阅读说明：本技术 一种复合干扰下的欠驱动auv反步自适应模糊滑模控制方法 (Under-actuated AUV (autonomous Underwater vehicle) backstepping self-adaptive fuzzy sliding mode control method under combined interference ) 是由 魏延辉 蒋志龙 贺佳林 ***强 马博也 牛家乐 刘东东 姜瑶瑶 于 2019-09-30 设计创作，主要内容包括：本发明公开了一种复合干扰下的欠驱动AUV反步自适应模糊滑模控制方法。首先建立AUV的运动学与动力学模型,建立基于Serret-Frenet坐标系的轨迹跟踪误差模型；根据误差模型,考虑在无干扰情况下,分别设计水平面和垂直面的轨迹跟踪反步滑模控制器,实现轨迹跟踪功能；在前述基础上,考虑系统在复合干扰条件下的工作状态,在原有控制器上增加自适应模糊逻辑系统,提高系统的抗干扰能力。以实现在外界复合干扰条件下对欠驱动AUV的轨迹跟踪控制。本发明能够辨识欠驱动AUV复合干扰,为水下机器人的轨迹跟踪精确控制提供了一种具有自适应,鲁棒性强等优点的参考方案。(The invention discloses an under-actuated AUV (autonomous Underwater vehicle) backstepping self-adaptive fuzzy sliding mode control method under combined interference. Firstly, establishing a kinematics and dynamics model of the AUV, and establishing a track tracking error model based on a Serret-Frenet coordinate system; according to the error model, considering the situation without interference, respectively designing track tracking backstepping sliding mode controllers of a horizontal plane and a vertical plane to realize a track tracking function; on the basis, the working state of the system under the condition of composite interference is considered, and a self-adaptive fuzzy logic system is added on the original controller, so that the anti-interference capability of the system is improved. The trajectory tracking control of the under-actuated AUV under the condition of external composite interference is realized. The method can identify the under-actuated AUV composite interference, and provides a reference scheme with the advantages of self-adaption, strong robustness and the like for the accurate control of the trajectory tracking of the underwater robot.)

1. An under-actuated AUV (autonomous Underwater vehicle) backstepping self-adaptive fuzzy sliding-mode control method under combined interference is characterized by comprising the following steps of:

step 1: setting an expected trajectory, an initial position and a speed of the AUV, and establishing a dynamic model and a kinematic model of a vertical plane and a horizontal plane of the AUV;

step 2: establishing a track tracking error model based on a Serret-Frenet coordinate system;

and step 3: constructing a backstepping sliding mode controller for the horizontal plane and the vertical plane respectively by using the trajectory tracking error model and the dynamic model, and acquiring controller outputs under the horizontal plane and the vertical plane respectively;

and 4, step 4: and (3) designing a self-adaptive backstepping sliding mode fuzzy controller on the basis of the controller in the step (3), adding a self-adaptive fuzzy control system, and realizing the under-actuated AUV trajectory tracking control under the composite interference.

2. The under-actuated AUV (autonomous Underwater vehicle) backstepping adaptive fuzzy sliding-mode control method under the combined interference according to claim 1, characterized in that:

the dynamic model in the step 1 comprises a horizontal plane dynamic model and a vertical plane dynamic model, wherein the horizontal plane dynamic model meets the following requirements:

the vertical plane dynamics model satisfies:

the kinematic model in the step 1 comprises a horizontal plane kinematic model and a vertical plane kinematic model, wherein the horizontal plane kinematic model satisfies the following conditions:

the vertical surface kinematics model satisfies:

where m represents the actual mass of the AUV in motion,representing the projection of the acceleration on three axes of motion, x, respectively_g、y_g、z_gRespectively representing the components of the gravitational acceleration in the x, y, z directions, I_x、I_y、I_zRepresenting the moment of inertia in the x, y, z axes, m₁₁，m₂₂，m₃₃Additional mass and coriolis force for the longitudinal, lateral and heading of the AUV; x represents the thrust to which the simplified AUV is subjected; n represents the yaw moment to which the simplified AUV is subjected; x_uu，X_u|u|，Y_vv，Y_v|v|，N_rr，N_r|r|The viscous damping coefficient between the AUV and the water environment when the AUV translates and rotates in x, y and z axes is shown, and is a positive number.

