Self-adaptive fault-tolerant generalization control method for autonomous underwater vehicle

Abstract

The invention relates to a self-adaptive fault-tolerant generalization control method for an autonomous underwater vehicle, which comprises the following steps of: considering primary and quadratic term damping effects of water, unknown constant matrixes of a mass matrix and an inertia matrix of the autonomous underwater vehicle and external interference factors; an actuator effectiveness index matrix is introduced to model the autonomous underwater vehicle into an under-actuated model, and meanwhile it is ensured that the resultant force of gravity and buoyancy is zero, and kinematics and dynamics equations of the autonomous underwater vehicle are obtained; a controller is designed based on a backstepping method, a position error and a saturation function are defined, a Lyapunov function is selected, the position error is driven to be within a preset fixed constant range, an estimation rule and a projection function are introduced for solving the problem of unknown parameters to calculate thrust and control input, and high-precision trajectory tracking control over the autonomous underwater vehicle is achieved. Compared with the prior art, the method does not need linearization or conversion dynamics, can solve the problems of fault tolerance and time-varying interference, is better in performance, and effectively improves the control precision and stability of the autonomous underwater vehicle.

Description

Technical Field

[0001] The present invention relates to the technical field of autonomous underwater vehicle (AUV) control, and in particular to an adaptive fault-tolerant generalized control method for an autonomous underwater vehicle. Background Art

[0002] Autonomous underwater vehicles (AUVs), as advanced underwater exploration and operation tools, have attracted widespread attention in recent years due to their flexible mobility and continuously improving technology. AUVs have important applications in marine scientific research, resource exploration, environmental monitoring, military reconnaissance, and other fields. However, AUVs face numerous challenges in practical operation, including nonlinear dynamics, model uncertainty, external interference (such as ocean currents, waves, and wind), and system failures. If these factors are not effectively controlled, they will seriously affect the AUV's maneuverability and navigation stability, and thus its ability to perform its mission.

[0003] Since the AUV system has strong nonlinear dynamic characteristics and faces model uncertainty and external interference (such as ocean currents, waves, etc.) in the actual underwater environment. Existing methods require linearization of the AUV dynamic model, which is difficult to be directly applied to nonlinear systems, resulting in a decrease in control accuracy. CN112527018A discloses a three-dimensional stabilization control method for an underactuated autonomous underwater vehicle, comprising: applying Lyapunov theory and backstepping to design a three-dimensional stabilization kinematic controller for generating a desired speed signal; applying sliding mode control technology to design a three-dimensional stabilization dynamic controller, and outputting an actual control signal according to the desired speed signal. This method uses Lyapunov theory and backstepping to design a kinematic controller, and designs a dynamic controller based on sliding mode control (SMC) technology, thereby realizing three-dimensional stabilization control of an underactuated AUV in an ocean current environment. However, this method ignores roll and linearizes the nonlinear equation, resulting in a decrease in control accuracy, and it does not consider external interference, making it difficult to cope with complex underwater environments. Summary of the Invention

[0004] The purpose of the present invention is to provide an adaptive fault-tolerant generalized control method for autonomous underwater vehicles to solve the trajectory tracking control problem of AUVs under uncertain dynamic parameters and external disturbances, and achieve global consistent ultimate boundedness (GUUB). The method has the characteristics of simple structure, good robustness, and strong adaptability. In practical applications, it can better cope with various challenges in AUV control and improve the AUV's mission execution capability and environmental adaptability.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] An adaptive fault-tolerant generalized control method for an autonomous underwater vehicle comprises the following steps:

[0007] Considering the primary and secondary damping effects of water, the mass matrix and inertia matrix of the autonomous underwater vehicle are unknown constant matrices and external interference factors. The actuator effectiveness index matrix is ​​introduced to model the autonomous underwater vehicle as an underactuated model. At the same time, the net force of gravity and buoyancy is ensured to be zero. The kinematic and dynamic equations of the autonomous underwater vehicle are obtained.

[0008] A controller is designed based on the backstepping method. The position error and saturation function are defined. The Lyapunov function is selected to drive the position error into a preset fixed constant range. To address the problem of unknown parameters, estimation rules and projection functions are introduced to calculate the thrust and control input to ensure globally consistent final boundedness and realize high-precision trajectory tracking control of autonomous underwater vehicles.

