CN110262494B - Collaborative learning and formation control method for isomorphic multi-unmanned ship system - Google Patents

Abstract

The invention discloses a collaborative learning and formation control method for a homogeneous multi-unmanned boat system. The method proposes a distributed collaborative learning based on a communication connection topology map for a plurality of unmanned boat systems that are fully driven and have the same structure. A control method, which solves the problem of collision and connection keeping between isomorphic unmanned boats maintaining communication, including the following steps: establishing a dynamic model of the unmanned boat; designing a graph theory-based communication between unmanned boats maintaining communication error; design the error transfer function that meets the preset performance; design the virtual controller based on the dynamic surface control technology; design the weight update rate of the radial basis function (RBF) neural network; design the formation controller and the experience-based controller. The formation control method that satisfies connection retention and has collaborative learning proposed by the present invention can ensure that if two unmanned boats maintain communication at the initial moment, they will always keep a safe distance and within the range of communication connection at any time thereafter.

Description

A Collaborative Learning and Formation Control Method for Isomorphic Multi-UAV Systems

technical field

The invention relates to the field of formation control of unmanned boats, in particular to a collaborative learning and formation control method of a homogeneous multi-unmanned boat system.

Background technique

With the development of science and technology and the needs of society, maritime tasks require multiple unmanned boats to work at the same time, and multiple sailing and supply unmanned boats to provide different services. Therefore, multi-boat cooperation and control technology has been developed rapidly. At present, the application of multi-boat cooperation and control technology has involved many fields such as submarine uranium symbols, marine refueling, marine fishing, and military maritime exercises. Multi-boat cooperative control technology can not only complete complex tasks in complex environments, but also free people from some dangerous jobs. In addition, the multi-boat cooperation and control technology has the characteristics of working according to people's wishes, which can greatly reduce people's labor intensity and improve people's quality of life. In the near future, people's desire to find seabed resources will create a broader market for multi-vessel cooperation and control technology, and will also promote the faster development of multi-vessel cooperation and control technology.

Compared with a single unmanned boat, the multi-boat formation has the following advantages:

(1) Multi-boat formations perform tasks with better robustness, fault tolerance and system survivability. Even if one of the unmanned boats fails, it will not affect the overall mission;

(2) The multi-boat formation does not require a single unmanned boat to be equipped with high-performance sensor equipment, and replaces it with a group of low-cost unmanned boats, thereby reducing operating costs;

(3) The perception range of a single UAV is limited. The cooperative operation of multiple boats can expand the sensing area of the entire group, so specific search tasks can be completed quickly and efficiently.

Through the interaction of local information, multiple unmanned boats are more effective and more powerful than a single unmanned boat, which greatly expands the use range of autonomous unmanned boats and realizes tasks that a single unmanned boat cannot complete. Based on the above reasons, unmanned boat formations have wide application potential in both civilian and military fields. In addition, since the sensing range of each unmanned boat is limited, in order to ensure that each unmanned boat can sense the status information of its neighbors through sensors during the entire process of formation movement, each unmanned boat should also be considered. The maximum distance and azimuth angle constraints need to be met between the boat, its leader and its neighbors.

SUMMARY OF THE INVENTION

The purpose of the invention is to overcome the shortcomings and deficiencies in the prior art, and to provide a collaborative learning and formation control method for a homogeneous multi-UAV system. The method designs a formation controller for the homogeneous multi-UAV with uncertain models, It can not only ensure that in the distributed leader-follower formation structure, each unmanned boat can always obtain the information of its leader and neighbors, and at the same time guarantee the transient performance of the formation error.

The purpose of the present invention can be realized by following technical scheme:

A collaborative learning and formation control method for a homogeneous multi-unmanned boat system, the method comprises the following steps:

Step (1), establish a plurality of dynamic models of unmanned boats with the same structure;

Step (2), design tracking error constraints according to the safety distance constraints and communication connection range constraints between adjacent unmanned boats;

Step (3), in order to meet the preset performance requirements, design a tracking error conversion function, and convert the tracking error to obtain the converted conversion error;

Step (4), applying the dynamic surface control technology to design the virtual controller: combining the dynamic surface control technology and the step-by-step pushback controller design technology to avoid the derivation of the virtual controller, thereby avoiding that the input of the controller contains the acceleration information of the neighbor;

Step (5), design the weight update rate of the RBF neural network: apply the RBF neural network to estimate the damping term in the unmanned boat system;

Step (6), designing a state feedback tracking controller: applying the Lyapunov stability theory and combining the step-by-step backward design method to construct a stable tracking controller;

Step (7), utilize the stored knowledge, complete the knowledge utilization, and design an experience-based state feedback tracking controller;

来描述无人艇编队系统中各个体间的信息交互，

是有限非空集合，称为顶点集，集合

中的每个顶点对应有相同编号的跟随者；

是有限集合，称之为边集，每条边对应有相同编号且能互相通信的相邻无人艇，无向图

的邻接矩阵A＝(a_il)_(N)×(N)的元素a_il∈{0,1}，当无人艇i能够获取无人艇j的信息时，此时j称为尾部，i称为头部，a_il＝1，否则a_il＝0；In step (2): use an undirected graph

To describe the information interaction between the various entities in the UAV formation system,

is a finite non-empty set, called the vertex set, the set

Each vertex in corresponds to a follower with the same number;

is a finite set, called an edge set, each edge corresponds to adjacent UAVs with the same number and can communicate with each other, undirected graph

The element a _il ∈{0,1} of the adjacency matrix A=(a _il ) _(N)×(N) , when the unmanned boat i can obtain the information of the unmanned boat j, then j is called the tail, i is called the head, a _il = 1, otherwise a _il = 0;

来描述包含领航者在内的编队系统中各成员间的信息交互，

为虚拟领导者，虚拟领导与部分跟随者保持通信；邻接矩阵A₀＝diag[a₁₀,…,a_N0]^T的元素a_i0∈{0,1}，并且

Further use of expansion diagrams

to describe the information interaction among the members of the formation system including the navigator,

For the virtual leader, the virtual leader maintains communication with the partial followers; the adjacency matrix A ₀ =diag[a ₁₀ ,...,a _N0 ] element a _i0 ∈ {0,1} of ^T , and

为设计常数，G(0)为G(t)的初始值；认为每个无人艇的通信范围有限且最大为

如果满足

其中

i≠k，G_x(0)为G(t)在纵向上的初始值，G_y(0)为G(t)在横荡方向的初始值，则无人艇i与无人艇k之间具有通信，其中

因此定义每个邻居为：

增广邻居集为：

和

为纵向的设计常数，

和

为横荡方向的设计常数，

和

为航向角上的设计常数；Design a continuously differentiable monotone decreasing function vector G(t), G(t) satisfies the first-order and second-order derivables,

is a design constant, G(0) is the initial value of G(t); it is considered that the communication range of each UAV is limited and the maximum is

if satisfied

in

i≠k, G _x (0) is the initial value of G(t) in the longitudinal direction, G _y (0) is the initial value of G(t) in the sway direction, then the relationship between the unmanned boat i and the unmanned boat k communication between

So define each neighbor as:

The augmented neighbor set is:

and

is the longitudinal design constant,

and

is the design constant for the sway direction,

and

is the design constant on the heading angle;

The undirected communication topology diagram is used to represent the information interaction between multiple unmanned boats, so that when a group of unmanned boats with limited communication range follows the given leader trajectory in the form of leader-follower formation, each unmanned boat at the same time The human-vessel also needs to meet the constraints of distance and azimuth to ensure that each unmanned boat can detect the information of its neighbors and maintain connection with it; the error is defined as:

x_k表示第k个无人艇在大地坐标O_eX_eY_e下纵向的位置，y_k表示第k个无人艇在大地坐标O_eX_eY_e下横荡方向的位置，ψ_k为第k个无人艇的航向角，G_x(t)为纵向的衰减函数，G_y(t)为横荡方向的衰减函数，G_ψ(t)为航向角上的衰减函数；where e _i,1 =[e _ix,1 ,e _iy,1 ,e _iψ,1 ] ^T , e _i,1 is the vector summed after transforming the position difference between the UAV and all its neighbors, e _ix,1 is the component of e _i,1 in the longitudinal direction, e _iy,1 is the component of e _i,1 in the sway direction, e _iψ,1 is the component of e _i,1 in the heading angle, a _ik represents the i-th Whether the unmanned boat remains connected to the k-th unmanned boat, if the connection a _ik =1, otherwise a _ik =0; ξ _i,k =[ξ _ix,k ,ξ _iy,k ,ξ _iψ,k ] ^T , ξ _ix,k , ξ _iy,k , ξ _iψ,k are the components of ξ _i,k in the longitudinal direction, yaw direction, and heading angle direction, respectively,

x _k represents the longitudinal position of the k-th unmanned boat under the geodetic coordinates O _e X _e Y _e , y _k represents the position of the k-th unmanned boat in the sway direction under the geodetic coordinates O _e X _e Y _e , ψ _k is the heading angle of the k-th unmanned boat, G _x (t) is the attenuation function in the longitudinal direction, G _y (t) is the attenuation function in the sway direction, and G _ψ (t) is the attenuation function on the heading angle;

"ξ _i,k is the vector converted in the second step of the position difference between the i-th unmanned boat and the k-th unmanned boat".

