Model-free unmanned underwater vehicle trajectory tracking method and system

Abstract

The invention discloses a model-free unmanned underwater vehicle trajectory tracking method and system, and the method comprises the steps: 1, calculating a tracking error and a tracking error change rate according to a given expected trajectory and the pose of an unmanned underwater vehicle obtained through measurement, and constructing a nonlinear nonsingular terminal sliding mode surface; step 2, calculating a dynamic regression matrix according to the pose, the speed and the expected trajectory of the unmanned underwater vehicle; step 3, according to the sliding mode surface and the dynamic regression matrix, designing a nonlinear adaptive law, obtaining an unknown upper bound of model uncertainty, inputting a reciprocal of a lower bound of a saturation reverse scale factor and an estimated value of an unknown physical parameter of the unmanned underwater vehicle; and 4, designing a model-free robust adaptive finite time control law according to the estimated value obtained in the step 3 in combination with a control law gain coefficient and a dynamic regression matrix. According to the method, the problem of trajectory tracking control of unknown physical parameters of the unmanned underwater vehicle under the conditions of input saturation and model uncertainty can be solved.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned underwater vehicles, and particularly to a model-free trajectory tracking method and system for unmanned underwater vehicles. Background Art

[0002] As an intelligent device integrating underwater detection, environmental perception, and autonomous decision-making functions, unmanned underwater vehicles have been widely used in fields such as marine resource exploration, submarine pipeline maintenance, underwater target reconnaissance, and military operations. The trajectory tracking control performance, which is one of its core technologies, directly affects the mission execution accuracy and reliability of the vehicle in complex marine environments.

[0003] Current mainstream control methods usually construct control algorithms based on accurate dynamic models. However, in practical applications, the hydrodynamic parameters of the vehicle are easily affected by factors such as carrier deformation, fouling accumulation, and fluid environment changes, resulting in significant time-varying characteristics of the model parameters. In addition, factors such as the thrust saturation constraint of the actuator and external disturbances further increase the design complexity of the control system.

[0004] In the prior art, patent document CN118625841A proposed a trajectory tracking method based on online modeling and model predictive control. This technique extracts features from offline data through fuzzy C-means clustering and uses a least squares support vector machine to establish a non-parametric model, and then realizes trajectory tracking through a model predictive controller. However, this solution has the following technical defects: (1) The control performance highly depends on the accuracy of online modeling, and it is easy to cause tracking instability when the vehicle encounters unmodeled dynamics or sudden disturbances; (2) The input saturation non-linear effect caused by the limited output torque of the thruster is not considered, which may cause integral saturation; (3) Using an asymptotic convergence control strategy, it cannot meet the strict requirements of finite-time convergence of tracking errors in high-dynamic scenarios.

[0005] Another related patent document CN118915475A discloses a trajectory tracking method based on super-twisting sliding mode control, and designs an anti-disturbance control law by establishing an accurate mathematical model. Although this technical solution can suppress the influence of external disturbances, it has obvious limitations: (1) The design of the control law requires an accurate mathematical model as a prerequisite and cannot effectively handle model uncertainties caused by parameter perturbations; (2) An input saturation compensation mechanism is not constructed, and the physical constraints of the actuator may destroy the reaching condition of the sliding surface; (3) The tracking error can only achieve asymptotic convergence and it is difficult to meet the requirements of time-sensitive tasks such as emergency obstacle avoidance and rapid approach.

[0006] In summary, there are three common defects in the existing technologies: First, over-reliance on precise mathematical models leads to insufficient robustness; second, there is a lack of a stability guarantee mechanism under input saturation constraints; third, the control convergence speed cannot meet the requirements of finite-time performance indicators. These defects severely restrict the reliable operation ability of unmanned underwater vehicles in dynamic uncertain environments. Summary of the Invention

[0007] The purpose of the present invention is to provide a model-free trajectory tracking method and system for unmanned underwater vehicles to overcome or at least mitigate at least one of the above-mentioned defects in the existing technologies.

[0008] To achieve the above purpose, the present invention provides a model-free trajectory tracking method for unmanned underwater vehicles, which includes:

[0009] Step 1: Calculate the tracking error and the rate of change of the tracking error based on the given desired trajectory and the measured pose of the unmanned underwater vehicle, and construct a nonlinear non-singular terminal sliding mode surface;

[0010] Step 2: Calculate the dynamic regression matrix according to the pose, velocity of the unmanned underwater vehicle and the desired trajectory;

[0011] Step 3: Design a nonlinear adaptive law based on the sliding mode surface and the dynamic regression matrix to obtain the estimated values of the unknown upper bound of model uncertainty, the reciprocal of the lower bound of the input saturation inverse scaling factor, and the unknown physical parameters of the unmanned underwater vehicle;

[0012] Step 4: Design a model-free robust adaptive finite-time control law according to the estimated values obtained in Step 3, in combination with the control law gain coefficient and the dynamic regression matrix.

[0013] Further, the nonlinear non-singular terminal sliding mode surface in Step 1 is expressed as S n :

[0014] S n = k 1 f 1 (e t ) + k 2 f 2 (e t ) + e tv

[0015] where f 1 (e t ) and f 2 (e t ) are both intermediate parameters, which are respectively expressed as follows:

[0016] f 1 (e) = |e tx | sign(e tx ), |ety |sign(e ty ),|e tz |sign(e tz ),|e tφ |sign(e tφ ),|e tθ |sign(e tθ ),|e tψ |sign(e tψ )] T

[0017]

[0018] Among them, k 1 ≥0.5, k 2 ≥0, 0 < p i < 1, | | represents the absolute value, and sign( ) represents the sign function.

