AuH formation cooperative control method under a limited time framework

Abstract

The application discloses an AUH formation cooperative control method under a limited time framework, which comprises the following steps: (1) constructing a dynamic model of a leader-AUH and a parameterized path; (2) introducing the parameterized path in the design of a trajectory tracking control rate of the leader, and using a limited time state expansion observer to estimate dynamic lumped uncertainty, so as to ensure that an observation error converges in a limited time; (3) introducing a limited time preset performance control method into a control rate of a follower; (4) using a RBFNN to approximate dynamic uncertainty in the control rate of the follower; and (5) designing an experience-based formation configuration maintaining control rate, and realizing accurate tracking of the follower to the leader to maintain the formation configuration. According to the application, the leader can accurately track the parameterized path, the follower can accurately track the leader to maintain the formation configuration, and the control performance of the system is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of underwater helicopter control, and particularly relates to an AUH formation cooperative control method under a limited time framework. BACKGROUND

[0002] In recent years, autonomous underwater vehicles (AUVs) have attracted extensive attention from researchers due to their outstanding advantages in application fields such as pipeline detection, military defense and ocean observation. A new type of AUV, called autonomous underwater helicopter (AUH), is more suitable for the above underwater tasks due to its special structure. Meanwhile, in some special cases, multiple AUVs need to track a given trajectory while maintaining a formation configuration, so the formation control problem of AUVs has become a research hotspot.

[0003] The complexity of AUV formation control comes from multiple aspects, including that the AUV has complex unknown nonlinear dynamics, it is difficult for tracking errors to converge quickly due to the complexity of the underwater environment, etc. Existing research has proposed some effective solutions to the above problems, radial basis function neural networks (RBFNNs) are widely used to approximate the uncertain terms of the system dynamics, state expansion observers are used to estimate the dynamic uncertainties, and preset performance control methods are used in the control of AUVs to speed up the convergence of errors, etc.

[0004] A kind of underactuated AUV formation trajectory tracking control method based on distributed model predictive control is disclosed in Chinese patent document with publication number CN113821028A, which uses a radial basis function neural network to approximate the uncertain part of the system equation, combines the minimum learning parameter method, and reduces the computational complexity.

[0005] Chinese patent document with publication number CN113009826A discloses an AUV preset performance trajectory tracking control method based on a new error transformation method, which uses an improved performance function and a new error transformation method to make the AUV trajectory tracking error converge within a specified time.

[0006] The above scheme fully studies the use of various strategies to control the AUV to accurately track the reference trajectory, however, these trajectory tracking methods only consider the spatial dimension and do not consider the time dimension, and the motion speed of the AUV when controlling the path tracking has not been controlled. At the same time, when the state expansion observer estimates the dynamic uncertainty, it cannot guarantee that the observation error converges in a finite time, and similarly, the preset performance control method used in the prior art can accelerate the convergence speed of the tracking error, but cannot set the convergence time in advance. In addition, the existing research fully utilizes the global approximation ability of the RBFNN, but ignores the local learning of the RBFNN. SUMMARY

[0007] The application provides an AUH formation cooperative control method in a finite time framework, which can realize accurate tracking of a parameterized path by a leader, and at the same time, realize accurate tracking of the leader by a follower to maintain the formation configuration and improve the control performance of the system.

[0008] An AUH formation cooperative control method in a finite time framework, characterized in that it comprises:

[0009] (1) constructing a dynamic model of the leader-AUH and a parameterized reference path;

[0010] (2) introducing the parameterized path when designing the trajectory tracking control rate of the leader, and using a finite time state expansion observer to estimate the dynamic lumped uncertainty, so as to guarantee that the observation error converges in a finite time;

[0011] (3) introducing a finite time preset performance control method into the control rate of the follower;

[0012] (4) using an RBFNN to approximate the dynamic uncertainty in the control rate of the follower;

[0013] (5) designing an experience-based formation configuration maintenance control rate to realize accurate tracking of the leader by the follower to maintain the formation configuration.