Further, in step (1), the dynamic model of the i-th unmanned boat is:

N表示无人艇的总个数，(x_i,y_i)表示第i个无人艇在大地坐标O_eX_eY_e下的位置，x_i为第i个无人艇的纵向位置，y_i为第i个无人艇的横荡方向位置，ψ_i为第i个无人艇的航向角；u_i表示第i个无人艇的纵向速度，v_i表示第i个无人艇的横荡速度，r_i表示第i个无人艇的转向角速度；M表示无人艇的质量矩阵，

表示第i个无人艇在u、v、r方向上的加速度构成的向量，C(v_i)表示科氏力矩阵，其中v_i＝[u_i,v_i,r_i]^T为速度向量，D(v_i)表示阻尼矩阵，由于多艘无人艇具有相同结构，所以每艘无人艇具有相同的M矩阵；τ_i＝[τ_ui,τ_vi,τ_ri]^T为需要设计的控制器向量，τ_ui表示第i个无人艇纵向的推力，τ_vi表示第i个无人艇横荡方向的推力，τ_ri表示第i个无人艇转向的力矩；τ_ωi＝[τ_ωui,τ_ωvi,τ_ωri]^T为外界时变扰动，τ_ωui表示第i个无人艇在纵向方向受到的外部时变扰动，τ_ωvi表示第i个无人艇在横荡方向受到的外部时变扰动，τ_ωri表示第i个无人艇在转向角方向受到的外部时变扰动；矩阵M、C(v_i)、D(v_i)、J(η_i)的具体形式分别如下所示：The first three terms in the above formula are the kinematic equations of the system, where,

N represents the total number of unmanned boats, ( _xi , y _i ) represents the position of the ith unmanned boat under the geodetic coordinates O _e X _e Y _e , and _xi is the longitudinal position of the ith unmanned boat, y _i is the sway direction position of the ith unmanned boat, ψ _i is the heading angle of the ith unmanned boat; _ui represents the longitudinal speed of the ith unmanned boat, and vi represents the _ith unmanned boat s sway speed, ri represents the steering angular velocity of the _i -th unmanned boat; M represents the mass matrix of the unmanned boat,

Represents the vector formed by the acceleration of the i-th unmanned boat in the u, v, and r directions, C(vi ) represents the Coriolis force matrix, where v _i =[ _{u i} ,vi _{,r i ]} ^T is the velocity vector , D(v _i ) represents the damping matrix. Since multiple unmanned boats have the same structure, each unmanned boat has the same M matrix; τ _i =[τ _ui ,τ _vi ,τ _ri ] ^T is the required design Controller vector, τ _ui represents the longitudinal thrust of the ith unmanned boat, τ _vi represents the thrust of the ith unmanned boat in the sway direction, τ _ri represents the turning moment of the ith unmanned boat; τ _ωi = [τ _ωui ,τ _ωvi ,τ _ωri ] ^T is the external time-varying disturbance, τ _ωui represents the external time-varying disturbance received by the i-th unmanned boat in the longitudinal direction, and τ _ωvi represents the external time-varying disturbance received by the i-th unmanned boat in the yaw direction Time-varying disturbance, τ _ωri represents the external time-varying disturbance received by the i-th unmanned boat in the direction of the steering angle; the specific forms of the matrices M, C(vi), D(vi ₎ , and J(η _{i )} are respectively as follows: Show:

Among them, m ₁₁ , m ₂₂ , m ₂₃ , and m ₃₃ are constants, d ₁₁ (u _i ) is a function of u _i , d ₂₂ (vi , _{ri )} , d ₂₃ (vi , _{ri )} , d ₃₂ (vi , _ri ), d ₃₃ (vi , _{ri )} are functions of v _{i , ri} ; transform the kinetic equation into the following form:

τ′_i＝J(η_i)M^-1τ_i，τ′_ωi＝J(η_i)M^-1τ_ωi，

为旋转矩阵J(η_i)的导数，J^-1(η_i)为旋转矩阵J(η_i)的逆，M^-1为质量矩阵M的逆。where v′ _i =J(η _i )v _i ,

τ′ _i =J(η _i )M ^-1 τ _i , τ′ _ωi =J(η _i )M ^-1 τ _ωi ,

is the derivative of the rotation matrix J(η _i ), J ⁻¹ (η _i ) is the inverse of the rotation matrix J(η _i ), and M ⁻¹ is the inverse of the mass matrix M.

Further, in step (3), the design tracking error constraints are as follows:

e _ji(t)表示e_ji(t)的下界性能函数，

表示e_ji(t)的上界性能函数，

表示性能函数

的初始值，

表示性能函数

的稳态值，e _ji,0表示性能函数e _ji(t)的初始值，e _ji,∞表示性能函数e _ji(t)的稳态值，k_ji表示其收敛速度；因此误差跟踪转换函数设计为：where j=x, y, ψ,

e _ji (t) represents the lower bound performance function of e _ji (t),

represents the upper bound performance function of e _ji (t),

Represents a performance function

the initial value of ,

Represents a performance function

The steady state value of , e _ji,0 represents the initial value of the performance function e _ji (t), e _ji,∞ represents the steady state value of the performance function e _ji (t), and k _ji represents its convergence speed; therefore, the error tracking transfer function Designed to:

表示自然底数的z_ji,1次幂，

表示自然底数的-z_ji,1次幂，-γ_ji＜T_ji(z_ji,1,γ_ji)＜1,

当且仅当z_ji,1＝0时，T_ji(z_ji,1,γ_ji)＝0；得到如下转换误差：Among them, z _ji,1 represents the conversion error of the i-th unmanned boat,

Represents the natural base z _{ji, the power of 1} ,

Represents the -z _{ji, 1} power of the natural base, -γ _ji <T _ji (z _ji,1 ,γ _ji ) < 1,

T _ji (z _ji,1 ,γ _ji )=0 if and only if z _ji,1 =0; the following conversion error is obtained:

Further, in step (4), the filter error is defined as:

e _i,f =α _i,f -α _i

z _i,2 =v′ _i -α _i,f

e_i,f＝[e_ix,f,e_iy,f,e_iψ,f]^T为滤波误差向量，e_ix,f为e_i,f在纵向上的分量，e_iy,f为e_i,f在横荡方向上的分量，e_iψ,f为e_i,f在航向角上的分量；α_i＝[α_ix,α_iy,α_iψ]^T为虚拟控制输入向量，α_ix为α_i在纵向上的分量，α_iy为α_i在横荡方向上的分量，α_iψ为α_i在航向角上的分量；α_i,f＝[α_ix,f,α_iy,f,α_iψ,f]^T为滤波虚拟控制输入向量，α_ix,f表示α_ix的滤波虚拟控制，α_iy,f表示α_iy的滤波虚拟控制，α_iψ,f表示α_iψ的滤波虚拟控制；z_i,2＝[z_iu,2,z_iv,2,z_ir,2]^T为转换速度误差，z_iu,2为z_i,2在纵向上的分量，z_iv,2为z_i,2在横荡方向上的分量，z_ir,2为z_i,2在航向角上的分量；in

e _i,f =[e _ix,f ,e _iy,f ,e _iψ,f ] ^T is the filtering error vector, e _ix,f is the vertical component of e _i,f , e _iy,f is e _i, The component of _f in the sway direction, e _iψ,f is the component of e _i,f in the heading angle; α _i =[α _ix ,α _iy ,α _iψ ] ^T is the virtual control input vector, α _ix is α _i Component in the longitudinal direction, α _iy is the component of α _i in the sway direction, α _iψ is the component of α _i in the heading angle; α _i,f =[α _ix,f ,α _iy,f ,α _{iψ, f} ] ^T is the filtering virtual control input vector, α _ix,f represents the filtering virtual control of α _ix , α _iy,f represents the filtering virtual control of α _iy , α _iψ,f represents the filtering virtual control of α _{iψ ;} ＝[z _iu,2 ,z _iv,2 ,z _ir,2 ] ^T is the conversion speed error, z _{iu,2 is} the vertical component of zi,2, z _iv,2 is the sway of zi _,2 The component in the direction, z _ir,2 is the component of z _i,2 in the heading angle;

