CN111650948B - Quick tracking control method for horizontal plane track of benthonic AUV - Google Patents

Abstract

The invention discloses a fast tracking control method for a horizontal plane trajectory of a bottom-dwelling AUV, which belongs to the technical field of trajectory tracking control of autonomous underwater robots. The invention solves the problems of limited control precision and slow adjustment speed when the current control method is applied to the bottom-dwelling AUV. The invention combines current disturbance and model uncertainty into a disturbance lumped term, uses a finite-time disturbance observer to approximate the disturbance lumped term value, and introduces a neural network to estimate the observation error. Furthermore, an adaptive neural network backstepping controller based on the finite-time disturbance observer is proposed to realize the finite-time high-precision trajectory tracking control of the benthic AUV. The present invention can be applied to the trajectory tracking control of the bottom-dwelling AUV.

Description

A fast tracking control method of horizontal plane trajectory for bottom-dwelling AUV

technical field

The invention belongs to the technical field of trajectory tracking control of autonomous underwater robots, and in particular relates to a horizontal plane trajectory fast tracking control method of a bottom-dwelling AUV.

Background technique

As an important tool for human exploration and development of the ocean, autonomous underwater vehicles (AUVs) have great development prospects in both military and civilian fields. At present, according to the working characteristics of AUVs, they can be divided into cruising AUVs for large-scale surveys and hovering AUVs for small-scale observations. Although both types of AUVs have great effects, the corresponding defects are also obvious, such as the poor fixed-point observation ability of cruise AUVs and the poor ability of hovering AUVs to investigate in large areas. Therefore, in order to realize further observation of the ocean, it is very meaningful to develop a new type of AUV that is highly autonomous and has the characteristics of both cruising AUV and hovering AUV. Therefore, the concept of benthic AUV was also proposed. The benthic AUV is a new type of underwater vehicle that combines the characteristics of seabed observation nodes and AUVs. At the same time of high-precision coordinate detection tasks, it can meet the needs of small target recognition. At the same time, this modified AUV is also a typical nonlinear strongly coupled system, which not only has the common research obstacles of AUV such as complex working environment and difficult to solve hydrodynamic parameters accurately, but also has large-scale deployment and accurate submerged operations on the seabed. Under the requirements, there are influencing factors such as the perturbation of hydrodynamic coefficient and the possibility of collision of the carrier.

In order to complete the submarine oil and gas seismic exploration in the designated area completely and efficiently, the benthic AUV needs to have good navigation ability, anti-interference ability and high-precision path tracking performance from the seabed surface, that is, to design an effective motion control law, so that The bottom-dwelling AUV can track the set trajectory from the initial state and complete the specified tasks, and ensure the global consistent and progressive stability of the tracking position error in a relatively short period of time, thereby achieving high-precision and rapid deployment operations in designated areas. At present, the common AUV control methods are usually to design a robust controller for external disturbances or use neural networks to approximate the total disturbance of the system. However, the control accuracy of such methods is limited and the adjustment speed is slow. When applied to AUVs such as bottom-dwelling AUVs that have harsh working environments, require high trajectory tracking accuracy, and need to quickly respond to external disturbances , it is difficult to achieve limited-time high-precision trajectory tracking control.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the problems of limited control accuracy and slow adjustment speed when the current control method is applied to the benthic AUV, and proposes a horizontal plane trajectory fast tracking control method of the benthic AUV .

The technical scheme adopted by the present invention to solve the above-mentioned technical problems is: a fast tracking control method of the horizontal plane trajectory of the bottom-dwelling AUV, the method specifically comprises the following steps:

Step 1. Consider the model uncertainty and current disturbance as a disturbance lumped term τ′ _d , and establish the kinematics and dynamics equations of the benthic AUV considering the disturbance lumped term;

Step 2. Based on the kinematics and dynamics equations established in step 1, use the backstepping control method to establish an error system for trajectory tracking;

Step 3: Design a sliding mode disturbance observer according to the trajectory tracking error system established in step 2, and use the designed sliding mode disturbance observer to approximate the disturbance lumped term τ′ _d to obtain the observation value of the disturbance lumped term τ′ _d ;

进行估计，获得观测误差

的估计值；Step 4. Using radial basis function neural network to measure the observation error of the perturbed lumped term

make an estimate, get the observation error

estimated value;

的估计值来设计控制器，使可底栖式AUV的位姿在有限时间内跟踪期望值，且跟踪误差在有限时间内收敛。Step 5. According to the observation value of the disturbance lumped term τ′ _d and the observation error

The estimated value of , to design the controller, so that the pose of the bottom-dwelling AUV can track the expected value in a limited time, and the tracking error converges in a limited time.

The beneficial effects of the present invention are as follows: the present invention proposes a fast tracking control method for the horizontal plane trajectory of the bottom-dwelling AUV, the present invention combines the current disturbance and model uncertainty into a disturbance lumped term, and uses a finite time disturbance observer to approximate The lumped term values are perturbed and a neural network is introduced to estimate the observation error. Furthermore, an adaptive neural network backstepping controller based on the finite-time disturbance observer is proposed to realize the finite-time high-precision trajectory tracking control of the benthic AUV.