[0009] The kinematic equation of the autonomous underwater vehicle is:

[0010]

[0011] Where p is the position of the autonomous underwater vehicle in the inertial coordinate system {I}, R is the rotation matrix from the body coordinate system {B} attached to the center of mass of the autonomous underwater vehicle to the inertial coordinate system {I}, v is the linear velocity of the autonomous underwater vehicle, ω is the angular velocity of the autonomous underwater vehicle, and S(·) represents a rotation matrix from arrive The mapping transforms the input variable x into an antisymmetric matrix that satisfies any vector x and S(x)=x×y, where × represents the cross product operation and · represents the derivative.

[0012] The dynamic equation of the autonomous underwater vehicle is:

[0013]

[0014] Where M is a positive definite mass matrix, M = diag(m1, m2, m3), m1, m2, m3 are the masses of the vehicle on the x, y, and z axes respectively, v is the linear velocity of the autonomous underwater vehicle, ω is the angular velocity of the autonomous underwater vehicle, d v ,d w is the linear damping vector, d v|v| ,d ω|ω| is the secondary damping vector, Represents vector dot product, g b is the combined force of gravity and buoyancy of the autonomous underwater vehicle, R is the rotation matrix from the body coordinate system {B} to the inertial coordinate system {I}, and e3 is a unit vector, e3 = [0,0,1] T , T is thrust, bv ,b w is the external disturbance in the inertial coordinate system {I}, τ is the control input, · represents the derivative, Π v 、Π ω is the actuator effectiveness index matrix, J is the positive definite inertia matrix, J = diag(J1, J2, J3), S(·) represents a arrive 's mapping.

[0015] The actuator effectiveness index matrix π v and Π ω Set as:

[0016]

[0017] in, i=1,2,3, all are uncertain constants.

[0018] when When both are not 0, the autonomous underwater vehicle is in full drive mode. When at least one is 0, the autonomous underwater vehicle is in underactuated mode.

[0019] The controller design based on the backstepping method includes the following steps:

[0020] Define the first error term z1 as:

[0021] z1=pp d +Rζ a

[0022] Where p is the position of the autonomous underwater vehicle in the inertial coordinate system {I}, p d is the desired position, ζ a is a constant vector defining the additional offset between the position and the desired position based on the orientation of the autonomous underwater vehicle, ζ a =[ζ a ,0,0] T ,ζ a ≠0, R is the rotation matrix from the body coordinate system {B} to the inertial coordinate system {I};

[0023] Define the second error term z2 as:

[0024]

[0025] Among them, b is a constant vector that defines the additional offset between the velocity of the autonomous underwater vehicle and the desired velocity, ζ b =[ζ b ,0,0] T ,ζ b≠0;

[0026] Define the first Lyapunov function V1 as:

[0027]

[0028] Among them, σ max To control the maximum value of the saturation function, κ is used to limit the maximum acceptable value of the error. a is a scaling factor for the position error, which helps adjust the controller response, z c =κ a (z1+δz2), δ is a positive constant, and u is a small positive constant used to prevent division by zero or excessive errors;

[0029] Compute the derivative of the first Lyapunov function V1 get:

[0030]

[0031] Among them, W(z1,z c )=δσ(z c ) T σ(z c )+k c (z2+δσ(z c )) T σ(z2+δσ(z c )), σ(x) is the saturation function of the independent variable x, z c =κ a (z1+δz2), M is the positive definite mass matrix, T x is the thrust of the spacecraft in the x-axis direction, e1 is a unit vector, and e3 = [1,0,0] T , v is the linear velocity of the autonomous underwater vehicle, ω is the angular velocity of the autonomous underwater vehicle, S(·) represents a arrive The mapping of , J is the positive definite inertia matrix, τ is the control input, d v ,d w is the linear damping vector, d v|v| ,d ω|ω| is the secondary damping vector, represents vector dot product, b v ,b w is the external disturbance in the inertial coordinate system {I};

[0032] The unknown parameters in the system are explicitly expressed as linear combinations of state variables and parameters:

[0033]

