Quasi-linear parameter change motion modeling method for unmanned underwater heading device

Abstract

The invention discloses a quasi-linear parameter change motion modeling method for an unmanned underwater heading device. The method comprises the following steps: firstly, establishing a non-linear motion model of a full-drive unmanned underwater vehicle; then scheduling parameters are selected based on the model features of the unmanned underwater vehicle; then, nonlinear terms in the unmanned underwater vehicle model are reconstructed by using the scheduling parameters; and finally, establishing a quasi-linear parameter change model of the unmanned underwater vehicle based on the reconstructed nonlinear term. According to the method, the scheduling parameters are incorporated into the nonlinear model of the unmanned underwater vehicle, so that the quasi-linear parameter change model can explicitly allow the state matrix to depend on the scheduling parameters and time derivatives of all orders, the fidelity of the model of the unmanned underwater vehicle is improved, and the degree of freedom of controller design is increased.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of underwater unmanned vehicles, and particularly relates to a quasi-linear parameter variation motion modeling method for an unmanned underwater vehicle. BACKGROUND

[0002] As important equipment for developing and utilizing marine resources, unmanned underwater vehicles (UUVs) play a key role in the fields of civil use and scientific research. With the development of artificial intelligence, sensor technology and energy technology, unmanned underwater vehicles are developing towards higher autonomy, longer endurance, stronger operation capacity and cluster cooperation, which puts unprecedentedly high requirements on the motion control precision and robustness of unmanned underwater vehicles.

[0003] An accurate mathematical model is the basis for realizing high-precision motion control of unmanned underwater vehicles. However, the motion of an unmanned underwater vehicle is an extremely complex nonlinear, strongly coupled and time-varying process. The dynamic model of the unmanned underwater vehicle not only contains nonlinear terms of six degrees of freedom of a rigid body (such as the Coriolis and centripetal force matrix), but also involves complex hydrodynamic terms generated by the interaction between the vehicle body and the fluid, such as added mass, damping force, lift, etc. These hydrodynamic coefficients are usually nonlinear functions of the motion state of the vehicle.

[0004] This inherent high-order nonlinearity, parameter uncertainty and external disturbance bring great challenges to the design and analysis of the control system: first, directly designing a controller based on the complete nonlinear model often leads to a complex controller structure and a huge amount of online calculation, which is difficult to meet the limited computing power and real-time requirements of the onboard processor of the unmanned underwater vehicle; second, the stability analysis and performance synthesis theory of nonlinear systems is far from mature compared with linear systems, and it is difficult to guarantee the global stability and performance index of the controller within the entire working envelope.

[0005] In order to solve the above problems, the following methods are usually used in the prior art to deal with the nonlinear model of the unmanned underwater vehicle. The most common method is to perform Taylor expansion on the nonlinear model at a certain equilibrium point (such as the uniform straight sailing state) and ignore the high-order terms, thereby obtaining a linear time-invariant model. Based on the linear time-invariant model, mature linear control theories such as proportional-integral-derivative, linear quadratic regulator, etc. can be applied to design the controller. However, the disadvantage of this method is that the linearized model only has sufficient accuracy near the equilibrium point, and once the unmanned underwater vehicle performs large-scale maneuvering (such as high-speed turning, ascending and descending), the model mismatch error will increase sharply, resulting in a serious decline in control performance or even system instability.

[0006] To extend the operating range, researchers have proposed more advanced nonlinear control strategies, such as feedback linearization, sliding mode control, and backstepping. Feedback linearization exactly cancels the system nonlinearity through nonlinear state feedback, but its effectiveness is highly dependent on the accuracy of the model parameters and is sensitive to model uncertainties and external disturbances. Sliding mode control has strong robustness to parameter perturbations and external disturbances, but the inherent "chattering" problem can cause frequent switching of the actuator, damaging the equipment life. Backstepping provides a systematic controller design framework for a class of nonlinear systems, but the derivation process is tedious. In addition, intelligent control methods based on data-driven, such as neural networks and fuzzy logic, are also used to approximate the unknown dynamics of the system, but their performance depends on a large amount of training data, and the "black box" nature makes it difficult to conduct rigorous theoretical analysis of system stability.