3. The under-actuated AUV (autonomous Underwater vehicle) backstepping adaptive fuzzy sliding-mode control method under the combined interference according to claim 1, characterized in that:

the track tracking error model in the step 2 comprises a horizontal plane track tracking error model and a vertical plane track tracking error model, wherein the horizontal plane track tracking error model satisfies the following conditions:

wherein psi_eFor course angle tracking error, psi_e＝ψ-ψ_P，Is the derivative of the course angle error, Up is the speed of movement of the reference point along the reference track, τ_e、n_eRespectively representing the tracking errors of the tracking points in the tangential direction and the normal direction of the tracking track; r and r_pRespectively representing along the z-axis and pointing U_pAngular velocity of the direction;

wherein the vertical plane trajectory tracking error model satisfies:

wherein theta is_eIndicating a pitch tracking error.

4. The under-actuated AUV (autonomous Underwater vehicle) backstepping adaptive fuzzy sliding-mode control method under the combined interference according to claim 1, characterized in that:

step 3, the backstepping sliding mode controller comprises a horizontal surface backstepping sliding mode longitudinal speed controller, a horizontal surface backstepping sliding mode course controller and a vertical surface backstepping sliding mode trim angle controller;

wherein, the horizontal plane backstepping sliding mode longitudinal speed controller satisfies:

the horizontal surface backstepping sliding mode course controller meets the following requirements:

the vertical surface backstepping sliding mode pitch angle controller meets the following requirements:

5. the under-actuated AUV (autonomous Underwater vehicle) backstepping adaptive fuzzy sliding-mode control method under the combined interference according to claim 1, characterized in that:

step 4 the adaptive backstepping sliding mode fuzzy controller comprises: a horizontal plane backstepping self-adaptive fuzzy sliding mode longitudinal speed controller, a horizontal plane backstepping self-adaptive fuzzy sliding mode course angle controller and a vertical plane backstepping self-adaptive fuzzy sliding mode pitch angle controller;

wherein, the horizontal plane backstepping self-adaptive fuzzy sliding mode longitudinal speed controller meets the following requirements:

the horizontal plane backstepping self-adaptive fuzzy sliding mode course angle controller meets the following requirements:

the vertical surface backstepping self-adaptive fuzzy sliding mode pitch angle controller meets the following requirements:

whereinIs the output of the fuzzy logic system and,is the output of the fuzzy logic system and,disturbance terms for fuzzy logic systems, S₁＝u-u_dH and beta each represent a real number having a positive value, z₁＝ψ-ψ_d，The index numbers of the subscripts indicate the representation of the parameters in the different controllers.

Technical Field

The invention relates to the field of track tracking control of underwater robots, in particular to a backstepping self-adaptive fuzzy sliding mode control method which can enable an AUV to stably track a preset track under compound interference.

Background

The ocean is a vital resource treasury on the earth, and is gradually the object of human key development due to the imminent exhaustion of land resources. According to the detection of human beings, a large amount of fossil fuels, metal deposits and biological resources exist in the ocean, and the ocean is a treasure place capable of carrying out transportation and wave power generation. In recent years, mankind has accelerated the pace of ocean development, which is an important area of research and development in various countries. However, the marine environment is special compared with the land, the underwater environment is very severe, and factors such as underwater pressure, temperature, illumination and the like can be greatly changed along with the increase of water depth. Due to the danger and complexity of the submarine environment, manned underwater operation is very dangerous, so that the research of a high-technology unmanned underwater detector and the research and development of an intelligent underwater robot (Autonomous underwater vehicle) as a high-tech ocean detection carrier are urgently required, and the research and development of an AUV are products under the background of the era and are organic combination of science and technology and information. At present, a plurality of AUVs of different models are put into use successively, and the application of the AUV plays a great role in human development and ocean utilization. The AUV can explore underwater resources, collect marine samples, observe marine life, explore submarine topography, and the like.

The intelligent underwater robot can be divided into three categories according to whether the input number is matched with the controlled degree of freedom: the system comprises a fully-driven underwater robot, an over-driven underwater robot and an under-driven underwater robot. In consideration of saving cost and reducing weight, the invention adopts the under-actuated AUV for research, the under-actuated AUV is an underwater robot with the dimension of control input less than the degree of freedom of a body, the under-actuated AUV has the advantages of high system reliability, low energy consumption, high system propulsion efficiency and the like, and has great effect in the fields of marine exploration, hydrological investigation, target detection, biological sampling and the like. However, the under-actuated AUV system has strong coupling, the model has nonlinearity and time-varying property, the model parameters have uncertainty, and the under-actuated AUV is easily influenced by external interference. Therefore, the quality of the design of the control algorithm determines the quality of the AUV trajectory tracking performance.