[0014] In step (1), the dynamic model of the leader-AUH is represented as:

[0015]

[0016] In the formula, χ0=M -1 [-C(ν0)ν0-D(ν0)ν0-Δ(η0,ν0)] represents the lumped uncertainty; J(η i ) represents the coordinate conversion matrix between the world coordinate system and the body coordinate system, C(v i ) represents the Coriolis force and centripetal force matrix with uncertainty, D(v i ) represents the hydrodynamic damping matrix with uncertainty, and Δ(η i,ν i ) represents the un-modeled dynamics of the system, τ i ∈R 6 represents the control input; represents the displacement and the yaw angle in the world coordinate system, where x i ,y i ,z i represent the coordinate values of the AUH in the world coordinate system x-axis, y-axis and z-axis, respectively, θ i ,ψ i represent the roll angle, pitch angle and yaw angle of the AUH in the world coordinate system, respectively; ν i =[u i ,υ i ,w i ,p i ,q i ,r i ] T represents the linear velocity and angular velocity in the body coordinate system, where u i ,υ i ,w i represent the velocities of the AUH in the body coordinate system along the x-axis, y-axis and z-axis, respectively, p i ,q i ,r i represent the roll angular velocity, pitch angular velocity and yaw angular velocity of the AUH in the body coordinate system, respectively; M represents the inertia matrix containing the additional mass; subscript i represents the i-th AUH agent, where 0 represents the leader-AUH, and 1, 2,..., N represent the follower-AUHs, respectively; represents the first-order derivative of η0 with respect to time, represents the first-order derivative of v0 with respect to time.

[0017] In step (1), the parameterized reference path is represented as:

[0018]

[0019] where x ro (σ), y r0 (σ), z ro (σ) represent the reference coordinate values of the parameterized reference path in the world coordinate system x-axis, y-axis and z-axis, respectively; θ r0 (σ), ψ r0 (σ) represent the reference roll angle, pitch angle and yaw angle of the parameterized path in the world coordinate system, respectively; σ(t) is the parameter variable of the path.

[0020] In step (2), the finite-time state extended observer is designed as

[0021]

[0022] where the function sig() is defined as sig α (m) = sign(m) |m| α where is a sign function. m is the observer gain, β11∈(0, 1) is a tuning parameter, and denote the estimates of η0, v0and χ0, respectively, and denote the first order derivatives of and , respectively, denotes the estimation error of η0, which is calculated as

[0023] The design process of the trajectory tracking control rate of the leader is as follows:

[0024] The tracking error of the leader is denoted as

[0025] z 1,0 = η0- η r,0 (σ)

[0026] The derivative is calculated as

[0027]

[0028] where is the ideal path parameter update rate, p is an externally introduced path update control variable, satisfying the relationship

[0029] The v0is selected as the virtual control variable, and the virtual control rate α0is designed as

[0030]

[0031] where K 1,0 is a positive definite gain diagonal matrix;

[0032] The update rate of the path parameter control variable is designed as

[0033]

[0034] where k p > 0 is a gain to be designed;

[0035] The error variable z 2,0 is calculated as

[0036] z 2,0 = v0- α0

[0037] Its first derivative is calculated as follows

[0038]

[0039] The navigator's parameterized trajectory tracking control rate is designed to be

[0040]

[0041] In the formula, K 2,0 It is a positive definite gain diagonal matrix.

[0042] Step (3) specifically involves:

[0043] The reference tracking trajectory of the i-th AUH is represented as

[0044]

[0045] In the formula, The relative position vectors that determine the formation configuration;

[0046] Tracking error is calculated as follows

[0047] e 1,i =η i -η r,i =[e 1,i1 ,...,e 1,i6 ] T

[0048] Under the performance preset control framework, the error transformation relationship is described as follows:

[0049] e 1,ij =h ij (t)G ij (z 1,ij )

[0050] In the formula, G ij Let z be the error transformation function. 1,ij Conversion error

[0051]

[0052] h ij (t) is a finite-time performance function, constrained to converge in finite time. The finite-time performance function is designed as follows:

[0053]

[0054] In the formula, T 2,i h is the preset time. ij (0) > 1 and h ij (∞)v0 are design parameters used to limit overshoot and steady-state error, respectively;

[0055] conversion error z 1,ij is calculated as

[0056]

[0057] Step (4) is specifically:

[0058] derivative of conversion error is calculated as

[0059]

[0060] where z 1,i = [z 1,i1 ,...,z 1,i6 ] T , Φ i = diag[c i1 ,...,c i6 ], Ξ i = diag[g i1 ,...,g i6 ], where c ij and g ij are defined as follows

[0061]

[0062] ν i is selected as a virtual control variable, then the virtual control rate α i is designed as