[0007] To seek a better balance between model accuracy and control law design complexity, linear parameter-varying system theory emerged. Linear parameter-varying system describes the dynamic characteristics of a nonlinear system as a linear state space structure, but its state matrix varies with a set of real-time measurable, time-varying scheduling parameters. The significance of this modeling approach is to embed the behavior of the original nonlinear system into a family of continuously changing linear models, allowing the mature linear robust control theory (such as robust control, linear matrix inequality techniques, etc.) to be applied to the analysis and synthesis of nonlinear systems, ensuring the stability and performance of the system throughout the operating envelope.

[0008] However, when converting the nonlinear system of an unmanned underwater vehicle into a standard linear parameter-varying model, due to the presence of derivative terms of scheduling parameters in the state matrix of the system, certain approximations or omissions are required. SUMMARY

[0009] To overcome the shortcomings of the prior art, the present application provides a quasi-linear parameter-varying motion modeling method for an unmanned underwater vehicle, which first establishes a full-drive unmanned underwater vehicle nonlinear motion model; then selects scheduling parameters based on the model characteristics of the unmanned underwater vehicle; next, the nonlinear terms in the unmanned underwater vehicle model are reconstructed using the scheduling parameters; finally, a quasi-linear parameter-varying model of the unmanned underwater vehicle is established based on the reconstructed nonlinear terms. By incorporating scheduling parameters into the nonlinear model of the unmanned underwater vehicle, the quasi-linear parameter-varying model can explicitly allow the state matrix to depend on the scheduling parameters and their time derivatives of various orders, not only improving the fidelity of the unmanned underwater vehicle model, but also increasing the degree of freedom for controller design.

[0010] The technical solution adopted by the application to solve its technical problems is as follows:

[0011] Step 1: Establish a full-drive unmanned underwater vehicle nonlinear motion model;

[0012] Step 2: Select scheduling parameters based on model characteristics of the unmanned underwater vehicle;

[0013] Step 3: Reconstruct nonlinear terms in the unmanned underwater vehicle model using scheduling parameters;

[0014] Step 4: Establish a quasi-linear parameter-varying model of the unmanned underwater vehicle based on the reconstructed nonlinear terms.

[0015] Preferably, the step 1 is specifically:

[0016] Step 1-1: Simplify the spatial motion of the unmanned underwater vehicle into planar motion, and establish a nonlinear kinematic model and a dynamic model of the unmanned underwater vehicle;

[0017] Step 1-2: Establish a global coordinate system for the motion of the unmanned underwater vehicle;

[0018] Global coordinate system O E -x E y E z E An earth-fixed coordinate system is used to describe the position and attitude of the unmanned underwater vehicle; the origin O E of the earth-centered inertial system is selected as the reference point on the surface of the earth, x E points to an appropriate direction in the horizontal plane, y E is located in the horizontal plane x E O E z E and is perpendicular to the plane, and its direction makes the coordinate system satisfy the right-hand rule;

[0019] Step 1-3: Define the state vector of the unmanned underwater vehicle as:

[0020]

[0021] where x and y represent the position of the unmanned underwater vehicle in the earth-fixed coordinate system, and ψ represents the heading angle of the unmanned underwater vehicle;

[0022] Define the velocity vector of the unmanned underwater vehicle as:

[0023]

[0024] where u and v represent the forward speed and lateral speed of the unmanned underwater vehicle, respectively, and r represents the heading angular velocity of the unmanned underwater vehicle;

[0025] Through coordinate transformation, the rotation matrix between the earth-fixed reference frame and the body-fixed reference frame is defined as:

[0026]

[0027] Thus, the kinematic model of the unmanned underwater vehicle is described as

[0028]

[0029] Step 1-4: Establish the dynamic model of the unmanned underwater vehicle;

[0030] In the carrier-fixed coordinate system O B -x B y B z B , the center of buoyancy of the unmanned underwater vehicle is defined as the coordinate origin O B , x B extends along the vertical axis of the unmanned underwater vehicle and points forward, y B is perpendicular to the Ox B z B plane and points to the right; thus, the dynamic model of the unmanned underwater vehicle is represented as:

[0031]

[0032] wherein the system inertia matrix M is composed of the rigid body mass matrix M RB = diag(m, m, I z ) and the added mass matrix is represented as:

[0033]