The method of the invention enables the bottom-dwelling AUV motion control system to track the expected value η _d within a limited time in the presence of external interference, and the tracking error e ₁ =η-η _d within a limited time convergence. It can ensure that the control input is a limited value, which is closer to the actual engineering.

Description of drawings

Fig. 1 is the surging tracking curve diagram of the bottom-dwelling AUV;

Fig. 2 is the sway tracking curve diagram of the bottom-dwelling AUV;

Fig. 3 is the bow tracking curve diagram of the benthic AUV;

Fig. 4 is the observation curve diagram of disturbance observer to longitudinal disturbance;

In the figure, H1 represents the longitudinal interference value, and d1 represents the longitudinal interference observation value;

Fig. 5 is the observation curve diagram of interference observer to lateral interference;

In the figure, H2 represents the lateral interference value, and d2 represents the lateral interference observation value;

Fig. 6 is the observation curve diagram of the disturbance observer to the yaw disturbance;

In the figure, H3 represents the yaw disturbance value, and d3 represents the observable yaw disturbance value;

Fig. 7 is the output curve diagram of the longitudinal control force of the actuator;

Fig. 8 is the output curve diagram of the lateral control force of the actuator;

FIG. 9 is an output curve diagram of the actuator yaw control torque.

Detailed ways

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 1. A method for fast tracking and controlling a horizontal plane trajectory of a bottom-dwelling AUV described in this embodiment, the method specifically includes the following steps:

Step 1. Consider the model uncertainty and current disturbance as a disturbance lumped term τ′ _d , and establish the kinematics and dynamics equations of the benthic AUV considering the disturbance lumped term;

Step 2. Based on the kinematics and dynamics equations established in step 1, use the backstepping control method to establish an error system for trajectory tracking;

Step 3: Design a sliding mode disturbance observer according to the trajectory tracking error system established in step 2, and use the designed sliding mode disturbance observer to approximate the disturbance lumped term τ′ _d to obtain the observation value of the disturbance lumped term τ′ _d ;

进行估计，获得观测误差

的估计值；Step 4. Using radial basis function neural network to measure the observation error of the perturbed lumped term

make an estimate, get the observation error

estimated value;

的估计值来设计控制器，使可底栖式AUV的位姿在有限时间内跟踪期望值，且跟踪误差在有限时间内收敛。Step 5. According to the observation value of the disturbance lumped term τ′ _d and the observation error

The estimated value of , to design the controller, so that the pose of the bottom-dwelling AUV can track the expected value in a limited time, and the tracking error converges in a limited time.

The kinematics and dynamics equations of the benthic AUV are expressed by the Newton-Eulerian equations based on the motion of a rigid body in a fluid:

In the formula, M is the mass inertia matrix, η=[x, y, ψ] ^T represents the three-degree-of-freedom position and attitude of the benthic AUV in the horizontal plane under the fixed coordinate system, v=[u, v, r] ^T Represents the velocity and angular velocity in the horizontal plane under the carrier coordinate system, J∈R ^3×3 represents the coordinate transformation matrix between the fixed coordinate system and the carrier coordinate system; C(v)∈R ^3x3 is the Coriolis containing the additional mass term Centripetal force matrix; D(v)∈R ^3x3 is the fluid damping matrix; g(η)∈R ^{3 is the restoring force and restoring moment vector generated by gravity and buoyancy acting on the hull; τ∈R 3 is} generated when the actuator is running Control force and moment vector; τ _d ∈ R ³ is the disturbance vector caused by external disturbance.

The present invention considers model uncertainty and ocean current disturbance, considers it as a disturbance lumped term, and considers its feasible mathematical expression form.

Embodiment 2: The difference between this embodiment and Embodiment 1 is that in the first step, the kinematics and dynamics equations of the bottom-dwelling AUV considering the perturbation lumped term are established, which are specifically:

是η的一阶导数，

代表可底栖式AUV在固定坐标系下的速度与角速度向量；

是v的一阶导数，

代表可底栖式AUV在载体坐标系下的加速度与角加速度向量；M₀代表质量惯性矩阵的标称值；上角标-1代表矩阵的逆，C₀(v)代表科里奥利向心力矩阵的标称值；D₀(v)代表流体阻尼矩阵的标称值；g₀代表恢复力和恢复力矩向量的标称值；In the formula, v=[u, v ₀ , r] ^T , v represents the velocity and angular velocity vector of the benthic AUV in the horizontal plane under the carrier coordinate system, u represents the surge speed, v ₀ represents the sway speed, and r represents the sway speed Yaw angular velocity; superscript T stands for transposition; η=[x,y,ψ] ^T stands for the three-degree-of-freedom pose vector of the bottom-dwelling AUV in the horizontal plane in a fixed coordinate system, and x and y represent the bottom-mountable AUV respectively The longitudinal and lateral position coordinates of the perched AUV in the fixed coordinate system, ψ represents the heading angle; J(η) represents the coordinate transformation matrix between the fixed coordinate system and the carrier coordinate system, J(η)∈R ^3×3 , R Represents a real number; τ′ _d represents the disturbance lumped term of the system; τ represents the control input vector, which can also be called the control force and torque vector generated when the actuator is running;

is the first derivative of η,

Represents the velocity and angular velocity vectors of the benthic AUV in a fixed coordinate system;

is the first derivative of v,

Represents the acceleration and angular acceleration vectors of the benthic AUV in the carrier coordinate system; M ₀ represents the nominal value of the mass-inertia matrix; the superscript -1 represents the inverse of the matrix, and C ₀ (v) represents the Coriolis centripetal force the nominal value of the matrix; D ₀ (v) represents the nominal value of the fluid damping matrix; g ₀ represents the nominal value of the restoring force and restoring moment vectors;