[0063]

[0064] Define the error variable z 2,i = ν i - α i , and its derivative is calculated as

[0065]

[0066] 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 is the dynamic lumped uncertainty term, which is approximated using RBFNN;

[0067]

[0068] wherein,

[0069] The formation keeping control rate τ of the follower i is designed as

[0070]

[0071] wherein, is an estimated value of

[0072] The update rate of the RBFNN weight coefficient is designed as

[0073]

[0074] wherein, Λ 1,ij > 0 is a gain matrix to be designed, k W,ij is a normal number, -Λ 1,ij S j (γ i )z 2,ij is an adaptive term, is a cooperative term.

[0075] Step (5) is specifically:

[0076] The input of the RBFNN is a periodic signal, and the regression sub-vector S p (x) is continuously activated, and the accurate approximation of the dynamic uncertain term f(x) is realized by

[0077]

[0078] wherein, is an experienced value obtained by learning

[0079]

[0080] wherein, T i = inf{z 1,0 (t)≤ι1,e 1,i (t)≤l2} represents the time when the AUHs formation enters the steady-state stage of the tracking periodic reference trajectory;

[0081] The formation keeping control rate based on experience is designed as

[0082]

[0083] ​Compared with the prior art, the present application has the following beneficial effects:

[0084] 1、The present application introduces a parameterized path in the trajectory tracking control method of the leader, which realizes independent control of the tracking speed while ensuring accurate tracking of the reference path, further, uses a finite-time state expansion observer to estimate the lumped uncertainty and ensures that the observation error converges in a finite time.

[0085] 2、The control of the follower is realized in the framework of leader-follower formation, so the tracking speed control of the follower will be realized through the fixed formation configuration. At the same time, the RBFNN is used to approximate the dynamic uncertainty in the control rate of the follower, the finite-time preset performance control method is introduced into the control rate, and the error is ensured to converge in a fixed time. In addition, when the AUHs track the periodic reference trajectory, the dynamic uncertainty will be learned by using the deterministic learning method, and the experience value obtained by learning will be used to build an experience-based cooperative formation controller. BRIEF DESCRIPTION OF DRAWINGS

[0086] Figure 1 It is a flow chart of the AUH formation cooperative control method under the finite-time framework of the present application;

[0087] Figure 2 It is an AUH communication topology structure schematic diagram in the embodiment of the present application;

[0088] Figure 3 It is a control path tracking speed schematic diagram of the parameterized path method in the embodiment of the present application;

[0089] Figure 4a It is the surge tracking error under the action of the adaptive-based control algorithm in the embodiment of the present application;

[0090] Figure 4b It is the sway tracking error under the action of the adaptive-based control algorithm in the embodiment of the present application;

[0091] Figure 4c It is the yaw angle tracking error under the action of the adaptive-based control algorithm in the embodiment of the present application;

[0092] Figure 5 It is the radial basis function neural network approximation error in the embodiment of the present application;

[0093] Figure 6a It is the surge tracking error under the action of the experience-based control algorithm in the embodiment of the present application;

[0094] Figure 6b It is the sway tracking error under the action of the experience-based control algorithm in the embodiment of the present application;

[0095] Figure 6c This refers to the yaw angle tracking error under the action of the experience-based control algorithm in this embodiment of the invention.

[0096] Figure 7 This is a schematic diagram of AUH formation path tracking in an embodiment of the present invention. Detailed Implementation

[0097] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be noted that the embodiments described below are intended to facilitate the understanding of the present invention and do not constitute any limitation thereof.

[0098] The research object of this invention is a multi-agent system with nonlinear uncertain dynamics, consisting of N+1 underwater helicopters (AUHs). The dynamic model of the system is expressed as follows:

[0099]

[0100] In the formula, the subscript i represents the i-th intelligent agent. Where 0 represents the leader (AUH), and 1, 2, ..., N represent the followers (AUHs). ν represents the displacement and heading angle in the world coordinate system. i =[u i ,υ i ,w i ,p i ,q i ,r i ] T Represents the linear and angular velocities in body coordinates, M represents the inertia matrix including the added mass, and J(η) represents the linear and angular velocities in body coordinates. i C(ν) represents the coordinate transformation matrix between the world coordinate system and the volume coordinate system. i D(v) represents the uncertain Coriolis and centripetal force matrices, where v is the variable. i ) represents the hydrodynamic damping matrix with uncertainty, Δ(η) i ,v i ) represents the unmodeled dynamics of the system, τ i ∈R 6 This indicates a control input.