Design the virtual controller as:

j＝x,y,ψ，

为e _ij,1的导数，

为

的导数，

为

在纵向上的分量，

为

在横荡方向上的分量，

为

在航向角上的分量；where k _i,1 =diag[k _ix,1 ,kiy, ₁ ,k _iψ,1 ] are design parameters, k _ix,1 is the vertical component of k _i,1 , k _ix,1 is k _{i, 1} is the component in the sway direction, k _iψ,1 is the component of k _i,1 in the heading angle; G _i =diag[G _ix ,G _iy ,G _iψ ], G _ix is the longitudinal component of G _i , G _iy is the component of G _i in the sway direction, G _iψ is the component of G _i in the heading angle, k _i,k =diag[k _ix,k ,k _iy,k ,k _iψ,k ], k _ix,k is the component of _ki,k in the longitudinal direction, kiy, _k is the component of _ki,k in the sway direction, _kiψ,k is the component of ki _,k in the heading angle; θ _{i, 1} =diag[θ _ix,1 ,θ _iy,1 ,θ _iψ,1 ], θ _ix,1 is the component of θ _i,1 in the longitudinal direction, θ _iy,1 is the component of θ _i,1 in the yaw direction Component, θ _iψ,1 is the component of θ _i,1 on the heading angle; p _i,k =diag[pi _ix,k ,p _iy,k ,p _iψ,k ], p _ix,k is p _i,k Component in the longitudinal direction, p _iy,k is the component of p _i,k in the sway direction, p _iψ,k is the component of p _i,k in the heading angle; h _i =diag[hi _ix ,hi _iy , hi _iψ ], h _ix is the component of _hi in the longitudinal direction, hi _iy is the component of hi in the sway direction, hi _iψ is the component of _hi in the heading angle; q _{i ,k} =diag[q _{ix, k} , q _iy,k , q _iψ,k ], q _ix,k is the component of qi _,k in the longitudinal direction, q _iy,k is the component of qi _,k in the sway direction, q _ix,k is The component of q _i,k on the heading angle;

j = x, y, ψ,

is the derivative of e _ij,1 ,

for

the derivative of ,

for

component in the longitudinal direction,

for

the component in the sway direction,

for

component in the heading angle;

Introducing the dynamic surface control technology and designing the first-order filter of the virtual controller is:

表示α_fi的导数，π_i＝diag[π₁,π₂,π₃]为滤波器时间常数矩阵，π₁为π_i在纵向上的分量，π₂为π_i在横荡方向上的分量，π₃为π_i在航向角上的分量；z_i,1＝diag[z_ix,1,z_iy,1,z_iψ,1]为转换误差，z_ix,1为z_i,1在纵向上的分量，z_iy,1为z_i,1在横荡方向上的分量，z_iy,1为z_i,1在航向角上的分量；α_i,f(0)表示滤波虚拟控制α_i,f的初始值；where α _i,m =π _i -π _i h _i ^-1 z _i,1 ,

Represents the derivative of α _fi , π _i =diag[π ₁ ,π ₂ ,π ₃ ] is the filter time constant matrix, π ₁ is the component of π _i in the longitudinal direction, π ₂ is the component of π _i in the sway direction , π ₃ is the component of π _i on the heading angle; z _i,1 =diag[z _ix,1 ,z _iy,1 ,z _iψ,1 ] is the conversion error, z _ix,1 is the longitudinal direction of z _i,1 , _ziy,1 is the component of zi _,1 in the sway direction, _ziy,1 is the component of zi _,1 on the heading angle; α _i,f (0) represents the filtering virtual control α _{i , the initial value of f} ;

a _ik is whether the i-th unmanned boat maintains connection with the k-th unmanned boat, if the connection is maintained a _ik =1, otherwise a _ik =0; e _i,1 is to convert the position difference between the unmanned boat and all its neighbors post-summed vector;

α _i,m (0) is the value of the virtual controller at time zero;

G _i is the decay function; k _i,k is the design constant vector; θ _i,1 is the variable coefficient of the error e _i,1 in the virtual controller; p _i,k is the ith unmanned boat and the kth unmanned boat The _vector of the first _conversion of the position difference of the human-boat The transformation vector of _i,k ; χ _i is composed of the upper bound function of ei _{, 1} , _ei,1 and the lower bound function of ei,1, the inverse vector of χ _i is the error of _ei,1 in the virtual controller variable coefficient;

Further, the RBF neural network in step (5):

为理想RBF神经网络权值，

为W^*在纵向上的分量，

为W^*在横荡方向上的分量，

为W^*在航向角上的分量；S(Z_i)为回归向量；RBF神经网络权值更新率设计如下：Among them, ω(Z _i )=[ω _u (Z _i ), ω _v (Z _i ), ω _r (Z _i )] ^T is the neural network compensation function, ω _u (Z _i ) is ω(Z _i ) in The longitudinal component, ω _v (Z _i ) is the component of ω(Z _i ) in the sway direction, and ω _r (Z _i ) is the component of ω(Z _i ) in the heading angle;

is the ideal RBF neural network weight,

is the component of W ^* in the longitudinal direction,

is the component of W ^* in the sway direction,

is the component of W ^* on the heading angle; S(Z _i ) is the regression vector; the RBF neural network weight update rate is designed as follows:

为

的导数，

为第i个无人艇

方向上的权值，

为第l个无人艇

方向上的权值，

为回归函数，

为第i个无人艇

方向上的速度误差，

为设计参数，

为

修正项，

为协同调整系数；in,

for

the derivative of ,

is the i-th unmanned boat

weights in the direction,

for the lth unmanned boat

weights in the direction,

is the regression function,

is the i-th unmanned boat

velocity error in direction,

are design parameters,

for

corrections,

is the synergistic adjustment factor;

为第i个无人艇

方向上的神经网络权值误差，W^*为理想RBF神经网络权值，

的一阶导数为：consider

is the i-th unmanned boat

The neural network weight error in the direction, W ^* is the ideal RBF neural network weight,

The first derivative of is:

为第l个无人艇

方向上的神经网络权值误差；in,

for the lth unmanned boat

The neural network weight error in the direction;

ε _i (Z _i ) is the approximation error of the neural network; Z _i is the input vector of the neural network;

a _il is whether the i-th unmanned boat remains connected to the l-th unmanned boat, if the connection is maintained, a _il =1, otherwise a _il =0.

Further, the state feedback tracking controller designed in step (6) is as follows:

为虚拟控制器α_i,f的导数，

为神经网络权值的转置，h_i ^-1为函数h_i的逆；Among them, τ _i ′=[τ′ _iu ,τ′ _iv ,τ′ _ir ] ^T is the design controller, τ′ _iu is the component of τ _i ′ in the longitudinal direction, τ′ _iv is the τ _i ′ in the yaw direction , τ′ _ir is the component of τ _i ′ on the heading angle; k _i,2 =diag[k _ix,2 ,k _iy,2 ,k _iψ,2 ] is the diagonal matrix, k _ix,2 represents the formation The design parameters of the controller τ′ _ix , k _iy,2 represents the design parameters of the formation controller τ′ _iy , and k _iψ,2 represents the design parameters of the formation controller τ′ _iψ ;

is the derivative of the virtual controller α _i,f ,

is the transpose of the neural network weights, h _i ^-1 is the inverse of the function h _i ;

z _i,2 is the conversion speed error.

Further, the experience-based state feedback tracking controller designed in step (7) is as follows:

为第i个无人艇的神经网络权值常数，

为

在纵向上的分量，

为

在横荡方向上的分量，

为

航向角上的分量，

为

的转置。in,

is the neural network weight constant of the i-th UAV,

for

component in the longitudinal direction,

for

the component in the sway direction,

for

component on the heading angle,

for

transposition of .

Compared with the prior art, the present invention has the following advantages and beneficial effects:

1. The collaborative learning and formation control method of a homogeneous multi-unmanned boat system provided by the present invention introduces a tracking error conversion function to ensure the boundedness of the constraint error to satisfy the original constraint tracking problem, and this function is selected as a time-varying index function to ensure that the target error is always within the range specified by the boundary function, and the transient performance of the error (convergence speed and maximum overshoot) can be preset by adjusting the parameters of the boundary function.

2. A collaborative learning and formation control method for a homogeneous multi-unmanned boat system provided by the present invention utilizes the nonlinear approximation capability of the RBF neural network to estimate the uncertain part in the model, and uses the estimated value in the controller to estimate the model. The uncertain part is compensated, and the adaptive update rate of the parameter estimation value is selected to achieve the convergence of the formation error.