The fixed coordinate system O-XYZ is: take the sea surface or any point in the sea as the origin O, the X axis is located on the horizontal plane, and the specified true north direction is the positive direction; the Y axis is located on the horizontal plane, and the specified true east direction is the positive direction. Direction, that is, the OY axis is obtained by rotating the OX axis 90° clockwise according to the right-hand rule; the Z axis is perpendicular to the XOY coordinate plane, and the geocentric direction is positive;

The carrier coordinate system O ₀ -X ₀ Y ₀ Z ₀ is: taking the position of the center of gravity of the benthic AUV as the origin O ₀ , the X ₀ axis is in the longitudinal section of the benthic AUV, and the water The line plane is parallel and the bow direction is the positive direction; the Y ₀ axis is perpendicular to the longitudinal section of the benthic AUV, parallel to the horizontal plane and the starboard direction is the positive direction; the Z ₀ axis is in the longitudinal section of the benthic AUV, and the The bottom-dwelling AUV water plane is vertical and the direction of the bottom of the boat is the positive direction;

where ΔM represents the uncertainty value of the mass inertia matrix; ΔC(v) represents the uncertainty value of the Coriolis centripetal force matrix; ΔD(v) represents the uncertainty value of the fluid damping matrix; Δg represents the restoring force and restoring moment vector The uncertainty value of τ _d represents the uncertainty value of the disturbance vector caused by the external disturbance.

Embodiment 3: The difference between this embodiment and Embodiment 2 is that the specific process of the second step is:

Define tracking error:

是η_d的一阶导数；

是e₁的一阶导数；v_d表示可底栖式AUV在载体坐标系下水平面的速度与角速度期望向量；In the formula, e ₁ represents the trajectory tracking error; e ₂ represents the velocity tracking error; η _d = [x _d , y _d , ψ _d ] ^T represents the three-degree-of-freedom pose of the benthic AUV in the horizontal plane in a fixed coordinate system Expected value, x _d is the expected value of x, y _d is the expected value of y, ψ _d is the expected value of ψ;

is the first derivative of η _d ;

is the first derivative of e ₁ ; v _d represents the expected vector of velocity and angular velocity on the horizontal plane of the bottom-dwelling AUV in the carrier coordinate system;

Then according to formula (2), the error system of trajectory tracking is established as:

是e₂的一阶导数；

是J(η)的一阶导数；

为v_d的一阶导数；In the formula,

is the first derivative of _e2 ;

is the first derivative of J(η);

is the first derivative of v _d ;

Define the dummy error z:

z=e ₂ -α ₁ (6)

In the formula, α ₁ is the virtual control law one;

Take the virtual error integral term as ε:

Then the error system of trajectory tracking is transformed into:

为ε的一阶导数；

为z的一阶导数；

为α₁的一阶导数。In the formula,

is the first derivative of ε;

is the first derivative of z;

is the _first derivative of α1.

There is a disturbance lumped term τ′ _d in formula (2). In order to estimate the disturbance value in a short time, a sliding mode disturbance observer is used for approximation. The basic idea of backstepping control is feedback control, but on this basis, the system is divided into multiple subsystems with the next-order output as the input of the previous-order subsystem, and the Lyapunov function is used to process each order subsystem to obtain The corresponding virtual input is obtained, and the input of the next-order subsystem is designed in this way, until the actual input is finally obtained, and the design of the backstep control law can be completed by combining the above processing steps.

Embodiment 4: The difference between this embodiment and Embodiment 3 is that the specific process of the third step is:

The sliding mode surface function s is chosen as:

s=ρ-v (9)

为ρ的一阶导数，且

的形式为：In the formula, ρ is an intermediate variable,

is the first derivative of ρ, and

of the form:

m＝1,2,3，

为三自由度上扰动的最大值；0＜r＜1；sign代表符号函数；s＝[s₁,s₂,s₃]^T，s₁,s₂,s₃均为s中的元素，有|s|^r＝[|s₁|^r,|s₂|^r,|s₃|^r]^T，|·|代表取绝对值；In the formula, k ₇ is a positive definite diagonal matrix, k ₇ ∈R ^3×3 ; L is a positive definite diagonal matrix, L=diag[L ₁ ,L ₂ ,L ₃ ]∈R ^3×3 ,L ₁ ,L ₂ , L ₃ are all elements in L,

m=1,2,3,

is the maximum value of disturbance on three degrees of freedom; 0<r<1; sign represents the sign function; s=[s ₁ , s ₂ , s ₃ ] ^T , s ₁ , s ₂ , s ₃ are all elements in s, There is |s| ^r = [|s ₁ | ^r , |s ₂ | ^r , |s ₃ | ^r ] ^T , |·| represents the absolute value;

Then the observed value of the disturbance lumped term τ′ _d is

为扰动集总项τ′_d的观测值；

为s的一阶导数。In the formula,

is the observed value of the disturbance lumped term τ′ _d ;

is the first derivative of s.