At present, most of research on AUV control at home and abroad is based on a controller designed according to a nominal model, the self dynamic characteristics of the under-actuated AUV are ignored, and the influence of external interference and parameter uncertainty is not considered.

Disclosure of Invention

Aiming at the prior art, the invention aims to provide an under-actuated AUV (autonomous Underwater vehicle) backstepping self-adaptive fuzzy sliding mode control method under the composite interference, which can self-adaptively identify the composite interference and inhibit the influence of the interference, so that a system can stably track and has the characteristic of strong robustness.

In order to solve the technical problem, the under-actuated AUV backstepping self-adaptive fuzzy sliding-mode control method under the composite interference comprises the following steps of:

step 1: setting an expected trajectory, an initial position and a speed of the AUV, and establishing a dynamic model and a kinematic model of a vertical plane and a horizontal plane of the AUV;

step 2: establishing a track tracking error model based on a Serret-Frenet coordinate system;

and step 3: constructing a backstepping sliding mode controller for the horizontal plane and the vertical plane respectively by using the trajectory tracking error model and the dynamic model, and acquiring controller outputs under the horizontal plane and the vertical plane respectively;

and 4, step 4: and (3) designing a self-adaptive backstepping sliding mode fuzzy controller on the basis of the controller in the step (3), adding a self-adaptive fuzzy control system, and realizing the under-actuated AUV trajectory tracking control under the composite interference.

The invention also includes:

1. the dynamic model in the step 1 comprises a horizontal plane dynamic model and a vertical plane dynamic model, wherein the horizontal plane dynamic model meets the following requirements:

the vertical plane dynamics model satisfies:

the kinematic model in the step 1 comprises a horizontal plane kinematic model and a vertical plane kinematic model, wherein the horizontal plane kinematic model satisfies the following conditions:

the vertical surface kinematics model satisfies:

where m represents the actual mass of the AUV in motion,representing the projection of the acceleration on three axes of motion, x, respectively_g、y_g、z_gRespectively representing the components of the gravitational acceleration in the x, y, z directions, I_x、I_y、I_zRepresenting the moment of inertia in the x, y, z axes, m₁₁，m₂₂，m₃₃Additional mass and coriolis force for the longitudinal, lateral and heading of the AUV; x represents the thrust to which the simplified AUV is subjected; n represents the yaw moment to which the simplified AUV is subjected; x_uu，X_u|u|，Y_vv，Y_v|v|，N_rr，N_r|r|The viscous damping coefficient between the AUV and the water environment when the AUV translates and rotates in x, y and z axes is shown, and is a positive number.

2. The trajectory tracking error model in the step 2 comprises a horizontal plane trajectory tracking error model and a vertical plane trajectory tracking error model, wherein the horizontal plane trajectory tracking error model satisfies the following conditions:

wherein psi_eFor course angle tracking error, psi_e＝ψ-ψ_P，Is the derivative of the course angle error, Up is the speed of movement of the reference point along the reference track, τ_e、n_eRespectively representing the tracking errors of the tracking points in the tangential direction and the normal direction of the tracking track; r and r_pRespectively representing along the z-axis and pointing U_pAngular velocity of the direction;

wherein the vertical plane trajectory tracking error model satisfies:

wherein theta is_eIndicating a pitch tracking error.

3. Step 3, the backstepping sliding mode controller comprises a horizontal surface backstepping sliding mode longitudinal speed controller, a horizontal surface backstepping sliding mode course controller and a vertical surface backstepping sliding mode trim angle controller;

wherein, the horizontal plane backstepping sliding mode longitudinal speed controller satisfies:

the horizontal surface backstepping sliding mode course controller meets the following requirements:

the vertical surface backstepping sliding mode pitch angle controller meets the following requirements:

4. step 4 the adaptive backstepping sliding mode fuzzy controller comprises: a horizontal plane backstepping self-adaptive fuzzy sliding mode longitudinal speed controller, a horizontal plane backstepping self-adaptive fuzzy sliding mode course angle controller and a vertical plane backstepping self-adaptive fuzzy sliding mode pitch angle controller;

wherein, the horizontal plane backstepping self-adaptive fuzzy sliding mode longitudinal speed controller meets the following requirements:

the horizontal plane backstepping self-adaptive fuzzy sliding mode course angle controller meets the following requirements:

the vertical surface backstepping self-adaptive fuzzy sliding mode pitch angle controller meets the following requirements:

whereinIs the output of the fuzzy logic system and,is the output of the fuzzy logic system and,disturbance terms for fuzzy logic systems, S₁＝u-u_dH and beta each represent a real number having a positive value, z₁＝ψ-ψ_d，The index numbers of the subscripts indicate the representation of the parameters in the different controllers.