[0101] Definition diagram In the formula, This represents the node set. Let b represent the set of adjacent edges, where vertex b is the vertex b. i The neighbor set of node b i ) is defined as This represents the weighted adjacency matrix. If (b) i ,b k If )∈ε, then a ik >0, otherwise a ik =0. The Laplacian operator matrix. Defined as In addition, if Then define It is an undirected graph, otherwise Let's consider a directed graph. In a directed graph, if there exist (b1, b2), ..., (b...), then... k-1 ,b k If a sequence of edges is of the form b1, then it is called a sequence of edges from vertex b1 to vertex b2. k A directed path, and vertex b k Vertex b1 is reachable. In an undirected graph, (b1, b2),...,(b...) k-1 ,b k The edge sequence in the form of ) represents the path from vertex b1 to vertex b. k An undirected graph is a graph where there is no undirected path between every pair of nodes. Furthermore, an undirected graph is connected if there is an undirected path between every pair of nodes. In a directed graph, a directed edge is represented as (b... i ,b k )∈ε, where b i Called the parent vertex, b k A child vertex is called a child vertex. A directed tree is a directed graph in which each node has only one parent node, there is only one node called the root node that has no parent node, and all other nodes are reachable from the root node. A directed graph contains a directed spanning tree if and only if at least one node in the directed graph is reachable from every other node.

[0102] The communication topology between AUH formations is described using graph theory, where the leader AUH is represented by 0, and the follower AUHs are represented by 1, ..., n. The communication topology between followers is an undirected graph. Description. The communication topology of the entire AUHs formation can be represented by a directed graph. Establish, among which, Communication between navigators and followers is unidirectional, meaning that information transmission can only be initiated by the navigator. Defined as the weighted adjacency matrix of the leader, where the subscripts are... c i >0 indicates that the i-th follower is connected to the leader; otherwise, c i= 0.

[0103] In this invention, RBFNN will be used to approximate an unknown nonlinear function f(x): R m → R.

[0104] f(x) = W *T S(x) + ε

[0105] where, is the optimal weight coefficient vector, and ε is the inherent approximation error, satisfying where, is an unknown small constant, and S(x) = s q (x)] T ∈ R q is the basis function vector, where q is the number of nodes of the neural network, and s i (x) is the Gaussian activation function.

[0106]

[0107] where, μ i and σ represent the center and basis width of the i-th node, respectively.

[0108] Consider a continuous periodic signal x(t) that is confined in a certain bounded set Ω x Then for a radial basis neural network W T S(x) with uniformly distributed centers and basis width that can cover the region Ω x , the corresponding regression sub-vector S p (x) is persistently exciting.

[0109] For a local RBFNN with persistently exciting regression sub-vector S p (x), the following conclusions are true

[0110] (1) The weight estimate value of the local RNFBB will converge to a small neighborhood of the optimal value .

[0111] (2) The exact approximation of the unknown nonlinear function f(x) can be achieved by .

[0112]

[0113] where, is the experience value obtained through learning, and ε E is the error of using experience approximation

[0114]

[0115] The present application satisfies the following three assumptions:

[0116] Assumption One: The undirected graph is connected.

[0117] Assumption Two: The adjacency weight matrix of the leader

[0118] Assumption Three: The parameterized trajectory η r,0 and its derivative are periodic and bounded. At the same time, and are bounded.

[0119] The core of the present application is realized in two steps. First, the trajectory tracking control law of the leader is designed to achieve accurate tracking of the parameterized path by the leader while ensuring that the tracking speed can be independently designed. Second, the leader tracking control law of the follower is designed to achieve accurate tracking of the leader by the follower to maintain the formation configuration. On this basis, the knowledge obtained in the adaptive process is used to construct an experience-based formation control law to improve control performance.

[0120] Specifically, as shown in Figure 1 , an AUH formation cooperative control method under a finite time framework includes the following steps:

[0121] Step 1, constructing the dynamics model of the leader-AUH and the parameterized path.

[0122] The dynamics model of the leader-AUH can be represented as

[0123]

[0124] where χ0=M -1 [-C(v0)v0-D(v0)v0-Δ(η0,v0)] represents the lumped uncertainty.

