ i ，w i Representing the speed of the AUH along the x, y and z axes, p, respectively, in a volumetric coordinate system i ，q i ，r i Respectively representing the rolling angular velocity, the pitch angle velocity and the yaw angular velocity of the AUH in a body coordinate system; m represents an inertial matrix containing additional mass; subscript i indicates the ith AUH agent,>wherein 0 represents a navigator-AUH, 1, 2..n represents a follower-AUH, respectively; />Representing eta 0 First derivative of time, +.>Representing v 0 The first derivative with respect to time.
3. The cooperative control method for AUH formation under a finite time frame according to claim 1, wherein in step (1), the parameterized reference path is expressed as:
wherein x is ro (σ)，y r0 (σ)，z ro (sigma) represents reference coordinate values of the parameterized reference path in the x-axis, y-axis and z-axis of the world coordinate system, respectively;θ r0 (σ)，ψ r0 (sigma) represents the reference roll, pitch and yaw angles, respectively, of the parameterized path in the world coordinate system; σ (t) is a parameter variable of the path.
4. The cooperative control method of AUH formation under a finite time frame according to claim 2, wherein in step (2), the finite time state dilation observer is designed to
In the formula, the function sig () is defined as sig α (m)＝sign(m)|m| α WhereinAs a sign function, m is the observer gain, beta 1 E (0, 1) is the adjustment parameter, < ->And->Respectively represent eta 0 、v 0 And χ (x) 0 Estimated value of ∈10->And->Respectively indicate->And->First derivative of>Representing eta 0 Is calculated as +.>
5. The cooperative control method for AUH formation under a finite time frame according to claim 4, wherein in the step (2), the design process of the trace tracking control rate of the pilot is as follows:
tracking error of the pilot is expressed as
z 1，0 ＝η 0 -η r，0 (σ)
Its derivative is calculated as
In the method, in the process of the invention,for ideal path parameter update rate, p is externally introduced path update control variable, satisfying the relation
Selecting v 0 Virtual control rate alpha as virtual control amount 0 Designed as
Wherein K is 1，0 Determining a gain diagonal matrix for positive;
update rate of path parameter control variablesDesigned as
Wherein k is p >0 is the gain to be designed;
error variable z 2，0 Calculated as
z 2，0 ＝v 0 -α 0
Its first derivative is calculated as
The parameterized track tracking control rate of the navigator is designed as follows
Wherein K is 2，0 The gain diagonal matrix is determined for positive.
6. The cooperative control method for AUH formation under a finite time frame according to claim 1, wherein the step (3) specifically comprises:
the reference tracking trace of the ith AUH is expressed as
In the method, in the process of the invention,a relative position vector for determining a formation configuration;
the tracking error is calculated as
e 1，i ＝η i -η r，i ＝[e 1，i1 ，...，e 1，i6 ] T
Under the performance preset control framework, the error conversion relation is described as
e 1，ij ＝h ij (t)G ij (z 1，ij )
Wherein G is ij As an error transfer function, z 1，ij To convert errors
h ij (t) is a finite time performance function, the constraint error converges in a finite time, the finite time performance function is designed as
Wherein T is 2，i For a preset time, h ij (0)>1 and h ij (∞)>0 is a design parameter for limiting overshoot and steady state error, respectively;
conversion error z 1，ij Calculated as
7. The cooperative control method for AUH formation under a finite time frame according to claim 1, wherein the step (4) specifically comprises:
derivative of conversion errorCalculated as
Wherein z is 1，i ＝[z 1，i1 ，...，z 1，i6 ] T ，Φ i ＝diag[c i1 ，...，c i6 ]，Ξ i ＝diag[g i1 ，...，g i6 ]Wherein c ij And g ij The definition is as follows
Selecting v i As a virtual control variable, the virtual control rate alpha i Designed as
Defining an error variable z 2，i ＝v i -α i Its derivative is calculated as
Let F i (γ i )＝M -1 [C(v i )v i +D(v i )v i +Δ(η i ，v i )]＝[f i1 (γ i )，...，f i6 (γ i )] T Approximation of the dynamic set total uncertainty term using RBFNN;
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 W i *T Estimated value of ∈10->
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.
8. The cooperative control method for AUH formation under a finite time frame according to claim 7, wherein the step (5) specifically comprises:
input of RBFNNIs a periodic signalRegression sub-vector S p (x) Is continuously active, the exact approximation of the dynamics uncertainty term f (x) is made by +.>Realization of
In the method, in the process of the invention,for empirical values obtained by learning
Wherein T is i ＝inf{z 1，0 (t)≤ι 1 ，e 1，i (t)≤ι 2 -indicating the moment when the auss formation enters the steady-state phase of the reference trajectory of the tracking cycle;
the formation configuration maintenance control rate based on experience is designed as
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