The invention has the beneficial effects that: the method comprises the steps of generating an error variable, designing a backstepping sliding mode controller under the condition of no interference by utilizing the error variable and a dynamic model, realizing stable tracking of the AUV, further adding composite interference, adding a fuzzy logic system, designing a self-adaptive backstepping sliding mode fuzzy controller, and realizing accurate control of the trajectory tracking of the AUV under the composite interference. Compared with the prior art, the method has the advantages of more accurate tracking effect, no buffeting, better composite interference suppression and higher stability.

Drawings

Fig. 1 is an AUV coordinate system reference diagram.

Fig. 2 is a flow chart of adaptive backstepping sliding mode fuzzy control.

Fig. 3 is a structure diagram of adaptive backstepping sliding mode fuzzy control.

FIG. 4 is a horizontal backstepping sliding mode control trajectory tracking diagram.

FIG. 5 is a vertical surface backstepping sliding mode control trajectory tracking diagram.

Fig. 6 is a graph of horizontal circular trajectory tracking under the composite interference.

Fig. 7 is a graph of vertical circular trajectory tracking under a compound disturbance.

Detailed Description

The following further describes the embodiments of the present invention with reference to the drawings.

The invention discloses an under-actuated AUV (autonomous Underwater vehicle) backstepping self-adaptive fuzzy sliding mode control method under combined interference. Firstly, establishing a kinematics and dynamics model of the AUV, and establishing a track tracking error model based on a Serret-Frenet coordinate system; according to the error model, considering the situation without interference, respectively designing track tracking backstepping sliding mode controllers of a horizontal plane and a vertical plane to realize a track tracking function; on the basis, the working state of the system under the condition of composite interference is considered, and a self-adaptive fuzzy logic system is added on the original controller, so that the anti-interference capability of the system is improved. The trajectory tracking control of the under-actuated AUV under the condition of external composite interference is realized. The method can identify the under-actuated AUV composite interference, and provides a reference scheme with the advantages of self-adaption, strong robustness and the like for the accurate control of the trajectory tracking of the underwater robot.

The specific technical scheme is as follows:

an under-actuated AUV (autonomous Underwater vehicle) backstepping self-adaptive fuzzy sliding-mode control method under compound interference comprises the following contents:

step 1, setting initial conditions and an expected track of an AUV, and establishing a dynamics and kinematics model of a vertical plane and a horizontal plane of the AUV;

step 2, establishing a track tracking error model based on a Serret-Frenet coordinate system;

step 3, constructing a backstepping sliding mode control controller for the horizontal plane and the vertical plane respectively by using the error variable and the AUV dynamic model, and acquiring controller outputs under the horizontal plane and the vertical plane respectively to realize under-actuated AUV trajectory tracking control under the condition of no interference;

and 4, adding a self-adaptive fuzzy control system to the trajectory tracking controller under the undisturbed control to realize the identification and inhibition of the compound interference and weaken the buffeting of the sliding mode. And the under-actuated AUV trajectory tracking control under the composite interference is realized.

The mathematical model of the AUV is as follows:

the horizontal plane kinematic equation is:

the vertical plane kinematic equation is:

the horizontal plane kinetic equation is:

the vertical plane kinetic equation is:

wherein: m is₁₁，m₂₂，m₃₃Additional mass and coriolis force for the longitudinal, lateral and heading of the AUV;

AUV propulsion direction is X-axis direction, X and Y are thrust of AUV along X coordinate axis and Y coordinate axis direction, N represents torque along z-axis direction, and X represents torque_uu，X_u|u|，Y_vv，Y_v|v|，N_rr，N_r|r|The viscous damping coefficients of the AUV and the water environment during translation and rotation of the AUV on the x axis, the y axis and the z axis are positive numbers;

the AUV horizontal trajectory tracking error equation is as follows:

the AUV vertical plane trajectory tracking error equation is as follows:

the backstepping sliding mode controller comprises:

horizontal surface backstepping sliding mode longitudinal speed controller:

horizontal surface backstepping sliding mode course controller

Vertical surface backstepping sliding mode trim angle controller

The backstepping self-adaptive fuzzy sliding mode controller comprises the following steps:

horizontal surface backstepping self-adaptive fuzzy sliding mode longitudinal speed controller