[0125] The parameterized path tracked by the leader-AUH is represented as

[0126]

[0127] where σ(t) is the parameter variable of the path.

[0128] Step 2, designing the trajectory tracking control law of the leader, and using a finite time state expanding observer to estimate the dynamics lumped uncertainty.

[0129] The finite time state expanding observer is designed as

[0130]

[0131] where m is the observer gain, β1∈(0, 1) is the tuning parameter, and denote the estimates of η0, v0and χ0, respectively.

[0132] The tracking error of the leader is denoted as

[0133] z 1,0 = η0- η r,0 (σ)

[0134] The derivative of z is calculated as

[0135]

[0136] where is the ideal path parameter update rate, p is the externally introduced path update control variable, satisfying the relationship

[0137] The virtual control variable v0is chosen, and the virtual control rate α0is designed as

[0138]

[0139] where K 1,0 is a positive definite gain diagonal matrix.

[0140] The update rate of the path parameter control variable p is designed as

[0141]

[0142] where k p > 0 is the gain to be designed.

[0143] The error variable z 2,0 is calculated as

[0144] z 2,0 = v0- α0

[0145] The first-order derivative of z is calculated as

[0146]

[0147] The parameterized trajectory tracking control rate of the leader is designed as

[0148]

[0149] where K 2,0 is a positive definite gain diagonal matrix.

[0150] Step 3: Introduce the finite-time preset performance control method into the control rate of the follower.

[0151] The reference tracking trajectory of the ith AUH is denoted as

[0152]

[0153] where, is the relative position vector of the platoon configuration.

[0154] The tracking error can be calculated as

[0155] e 1,i = η i - η r,i = [e 1,i1 ,...,e 1,i6 ] T

[0156] Under the performance pre-set control framework, the error conversion relationship can be described as

[0157] e 1,ij = h ij (t)G ij (z 1,ij )

[0158] where, G ij is the error conversion function, z 1,ij is the conversion error

[0159]

[0160] h ij (t) is a finite-time performance function, which limits the error to converge in a finite time. In this patent, the finite-time performance function is designed as

[0161]

[0162] where, T 2,i is the preset time, h ij (0) > 1 and h ij (∞) > 0 are design parameters used to limit the overshoot and steady-state error, respectively.

[0163] The conversion error z 1,ij is calculated as

[0164]

[0165] Step 4: Use RBFNN to approximate the dynamics uncertainty in the control rate of the follower.

[0166] The derivative of the conversion error z is calculated as

[0167]

[0168] where, z1,i = [z 1,i1 ,...,z 1,i6 ] T , Φ i = diag[c i1 ,...,c i6 ], Ξ i = diag[g i1 ,...,g i6 ], where c ij and g ij are defined as follows

[0169]

[0170] The virtual control variable v i is chosen as the virtual control variable, then the virtual control rate a i is designed as

[0171]

[0172] The error variable z 2,i = v i - a i is defined, and its derivative is calculated as

[0173]

[0174] 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 be the dynamic lumped uncertainty term, which is approximated by using RBFNN;

[0175]

[0176] where,

[0177] where, is the estimated value of

[0178] The update rate of the RBFNN weight coefficient is designed as

[0179] ​

[0180] wherein, Λ 1,ij is the gain matrix to be designed, k W,ij is a constant, -Λ 1,ij S j (x i )z 2,ij is the adaptive term, is the cooperative term.

[0181] Step 5, design the experience-based formation configuration keeping control rate.

[0182] The input of RBFNN is a periodic signal, the regression sub-vector S p (x) is continuously active, and the accurate approximation of the dynamic uncertain term f(x) is realized by

[0183]

[0184] wherein, is the experience value obtained by learning

[0185]

[0186] wherein, T i = inf{z 1,0 (t)≤ι1,e 1,i (t)<ι2} represents the time when the AUHs formation enters the steady state stage of the tracking periodic reference trajectory;

[0187] The experience-based formation configuration keeping control rate is designed as

[0188]

[0189] To verify the effectiveness of the present application, the following simulation experiment is carried out on the AUHs formation system composed of 5 AUHs.

[0190] The formation configuration vector is The unmodeled dynamics is Δ(η i ,v i ) = [Δ1,...,Δ6] T wherein, The communication topology structure of the AUH formation is shown in Figure 2 , and the parameterized path and the initial state of the AUH are shown in Table 1.