If there are 0<a ₁ <1 and 0<a ₂ <2, then for ri ( _i =1,...,n), the following inequalities are satisfied:

sign represents the sign function, for a vector

ξ=[ζ ₁ …ζ _n ] ^T (14)

There is the following equation

ζ ^α = [|ζ ₁ | ^α sign(ζ ₁ )…|ζ _n | ^α sign(ζ _n )] ^T (15)

sign(ζ)=[sign(ζ ₁ )…sign(ζ _n )] ^T (16)

Although the estimated value of the disturbance has been obtained in the system (11), since the value of L is not easy to clarify, it will lead to observation errors in the system

The basic design principle of the disturbance observer is to combine the parameter perturbation terms, model uncertainties and external disturbances existing in the AUV control system into a perturbation lumped term, and then construct the observer system according to the measurable system state. The disturbance lumped term is approximated online, and the corresponding controller is designed by using the observation value of the disturbance lumped term, so as to improve the tracking performance of the system to the preset trajectory.

Embodiment 5: The difference between this embodiment and the fourth embodiment is that the specific process of the fourth step is:

为：observation error

for:

进行估计，径向基函数神经网络的输入x为：

则径向基函数神经网络输出观测误差

的估计值为：Observation error of perturbed lumped term using radial basis function neural network

To estimate, the input x of the radial basis function neural network is:

Then the radial basis function neural network outputs the observation error

is estimated to be:

为权值矩阵的估计值，

均为

中的子矩阵，

j＝1,2,3，

代表第j行第i个神经网络权值的估计值，i＝1,2,…,6，φ(x)为中间变量，φ(x)＝[φ₁(x),φ₂(x),...,φ₆(x)]^T，φ_i(x)代表第i个神经网络的高斯形式的径向基函数。In the formula,

is the estimated value of the weight matrix,

both

A submatrix in ,

j=1,2,3,

Represents the estimated value of the ith neural network weight in the jth row, i=1,2,...,6, φ(x) is the intermediate variable, φ(x)=[φ ₁ (x),φ ₂ (x) ,...,φ ₆ (x)] ^T , φ _i (x) represents the radial basis function of the Gaussian form of the ith neural network.

Radial basis function neural network is a kind of forward network based on function approximation theory, which has the characteristics of simple structure, concise training, fast learning convergence speed, and can approximate any nonlinear function. The learning of such networks is equivalent to finding the best fit plane for the training data in a multidimensional space.

Embodiment 6: The difference between this embodiment and Embodiment 5 is that the specific process of step 5 is:

Due to the physical limitation of the actuator, the maximum value of the execution input is a finite value, so it is necessary to limit the control input with the upper bound of the maximum output value;

The control input vector τ is constrained by the saturation value:

sat(τ)=[sat(τ ₁ ), sat(τ ₂ ), sat(τ ₃ )] ^T (19)

In the formula, sat(τ) is the output value of the control input vector after saturation limit processing, which is generated by the control input vector τ and the saturated control function sat(τ _j ), where τ _j represents the j-th value of the control input vector τ, j=1,2,3;

sat(τ _j ) represents the nonlinear saturation characteristic of the actuator, and the saturation control function is described as:

sat(τ _j )=τ _j (t)+θ _j (t) (20)

in

In the formula, θ _j (t) is the saturation control term, and τ _mj is the maximum allowable value of the j-th value τ _j of the control input vector τ;

The adaptive backstepping control law is designed as follows:

是

的一阶导数，c为待设计的控制参数及自适应增益，c＞0，λ为常数，λ＞0。In the formula, τ _s represents the nominal value of the control input vector, α ₂ is the second virtual control law, _ki is a positive definite diagonal matrix, i=1, 2,...6, _ki ∈ R ^3×3 , a is a constant, 0<a<1,

Yes

The first derivative of , c is the control parameter and adaptive gain to be designed, c>0, λ is a constant, λ>0.

1. Theoretical basis

1.1 Mathematical model of the motion system of the bottom-dwelling AUV

The kinematics and dynamics equations of the benthic AUV can be expressed by the Newton-Eulerian equation based on the motion of a rigid body in a fluid:

M is the mass inertia matrix, η=[x, y, ψ] ^T represents the three-degree-of-freedom position and attitude of the benthic AUV in the horizontal plane under the fixed coordinate system, v=[u, v ₀ , r] ^T represents the carrier The velocity and angular velocity in the horizontal plane under the coordinate system, J∈R ^3×3 represents the coordinate transformation matrix between the fixed coordinate system and the carrier coordinate system; C(v)∈R ^3×3 is the Coriolis containing the additional mass term Centripetal force matrix; D(v)∈R ^3×3 is the fluid damping matrix; g(η)∈R ^{3 is the restoring force and restoring moment vector generated by gravity and buoyancy acting on the hull; τ∈R 3 is} the actuator running The generated control force and torque vector; τ _d ∈ R ³ is the disturbance vector caused by the external disturbance.