[0034] in, τ n =diag(τ1,τ2,τ3), m1 is the mass of the spacecraft on the x-axis, τ1, τ2, τ3 are the input torques of the spacecraft on the x-axis, y-axis, and z-axis, J1, J2, J3 are the moments of inertia of the spacecraft on the x-axis, y-axis, and z-axis, Ω is the state correlation matrix, is a set of unknown constant parameters;

[0035] Will Rewritten as:

[0036]

[0037] Introducing the Estimation Rule Indicates m n ,J n , The corresponding estimation error is:

[0038]

[0039] Taking into account the estimation error, a new Lyapunov function V2 is defined:

[0040]

[0041] Among them, λ m is a constant coefficient, is the projection function, s corresponds to the integral variable, and γ i are all constant coefficients, is a positive number, for a vector x,

[0042] The time derivative of V2 is:

[0043]

[0044] in, Γ=diag(γ1,γ2,...,γ 30 );

[0045] Calculate thrust T x And the control input τ:

[0046]

[0047] where Ξ T =[1,0 1×3 ] T ,Ξ τ =[0 3×1 ,1 3×3 ]T , The expression of Υ is as follows:

[0048]

[0049] The saturation function is:

[0050]

[0051] Here, μ is a small positive constant used to prevent division by zero or excessive errors.

[0052] The projection function is:

[0053]

[0054] in, For the independent variable The projection function, are all preset constants, ε is a positive number,

[0055] The estimation rule is:

[0056]

[0057] Apply the estimation law and calculate the thrust T x and the control input τ into the time derivative of V2 get:

[0058]

[0059] Compared with the prior art, the present invention has the following beneficial effects:

[0060] (1) The present invention is directly based on nonlinear model design and does not require a linearization process or conversion of the AUV dynamics into the so-called canonical form. It is applicable to both underactuated and fully actuated AUVs, which expands the scope of application of the method.

[0061] (2) The present invention realizes robust adaptive fault-tolerant control of external constant disturbances and system failures by designing estimation rules for model uncertainty and external disturbances and incorporating them into the control input, achieving globally consistent ultimate boundedness and significantly improving the stability and reliability of the system.

[0062] (3) The present invention can solve the trajectory tracking control problem with fewer backstepping iterations and achieve global consistent final boundedness. The proposed control scheme with a simplified structure can be extended to underactuated surface unmanned vessels and rotorcraft to solve the trajectory tracking problem, and has a wide range of applications.

[0063] (4) The drive signals designed in the present invention, namely the thrust and control input torque, are bounded relative to the position error, which is a desirable characteristic. In particular, when considering that the initial position error can be arbitrarily large, effective control can be achieved by making the actuation signal proportional to the position error.

[0064] (5) The present invention takes into account the uncertainty of the model and external interference, and designs a projection function to achieve robust control of external interference, which is more applicable. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 is a flow chart of the method of the present invention;

[0066] Figure 2 Schematic diagram of the horizontal motion of the AUV of the present invention;

[0067] Figure 3 Graph showing the expected and actual trajectories of an AUV in one embodiment. DETAILED DESCRIPTION

[0068] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0069] This embodiment provides an adaptive fault-tolerant generalized control method for an autonomous underwater vehicle (AUV). In response to the challenges faced by AUV control, such as nonlinear dynamics, model uncertainty, external interference and system failure, existing control methods have many limitations. Based on backstepping technology, the present invention first establishes an AUV model, defines the inertial system position error and related terms, selects the Lyapunov function, and introduces estimation rules and projection functions to design a controller to handle unknown parameters. Stability has been proven to make the error term converge globally to the zero neighborhood to achieve global consistent ultimate boundedness (GUUB). Simulation results show that the controller can guide the AUV to closely track the reference trajectory. The control signal of this method is bounded and is suitable for under-driven and fully-driven AUVs. Compared with existing methods, it does not require linearization or conversion dynamics, can solve fault tolerance and time-varying interference problems, has better performance, and effectively improves the control accuracy and stability of the AUV.

[0070] Specifically, such as Figure 1 As shown, the method includes the following steps:

[0071] S1, considering the primary and secondary damping effects of water, the mass matrix and inertia matrix of the autonomous underwater vehicle are unknown constant matrices and external interference factors. The actuator effectiveness index matrix is ​​introduced to model the autonomous underwater vehicle as an under-actuated model, while ensuring that the resultant force of gravity and buoyancy is zero, and the kinematic and dynamic equations of the autonomous underwater vehicle are obtained.