[0191] Table 1 Parameterized path and initial state of AUH

[0192] ​

[0193] 1. Simulation experiment of path tracking speed control

[0194] A numerical simulation experiment is conducted to verify the effectiveness of the parameterized path tracking control law on the path tracking speed control of the leader.

[0195] The control gain is designed as 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 extended state observer are designed as m = 2, β1= 0.8. The parameterized path is given in Table 1, and the ideal path parameter update rate is initially set to 1 and stepped to 2 after 15 seconds.

[0196] The simulation results are shown in Figure 3 , where (a) shows that under the action of the control law Figure 3 , the path parameter update rate quickly converges to the desired value . Figure 3 (b) shows that the tracking speed of the leader can be independently designed by specifying .

[0197] 2. Simulation experiment of formation control based on adaptive method

[0198] The simulation control objectives of the AUHs formation are specified as follows

[0199] (1) The steady-state error of path tracking is not more than 0.02.

[0200] (2) The steady-state error of tracking speed is controlled within 0.1.

[0201] (3) The maximum convergence time of the entire system is not more than 20s.

[0202] In order to achieve the above objectives, the parameter values of the observer and the control law are designed as shown in Table 2.

[0203] Table 2 Parameter values of the observer and the control law

[0204]

[0205] The radial basis function neural network with 21 nodes is used to approximate the dynamic uncertainty, and the nodes are evenly distributed in the interval [-1, 1] with a basis width of 2.

[0206] First, the effectiveness of the formation control algorithm based on the adaptive method is verified, and the simulation results are shown in Figure 4, Figure 5 .Figures 4a to 4c It is shown that the tracking errors of the leader and the follower converge in finite time under the control of the control algorithm, Figure 5 The approximation error of the dynamic uncertainty is shown, and the effectiveness of the RBFNN approximation is verified.

[0207] 3. Experience-based formation control simulation experiment

[0208] Under the control of the experience-based formation control algorithm, the tracking error of the AUH formation is as shown in Figures 6a to 6c The path tracking of the AUH is as shown in Figure 7 The tracking error converges in finite time, and the AUH formation can effectively track the parameterized path, which verifies the effectiveness of the control algorithm.

[0209] The above-described embodiments have described the technical solutions and beneficial effects of the present application in detail. It should be understood that the above-described is only a specific embodiment of the present application, and is not used to limit the present application. Any modification, supplement and equivalent replacement made within the principle range of the present application should be included in the protection range of the present application.

Claims

1. A method for AUH formation cooperative control under a limited time frame, characterized in that, Comprise: (1) constructing the dynamics model and parameterized reference path of the leader-AUH; (2) introducing the parameterized path in the design of the trajectory tracking control law of the leader, and using the finite time state extended observer to estimate the dynamics lumped uncertainty, so as to ensure that the observation error converges in finite time; (3) introducing the finite time preset performance control method into the control law of the follower; (4) using RBFNN to approximate the dynamics uncertainty in the control law of the follower; (5) designing the experience-based formation configuration keeping control law to realize the accurate tracking of the follower to the leader to keep the formation configuration; Specifically: Inputs to the RBFNN The regression sub-vector S is periodic p (x) is persistently active, an exact approximation of the dynamics-uncertain term f(x) by Achieved In the formula, Experience value acquired through learning In the formula, T i = inf{z 1,0 (t)≤ι1,e 1,i (t)≤ι2} represents the time when the AUHs platoon enters the steady-state stage of the tracking period reference trajectory. The experience-based formation configuration keeping control law is designed as 2. The AUH formation cooperative control method under a limited time framework according to claim 1, characterized in that, In step (1), the dynamics model of the leader-AUH is represented as: where χ0= M -1 [-C(ν0)ν0-D(ν0)ν0-Δ(η0,ν0)] represents the lumped uncertainty; J(η i ) represents the coordinate transformation matrix between the world coordinate system and the body coordinate system, C(ν i ) represents the Coriolis and centripetal force matrix with uncertainty, D(ν i ) represents the hydrodynamic damping matrix with uncertainty, Δ(η i ,ν i ) represents the unmodeled dynamics of the system, τ i ∈R 6 represents the control input; represents the displacement and the yaw angle in the world coordinate system, where x i , y i , z i represent the coordinate values of the AUH in the world coordinate system x-axis, y-axis and z-axis, respectively, θ i , ψ i represent the roll angle, pitch angle and yaw angle of the AUH in the world coordinate system, respectively; ν i = [u i , υ i , w i , p i , q i , r i ] T represents the linear velocity and angular velocity in the body coordinate system, where u i , υ i , w i represent the velocities of the AUH along the x-axis, y-axis and z-axis in the body coordinate system, respectively, p i , q i , r i represent the roll angular velocity, pitch angular velocity and yaw angular velocity of the AUH in the body coordinate system, respectively; M represents the inertia matrix including the added mass; the subscript i represents the i-th AUH intelligent agent, where 0 represents the leader-AUH, and 1, 2, …, N represent the follower-AUHs, respectively; represents the first-order derivative of η0with respect to time, represents the first-order derivative of ν0with respect to time.