3. A method for collaborative learning and formation control of a homogeneous multi-UAV system provided by the present invention is based on the deterministic learning theory, adopts radial basis neural network to obtain system dynamic knowledge, and uses constant neural network weights for the learned knowledge. Stored in the form of values, the same or similar control tasks no longer need to retrain the neural network, but reuse the knowledge already learned.

Description of drawings

FIG. 1 is a schematic structural diagram of a distributed leader-follower formation of an unmanned boat according to an embodiment of the present invention.

FIG. 2 is a phaseless communication topology diagram of an unmanned boat formation system according to an embodiment of the present invention.

FIG. 3 is an overall control block diagram of formation control of an unmanned boat according to an embodiment of the present invention.

FIG. 4 is a phase plan view of a group of isomorphic unmanned boat formation movement according to an embodiment of the present invention.

FIG. 5 is a schematic diagram of longitudinal tracking errors e _ix,1 (t) of a group of isomorphic unmanned boats according to an embodiment of the present invention.

FIG. 6 is a schematic diagram of the tracking error e _iy,1 (t) of a group of isomorphic UAVs in the sway direction according to an embodiment of the present invention.

7 is a schematic diagram of tracking errors e _iψ,1 (t) of a group of isomorphic UAV heading angles according to an embodiment of the present invention.

的示意图。FIG. 8 is the second norm of the neural network weight for estimating the damping term of the unmanned boat according to the embodiment of the present invention

schematic diagram.

FIG. 9 is a schematic diagram of the longitudinal thrust τ _ix of the unmanned boat according to the embodiment of the present invention.

FIG. 10 is a schematic diagram of the thrust τ _iy in the sway direction of the unmanned boat according to the embodiment of the present invention.

FIG. 11 is a schematic diagram of the thrust τ _iψ of the steering of the unmanned boat according to the embodiment of the present invention.

12 is a schematic diagram of longitudinal tracking errors e _ix,1 (t) of a group of isomorphic unmanned boats according to an embodiment of the present invention.

FIG. 13 is a schematic diagram of the tracking error e _iy,1 (t) of a group of isomorphic UAVs in the sway direction according to an embodiment of the present invention.

14 is a schematic diagram of the tracking error e _iψ,1 (t) of a group of isomorphic UAV heading angles according to an embodiment of the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, and not to limit the present invention.

Example:

This embodiment provides a collaborative learning and formation control method for a homogeneous multi-UAV system. The method proposes a distributed leader-follower structure based on the problem of maintaining connection and cooperative control in the formation control of UAVs. Formation control method, the schematic diagram of the distributed leader-follower formation structure is shown in Figure 1, Figure 2 is the phaseless communication topology diagram of the homogeneous unmanned boat formation system, and Figure 3 is the overall formation control of the homogeneous unmanned boat. Control block diagram, the method specifically includes the following steps:

Step (1): The tasks of each unmanned boat in the unmanned boat formation are the same or similar, and the environment of each unmanned boat is similar (the communication range of the unmanned boat is limited, and each unmanned boat in the formation has at least One unmanned boat maintains communication), so in this design, multiple unmanned boats with the same structure are used for formation control, the dynamic model of the unmanned boat in the distributed formation structure is established, and the dynamic model in the form of a vector is expanded into a scalar form;

个无人艇的动态模型为：the first

The dynamic model of each UAV is:

表示第i个无人艇在u，v，r方向上的加速度构成的向量，C(v_i)表示科氏力矩阵，其中v_i＝[u_i,v_i,r_i]^T为速度向量，D(v_i)表示阻尼矩阵，由于多艘无人艇具有相同结构，所以每艘无人艇具有相同的M矩阵；τ_i＝[τ_ui,τ_vi,τ_ri]^T为需要设计的控制器向量，τ_ui表示第i个无人艇纵向的推力，τ_vi表示第i个无人艇横荡方向的推力，τ_ri表示第i个无人艇转向的力矩；τ_ωi＝[τ_ωui,τ_ωvi,τ_ωri]^T为外界时变扰动，τ_ωui表示第i个无人艇在纵向方向受到的外部时变扰动，τ_ωvi表示第i个无人艇在横荡方向受到的外部时变扰动，τ_ωri表示第i个无人艇在转向角方向受到的外部时变扰动。矩阵M、C(v_i)、D(v_i)、J(η_i)的具体形式分别如下所示：The first three terms in the above formula are the kinematic equations of the system. Among them, ( _xi , y _i ) represents the position of the ith unmanned boat under the geodetic coordinates O _e X _e Y _e , _xi is the longitudinal position of the ith unmanned boat, and _yi is the ith unmanned boat The sway direction position of the boat, ψ _i is the heading angle of the i-th unmanned boat; u _i represents the longitudinal speed of the _i -th unmanned boat, vi represents the sway speed of the _i -th unmanned boat, and ri means The steering angular velocity of the i-th unmanned boat; M represents the mass matrix of the unmanned boat,

Represents the vector formed by the acceleration of the i-th unmanned boat in the u, v, and r directions, C(vi ) represents the Coriolis force matrix, where v _i =[ _{u i} ,vi _{,r i ]} ^T is the velocity vector , D(v _i ) represents the damping matrix. Since multiple unmanned boats have the same structure, each unmanned boat has the same M matrix; τ _i =[τ _ui ,τ _vi ,τ _ri ] ^T is the required design Controller vector, τ _ui represents the longitudinal thrust of the ith unmanned boat, τ _vi represents the thrust of the ith unmanned boat in the sway direction, τ _ri represents the turning moment of the ith unmanned boat; τ _ωi = [τ _ωui ,τ _ωvi ,τ _ωri ] ^T is the external time-varying disturbance, τ _ωui represents the external time-varying disturbance received by the i-th unmanned boat in the longitudinal direction, and τ _ωvi represents the external time-varying disturbance received by the i-th unmanned boat in the yaw direction Time-varying disturbance, τ _ωri represents the external time-varying disturbance in the steering angle direction of the ith UAV. The specific forms of the matrices M, C(v _i ), D(vi ), and J(η _{i )} are as follows:

In this example, four identical dynamic models of the unmanned boat are selected, and the system parameters of the unmanned boat are:

m ₁₁ = 25.8 kg, m ₂₂ = 33.8 kg, m ₂₃ = m ₃₂ = 1.0948 kg, m ₃₃ = 2.76 kg,

c ₁₃ (vi )=-m _22i v _i -m _{23i ri ,} the hull length is Li = _1.225m .

d ₂₂ (vi )=0.8612+36.2823*|v _i |+0.805*|r _i | _,

d ₂₃ (vi )=-0.1079+0.845*|v _i |+3.45*|r _i | _,

d ₃₂ (vi )=-0.1052-5.0437*|v _i |-0.13*|r _i | _,

d ₃₃ (vi )= _1.9−0.08 *|v _i |+0.75*| _ri |.

The form of external disturbance is:

The reference trajectory produced by the virtual leader is:

η ₀ =[40sin(0.1t),20sin(0.2t),0.1] ^T

The initial positions of the four UAVs are: η ₁ (0)=[-8,0,0.1] ^T , η ₂ (0)=[0,-6,0.2] ^T , η ₃ (0)=[0 ,6,0] ^T , η ₄ (0)=[ _8,0,0.1 ] ^T , and the initial velocity is chosen as vi (0)=[0,0,0] ^T .

Transform the kinetic equations into the following form:

τ′_i＝J(η_i)M^-1τ_i，τ′_ωi＝J(η_i)M^-1τ_ωi，

为旋转矩阵J(η_i)的导数，J^-1(η_i)为旋转矩阵J(η_i)的逆，M^-1为质量矩阵M的逆。where v′ _i =J(η _i ),

τ′ _i =J(η _i )M ^-1 τ _i , τ′ _ωi =J(η _i )M ^-1 τ _ωi ,

is the derivative of the rotation matrix J(η _i ), J ⁻¹ (η _i ) is the inverse of the rotation matrix J(η _i ), and M ⁻¹ is the inverse of the mass matrix M.

来描述同构多无人艇编队系统中各个体间的信息交互。

是有限非空集合，称为顶点集，集合

中的每个顶点对应有相同编号的跟随者；

是有限集合，称之为边集，每条边对应有相同编号且能互相通信的相邻无人艇。无向图

的邻接矩阵A＝(a_il)_(N)×(N)的元素a_il∈{0,1}。当无人艇i可以获取无人艇j的信息时(此时j称为尾部，i称为头部)，a_il＝1，否则a_il＝0。Step (2): Use an undirected graph

To describe the information interaction among the various entities in the homogeneous multi-UAV formation system.

is a finite non-empty set, called the vertex set, the set

Each vertex in corresponds to a follower with the same number;

is a finite set, called an edge set, each edge corresponds to adjacent UAVs with the same number and can communicate with each other. Undirected graph

The adjacency matrix A=(a _il ) _(N)×(N) of elements a _il ∈ {0,1}. When the unmanned boat i can obtain the information of the unmanned boat j (the j is called the tail at this time, and the i is called the head), a _il =1, otherwise a _il =0.