Model uncertainty and current disturbance will lead to serious tracking error, which is considered as a disturbance lumped term, and its feasible mathematical expression is considered. Therefore, equation (23) can be transformed into:

In the formula, τ' _d represents the perturbation lumped term of the system, and its expression is as follows:

In the formula, the subscript 0 represents the coefficients of the nominal model, and Δ represents the uncertain value.

The goal of the present invention can be expressed as designing a suitable controller τ so that the motion control system of the benthic AUV can still track the expected value η _d within a limited time in the presence of external disturbances, and make the tracking error e ₁ =η-η _d converges in finite time and the control input is limited to less than the saturation value.

Combined with the actual engineering background, three hypotheses are proposed:

可测。Suppose 1 pose state η and its first derivative

measurable.

Suppose 2 disturbance observer observation error is bounded.

It is assumed that the expected value η _d of the 3 poses and its first and second derivatives are known and bounded.

It is assumed that the 4 perturbation lumped terms are bounded, that is, ||τ' _d ||≤χ, where χ is an unknown positive constant.

1.2 Definition of finite time control

Consider the following system:

上的光滑函数V(x)，并且存在实数p＞0，0＜α<1以及d>0，使得V(x)在

上正定和

在

上半负定或

在

上半负定，则系统的原点是有限时间稳定的，停止时间依赖于初始值。In the formula, f: U ₀ ×R→R ⁿ is continuous on U ₀ ×R, and U ₀ is a neighborhood at the origin x=0. For the considered system (26), the finite-time stability theory of nonlinear control systems is defined as follows: Suppose there is a neighborhood defined at the origin

A smooth function V(x) on , and there exist real numbers p>0, 0<α<1, and d>0, such that V(x) is in

Shangzheng Dinghe

exist

first half negative definite or

exist

If the upper half is negative definite, the origin of the system is stable for a finite time, and the stop time depends on the initial value.

x(0)=x ₀ (27)

1.3 Backstep control method

define tracking error

Then according to formula (26), the error system can be obtained as:

Define dummy error:

z=e ₂ -α ₁ (30)

Among them, α ₁ is the virtual control law.

Take points:

Then the error system becomes:

If the control law τ is designed to make z bounded, then _e1 and _e2 are bounded.

1.4 Design of Sliding Mode Interference Observer

There is a perturbation lumped term τ' _d in the system (24). In order to estimate the perturbation value in a relatively short time, the sliding mode disturbance observer is used for approximation, and the sliding mode surface function is selected as:

s=ρ-v (33)

In the formula, ρ is an intermediate variable, and its form can be described as:

In the formula, k ₇ ∈ R ^3×3 is a positive definite diagonal matrix, 0<r<1, L ∈ R ^3×3 is a positive definite diagonal matrix.

Then the observed value of the disturbance lumped term is:

For the system (32), the disturbance observer of the form (35) is designed, then the sliding mode surface formula (33) converges to zero within the finite time t ₀ , and the disturbance lumped term is valid by the disturbance observer within the finite time t ₀ . estimate.

Definition: If 0<a ₁ <1 and 0<a ₂ <2 exist, then for ri ( _i =1,...,n), the following inequalities are satisfied:

In addition, sign represents a sign function in the present invention, and for a vector

ξ=[ζ ₁ …ζ _n ] ^T (38)

There is the following equation

ζ ^α = [|ζ ₁ | ^α sign(ζ ₁ )…|ζ _n | ^α sign(ζ _n )] ^T (39)

sign(ζ) ₌ [sign(ζ1)...sign( _ζn )] ^T (40)

Proof: Using the following Lypunov function:

Derivation of the above formula can get:

From equations (41) and (42), we can get

Then according to the finite time theory, it can be known that the sliding mode disturbance observer can estimate the disturbance in a finite time.

1.5 Control Input Saturation Constraint

Due to the physical limitations of the actuator, the control signal τ is constrained by the saturation value. it's here,

sat(τ)=[sat(τ ₁ )…sat(τ _n )] ^T (44)

sat(τ) is the vector of actual control inputs, produced by the actuator and the saturation control function sat(τ _i ) (i=1,2,...,n), representing the nonlinear saturation characteristics of the actuator. The saturation control function can be described as:

sat(τ _i )=τ _i (t)+θ _i (t) (45)

in

In the formula, τ _mi is the maximum allowable value of the control input.