3. The AUH formation cooperative control method under a limited time framework according to claim 1, characterized in that, In step (1), the parameterized reference path is represented as: where x ro (σ),y r0 (σ),z ro (σ) respectively represent the reference coordinate values of the parameterized reference path on the x-axis, y-axis and z-axis of the world coordinate system; θ r0 (σ),ψ r0 (σ) respectively represent the reference roll angle, pitch angle and yaw angle of the parameterized path under the world coordinate system; σ(t) is the parameter variable of the path.

4. The AUH formation cooperative control method under a limited time framework according to claim 2, characterized in that, In step (2), the finite time state extended observer is designed as where the function sig() is defined as sig α (m) = sign(m) |m| α where is a sign function, m is an observer gain, β1∈(0,1) is a tuning parameter, and denote the estimates of η0, v0, and χ0, respectively, and denote the first order derivatives of and respectively, denotes the estimation error of η0, computed as 5. The AUH formation cooperative control method under the limited time framework according to claim 4, characterized in that, In step (2), the design process of the trajectory tracking control law of the leader is as follows: The tracking error of the leader is represented as z 1,0 = η0- η r,0 (σ) The derivative calculation is wherein is the ideal path parameter update rate, p is an externally introduced path update control variable, satisfying the relationship The virtual control quantity v0 is selected, and the virtual control law a0 is designed as In the formula, K 1,0 It is a positive definite gain diagonal matrix; Updating rate of path parameter control variable is designed to where k > 0 is the gain to be designed. p > 0 is the gain to be designed. Error variable z 2,0 Computed as z 2,0 = v0- a0 The first order derivative calculation is The parameterized trajectory tracking control law of the leader is designed as where K 2,0 is a positive definite gain diagonal matrix.

6. The AUH formation cooperative control method under a limited time framework according to claim 1, characterized in that, Step (3) is specifically: The reference tracking trajectory of the i-th AUH is represented as In the formula, is the relative position vector of the platoon 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 relationship is described as e 1,ij = h ij (t) G ij (z 1,ij ) In the formula, G ij is an error conversion function, z 1,ij is a conversion error h ij (t) is a finite-time performance function that limits the error to converge in finite time, the finite-time performance function is designed as In the formula, T 2,i is a preset time, h ij (0) > 1 and h ij (∞) > 0 are design parameters respectively used to limit the overshoot and steady-state error; conversion error z 1,ij computed as 7. The AUH formation cooperative control method under a limited time framework according to claim 1, characterized in that, Step (4) is specifically: derivative of the conversion error computed as where z 1,i = [z 1,i1 ,…,z 1,i6 ] T , Φ i = diag[c i1 ,…,c i6 ], Ξ i = diag[g i1 ,…,g i6 ], where c ij and g ij are defined as follows Selecting v i is a virtual control variable, then the virtual control rate a i is designed as Define the error variable z 2,i = v i - a i whose derivative is calculated as Let F i (Υ i ) = M -1 [C(ν i )ν i + D(ν i )ν i + Δ(η i ,ν i )] = [f i1 (Υ i ),…,f i6 (Υ i )] T are the kinetic lumped uncertainties, which are approximated by RBFNNs. In the formulae, The control rate τ of the formation configuration of the followers is maintained i is designed to wherein is W i *T an estimate of the value of The update rate of the RBFNN weight coefficient is designed as In the formula, Λ 1,ij > 0 is a gain matrix to be designed, k W,ij is a constant, -Λ 1,ij S j (Υ i )z 2,ij is an adaptive term, is a cooperative term.

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