来描述包含领航者在内的编队系统中各成员间的信息交互。

为虚拟领导者，虚拟领导与部分跟随者保持通信；邻接矩阵A₀＝diag[a₁₀,,a_N0]^T的元素a_i0∈{0,1}，并且

Further use of expansion diagrams

To describe the information exchange among the members of the formation system including the pilot.

is a virtual leader, which maintains communication with some of its followers; the adjacency matrix A ₀ =diag[a ₁₀ ,,a _N0 ] the element a _i0 ∈ {0,1} of ^T , and

(

为设计常数，G(0)为G(t)的初始值)。我们认为每个无人艇的通信范围有限且最大为

如果满足

G_x(0)为G(t)在纵向上的初始值，G_y(0)为G(t)在横荡方向的初始值，则无人艇i与无人艇k之间具有通信，其中

因此定义每个邻居为：

增广邻居集为：

和

为纵向的设计常数，

和

为横荡方向的设计常数，

和

为航向角上的设计常数。Design a continuously differentiable monotone decreasing function vector G(t), G(t) satisfies the first-order and second-order derivables,

(

is the design constant, G(0) is the initial value of G(t)). We believe that the communication range of each UAV is limited and the maximum is

if satisfied

G _x (0) is the initial value of G(t) in the longitudinal direction, G _y (0) is the initial value of G(t) in the sway direction, then there is communication between the unmanned boat i and the unmanned boat k, in

So define each neighbor as:

The augmented neighbor set is:

and

is the longitudinal design constant,

and

is the design constant for the sway direction,

and

is the design constant on the heading angle.

The undirected communication topology is used to represent the information interaction between homogeneous multi-UAVs, so that a group of UAVs with limited communication range follow a given leader trajectory in the form of a leader-follower formation (only some followers). When the leader information is available), each unmanned boat also needs to meet the constraints of distance and azimuth to ensure that each unmanned boat can detect the information of its neighbors and maintain a connection with it. Define the error as:

x_k表示第k个无人艇在大地坐标O_eX_eY_e下纵向的位置，y_k表示第k个无人艇在大地坐标O_eX_eY_e下横荡方向的位置，ψ_k为第k个无人艇的航向角，G_x(t)为纵向的衰减函数，G_y(t)为横荡方向的衰减函数，G_ψ(t)为航向角上的衰减函数。where e _i,1 =[e _ix,1 ,e _iy,1 ,e _iψ,1 ] ^T , e _i,1 is the vector summed after transforming the position difference between the UAV and all its neighbors, e _ix,1 is the component of e _i,1 in the longitudinal direction, e _iy,1 is the component of e _i,1 in the sway direction, e _iψ,1 is the component of e _i,1 in the heading angle, a _ik represents the i-th Whether the unmanned boat remains connected to the k-th unmanned boat, if the connection a _ik =1, otherwise a _ik =0; ξ _i,k =[ξ _ix,k ,ξ _iy,k ,ξ _iψ,k ] ^T , ξ _ix,k , ξ _iy,k , ξ _iψ,k are the components of ξ _i,k in the longitudinal direction, yaw direction, and heading angle direction, respectively,

x _k represents the longitudinal position of the k-th unmanned boat under the geodetic coordinates O _e X _e Y _e , y _k represents the position of the k-th unmanned boat in the sway direction under the geodetic coordinates O _e X _e Y _e , ψ _k is the heading angle of the k-th UAV, G _x (t) is the attenuation function in the longitudinal direction, G _y (t) is the attenuation function in the sway direction, and G _ψ (t) is the attenuation function on the heading angle.

如图4所示的是无人艇编队系统在相平面上的实际轨迹图。This example is shown in Figure 2. The neighbor sets of the four followers are

Figure 4 shows the actual trajectory of the UAV formation system on the phase plane.

Further, in step (3), the design tracking error constraints are as follows:

e_ji(t)表示e_ji(t)的下界性能函数，

表示e_ji(t)的上界性能函数，

表示性能函数

的初始值，

表示性能函数

的稳态值，e_ji,0表示性能函数e_ji(t)的初始值，e_ji,∞表示性能函数e_ji(t)的稳态值，k_ji表示其收敛速度。因此误差跟踪转换函数设计为：where j=x, y, ψ,

e _ji (t) represents the lower bound performance function of e _ji (t),

represents the upper bound performance function of e _ji (t),

Represents a performance function

the initial value of ,

Represents a performance function

The steady state value of , e _ji,0 represents the initial value of the performance function e _ji (t), e _ji,∞ represents the steady state value of the performance function e _ji (t), and k _ji represents its convergence speed. Therefore the error tracking transfer function is designed as:

表示自然底数的z_ji,1次幂，

表示自然底数的-z_ji,1次幂，-γ_ji＜T_ji(z_ji,1,γ_ji)＜1,

当且仅当z_ji,1＝0时，T_ji(z_ji,1,γ_ji)＝0；得到如下转换误差：Among them, z _ji,1 represents the conversion error of the i-th unmanned boat,

Represents the natural base z _{ji, the power of 1} ,

Represents the -z _{ji, 1} power of the natural base, -γ _ji <T _ji (z _ji,1 ,γ _ji ) < 1,

T _ji (z _ji,1 ,γ _ji )=0 if and only if z _ji,1 =0; the following conversion error is obtained:

In this example, the design parameters of the four UAVs are as follows:

The maximum communication distance of each unmanned boat is 17m, and the longitudinal G _x (t), sway direction G _y (t), and heading G _ψ (t) are:

G _y (t)=(10-3)×e ^-0.1t +3

G _x (t)=(10-3)×e ^-0.1t +3

G _ψ (t)=(0.4-0.2)×e ^-0.1t +0.2

The upper and lower bounds of the preset performance functions in the longitudinal direction, the yaw direction and the heading angle are:

Figure 5-7 shows the longitudinal tracking error e _ix,1 (t), the yaw direction tracking error e _iy,1 (t), and the heading angle tracking error e _iψ,1 (t). From the change process of e _ix,1 (t), e _iy,1 (t), and e _iψ,1 (t) in the figure, it can be known that the transient fluctuation process of the UAV spacing has never crossed the set upper and lower boundaries. This simulation figure shows that the control scheme can better solve the problems of collision avoidance and communication connection retention.

Step (4): Define the filter error as:

e _i,f =α _i,f -α _i

z _i,2 =v′ _i -α _i,f

e_i,f＝[e_ix,f,e_iy,f,e_iψ,f]^T为滤波误差向量，e_ix,f为e_i,f在纵向上的分量，e_iy,f为e_i,f在横荡方向上的分量，e_iψ,f为e_i,f在航向角上的分量；α_i＝[α_ix,α_iy,α_iψ]^T为虚拟控制输入向量，α_ix为α_i在纵向上的分量，α_iy为α_i在横荡方向上的分量，α_iψ为α_i在航向角上的分量；α_i,f＝[α_ix,f,α_iy,f,α_iψ,f]^T为滤波虚拟控制输入向量，α_ix,f表示α_ix的滤波虚拟控制，α_iy,f表示α_iy的滤波虚拟控制，α_iψ,f表示α_iψ的滤波虚拟控制；z_i,2＝[z_iu,2,z_iv,2,z_ir,2]^T为转换速度误差，z_iu,2为z_i,2在纵向上的分量，z_iv,2为z_i,2在横荡方向上的分量，z_ir,2为z_i,2在航向角上的分量。in

e _i,f =[e _ix,f ,e _iy,f ,e _iψ,f ] ^T is the filtering error vector, e _ix,f is the vertical component of e _i,f , e _iy,f is e _i, The component of _f in the sway direction, e _iψ,f is the component of e _i,f in the heading angle; α _i =[α _ix ,α _iy ,α _iψ ] ^T is the virtual control input vector, α _ix is α _i Component in the longitudinal direction, α _iy is the component of α _i in the sway direction, α _iψ is the component of α _i in the heading angle; α _i,f =[α _ix,f ,α _iy,f ,α _{iψ, f} ] ^T is the filtering virtual control input vector, α _ix,f represents the filtering virtual control of α _ix , α _iy,f represents the filtering virtual control of α _iy , α _iψ,f represents the filtering virtual control of α _{iψ ;} ＝[z _iu,2 ,z _iv,2 ,z _ir,2 ] ^T is the conversion speed error, z _{iu,2 is} the vertical component of zi,2, z _iv,2 is the sway of zi _,2 The component in the direction, z _ir,2 is the component of z _i,2 in the heading angle.