1.6 Design of finite-time trajectory tracking controller

且由于扰动集总项值范围不易确定会导致观测器参数较难选取，故采用RBF神经网络进行逼近扰动集总项估计误差，即Perturbation lumped term estimation error occurs when using sliding mode observers

And because the value range of the perturbation lumped term is not easy to determine, it will lead to difficulty in selecting the observer parameters, so the RBF neural network is used to approximate the perturbation lumped term estimation error, that is,

φ(x)为径向基函数，θ^*∈R^m是神经网络最优权值，m为神经网络隐含节点数。且θ^*满足

且

m为隐藏节点数，ε^*是最优逼近误差。in

φ(x) is the radial basis function, θ ^* ∈ R ^m is the optimal weight of the neural network, and m is the number of hidden nodes in the neural network. and θ ^* satisfies

and

m is the number of hidden nodes, and ε ^* is the optimal approximation error.

The optimal weight θ ^* is defined as:

In the present invention, the radial basis function φ(x) selects the Gaussian basis function:

In the formula, d _i =[d _i1 ,d _i2 ,...,d _im ] is the center of the i-th neuron in the hidden layer; b _i =[b _i1 ,b _i2 ,...,b _im ] is the i-th neuron The width of the meta Gaussian function.

则观测误差

的估计可以写为：Take the neural network input as

then the observation error

The estimate of can be written as:

为权值矩阵的估计值，

均为

中的子矩阵，

j＝1,2,3，

代表第j行第i个神经网络权值的估计值，i＝1,2,…,6，φ(x)为中间变量，φ(x)＝[φ₁(x),φ₂(x),…,φ₆(x)]^T，φ_i(x)代表第i个神经网络的高斯形式的径向基函数。In the formula,

is the estimated value of the weight matrix,

both

A submatrix in ,

j=1,2,3,

Represents the estimated value of the ith neural network weight in the jth row, i=1,2,...,6, φ(x) is the intermediate variable, φ(x)=[φ ₁ (x),φ ₂ (x) ,…,φ ₆ (x)] ^T , φ _i (x) represents the radial basis function of the ith neural network in Gaussian form.

Based on the above analysis process, the following adaptive backstepping control law is designed:

In the formula: α ₁ is the virtual control law 1, α ₂ is the virtual control law 2, z is the virtual error, ε is the virtual error integral term, k _i ∈ R ^3×3 (i=1,2,3,4,5 , 6) is a positive definite diagonal matrix, 0<a<1, λ>0, c>0 are the control parameters and adaptive gain to be designed. It can be seen that when the mathematical model (24) of the error system of the benthic AUV can be transformed into the error system (32) through the error transformations (28) and (30), if the control input vector τ, the virtual control laws α ₁ , α ₂ And the adaptive law is designed in the form of Equation (51), then the transformation error z is uniform and eventually bounded, and the tracking error e ₁ satisfies the finite-time convergence performance.

Proof: take

but

Substitute α ₁ into equation (32) to get:

where α=-λ _min (k ₁ ), β=-λ _min (k ₄ );

Then according to the finite time control theory, as long as z converges in a finite time, then e ₁ converges in a finite time.

Pick

为相应的估计误差，λ＝diag[λ₁,λ₂,λ₃,λ₄,λ₅,λ₆]。where:

is the corresponding estimation error, λ=diag[λ ₁ ,λ ₂ ,λ ₃ ,λ ₄ ,λ ₅ ,λ ₆ ].

but

代入得：Set τ, α ₂ ,

Substitute into:

为一标量，故有Analyze the last three terms of equation (57): since

is a scalar, so we have

also because

Therefore

Define variables:

且

则当

时because

and

then when

Time

so

时，when

hour,

so

Combining equations (62) and (64), we get

Substitute h into inequalities (61) and (60) to get

And because z ^T k ₃ z > 0, z ^T k ₆ z > 0, so

Among them, k _3min =λ _min (k ₃ )z ^T z, k _6min =λ _min (k ₆ )z ^T z, so it can be obtained from equations (36) and (37)

故根据有限时间控制理论，选择合适参数即可使可底栖式轨迹跟踪误差在有限时间内收敛，证毕。in,

Therefore, according to the finite-time control theory, the benthic trajectory tracking error can be converged in a finite time by selecting appropriate parameters, and the verification is completed.

The invention obtains the performance of fast tracking of the desired pose by introducing the sliding mode disturbance observer system and the finite time control method, and relaxes the requirements for the selection of control parameters to a certain extent.

The invention combines the current disturbance and model uncertainty into a disturbance lumped term, uses a finite-time disturbance observer to approximate the disturbance lumped term value, introduces a neural network to estimate the observation error, and selects a finite-time backstepping control method to weaken the chattering effect. Therefore, the ways to deal with several factors that affect the tracking accuracy of the bottom-dwelling AUV's horizontal trajectory are included in the design of the controller, which is closer to the actual engineering needs.

2. Simulation part

2.1 Simulation preparation

In order to verify the effectiveness of the motion control method designed in the present invention, it is applied to a bottom-dwelling AUV horizontal plane motion model for simulation verification, and the model uncertainty and the combined disturbance lumped term of the ocean current disturbance are considered. influences. The corresponding parameters of the benthic AUV model are shown in Table 1-3.

Table 1 Hydrodynamic coefficient of benthic AUV

Table 2 Inertia coefficient of benthic AUV

Table 3 OBFN position and attitude simulation initial value table

perturbation lumped term

In order to facilitate the simulation analysis, the present invention quantifies the uncertainty of the model, and combines it with the external disturbance to form the disturbance lumped term H=[2sin0.2t+0.01, 2sin0.2t+0.01, sin0.2t+0.01] ^T , and the It is incorporated into the simulation module.