Horizontal plane backstepping self-adaptive fuzzy sliding mode course angle controller design

Vertical surface backstepping self-adaptive fuzzy sliding mode pitch angle controller design

The specific implementation mode of the invention also comprises:

implementation 1: fig. 2 is a flow chart of adaptive backstepping sliding mode fuzzy control, and the implementation process is as follows:

step 1, establishing a dynamics and kinematics model of a vertical plane and a horizontal plane of the AUV;

step 2, establishing a track tracking error model based on a Serret-Frenet coordinate system;

step 3, constructing a backstepping sliding mode control controller for the horizontal plane and the vertical plane respectively by using the error variables and the dynamic model, and acquiring controller outputs under the horizontal plane and the vertical plane respectively to realize under-actuated AUV (autonomous underwater vehicle) trajectory tracking control under the condition of no interference;

and 4, adding a self-adaptive fuzzy control system to the trajectory tracking controller under the undisturbed control to realize the identification and inhibition of the compound interference and weaken the buffeting of the sliding mode. And the under-actuated AUV trajectory tracking control under the composite interference is realized.

Implementation 2: as shown in fig. 3, it can be seen that the fuzzy sliding mode controller mainly includes a fuzzy sliding mode controller, an adaptive backstepping controller and a control object. The invention establishes the kinematics and dynamics model of AUV:

the horizontal plane kinematic equation is:

the vertical plane kinematic equation is:

the horizontal plane kinetic equation is:

the vertical plane kinetic equation is:

then, a tracking error model is established under a Serret-Frenet coordinate system:

the AUV horizontal plane trajectory tracking error equation is as follows:

the AUV vertical plane trajectory tracking error equation is as follows:

implementation 3: designing a self-adaptive backstepping controller:

horizontal surface backstepping sliding mode longitudinal speed controller:

horizontal surface backstepping sliding mode course controller

Vertical surface backstepping sliding mode trim angle controller

Fig. 4 and 5 are obtained by applying this controller to the control target in embodiment 1. Fig. 4 is a graph of circular trajectory tracking in the horizontal plane, and fig. 5 is a graph of sinusoidal trajectory tracking in the vertical plane. The simulation assumes the same initial conditions, does not consider external interference, and the expected speed of AUV is u_dThe circle and the sine curve are respectively selected as the tracks to be tracked, and the initial state of the AUV is v (0) ═ r (0) ═ 0, and u (0) ═ 0.08 m/s. As can be seen from fig. 4 and 5, the horizontal plane trajectory tracking controller and the PID controller designed by the present invention can better track the target trajectory without external interference. The backstepping sliding mode controller can track the upper target track relatively more quickly, and the PID controller has larger offset in the early period; the backstepping sliding mode controller can achieve better tracking effect than the traditional PID under the condition of no interference.

Implementation 4: on the basis of implementation 3, the adaptive backstepping sliding mode fuzzy controller is designed as follows:

horizontal surface backstepping self-adaptive fuzzy sliding mode longitudinal speed controller

Horizontal plane backstepping self-adaptive fuzzy sliding mode course angle controller design

Vertical surface backstepping self-adaptive fuzzy sliding mode pitch angle controller design

WhereinIs the output of the fuzzy logic system and,is the output of the fuzzy logic system and,disturbance terms for fuzzy logic systems, S₁＝u-u_dH and beta each represent a real number having a positive value, z₁＝ψ-ψ_d，The index numbers of the subscripts indicate the representation of the parameters in the different controllers.

And (3) acting the controller on the control object in the implementation 2, adding compound interference, and simulating the horizontal plane. The simulation assumes the same initial conditions and the desired speed of AUV is u_d1m/s, and the initial state of the AUV is u (0) ═ 0.08m/s, v (0) ═ r (0) ═ 0, ψ (0) ═ 0, ξ (0) ═ η (0) ═ 0,and respectively selecting a circle and a straight line as the tracks to be tracked. In addition, model parameter estimatesAndinitial value is set to 0, and external interference estimated valueAndthe initial value is also set to 0 and it is assumed that the under-actuated AUV is subjected to [3N 3N 3N/m]Selecting the parameters of the controller as the horizontal plane path tracking control parameters in the table 2

(1) The parametric equation for the circular trajectory is:

as shown in fig. 6, which is a tracking curve of a horizontal plane circular trajectory under the combined interference, it can be known from fig. 6 that both the back-step sliding mode controller and the back-step adaptive fuzzy sliding mode controller can track the circular trajectory well, but the back-step adaptive fuzzy sliding mode controller has a relatively better tracking effect.