Design the virtual controller as:

为e_ij,1的导数，

为

的导数，

为

在纵向上的分量，

为

在横荡方向上的分量，

为

在航向角上的分量。where k _i,1 =diag[k _ix,1 ,kiy, ₁ ,k _iψ,1 ] are design parameters, k _ix,1 is the vertical component of k _i,1 , k _ix,1 is k _{i, 1} is the component in the sway direction, k _iψ,1 is the component of k _i,1 in the heading angle; G _i =diag[G _ix ,G _iy ,G _iψ ], G _ix is the longitudinal component of G _i , G _iy is the component of G _i in the sway direction, G _iψ is the component of G _i in the heading angle, k _i,k =diag[k _ix,k ,k _iy,k ,k _iψ,k ], k _ix,k is the component of _ki,k in the longitudinal direction, kiy, _k is the component of _ki,k in the sway direction, _kiψ,k is the component of ki _,k in the heading angle; θ _{i, 1} =diag[θ _ix,1 ,θ _iy,1 ,θ _iψ,1 ], θ _ix,1 is the component of θ _i,1 in the longitudinal direction, θ _iy,1 is the component of θ _i,1 in the yaw direction Component, θ _iψ,1 is the component of θ _i,1 on the heading angle; p _i,k =diag[pi _ix,k ,p _iy,k ,p _iψ,k ], p _ix,k is p _i,k Component in the longitudinal direction, p _iy,k is the component of p _i,k in the sway direction, p _iψ,k is the component of p _i,k in the heading angle; h _i =diag[hi _ix ,hi _iy , hi _iψ ], h _ix is the component of _hi in the longitudinal direction, hi _iy is the component of hi in the sway direction, hi _iψ is the component of _hi in the heading angle; q _{i ,k} =diag[q _{ix, k} , q _iy,k , q _iψ,k ], q _ix,k is the component of qi _,k in the longitudinal direction, q _iy,k is the component of qi _,k in the sway direction, q _ix,k is The component of q _i,k on the heading angle;

is the derivative of e _ij,1 ,

for

the derivative of ,

for

component in the longitudinal direction,

for

the component in the sway direction,

for

component in the heading angle.

Introducing the dynamic surface control technology and designing the first-order filter of the virtual controller is:

表示α_fi的导数，π_i＝diag[π₁,π₂,π₃]为滤波器时间常数矩阵，π₁为π_i在纵向上的分量，π₂为π_i在横荡方向上的分量，π₃为π_i在航向角上的分量；z_i,1＝diag[z_ix,1,z_iy,1,z_iψ,1]为转换误差，z_ix,1为z_i,1在纵向上的分量，z_iy,1为z_i,1在横荡方向上的分量，z_iy,1为z_i,1在航向角上的分量；α_i,f(0)表示滤波虚拟控制α_i,f的初始值。本实例中的滤波器时间常数矩阵设计为π_i＝diag[0.01,0.01,0.01]，k_i,1＝diag[0.01,0.1,1]。where α _i,m =π _i -π _i h _i ^-1 z _i,1 ,

Represents the derivative of α _fi , π _i =diag[π ₁ ,π ₂ ,π ₃ ] is the filter time constant matrix, π ₁ is the component of π _i in the longitudinal direction, π ₂ is the component of π _i in the sway direction , π ₃ is the component of π _i on the heading angle; z _i,1 =diag[z _ix,1 ,z _iy,1 ,z _iψ,1 ] is the conversion error, z _ix,1 is the longitudinal direction of z _i,1 , _ziy,1 is the component of zi _,1 in the sway direction, _ziy,1 is the component of zi _,1 on the heading angle; α _i,f (0) represents the filtering virtual control α _{i , the initial value of f} . The filter time constant matrix in this example is designed as π _i =diag[0.01,0.01,0.01], ki _,1 =diag[0.01,0.1,1].

Step (5): RBF neural network:

为理想RBF神经网络权值，

为W^*在纵向上的分量，

为W^*在横荡方向上的分量，

为W^*在航向角上的分量；S(Z_i)为回归向量。本实例中高斯径向基函数神经网络

包含1000个节点，分布在[0,0.2]×[-4,5]中，宽度为0.8；高斯径向基函数神经网络

和

均包含1500个节点，都分布在[0,0.2]×[-5,5]×[-0.1,0.1]中，宽度都为0.8；此外神经网络权值初始值

RBF神经网络权值更新率设计如下：Among them, ω(Z _i )=[ω _u (Z _i ), ω _v (Z _i ), ω _r (Z _i )] ^T is the neural network compensation function, ω _u (Z _i ) is ω(Z _i ) in The longitudinal component, ω _v (Z _i ) is the component of ω(Z _i ) in the sway direction, and ω _r (Z _i ) is the component of ω(Z _i ) in the heading angle;

is the ideal RBF neural network weight,

is the component of W ^* in the longitudinal direction,

is the component of W ^* in the sway direction,

is the component of W ^* on the heading angle; S(Z _i ) is the regression vector. Gaussian radial basis function neural network in this example

Contains 1000 nodes distributed in [0, 0.2] × [-4, 5] with a width of 0.8; Gaussian radial basis function neural network

and

Both contain 1500 nodes, all distributed in [0, 0.2] × [-5, 5] × [-0.1, 0.1], and the width is 0.8; in addition, the initial value of the neural network weights

The weight update rate of RBF neural network is designed as follows:

为

的导数，

为第i个无人艇

方向上的权值，

为第l个无人艇

方向上的权值，

为回归函数，

为第i个无人艇

方向上的速度误差，其中设计参数：Γ_iu＝1.5，Γ_iv＝1.5，Γ_ir＝3，

RBF神经网络权值二范数

为图8所示。in,

for

the derivative of ,

is the i-th unmanned boat

weights in the direction,

for the lth unmanned boat

weights in the direction,

is the regression function,

is the i-th unmanned boat

Velocity error in direction with design parameters: Γ _iu = 1.5, Γ _iv = 1.5, Γ _ir = 3,

RBF neural network weights two norm

As shown in Figure 8.

为第i个无人艇

方向上的神经网络权值误差，W^*为第i个无人艇

方向上的神经网络最优值，

的一阶导数为：consider

is the i-th unmanned boat

Neural network weight error in the direction, W ^* is the i-th UAV

The optimal value of the neural network in the direction,

The first derivative of is:

为第l个无人艇

方向上的神经网络权值误差。in,

for the lth unmanned boat

Neural network weight error in direction.

Step (6): The designed formation tracking controller is as follows:

为虚拟控制器α_i,f的导数，

为神经网络权值的转置，h_i ^-1为函数h_i的逆。在本实例中

k_2,2＝k_3,2＝k_4,2＝diag[100,100,100]；图9-11分别为无人艇纵向的推力τ_iu、横荡方向推力τ_iv、转向的的推力τ_ir。Among them, τ _i ′=[τ′ _iu ,τ′ _iv ,τ′ _ir ] ^T is the design controller, τ′ _iu is the component of τ _i ′ in the longitudinal direction, τ′ _iv is the τ _i ′ in the yaw direction The component of τ′ _ir is the component of τ _i ′ on the heading angle;

is the derivative of the virtual controller α _i,f ,

is the transpose of the neural network weights, and h _i ^-1 is the inverse of the function h _i . In this instance

k _2,2 =k _3,2 =k _4,2 =diag[100,100,100]; Figures 9-11 are the longitudinal thrust τ _iu , the yaw direction thrust τ _iv , and the steering thrust τ _ir , respectively.

Step (7): The designed experience-based formation controller is as follows:

为第i个无人艇的神经网络权值常数，

为

在纵向上的分量，

为

在横荡方向上的分量，

为

航向角上的分量，

为

的转置。图12-14分别为纵向的跟踪误差e_ix,1(t)、横荡方向的跟踪误差e_iy,1(t)、航向角的跟踪误差e_iψ,1(t)。in,

is the neural network weight constant of the i-th UAV,

for

component in the longitudinal direction,

for

the component in the sway direction,

for

component on the heading angle,

for

transposition of . Figures 12-14 show the longitudinal tracking error e _ix,1 (t), the yaw direction tracking error e _iy,1 (t), and the heading angle tracking error e _iψ,1 (t).