[0072] In this step, this embodiment introduces an inertial coordinate system and a body coordinate system to determine the kinematic equation and the dynamic equation, and determines the driving state through the actuator effectiveness index.

[0073] like Figure 2 As shown in , according to the horizontal motion relationship of AUV, the kinematic equation of autonomous underwater vehicle is:

[0074]

[0075] Where p is the position of the autonomous underwater vehicle in the inertial coordinate system {I}, R is the rotation matrix from the body coordinate system {B} attached to the center of mass of the autonomous underwater vehicle to the inertial coordinate system {I}, v is the linear velocity of the autonomous underwater vehicle, ω is the angular velocity of the autonomous underwater vehicle, and S(·) represents a rotation matrix from arrive The mapping transforms the input variable x into an antisymmetric matrix that satisfies any vector x and S(x)=x×y, where × represents the cross product operation and · represents the derivative.

[0076] The dynamic equation of the autonomous underwater vehicle is:

[0077]

[0078] Where M is a positive definite mass matrix, M = diag(m1, m2, m3), m1, m2, m3 are the masses of the spacecraft on the x, y, and z axes respectively, d v ,d w is the linear damping vector, d v|v| ,d ω|ω| is the secondary damping vector, Represents vector dot product, g b is the combined force of gravity and buoyancy of the autonomous underwater vehicle, e3 is a unit vector, e3 = [0,0,1] T , T is thrust, b v ,b w is the external disturbance in the inertial coordinate system {I}, τ is the control input, Π v 、Π ω is the actuator effectiveness index matrix, J is the positive definite inertia matrix, J = diag(J1, J2, J3).

[0079] Most methods will linearize the model, which makes it difficult to directly apply it to nonlinear systems, resulting in reduced control accuracy, or rely on a full-drive model, which is not very applicable. The present invention considers the first-order and second-order hydrodynamic damping effects when modeling the system dynamics. The mass matrix and inertia matrix are unknown constant matrices, and external interference factors are introduced. It should be noted that the actuator effectiveness index matrix Π v and Π ω Used to determine the drive status, set to:

[0080]

[0081] in, i=1,2,3, all are uncertain constants.

[0082] when When all are not 0, the autonomous underwater vehicle has 6 inputs and is in full drive mode. When at least one is 0, the autonomous underwater vehicle is in underactuated mode. If is zero, the AUV has five inputs and is in underactuated mode. Ensure that the gravity and buoyancy of the AUV are b It is set to zero to adapt to under-drive and full-drive modes, and has good drive compatibility.

[0083] In this step, the kinematic equations accurately describe the geometric relationship between the AUV's position, velocity, and attitude, while the dynamic equations precisely describe the relationship between the forces and torques acting on the AUV and the changes in the AUV's motion state. The modeling process fully considers the primary and secondary damping of water, as well as the unknown constant matrices of the AUV's mass matrix and inertia matrix, and external interference. The actuator effectiveness index matrix can flexibly adjust the AUV's driving state according to the settings, modeling it as an under-actuated model while ensuring that the resultant force of gravity and buoyancy is zero, providing an accurate model foundation for the design of subsequent control strategies.

[0084] S2, a controller is designed based on the backstepping method, the position error and saturation function are defined, and the Lyapunov function is selected to drive the position error into a preset fixed constant range. For the problem of unknown parameters, estimation rules and projection functions are introduced to calculate the thrust and control input to ensure the globally consistent final boundedness and realize high-precision trajectory tracking control of autonomous underwater vehicles.

[0085] Based on backstepping techniques, this step develops a robust, adaptive, fault-tolerant trajectory tracking controller for an underactuated AUV. To compensate for uncertain model parameters and external disturbances, a set of estimation laws is designed and embedded into the control law. The design begins by defining the position error in the inertial frame. First, the first error term is defined. By introducing a constant vector, the number of backstepping steps is reduced, simplifying the control complexity while still achieving the desired control objective. The first error term, z1, is defined as:

[0086] z1=pp d +Rζ a (3)

[0087] Where p is the position of the autonomous underwater vehicle in the inertial coordinate system {I}, p d is the desired position, ζ a is a constant vector defining the additional offset between the position and the desired position based on the orientation of the autonomous underwater vehicle, ζ a =[ζ a ,0,0] T ,ζ a ≠0, R is the rotation matrix from the body coordinate system {B} to the inertial coordinate system {I}.