[0034] m represents the mass of the unmanned underwater vehicle, I z represents the moment of inertia about the z axis, represents the surge added mass coefficient, represents the sway added mass coefficient, represents the yaw added moment of inertia coefficient; is the Coriolis centripetal matrix caused by the rotation and translation velocity of the unmanned underwater vehicle in the carrier-fixed coordinate system, for a 3-DOF model, C(v) is skew-symmetric, and is represented as:

[0035]

[0036] The damping matrix represents fluid power and moments opposite to the motion of the unmanned underwater vehicle:

[0037] D(v) = -diag(X u + X |u|u |u|, Y v + Y |v|v |v|, N r +N |r|r| r | ) (7) X u denotes the surge added mass coefficient, X |u|u denotes the quadratic surge damping coefficient, Y v denotes the sway added mass coefficient, Y |v|v denotes the quadratic sway damping coefficient, N r denotes the yaw added moment of inertia coefficient, N |r|r denotes the quadratic yaw damping moment coefficient; is the force and moment vector of the UUV motion;

[0038] Step 1-5: Further define the state vector to establish the UUV low speed motion model as:

[0039] where,

[0040]

[0041] Preferably, the step 2 is specifically:

[0042] The quasi-linear parameter-varying system scheduling parameters of the UUV are selected as ρ = [ψ u v r] T .

[0043] Preferably, the step 3 is specifically:

[0044] By selecting ρ = [ψ u v r] T , the nonlinear term rotation matrix J(η), the Coriolis centripetal force matrix C(v) and the hydrodynamic damping matrix D(v) are decomposed into the form of J(ρ), C(ρ) and D(ρ), thereby integrating the nonlinearity into the state matrix A(ρ).

[0045] Preferably, the step 4 is specifically:

[0046] Step 4-1: Discretize the continuous system by using the Newton-Euler method to obtain the discrete time motion model of the UUV nonlinear motion system:

[0047]

[0048] where, x k+1 and x k respectively represent the state vectors at k+1 and k time, T represents the sampling step, A k represents the state matrix at k time, B k represents the input matrix at k time, τ k represents the input vector at k time;

[0049] Step 4-2: Define the reference state and reference input as xd and τ d , so that the trajectory tracking error model is:

[0050]

[0051] wherein ξ k = x k - x d and u k = τ k - τ d are the trajectory tracking error and the control input error at time k, respectively; ξ k+1 denotes the trajectory tracking error vector at time k+1.

[0052] Step 4-3: The scheduling parameter vector is defined as ρ = [ψ u v r] T , and there exists a continuous homeomorphism such that The trajectory tracking error model is converted into a quasi-linear parameter-varying system:

[0053]

[0054] wherein the scheduling parameter and is defined as the compact set of scheduling parameters; A(ρ k ) denotes the state matrix of the quasi-linear parameter-varying error model at time k; B(ρ k ) denotes the input matrix of the quasi-linear parameter-varying error model at time k.

[0055] An electronic device, comprising: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device executes the above quasi-linear parameter-varying modeling method.

[0056] A computer readable storage medium, which stores a computer program, the computer program is executed by a processor to implement the above quasi-linear parameter-varying modeling method.

[0057] A chip, comprising: a processor, used to call and run a computer program from a memory, so that a device installed with the chip executes the above quasi-linear parameter-varying modeling method.

[0058] A computer program product, the computer program product comprises a computer storage medium, the computer storage medium stores a computer program, the computer program comprises instructions executable by at least one processor, when the instructions are executed by the at least one processor, the above quasi-linear parameter-varying modeling method is implemented.

[0059] The beneficial effects of the present application are as follows:

[0060] 1. The quasi-linear parameter-varying modeling method according to the present application can accurately reconstruct a large class of nonlinear systems into a parameterized linear structure in a more rigorous and direct mathematical way. It avoids structural model mismatch caused by neglecting derivative terms, thereby preserving the dynamic characteristics of the original nonlinear system to the greatest extent.

[0061] 2. The present application allows the state matrix to depend on scheduling parameters and their time derivatives of various orders by incorporating scheduling parameters into the nonlinear model of an unmanned underwater vehicle, which not only improves the fidelity of the unmanned underwater vehicle model, but also increases the degree of freedom of controller design.