Disturbance Observer Parameters

The interference observer designed to verify the inventive method can effectively approximate the external interference, and its simulation parameters are shown in Table 4.

Table 4 Interference observer parameter values

Controller parameters

It is required that the system has a fast convergence speed and the actuator input needs to be controlled. Based on this, the following simulation parameters are selected, as shown in Table 5.

Table 5 Motion control parameter values

The parameters for the neural network item are as follows:

λ _i = 15, c = 2; the number of nodes in the hidden layer of the RBF neural network is taken as j = 6, and the center of the Gaussian basis function is expressed as d = [d ₁ ,...,d ₆ ], and the value is shown in the formula ( 70), the base width b _j =40.

2.2 Simulation Analysis

Consider that if the expected trajectory is more complex, the test of the control law will be more representative. Therefore, the present invention selects a relatively complex horizontal plane navigation trajectory as the desired trajectory, and its specific expression is as follows:

η _d (t) = [x(t), y(t), ψ(t)] ^T (71)

where _ηd is the desired trajectory.

In the simulation analysis, considering the existence of model uncertainty and the disturbance lumped term composed of external disturbances, as well as the influence of saturated input on the bottom-dwelling AUV. Figures 1 to 3 show the 3-DOF trajectory tracking curves of the bottom-dwelling AUV. Figures 4 to 6 show the estimates of the disturbance lumped term by the disturbance observer. Figures 7 to 9 show the control inputs of the benthic AUV.

It can be seen from Fig. 1 to Fig. 9 that the method proposed in the present invention can better observe the external disturbance and can track the desired trajectory in a relatively short time, and also limit the control input, and obtain a good dynamic process , to quickly achieve the performance of trajectory tracking.

The above calculation examples of the present invention are only to illustrate the calculation model and calculation process of the present invention in detail, but are not intended to limit the embodiments of the present invention. For those of ordinary skill in the art, on the basis of the above description, other different forms of changes or changes can also be made, and it is impossible to list all the embodiments here. Obvious changes or modifications are still within the scope of the present invention.

Claims (3)

1. a kind of horizontal plane track fast tracking control method of bottom-dwelling type AUV, is characterized in that, described method specifically comprises the following steps: Step 1. Consider the model uncertainty and current disturbance as a disturbance lumped term τ′ _d , and establish the kinematics and dynamics equations of the benthic AUV considering the disturbance lumped term; In the step 1, the kinematics and dynamics equations of the bottom-dwelling AUV considering the perturbation lumped term are established, which are specifically:

In the formula, v=[u, v ₀ , r] ^T , v represents the velocity and angular velocity vector of the benthic AUV in the horizontal plane under the carrier coordinate system, u represents the surge speed, v ₀ represents the sway speed, and r represents the sway speed Yaw angular velocity; superscript T stands for transposition; η=[x,y,ψ] ^T stands for the three-degree-of-freedom pose vector of the bottom-dwelling AUV in the horizontal plane in a fixed coordinate system, and x and y represent the bottom-mountable AUV respectively The longitudinal and lateral position coordinates of the perched AUV in the fixed coordinate system, ψ represents the heading angle; J(η) represents the coordinate transformation matrix between the fixed coordinate system and the carrier coordinate system, J(η)∈R ^3×3 , R represents a real number; τ′ _d represents the disturbance lumped term of the system; τ represents the control input vector;

is the first derivative of η,

Represents the velocity and angular velocity vectors of the benthic AUV in a fixed coordinate system;

is the first derivative of v,

Represents the acceleration and angular acceleration vectors of the benthic AUV in the carrier coordinate system; M ₀ represents the nominal value of the mass-inertia matrix; the superscript -1 represents the inverse of the matrix, and C ₀ (v) represents the Coriolis centripetal force the nominal value of the matrix; D ₀ (v) represents the nominal value of the fluid damping matrix; g ₀ represents the nominal value of the restoring force and restoring moment vectors; The fixed coordinate system O-XYZ is: take the sea surface or any point in the sea as the origin O, the X axis is located on the horizontal plane, and the specified true north direction is the positive direction; the Y axis is located on the horizontal plane, and the specified true east direction is the positive direction. direction; the Z axis is perpendicular to the XOY coordinate plane, and the direction of the center of the earth is positive; The carrier coordinate system O ₀ -X ₀ Y ₀ Z ₀ is: taking the position of the center of gravity of the benthic AUV as the origin O ₀ , the X ₀ axis is in the longitudinal section of the benthic AUV, and the water The line plane is parallel and the bow direction is the positive direction; the Y ₀ axis is perpendicular to the longitudinal section of the benthic AUV, parallel to the horizontal plane and the starboard direction is the positive direction; the Z ₀ axis is in the longitudinal section of the benthic AUV, and the The bottom-dwelling AUV water plane is vertical and the direction of the bottom of the boat is the positive direction;

where ΔM represents the uncertainty value of the mass inertia matrix; ΔC(v) represents the uncertainty value of the Coriolis centripetal force matrix; ΔD(v) represents the uncertainty value of the fluid damping matrix; Δg represents the restoring force and restoring moment vector The uncertainty value of τ _d represents the uncertainty value of the disturbance vector caused by the external disturbance; Step 2. Based on the kinematics and dynamics equations established in step 1, use the backstepping control method to establish an error system for trajectory tracking; The specific process of the second step is: Define tracking error:

In the formula, e ₁ represents the trajectory tracking error; e ₂ represents the velocity tracking error; η _d = [x _d , y _d , ψ _d ] ^T represents the three-degree-of-freedom pose of the benthic AUV in the horizontal plane in a fixed coordinate system Expected value, x _d is the expected value of x, y _d is the expected value of y, ψ _d is the expected value of ψ;

is the first derivative of η _d ;

is the first derivative of e ₁ ; v _d represents the expected vector of velocity and angular velocity on the horizontal plane of the benthic AUV in the carrier coordinate system; Then according to formula (2), the error system of trajectory tracking is established as:

In the formula,

is the first derivative of _e2 ;

is the first derivative of J(η);

is the first derivative of v _d ; Define the dummy error z: z=e ₂ -α ₁ (6) In the formula, α ₁ is the virtual control law one; Take the virtual error integral term as ε:

Then the error system of trajectory tracking is transformed into:

In the formula,

is the first derivative of ε;

is the first derivative of z;

is the first derivative of α ₁ ; Step 3: Design a sliding mode disturbance observer according to the trajectory tracking error system established in step 2, and use the designed sliding mode disturbance observer to approximate the disturbance lumped term τ′ _d to obtain the observation value of the disturbance lumped term τ′ _d ; The specific process of the third step is: The sliding mode surface function s is chosen as: s=ρ-v (9) In the formula, ρ is an intermediate variable,

is the first derivative of ρ, and

of the form:

In the formula, k ₇ is a positive definite diagonal matrix, k ₇ ∈R ^3×3 ; L is a positive definite diagonal matrix, L=diag[L ₁ ,L ₂ ,L ₃ ]∈R ^3×3 ,L ₁ ,L ₂ , L ₃ are all elements in L,

is the maximum value of disturbance on three degrees of freedom; 0<r<1; sign represents the sign function; s=[s ₁ , s ₂ , s ₃ ] ^T , s ₁ , s ₂ , s ₃ are all elements in s, There is |s| ^r = [|s ₁ | ^r , |s ₂ | ^r , |s ₃ | ^r ] ^T , |·| represents the absolute value; Then the observed value of the disturbance lumped term τ′ _d is

In the formula,

is the observed value of the disturbance lumped term τ′ _d ;

is the first derivative of s; Step 4. Using radial basis function neural network to measure the observation error of the perturbed lumped term

make an estimate, get the observation error

estimated value; Step 5. According to the observation value of the disturbance lumped term τ′ _d and the observation error

The estimated value of , to design the controller, so that the pose of the bottom-dwelling AUV can track the expected value in a limited time, and the tracking error converges in a limited time. 2. a kind of horizontal plane trajectory fast tracking control method of bottom-dwelling AUV according to claim 1, is characterized in that, the concrete process of described step 4 is: observation error

for:

Observation error of perturbed lumped term using radial basis function neural network

For estimation, the input n of the radial basis function neural network is: n=[e ₁ ^T , e ₂ ^T , η _d ^T , v _d ^T ], then the radial basis function neural network outputs the observation error

is estimated to be:

In the formula,

is the estimated value of the weight matrix,

both

A submatrix in ,

Represents the estimated value of the ith neural network weight in the jth row, i=1,2,...,6, φ(n) is the intermediate variable, φ(n)=[φ ₁ (n),φ ₂ (n) ,…,φ ₆ (n)] ^T , φ _i (n) represents the radial basis function of the Gaussian form of the ith neural network. 3. a kind of horizontal plane trajectory fast tracking control method of bottom-dwelling type AUV according to claim 2, is characterized in that, the concrete process of described step 5 is: The control input vector τ is constrained by the saturation value: sat(τ)=[sat(τ ₁ ), sat(τ ₂ ), sat(τ ₃ )] ^T (19) In the formula, sat(τ) is the output value of the control input vector after saturation limit processing, τ _j represents the jth value of the control input vector τ, j=1, 2, 3; sat(τ _j ) represents the nonlinear saturation characteristic of the actuator, and the saturation control function is described as: sat(τ _j )=τ _j (t)+θ _j (t) (20) in

In the formula, θ _j (t) is the saturation control term, and τ _mj is the maximum allowable value of the j-th value τ _j of the control input vector τ; The adaptive backstepping control law is designed as follows:

In the formula, τ _s represents the nominal value of the control input vector, α ₂ is the second virtual control law, _ki is a positive definite diagonal matrix, i=1, 2,...6, _ki ∈ R ^3×3 , a is a constant, 0<a<1,

Yes

The first derivative of , c is the control parameter and adaptive gain to be designed, c>0, λ is a constant, λ>0.

Images