[0088] Define the second error term z2 as:

[0089]

[0090] Among them, b is a constant vector that defines the additional offset between the velocity of the autonomous underwater vehicle and the desired velocity, ζ b =[ζ b ,0,0] T ,ζ b ≠0.

[0091] Define the first Lyapunov function V1 as:

[0092]

[0093] Among them, σ max To control the maximum value of the saturation function, κ is used to limit the maximum acceptable value of the error. a is a scaling factor for the position error, which helps adjust the controller response, z c =κ a (z1+δz2), δ is a positive constant, and u is a small positive constant used to prevent division by zero or excessive errors.

[0094] Compute the derivative of the first Lyapunov function V1 get:

[0095]

[0096] Among them, W(z1,z c )=δσ(z c ) T σ(z c )+k c (z2+δσ(z c )) T σ(z2+δσ(z c )), σ(x) is the saturation function of the independent variable x, z c =κ a (z1+δz2), M is the positive definite mass matrix, T x is the thrust of the spacecraft in the x-axis direction, e1 is a unit vector, and e3 = [1,0,0] T , v is the linear velocity of the autonomous underwater vehicle, ω is the angular velocity of the autonomous underwater vehicle, S(·) represents a arrive The mapping of , J is the positive definite inertia matrix, τ is the control input, d v ,d w is the linear damping vector, d v|v| ,d ω|ω| is the secondary damping vector, represents vector dot product, b v ,b w is the external disturbance in the inertial coordinate system {I}.

[0097] In order to ensure a bounded driving signal relative to the position error, a saturation function is introduced to achieve control under any large value of the initial position error. Its expression is:

[0098]

[0099] Here, μ is a small positive constant used to prevent division by zero or excessive errors.

[0100] Since the uncertainty in Equation (6) cannot be included in the control law, T cannot be directly obtained. x To solve this problem, this embodiment uses a linear parameterization technique for unknown parameters. The core idea of ​​this method is to express the unknown parameters in the system as a linear combination of state variables and parameters, as shown below:

[0101]

[0102] in, m1 is the mass of the spacecraft on the x-axis, τ1, τ2, τ3 are the input torques of the spacecraft on the x-axis, y-axis, and z-axis, J1, J2, J3 are the moments of inertia of the spacecraft on the x-axis, y-axis, and z-axis, Ω is the state correlation matrix, is a set of unknown constant parameters;

[0103] Rewrite equation (6) as:

[0104]

[0105] As mentioned above, the unknown term m n ,J n , Cannot be directly in T x and τ, so the estimation rule is introduced Indicates m n ,J n , The corresponding estimation error is:

[0106]

[0107] Taking into account the estimation error, a new Lyapunov function V2 is defined:

[0108]

[0109] Among them, λ m is a constant coefficient, is the projection function, s corresponds to the integral variable, and γ i are all constant coefficients, is a positive number, for a vector x,

[0110] The projection function ensures that all estimates remain within a predefined bounded set, improving the system's robustness to unknowns and external interference, which can be expressed as:

[0111]

[0112] in, For the independent variable The projection function, are all preset constants, ε is a positive number,

[0113] The time derivative of V2 is:

[0114]

[0115] in, Γ=diag(γ1,γ2,…,γ 30).

[0116] Select the estimation rule as:

[0117]

[0118] Calculate thrust T x And the control input τ:

[0119]

[0120] where Ξ T =[1,0 1×3 ] T ,Ξ τ =[0 3×1 ,1 3×3 ] T , The expression of Υ is as follows:

[0121]

[0122] The estimated rule (12) and the calculated thrust T x Substitute the time derivative of V2 into Equation (13) and the control input τ Formula (11) yields:

[0123]

[0124] In summary, considering the designed estimation rule (12) and control input (13), the error terms z1 and z2 defined in (3) and (4) are driven globally to near zero, regardless of whether the uncertain model parameters exist, thus achieving globally consistent final boundedness.