[0062] 3. The theoretical analysis of the quasi-linear parameter-varying model proposed in the present application is relatively complex, but the resulting controller is usually a state feedback gain matrix. Although this gain matrix is a function of scheduling parameters, its online calculation amount is much smaller than solving complex nonlinear equations or performing iterative optimization, thereby making it possible to achieve high-performance control on the onboard computer of the resource-limited unmanned underwater vehicle. BRIEF DESCRIPTION OF DRAWINGS

[0063] Figure 1 Flowchart of the quasi-linear parameter-varying modeling method;

[0064] Figure 2 Schematic diagram of the global coordinate system and the carrier coordinate system;

[0065] Figure 3 Schematic diagram of state quantity changes in trajectory tracking of the embodiment of the present application;

[0066] Figure 4 Schematic diagram of control input quantity changes in trajectory tracking of the embodiment of the present application;

[0067] Figure 5 Schematic diagram of position error changes in trajectory tracking of the embodiment of the present application;

[0068] Figure 6 Schematic diagram of velocity error changes in trajectory tracking of the embodiment of the present application. DETAILED DESCRIPTION

[0069] The present application will be further described below in conjunction with the drawings and embodiments.

[0070] The object of the present application is to overcome the shortcomings and deficiencies of the prior art, and provide a quasi-linear parameter variation motion modeling method for an unmanned underwater vehicle, which provides a technical approach for solving the modeling and control problems of complex nonlinear systems such as unmanned underwater vehicles. Based on the method, the control system can significantly improve the tracking accuracy and robustness of the control system while ensuring low computational complexity.

[0071] The flow of the method is shown in Figure 1 The steps are as follows:

[0072] Step 1: Establish a full-drive unmanned underwater vehicle nonlinear motion model;

[0073] The research object of the present application is a class of full-drive unmanned underwater vehicles. The kinematic model of the unmanned underwater vehicle mainly describes the motion trajectory and attitude change law of the vehicle in the underwater space, which covers the mutual relationship between the key parameters such as the position, velocity, acceleration and attitude angle of the vehicle in the three-dimensional space. For ease of research, the spatial motion of the unmanned underwater vehicle is simplified as a plane motion. At the same time, in order to facilitate the establishment of the subsequent quasi-linear parameter variation model, so as to realize more accurate dynamic simulation and efficient control of the unmanned underwater vehicle, it is necessary to first establish the nonlinear kinematic model and dynamic model of the unmanned underwater vehicle.

[0074] Figure 2 The global coordinate system and the carrier coordinate system of the unmanned underwater vehicle motion are shown. The global coordinate system O E -x E y E z E The earth-fixed coordinate system is adopted to describe the position and attitude of the unmanned underwater vehicle. The origin O E of the earth-centered inertial system is selected as the reference point on the surface of the earth. x E points to an appropriate direction in the horizontal plane. y E is located in the horizontal plane x E O E z E and is perpendicular to the plane, and the direction makes the coordinate system satisfy the right-hand rule.

[0075] In the present application, the low-speed motion of the unmanned underwater vehicle is considered, and the pitch motion and roll motion are ignored to simplify the problem description. First, the state vector of the unmanned underwater vehicle needs to be defined as:

[0076]

[0077] For the convenience of describing the velocity in the body coordinate system of the unmanned underwater vehicle, the velocity vector of the unmanned underwater vehicle is defined as:

[0078]

[0079] By coordinate transformation, the rotation matrix between the earth-fixed reference frame and the body-fixed reference frame is defined as:

[0080]

[0081] Therefore, the kinematic model of the low-speed motion of the unmanned underwater vehicle can be described as:

[0082]

[0083] Next, the dynamic model of the unmanned underwater vehicle is established. The dynamic model describes the various forces and moments that the unmanned underwater vehicle experiences in the underwater environment and how these forces and moments affect its motion state. In the body-fixed coordinate system O B -x B y B z B The center of buoyancy of the unmanned underwater vehicle is defined as the coordinate origin O B , x B extends along the vertical axis of the unmanned underwater vehicle and points forward, y B is perpendicular to the Ox B z B plane and points to the right. Therefore, the dynamic model of the unmanned underwater vehicle can be represented as:

[0084] where the system inertia matrix M is usually composed of the rigid body mass matrix M RB = diag(m, m, I z ) and the added mass matrix , which can be represented as:

[0085]

[0086] is the Coriolis centripetal matrix caused by the rotation and translational velocity of the unmanned underwater vehicle in the body-fixed coordinate system. For a 3-DOF model, this matrix is skew-symmetric and can be represented as:

[0087]

[0088] The damping matrix represents the fluid dynamics and moments opposite to the motion of the unmanned underwater vehicle, and is represented as:

[0089] D(v) = -diag(X u + X |u|u |u|, Y v + Y |v|v |v|, N r + N |r|r |r|) (18)

[0090] For the force and moment vectors of the unmanned underwater vehicle motion. According to the above kinematic model and dynamic model, the state vector is further defined to establish the low-speed motion model of the unmanned underwater vehicle as:

[0091]

[0092] where,

[0093]

[0094] Step 2: Select appropriate scheduling parameters based on the model characteristics of the unmanned underwater vehicle;

[0095] Linear parameter-varying systems are a class of linear time-varying systems whose state-space matrices depend on measurable time-varying parameters. The parameters of quasi-linear parameter-varying systems depend on the system state or input, but can still be linearized by feedback control.

[0096] For the selection of scheduling parameters for the unmanned underwater vehicle system, the following criteria need to be met:

[0097] • Strong correlation: The scheduling parameter must be closely related to the main source of nonlinearity in the system. The selected parameter should be able to parameterize the terms that cause the system to deviate from linear behavior.

[0098] • Real-time measurability: The scheduling parameter must be able to be measured or estimated accurately in real time during the operation of the unmanned underwater vehicle.

[0099] • Boundedness: In order to design robust control (especially using linear matrix inequality techniques), we must know the range of values of the scheduling parameter ρ and its rate of change .

[0100] • Simplicity: On the premise of meeting the accuracy requirement, the minimum number of scheduling parameters should be selected as much as possible. Because the number of scheduling parameters and the dimension of the variation range directly determine the computational complexity of the linear matrix inequality control synthesis problem.

[0101] Taking the above into account, the scheduling parameter of the quasi-linear parameter-varying system of the unmanned underwater vehicle is selected as ρ = [ψ u vr] T .

[0102] First, the main source of nonlinearity in the dynamics model of the unmanned underwater vehicle is the Coriolis centripetal force matrix C(v) and the hydrodynamic damping matrix D(v), which are both directly functions of the velocity ρ. It meets the strong correlation.

[0103] Secondly, the state variables ψ, u, v, r in the scheduling parameter can be obtained by fusing multiple sensors. Doppler log can measure the linear velocity u and v of the AUV, while the inertial measurement unit can provide the heading angle ψ and the heading angle rate r of the AUV, which meets the real-time measurability.

[0104] After that, according to the design performance and task requirements of the AUV, its maximum speed and maximum angular velocity are known, so the boundary of ρ is clear. Similarly, the derivative of ρ is A reasonable boundary can also be set according to the propeller capacity and physical limitations. The boundedness is satisfied.

[0105] Therefore, based on the above conditions, the scheduling parameter of the quasi-linear parameter-varying system of the AUV is selected as ρ = [ψ u v r] T .

[0106] Step 3: Reconstruct the nonlinear terms in the AUV model using the scheduling parameter;

[0107] In the AUV motion model established in Step 1, we notice that the nonlinear terms in the matrix A can be represented using the scheduling parameter ρ. The rotation matrix J(η), the Coriolis centripetal force matrix C(v), and the hydrodynamic damping matrix D(v) are all direct functions of the scheduling parameter ρ. For example, the terms in C(v) are linear combinations of velocity (such as mv, mu, etc.). The terms in D(v) contain linear and quadratic terms of velocity (such as X |u|u |u|, Y |v|v |v|, N |r|r |r|, etc.). By selecting ρ = [ψ u v r] T , we can decompose these nonlinear terms into the form of J(ρ), C(ρ), and D(ρ), thereby incorporating the nonlinearity into the state matrix A(ρ) and improving the model accuracy.

[0108] Step 4: Establish the quasi-linear parameter-varying model of the AUV based on the reconstructed nonlinear terms;

[0109] Using the Newton-Euler method to discretize the continuous system, we obtain the discrete-time motion model of the AUV nonlinear motion system:

[0110]

[0111] where, To achieve trajectory tracking control of the AUV, define the reference state and reference input as x d and τ d , respectively, so that the trajectory tracking error model is

[0112]

[0113] where ξ k = x k - x d and u k = τ k - τ d are trajectory tracking error and control input error, respectively.