Aiming at the problem of distributed synchronous tracking and collaborative learning control of multiple isomorphic full-drive unmanned boats with uncertainty, the invention proposes a distributed unmanned boat formation control method that satisfies connection retention and has collaborative learning. The control goal is to use the undirected communication topology diagram to represent the information interaction between the homogeneous multi-UAVs, so that a group of UAVs with limited communication range follow the given leader trajectory in the form of leader-follower formation (only part of it). While the follower can obtain the leader information), each of the UAVs also satisfies the distance and azimuth constraints to ensure that each UAV can detect the information of its neighbors and maintain a connection with it. The original constraint tracking problem is satisfied by introducing a tracking error transfer function to ensure the boundedness of the constraint error; for the uncertainty of the same model, real-time online communication and sharing of weights between neural network weight adaptation rates according to communication topology For continuous nonlinear dynamic systems that generate regression trajectories, deterministic learning can achieve local accurate approximation of unknown closed-loop system dynamics. In this paper, RBF neural network is used to design a control algorithm for the synchronous tracking control of multiple unmanned boats, not only Finally, all signals of the closed-loop system are finally consistent and bounded, and in the stable control process, the partial neural network weights converge to the optimal value and the local accurate approximation of the unknown closed-loop system dynamics is realized. The learned knowledge is stored in the form of constant neural network weights, which can be used to improve the control performance of the system, and can also be applied to the same or similar subsequent control tasks.

The above-mentioned embodiments only represent several embodiments of the present invention, and the descriptions thereof are specific and detailed, but should not be construed as a limitation on the scope of the patent of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can also be made, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the claims.

Claims (7)

1. A collaborative learning and formation control method for a homogeneous multi-unmanned ship system is characterized by comprising the following steps:

step (1), establishing a plurality of dynamic models of unmanned boats with the same structure;

step (2), designing a tracking error constraint condition according to the safety distance constraint and the communication connection range constraint between adjacent unmanned boats;

step (3), in order to meet the preset performance requirement, designing a tracking error conversion function, and converting the tracking error to obtain a converted conversion error;

step (4), designing a virtual controller by applying a dynamic surface control technology: the derivation of the virtual controller is avoided by combining a dynamic surface control technology and a step-by-step backward controller design technology, so that the input of the controller is prevented from containing the acceleration information of neighbors;

step (5), designing the weight update rate of the RBF neural network: estimating a damping term in the unmanned ship system by applying an RBF neural network;

step (6), designing a state feedback tracking controller: a stable tracking controller is constructed by applying the Lyapunov stability theory and combining a step-by-step back-pushing design method;

step (7), utilizing the stored knowledge to complete knowledge utilization, and designing a state feedback tracking controller based on experience;

in the step (2): using undirected graphs

To describe the information interaction among the individuals in the unmanned boat formation system,

is a finite, non-empty set, called a set of vertices

Each vertex in the system corresponds to a follower with the same number;

is a finite set called as an edge set, each edge corresponds to adjacent unmanned boats with the same number and capable of communicating with each other, and an undirected graph

Is (a) of_il)_(N)×(N)Element a of_il∈ {0,1}, when unmanned boat i is able to obtain information about unmanned boat j, when j is called tail, i is called head, a_il1, otherwise a_il＝0；

Further using expansion diagram

To describe the information interaction among the members in the formation system including the pilot,

for a virtual leader, the virtual leader maintains communication with the partial follower; adjacency matrix A₀＝diag[a₁₀,…,a_N0]^TElement a of_i0∈ {0,1}, and

designing a continuous differentiable monotone decreasing function vector G (t), G (t) satisfies the first-order conductibility and the second-order conductibility,

g (0) is the initial value of G (t) for the design constant; the communication range of each unmanned boat is considered to be limited and maximum

If it is satisfied with

Wherein

i≠k，G_x(0) Is an initial value in the longitudinal direction, G (t)_y(0) G (t) initial value in the sway direction, then there is communication between unmanned boat i and unmanned boat k, where

Thus each neighbor is defined as:

the augmented neighbor set is:

and

for the design constant in the longitudinal direction,

and

for the design constant of the yaw direction,

and

is a design constant at the course angle;

when a group of unmanned boats with limited communication range follows a given leader track in a leader-follower formation mode, each unmanned boat needs to meet the constraint conditions of distance and azimuth angle to ensure that each unmanned boat can detect the information of the neighbor and keep connection with the unmanned boat; the defined error is:

wherein e_i,1＝[e_ix,1,e_iy,1,e_iψ,1]^T，e_i,1Vector for summing up the transformed differences between the unmanned surface vehicle and all its neighbors, e_ix,1Is e_i,1Component in the longitudinal direction, e_iy,1Is e_i,1Component in the direction of the yaw, e_iψ,1Is e_i,1Component at heading angle, a_ikIndicating whether the ith unmanned ship is kept connected with the kth unmanned ship or not, and if the connection a is kept_ik1, otherwise a_ik＝0；ξ_i,k＝[ξ_ix,k,ξ_iy,k,ξ_iψ,k]^T，ξ_ix,k、ξ_iy,k、ξ_iψ,kAre respectively ξ_i,kComponents in the longitudinal direction, the yaw direction, the course angle direction,

x_kindicating the kth unmanned ship at geodetic coordinate O_eX_eY_ePosition in the lower longitudinal direction, y_kIndicating the kth unmanned ship at geodetic coordinate O_eX_eY_ePosition in the lower yaw direction,. psi_kIs the heading angle, G, of the kth unmanned boat_x(t) is the longitudinal decay function, G_y(t) attenuation function in the sway directionNumber, G_ψ(t) is a decay function over the course angle;

“ξ_i,kand (5) carrying out vector conversion after the second step on the position difference between the ith unmanned ship and the kth unmanned ship.

2. The collaborative learning and formation control method of the isomorphic multi-unmanned ship system according to claim 1, wherein in the step (1), the dynamic model of the ith unmanned ship is:

the first three terms in the above equation are kinematic equations for the system, where,

n represents the total number of unmanned boats, (x)_i,y_i) Indicating the i-th unmanned ship at geodetic coordinate O_eX_eY_ePosition of lower, x_iLongitudinal position of the ith unmanned ship, y_iIs the yaw direction position of the ith unmanned ship, psi_iThe course angle of the ith unmanned ship; u. of_iRepresenting the longitudinal speed, v, of the ith unmanned boat_iRepresents the yaw rate, r, of the ith unmanned boat_iRepresenting the steering angular velocity of the ith unmanned boat; m represents the mass matrix of the unmanned vehicle,

a vector C (v) representing the acceleration of the i-th unmanned ship in the u, v, r directions_i) Represents a Coriolis force matrix, wherein v_i＝[u_i,v_i,r_i]^TAs a velocity vector, D (v)_i) Representing a damping matrix, each unmanned ship having the same M matrix since the plurality of unmanned ships have the same structure; tau is_i＝[τ_ui,τ_vi,τ_ri]^TFor the controller vector to be designed, τ_uiExpressing thrust in the longitudinal direction of the i-th unmanned ship, tau_viExpressing thrust in the yaw direction, τ, of the ith unmanned boat_riRepresenting the moment of steering of the ith unmanned boat; tau is_ωi＝[τ_ωui,τ_ωvi,τ_ωri]^TIs an external time-varying disturbance, tau_ωuiRepresenting the external time-varying disturbance, τ, experienced by the ith unmanned boat in the longitudinal direction_ωviRepresents the external time-varying disturbance, tau, received by the ith unmanned boat in the sway direction_ωriRepresenting the external time-varying disturbance to the ith unmanned boat in the direction of the steering angle; matrix M, C (v)_i)、D(v_i)、J(η_i) The specific forms of (A) and (B) are respectively as follows:

wherein m is₁₁、m₂₂、m₂₃、m₃₃Is a constant number d₁₁(u_i) Is about u_iFunction of d₂₂(v_i,r_i)、d₂₃(v_i,r_i)、d₃₂(v_i,r_i)、d₃₃(v_i,r_i) Is about v_i,r_iA function of (a); the kinetic equation is converted to the form:

wherein v'_i＝J(η_i)v，

τ′_i＝J(η_i)M^-1τ_i，τ′_ωi＝J(η_i)M^-1τ_ωi，

Is a rotation matrix J (η)_i) Derivative of (A), J^-1(η_i) Is a rotation matrix J (η)_i) Inverse of (A), M^-1Is the inverse of the mass matrix M.