[0125] In this step, a series of Lyapunov functions, based on the backstepping method, were selected to drive the position error within a fixed constant range. By designing control laws for the driving force and torque, global control of the AUV was achieved, achieving globally consistent ultimate boundedness. The introduced estimation law and projection function work together. The estimation law continuously updates the estimated values ​​of unknown parameters based on the system's real-time state and measurement information, compensating for the AUV's uncertain model parameters, namely the mass matrix, inertia matrix, and external disturbances. The projection function ensures that all estimated values ​​remain within a predefined bounded set, preventing abnormal fluctuations in the estimated values ​​from affecting the control effect, and jointly ensuring the effectiveness and stability of the controller.

[0126] In this embodiment, stability is proved based on the above control scheme, and the convergence of the error term is derived using inequalities.

[0127] For formula (14), using Young's inequality, we have:

[0128]

[0129] in, ε=||ζ b || 2 / 2.

[0130] From formula (15), we can further obtain:

[0131]

[0132] We can get ||z c ||,||σ(z c )||,||z2+δσ(z c )|| is ultimately bounded.

[0133] definition and in It is worth noting that by increasing and Can make and Arbitrarily small. Therefore, we can get:

[0134]

[0135] By z c The definition of We can further obtain:

[0136]

[0137] From Equations (16) and (17), it can be concluded that the error terms z1 and z2 globally converge to the neighborhood of zero.

[0138] Finally, simulations were conducted to verify the effectiveness and robustness of the control method. Specifically, by selecting appropriate parameters and setting a reference trajectory, the AUV was allowed to complete the trajectory tracking task along the reference trajectory, and the root mean square error was calculated to verify the effectiveness and robustness of the algorithm.

[0139] The reference trajectory is set to

[0140]

[0141] Where c1=13, c2=2.8, w=0.25. Figure 3 The reference trajectory and the true trajectory obtained by the proposed controller are shown. It can be seen that the proposed method can guide the AUV to move closely along the reference trajectory, and the root mean square error of ||z1|| in the steady state is 0.45(m).

[0142] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. An adaptive fault-tolerant generalized control method for an autonomous underwater vehicle, characterized in that: The following steps are involved: Considering the primary and secondary damping effects of water, the mass matrix and inertia matrix of the autonomous underwater vehicle are unknown constant matrices and external interference factors. The actuator effectiveness index matrix is ​​introduced to model the autonomous underwater vehicle as an underactuated model. At the same time, the net force of gravity and buoyancy is ensured to be zero. The kinematic and dynamic equations of the autonomous underwater vehicle are obtained. A controller is designed based on the backstepping method. The position error and saturation function are defined. The Lyapunov function is selected to drive the position error into a preset fixed constant range. To address the problem of unknown parameters, estimation rules and projection functions are introduced to calculate the thrust and control input to ensure globally consistent final boundedness and realize high-precision trajectory tracking control of autonomous underwater vehicles.

2. The adaptive fault-tolerant generalized control method for an autonomous underwater vehicle according to claim 1, characterized in that: The kinematic equation of the autonomous underwater vehicle is: Where p is the position of the autonomous underwater vehicle in the inertial coordinate system {I}, R is the rotation matrix from the body coordinate system {B} attached to the center of mass of the autonomous underwater vehicle to the inertial coordinate system {I}, v is the linear velocity of the autonomous underwater vehicle, ω is the angular velocity of the autonomous underwater vehicle, and S(·) represents a rotation matrix from arrive The mapping transforms the input variable x into an antisymmetric matrix that satisfies any vector x and S(x)=x×y, where × represents the cross product operation and · represents the derivative.

3. The adaptive fault-tolerant generalized control method for an autonomous underwater vehicle according to claim 1, characterized in that: The dynamic equation of the autonomous underwater vehicle is: Where M is a positive definite mass matrix, M = diag(m1, m2, m3), m1, m2, m3 are the masses of the vehicle on the x, y, and z axes respectively, v is the linear velocity of the autonomous underwater vehicle, ω is the angular velocity of the autonomous underwater vehicle, d v ,d w is the linear damping vector, d v|v| ,d ω|ω| is the secondary damping vector, Represents vector dot product, g b is the combined force of gravity and buoyancy of the autonomous underwater vehicle, R is the rotation matrix from the body coordinate system {B} to the inertial coordinate system {I}, and e3 is a unit vector, e3 = [0,0,1] T , T is thrust, b v ,b w is the external disturbance in the inertial coordinate system {I}, τ is the control input, · represents the derivative, Π v 、Π ω is the actuator effectiveness index matrix, J is the positive definite inertia matrix, J = diag(J1, J2, J3), S(·) represents a arrive 's mapping.