[0114] The scheduling parameter vector is defined as ρ = [ ψ u v r ] T in the above steps, and there is a continuous implicit function such that The trajectory tracking system error model is converted into a quasi-linear parameter-varying system:

[0115]

[0116] where the scheduling parameter and is defined as a tight set of scheduling parameters.

[0117] Step 5: Design trajectory tracking simulation experiments based on the quasi-linear parameter-varying model of the unmanned underwater vehicle.

[0118] In the present application, in order to verify the effectiveness of the quasi-linear parameter-varying model of the unmanned underwater vehicle established, the controller of the model is designed and verified by simulation using the proposed quasi-linear parameter-varying method. The initial state is set as x0 = [0, 3, -0.5π, 0, 0, 0], the sampling time is T = 0.1s, and the total simulation time is 60s. For easy comparison, we use the traditional nonlinear modeling method as a comparison to compare the tracking effect and results under the two modeling methods.

[0119] The reference trajectory used in this simulation is generated by the following trigonometric function:

[0120]

[0121] Figures 3 to 6 The trajectory tracking results are shown, and compared with the control results based on the nonlinear model, the proposed method has smaller tracking error and faster convergence speed. Figure 3 The tracking performance of the quasi-linear parameter-varying model and the control of the nonlinear model are compared with the sinusoidal reference trajectory, and a smoother transition is obtained, which indicates that the dynamic response is improved, thereby proving the effectiveness of the quasi-linear parameter-varying modeling method, and the unmanned underwater vehicle using the method can effectively track the reference trajectory.

[0122] Figure 4The tracking performance of the nonlinear model approach and the quasi-linear parameter variation approach are compared with the sinusoidal reference trajectory. From Figure 4 It can be seen that the two approaches almost overlap in terms of yaw error and remain stable within about 5 seconds. In terms of position error, the proposed approach is significantly better than the tracking result based on the nonlinear model. Figure 5 It is shown that, although the proposed approach has a slightly larger overshoot in the initial tracking, it achieves a smoother and faster speed tracking performance with better damping characteristics and shorter tuning time.

[0123] According to Figure 6 The proposed approach achieves a smoother and faster control input stabilization, which indicates an improved energy efficiency and reduced actuator wear compared to the nonlinear model approach, as shown by the control input curve.

Claims

1. A method for modeling the quasi-linear parameter variation motion of an unmanned underwater navigator, characterized in that, Includes the following steps: Step 1: Establish a nonlinear motion model for the fully driven unmanned underwater vehicle; Step 2: Select scheduling parameters based on the model characteristics of the unmanned underwater vehicle; Step 3: Reconstruct the nonlinear terms in the unmanned underwater vehicle model using scheduling parameters; Step 4: Establish a quasi-linear parameter variation model for the unmanned underwater vehicle based on the reconstructed nonlinear terms.