3. The collaborative learning and formation control method of the isomorphic multi-unmanned ship system according to claim 2, wherein in the step (3), the tracking error constraint conditions are designed as follows:

where j is x, y, ψ,

e_ji(t) represents e_ji(t) a lower bound performance function of,

denotes e_ji(t) an upper bound performance function,

representing a performance function

Is set to the initial value of (a),

representing a performance function

The steady-state value of (a) is,e _ji,0representing a performance functione _ji(t) initiation ofThe value of the one or more of,e _ji,∞representing a performance functione _jiSteady state value of (t), k_jiRepresents the convergence rate thereof; the error tracking transfer function is therefore designed to:

wherein z is_ji,1Indicating the conversion error of the ith unmanned boat,

z representing a natural base number_ji,1The power of the first power of the image,

z representing a natural base number_ji,1Power of the order, -gamma_ji＜T_ji(z_ji,1,γ_ji)＜1,

If and only if z_ji,1When equal to 0, T_ji(z_ji,1,γ_ji) 0; the following conversion errors were obtained:

4. the collaborative learning and formation control method of the homogeneous multi-unmanned ship system according to claim 3, wherein in the step (4), the filter error is defined as:

e_i,f＝α_i,f-α_i

z_i,2＝v′_i-α_i,f

wherein

e_i,f＝[e_ix,f,e_iy,f,e_iψ,f]^TTo filter the error vector, e_ix,fIs e_i,fComponent in the longitudinal direction, e_iy,fIs e_i,fComponent in the direction of the yaw, e_iψ,fIs e_i,fComponent at heading angle α_i＝[α_ix,α_iy,α_iψ]^TTo virtually control the input vector, α_ixIs α_iComponent in the longitudinal direction, α_iyIs α_iComponent in the direction of the yaw, α_iψIs α_iComponent at heading angle α_i,f＝[α_ix,f,α_iy,f,α_iψ,f]^TFor filtering the virtual control input vector, α_ix,fRepresentation α_ixFilter virtual control of α_iy,fRepresentation α_iyFilter virtual control of α_iψ,fRepresentation α_iψFiltering virtual control of (3); z is a radical of_i,2＝[z_iu,2,z_iv,2,z_ir,2]^TTo convert the speed error, z_iu,2Is z_i,2Component in the longitudinal direction, z_iv,2Is z_i,2Component in the direction of the yaw, z_ir,2Is z_i,2A component at a heading angle;

designing a virtual controller as follows:

wherein k is_i,1＝diag[k_ix,1,k_iy,1,k_iψ,1]To design the parameter, k_ix,1Is k_i,1Component in the longitudinal direction, k_ix,1Is k_i,1Component in the yaw direction, k_iψ,1Is k_i,1A component at a heading angle; g_i＝diag[G_ix,G_iy,G_iψ]，G_ixIs G_iComponent in the longitudinal direction, G_iyIs G_iComponent in the direction of the yaw, G_iψIs G_iComponent at heading angle, k_i,k＝diag[k_ix,k,k_iy,k,k_iψ,k]，k_ix,kIs k_i,kComponent in the longitudinal direction, k_iy,kIs k_i,kComponent in the yaw direction, k_iψ,kIs k_i,kA component at a heading angle; theta_i,1＝diag[θ_ix,1,θ_iy,1,θ_iψ,1]，θ_ix,1Is theta_i,1Component in the longitudinal direction, θ_iy,1Is theta_i,1Component in the direction of the yaw, θ_iψ,1Is theta_i,1A component at a heading angle; p is a radical of_i,k＝diag[p_ix,k,p_iy,k,p_iψ,k]，p_ix,kIs p_i,kComponent in the longitudinal direction, p_iy,kIs p_i,kComponent in the direction of the yaw, p_iψ,kIs p_i,kA component at a heading angle; h is_i＝diag[h_ix,h_iy,h_iψ]，h_ixIs h_iComponent in the longitudinal direction, h_iyIs h_iComponent in the direction of the yaw, h_iψIs h_iA component at a heading angle; q. q.s_i,k＝diag[q_ix,k,q_iy,k,q_iψ,k]，q_ix,kIs q_i,kComponent in the longitudinal direction, q_iy,kIs q_i,kComponent in the direction of the yaw, q_ix,kIs q_i,kA component at a heading angle;

is e_ij,1The derivative of (a) of (b),

is composed of

The derivative of (a) of (b),

is composed of

The component in the longitudinal direction is,

is composed of

The component in the direction of the yaw is,

is composed of

A component at a heading angle;

introducing a dynamic surface control technology and designing a first-order filter of a virtual controller as follows:

wherein,

representation α_fiDerivative of (a) (# n)_i＝diag[π₁,π₂,π₃]Is a filter time constant matrix, pi₁Is pi_iComponent in the longitudinal direction, pi₂Is pi_iComponent in the direction of the yaw, pi₃Is pi_iA component at a heading angle; z is a radical of_i,1＝diag[z_ix,1,z_iy,1,z_iψ,1]To convert errors, z_ix,1Is z_i,1Component in the longitudinal direction, z_iy,1Is z_i,1Component in the direction of the yaw, z_iy,1Is z_i,1Component at heading angle α_i,f(0) Representing filtering virtual controls α_i,fAn initial value of (1);

a_ikwhether the ith unmanned ship is kept connected with the kth unmanned ship or not is judged, and if the connection a is kept_ik1, otherwise a_ik＝0；e_i,1The vector is obtained by converting and summing the position differences of the unmanned ship and all neighbors of the unmanned ship;

α_i,m(0) is the value of the virtual controller at time zero;

G_iis a decay function; k is a radical of_i,kTo design a constant vector; theta_i,1For errors e in virtual controllers_i,1A variable coefficient of (d); p is a radical of_i,kVector after the first step of conversion is carried out on the position difference of the ith unmanned ship and the kth unmanned ship; h is_iThe reciprocal of the vector sum after the first step of conversion is carried out on the position difference of the ith unmanned ship and the kth unmanned ship; q. q.s_i,kIs p_i,kThe transformed vector of (2); chi shape_iIs formed by e_i,1、e_i,1Upper bound function of and e_i,1Is a lower bound function of_iThe inverse vector of (a) is the error e in the virtual controller_i,1Is measured.

5. The collaborative learning and formation control method of the isomorphic multi-unmanned ship system according to claim 4, wherein in the step (5), the RBF neural network:

ω(Z_i)＝D′(η_i,v′_i)v′_i＝W^*TS(Z_i)+_i(Z_i)

wherein, ω (Z)_i)＝[ω_u(Z_i),ω_v(Z_i),ω_r(Z_i)]^TAs a compensation function of the neural network, omega_u(Z_i) Is omega (Z)_i) Component in the longitudinal direction, ω_v(Z_i) Is omega (Z)_i) Component in the direction of the yaw, ω_r(Z_i) Is omega (Z)_i) A component at a heading angle;

is the weight of an ideal RBF neural network,

is W^*The component in the longitudinal direction is,

is W^*The component in the direction of the yaw is,

is W^*A component at a heading angle; s (Z)_i) Is a regression vector; the RBF neural network weight updating rate is designed as follows:

wherein,

is composed of

The derivative of (a) of (b),

is the ith unmanned ship

The weight in the direction is given to the user,

is the first unmanned boat

Direction of rotationThe weight of the upper node is higher than the weight of the lower node,

in the form of a regression function,

is the ith unmanned ship

The error in the speed in the direction of the direction,

in order to design the parameters of the device,

is composed of

The correction term is a term that is used to correct,

is a cooperative adjustment coefficient;

consider that

Is the weight error of the neural network in the l direction of the ith unmanned ship, W^*Is the weight of an ideal RBF neural network,

the first derivative of (d) is:

wherein,

is the first unmanned boat

Neural network weight error in direction;

_i(Z_i) Approximating the error for a neural network; z_iInputting a vector for the neural network;

a_ilwhether the ith unmanned ship is kept connected with the ith unmanned ship or not is judged, and if the ith unmanned ship is kept connected with the ith unmanned ship, a_il1, otherwise a_il＝0。

6. The collaborative learning and formation control method of the homogeneous multi-unmanned ship system according to claim 5, wherein the state feedback tracking controller designed in the step (6) is as follows:

wherein, tau_i′＝[τ′_iu,τ′_iv,τ′_ir]^TTo design the controller, τ'_iuIs tau_i'component in longitudinal direction, τ'_ivIs tau_i'component in the yaw direction, τ'_irIs tau_i' component at heading angle; k is a radical of_i,2＝diag[k_ix,2,k_iy,2,k_iψ,2]Is a diagonal matrix, k_ix,2Denotes a formation controller τ'_ixDesign parameter of (1), k_iy,2Denotes a formation controller τ'_iyDesign parameter of (1), k_iψ,2Denotes a formation controller τ'_iψThe design parameters of (1);

is a virtual controller α_i,fThe derivative of (a) of (b),

for transposition of weights of neural networks, h_i ^-1As a function h_iThe inverse of (1);

z_i,2to convert speed errors.

7. The collaborative learning and formation control method of a homogeneous multi-unmanned ship system according to claim 6, wherein the experience-based state feedback tracking controller designed in the step (7) is as follows:

wherein,

is the weight constant of the neural network of the ith unmanned ship,

is composed of

The component in the longitudinal direction is,

is composed of

The component in the direction of the yaw is,

is composed of

The component in the angle of the heading,

is composed of

The transposing of (1).

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