4. The adaptive fault-tolerant generalized control method for an autonomous underwater vehicle according to claim 3, characterized in that: The actuator effectiveness index matrix π v and Π ω Set as: in, i=1,2,3, all are uncertain constants.

5. The adaptive fault-tolerant generalized control method for an autonomous underwater vehicle according to claim 4, characterized in that: when When both are not 0, the autonomous underwater vehicle is in full drive mode. When at least one is 0, the autonomous underwater vehicle is in underactuated mode.

6. The adaptive fault-tolerant generalized control method for an autonomous underwater vehicle according to claim 1, characterized in that: The controller design based on the backstepping method includes the following steps: Define the first error term z1 as: z1=p-p d +Rζ a Where p is the position of the autonomous underwater vehicle in the inertial coordinate system {I}, p d is the desired position, ζ a is a constant vector defining an additional offset from the desired position based on the orientation of the autonomous underwater vehicle, ζ a ≠0, R is the rotation matrix from the body coordinate system {B} to the inertial coordinate system {I}; Define the second error term z2 as: Among them, b is a constant vector that defines the additional offset of the autonomous underwater vehicle speed from the desired speed, ζ b ≠0; Define the first Lyapunov function V1 as: Among them, σ max To control the maximum value of the saturation function, κ is used to limit the maximum acceptable value of the error. a is a scaling factor for the position error, which helps adjust the controller response, z c =κ a (z1+δz2), δ is a positive constant, and u is a small positive constant used to prevent division by zero or excessive errors; Compute the derivative of the first Lyapunov function V1 get: Among them, W(z1,z c )=δσ(z c ) T σ(z c )+k c (z2+δσ(z c )) T σ(z2+δσ(z c )), σ(x) is the saturation function of the independent variable x, z c =κ a (z1+δz2), M is the positive definite mass matrix, T x is the thrust of the spacecraft in the x-axis direction, e1 is a unit vector, and e3 = [1,0,0] T , v is the linear velocity of the autonomous underwater vehicle, ω is the angular velocity of the autonomous underwater vehicle, S(·) represents a arrive The mapping of , J is the positive definite inertia matrix, τ is the control input, d v ,d w is the linear damping vector, d v|v| ,d ω|ω| is the secondary damping vector, represents vector dot product, b v ,b w is the external disturbance in the inertial coordinate system {I}; The unknown parameters in the system are explicitly expressed as linear combinations of state variables and parameters: in, m1 is the mass of the spacecraft on the x-axis, τ1, τ2, τ3 are the input torques of the spacecraft on the x-axis, y-axis, and z-axis, J1, J2, J3 are the moments of inertia of the spacecraft on the x-axis, y-axis, and z-axis, Ω is the state correlation matrix, is a set of unknown constant parameters; Will Rewritten as: Introducing the Estimation Rule express The corresponding estimation error is: Taking into account the estimation error, a new Lyapunov function V2 is defined: Among them, λ m is a constant coefficient, is the projection function, s corresponds to the integral variable, and γ i are all constant coefficients, is a positive number, for a vector x, The time derivative of V2 is: Among them, Γ=diag(γ1,γ2,...,γ 30 ); Calculate thrust T x And the control input τ: in The expression of Υ is as follows:

7. The adaptive fault-tolerant generalized control method for an autonomous underwater vehicle according to claim 6, characterized in that: The saturation function is: Here, μ is a small positive constant used to prevent division by zero or excessive errors.

8. The adaptive fault-tolerant generalized control method for an autonomous underwater vehicle according to claim 6, characterized in that: The projection function is: in, For the independent variable The projection function, are all preset constants, ε is a positive number, 9. The adaptive fault-tolerant generalized control method for an autonomous underwater vehicle according to claim 6, characterized in that: The estimation rule is:

10. The adaptive fault-tolerant generalized control method for an autonomous underwater vehicle according to claim 9, characterized in that: Apply the estimation law and calculate the thrust T x and the control input τ into the time derivative of V2 get:

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