2. The method for quasi-linear parameter variation motion modeling of an unmanned underwater navigator according to claim 1, characterized in that, Step 1 specifically involves: Step 1-1: Simplify the spatial motion of the unmanned underwater vehicle into planar motion, and establish the nonlinear kinematic and dynamic models of the unmanned underwater vehicle; Step 1-2: Establish the global coordinate system for the motion of the unmanned underwater vehicle; Global coordinate system O E -x E y E z E A fixed Earth coordinate system is used to describe the position and attitude of the unmanned underwater vehicle; the origin O of the Earth-centered inertial frame is chosen. E As a reference point on the Earth's surface, x E Pointing in the appropriate direction in the horizontal plane, y E Located on the horizontal plane x E O E z E The coordinate system is perpendicular to the plane and its direction makes the coordinate system satisfy the right-hand rule; Steps 1-3: Define the state vector of the unmanned underwater vehicle as follows: Where x and y represent the position of the unmanned underwater navigator in the Earth-fixed coordinate system, and ψ represents the heading angle of the unmanned underwater navigator; Define the velocity vector of the unmanned underwater vehicle as: Where u and v represent the forward velocity and lateral velocity of the unmanned underwater navigator, respectively, and r represents the angular velocity of the unmanned underwater navigator. Through coordinate transformation, the rotation matrix between the Earth-fixed reference frame and the body-fixed reference frame is defined as: Therefore, the kinematic model of the unmanned underwater vehicle is described as Steps 1-4: Establish the dynamic model of the unmanned underwater vehicle; In the carrier fixed coordinate system O B -x B y B z B In this context, the center of buoyancy of the unmanned underwater vehicle is defined as the origin O. B x B Extending along the vertical axis of the unmanned underwater vehicle and pointing forward, y B Perpendicular to Ox B z B The plane points to the right; therefore, the dynamic model of the unmanned underwater vehicle is represented as: Wherein, the system inertia matrix M is composed of the rigid body mass matrix M RB =diag(m,m,I z ) and additional mass matrix The composition is represented as: m represents the mass of the unmanned underwater vehicle, I z This represents the moment of inertia about the z-axis. This represents the sway-additional mass coefficient. This represents the sway-added mass coefficient. Indicates the additional moment of inertia coefficient of bow roll; The Coriolis centripetal matrix is ​​caused by the rotational and translational velocities of the unmanned underwater vehicle within the fixed coordinate system of the vehicle. For a 3-DOF model, C(v) is obliquely symmetric and is expressed as: Damping matrix Representing the hydrodynamic forces and torques that are opposite to the motion of an unmanned underwater vehicle: D(v)=-diag(X u +X |u|u |u|,Y v +Y |v|v |v|,N r +N |r|r |r|) (7) X u X represents the oscillation-added mass coefficient. |u|u Y represents the quadratic oscillation damping coefficient. v Y represents the sway-added mass coefficient. |v|v N represents the quadratic sway damping coefficient. r N represents the additional moment of inertia coefficient of bow roll. |r|r This represents the quadratic bow roll damping moment coefficient; For the force and torque vectors of the unmanned underwater vehicle; Steps 1-5: Further define the state vector to establish a low-speed motion model for the unmanned underwater vehicle: in, 3. The quasi-linear parameter variation motion modeling method for an unmanned underwater navigator according to claim 2, characterized in that, Step 2 specifically involves: The quasi-linear parameter variation system scheduling parameters for the unmanned underwater vehicle are chosen as ρ = [ψu vr]. T .

4. The quasi-linear parameter variation motion modeling method for an unmanned underwater navigator according to claim 3, characterized in that, Step 3 specifically involves: By choosing ρ = [ψu vr] T The nonlinear term rotation matrix J(η), Coriolis centripetal force matrix C(v), and hydrodynamic damping matrix D(v) are decomposed into the forms J(ρ), C(ρ), and D(ρ), thereby incorporating the nonlinearity into the state matrix A(ρ).

5. The quasi-linear parameter variation motion modeling method for an unmanned underwater navigator according to claim 4, characterized in that, Step 4 specifically involves: Step 4-1: Discretize the continuous system using the Newton-Euler method to obtain the discrete-time motion model of the nonlinear motion system of the unmanned underwater vehicle: in, x k+1 and x k Let A represent the state vectors at times k+1 and k, respectively, where T represents the sampling step size, and A represents the state vectors at times k+1 and k, respectively. k B represents the state matrix at time k. k Let τ represent the input matrix at time k. k This represents the input vector at time k; Step 4-2: Define the reference state and reference input as x d and τ d Therefore, the trajectory tracking error model is as follows: Where, ξ k =x k -x d and u k =τ k -τ d Let ξ be the trajectory tracking error and the control input error at time k, respectively; k+1 This represents the trajectory tracking error vector at time k+1; Step 4-3: The scheduling parameter vector is defined as ρ = [ψu vr]. T And there exists a continuous implicit function f: Make The trajectory tracking error model is converted into a quasi-linear parameter variation system: Among them, scheduling parameters and Defined as a compact set of scheduling parameters; A(ρ) k B(ρ) represents the state matrix of the quasi-linear parameter change error model at time k; k ) represents the input matrix of the quasi-linear parameter change error model at time k.

6. An electronic device, characterized in that, include: Processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to cause the electronic device to perform the method as described in any one of claims 1 to 5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 5.

8. A chip, characterized in that, include: A processor for retrieving and running a computer program from memory, causing a device on which the chip is mounted to perform the method as described in any one of claims 1 to 5.

9. A computer program product, characterized in that, The computer program product includes a computer storage medium storing a computer program, the computer program including instructions executable by at least one processor, which, when executed by the at least one processor, implement the method as described in any one of claims 1 to 5.

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