Implementation 5: under the controller of the embodiment 4, the tracking simulation of the vertical plane is continued. The simulation assumes the same initial conditions and the desired speed of AUV is u_d1m/s, and the initial state of the AUV is u (0) ═ 0.06m/s, w (0) ═ q (0) ═ 0, θ (0) ═ 0, ξ (0) ═ ζ (0) ═ 0,and respectively selecting a sine curve and a straight line as the tracks to be tracked. In addition, model parameter estimatesAndis set to 0, and the external interference estimate is set toAndthe initial value is also set to 0 and it is assumed that the under-actuated AUV is subjected to [2N 2N 2N/m]The parameters of the selected controller are shown in table 3.

TABLE 3 vertical plane Path tracking control parameters

(1) The parametric equation for sinusoidal trajectory is:

as shown in fig. 7, which is a compound disturbance lower vertical sinusoidal track tracking curve, it can be seen that both controllers can track sinusoidal tracks well, but the backstepping sliding mode controller generates large buffeting. And the adaptive backstepping sliding mode fuzzy control can stably track under the composite interference.

The specific implementation mode of the invention also comprises:

step 1, establishing a dynamics and kinematics model of a vertical plane and a horizontal plane of the AUV;

step 2, a track tracking error model based on a Serret-Frenet coordinate system is solved to calculate a virtual control law;

step 3, constructing a backstepping sliding mode control controller for the horizontal plane and the vertical plane respectively by using the error variable and the virtual control law, and acquiring controller outputs under the horizontal plane and the vertical plane respectively to realize under-actuated AUV (autonomous underwater vehicle) trajectory tracking control under the condition of no interference;

and 4, adding a self-adaptive fuzzy control system to the trajectory tracking controller under the undisturbed control to realize the identification and inhibition of the compound interference and weaken the buffeting of the sliding mode. And the under-actuated AUV trajectory tracking control under the composite interference is realized.

TABLE 1 Underwater robot 6 degree of freedom motion identifier

The mathematical model of the AUV is (AUV six degrees of freedom motion identifier is shown in table 1):

the horizontal plane kinematic equation is:

where m represents the actual mass of the AUV in motion,respectively represent the accelerationThe projection on the three axes of motion is,

x_g、y_g、z_grespectively representing the components of the gravitational acceleration in the x, y, z directions, I_x、I_y、I_zRepresenting the moment of inertia in the x, y, z axes. The same applies below.

The vertical plane kinematic equation is:

the horizontal plane kinetic equation is:

the vertical plane kinetic equation is:

wherein: m is₁₁，m₂₂，m₃₃Additional mass and coriolis force for the longitudinal, lateral and heading of the AUV;

x represents the thrust to which the simplified AUV is subjected;

n represents the yaw moment to which the simplified AUV is subjected;

X_uu，X_u|u|，Y_vv，Y_v|v|，N_rr，N_r|r|the viscous damping coefficients are all positive numbers;

the AUV horizontal plane trajectory tracking error equation is as follows:

wherein: psi_eFor course angle tracking error, psi_e＝ψ-ψ_P，Is the derivative of the course angle error, Up is the speed of movement of the reference point along the reference track, τ_e、n_eRespectively representing the tracking error of the tracking point in the tangential direction and the normal direction of the tracking track, wherein the AUV vertical plane track tracking error equation is as follows:

wherein theta is_eIndicating pitch tracking error

Horizontal surface backstepping sliding mode longitudinal speed controller:

wherein h is₁Denotes a positive constant, S₁Surface for representing sliding form

Horizontal surface backstepping sliding mode course controller

Wherein c is₁、h₂Is a constant, S₂Is a slip form surface and is provided with a plurality of slip forms,

vertical surface backstepping sliding mode trim angle controller

Horizontal surface backstepping self-adaptive fuzzy sliding mode longitudinal speed controller

Horizontal plane backstepping self-adaptive fuzzy sliding mode course angle controller design

Vertical surface backstepping self-adaptive fuzzy sliding mode pitch angle controller design

Wherein the content of the first and second substances,to represent the input to the fuzzy system, h and β each represent a real number with a positive value. The index numbers of the subscripts indicate the representation of the parameters in the different controllers.