[0019] Furthermore, the dynamic regression matrix in step 2 is expressed as

[0020] where η(t) and ξ(t) are the measured pose and velocity respectively, η d (t) is the given desired trajectory, is the desired pose change rate, is composed of the physical parameters of the unmanned underwater vehicle. The superscript T represents the transpose, the superscript -1 represents the reciprocal, and the dot above the parameter represents the derivative of the parameter. χ, M * (η(t)), C * (η(t), ξ(t)), D * (η(t), ξ(t)) are all intermediate / process parameters used to simplify the formula, and the specific descriptions are as follows:

[0021]

[0022] M * (η(t)) = J -T (η(t))MJ -1 (η(t))

[0023]

[0024] D * (η(t), ξ(t)) = J -T (η(t))D(ξ(t))J -1 (η(t)).

[0025] Among them, \(J(\eta(t))\), \(M\), \(C(\xi(t))\), \(D(\xi(t))\) are the coordinate transformation matrix, the inertia matrix, the centripetal force and Coriolis force matrix of the rigid body, and the hydrodynamic damping matrix, respectively.

[0026] Furthermore, the nonlinear adaptive law in step 3 is expressed as the following formula:

[0027]

[0028] Among them, \(\tau\) dM is the unknown upper bound of model uncertainty, \(\gamma\) is the reciprocal of the lower bound of the input saturation inverse scaling factor, \(\Gamma\) is a set coefficient greater than 0, is a preset gain coefficient greater than 0. The hat on top of the parameter indicates the estimated value of the parameter, and the dot on top of the parameter indicates the derivative of the parameter. is the gain coefficient, which is expressed as follows:

[0029]

[0030] Furthermore, the model-free robust adaptive finite-time control law \(\tau(t)\) in step 4 is expressed as the following formula:

[0031]

[0032] The present invention also provides a model-free unmanned underwater vehicle trajectory tracking system, which includes an expected trajectory given module, a tracking control module and an unmanned underwater vehicle. Among them, the unmanned underwater vehicle specifically includes:

[0033] A nonlinear nonsingular terminal sliding mode surface construction unit, which is used to calculate the tracking error and the change rate of the tracking error according to the given expected trajectory and the measured pose of the unmanned underwater vehicle, and construct a nonlinear nonsingular terminal sliding mode surface;

[0034] A dynamic regression matrix calculation unit, which is used to calculate the dynamic regression matrix according to the pose, speed and expected trajectory of the unmanned underwater vehicle;

[0035] A nonlinear adaptive law design unit, which is used to design a nonlinear adaptive law according to the sliding mode surface and the dynamic regression matrix, and obtain the unknown upper bound of model uncertainty, the reciprocal of the lower bound of the input saturation inverse scaling factor, and the estimated values of the unknown physical parameters of the unmanned underwater vehicle;

[0036] A model-free robust adaptive finite-time control law design unit, which is used to design a model-free robust adaptive finite-time control law according to the estimated values of the nonlinear adaptive law design unit, in combination with the control law gain coefficient and the dynamic regression matrix.

[0037] Furthermore, the nonlinear nonsingular terminal sliding mode surface of the nonlinear nonsingular terminal sliding mode surface construction unit is expressed as \(S\) n:

[0038] S n = k 1 f 1 (e t ) + k 2 f 2 (e t ) + e tv

[0039] Wherein, f 1 (e t ) and f 2 (e t ) are both intermediate parameters, which are respectively represented as follows:

[0040] f 1 (e t ) = [|e tx | sign(e tx ), |e ty | sign(e ty ), |e tz | sign(e tz ), |e tφ | sign(e tφ ), |e tθ | sign(e tθ ), |e tψ | sign(e tψ )] T

[0041]

[0042] Wherein, k 1 ≥ 0.5, k 2 ≥ 0, 0 < p i < 1, || is the absolute value, and sign() is the sign function.

[0043] Furthermore, the dynamic regression matrix of the dynamic regression matrix calculation unit is represented as

[0044]

[0045] Wherein, η(t) and ξ(t) are the measured pose and velocity respectively, η d (t) is the given desired trajectory, is the desired pose change rate, is composed of the physical parameters of the unmanned underwater vehicle. The superscript T represents the transpose, the superscript -1 represents the reciprocal, and the dot above the parameter represents the derivative of the parameter. X, M * (η(t)), C * (η(t), ξ(t)), D* (η(t), ξ(t)) are both intermediate / process parameters used to simplify the formula, and the specific descriptions are as follows:

[0046]

[0047] M * J(η(t)) = J -T J(η(t))MJ -1 J(η(t))

[0048]

[0049] D * J(η(t), ξ(t)) = J -T J(η(t))D(ξ(t))J -1 J(η(t)).

[0050] Among them, J(η(t)), M, C(ξ(t)), and D(ξ(t)) are the coordinate transformation matrix, inertia matrix, rigid body centripetal force and Coriolis force matrix, and hydrodynamic damping matrix respectively.

[0051] Furthermore, the nonlinear adaptive law of the nonlinear adaptive law design unit is expressed as the following formula:

[0052]

[0053] Among them, τ dM is the unknown upper bound of model uncertainty, γ is the reciprocal of the lower bound of the input saturation inverse scaling factor, Γ is a set coefficient greater than 0, is a preset gain coefficient greater than 0. The hat on the parameter indicates the estimated value of the parameter, and the dot on the parameter head indicates the derivative of the parameter. is the gain coefficient, which is expressed as follows:

[0054]

[0055] Furthermore, the model-free robust adaptive finite-time control law τ(t) is expressed as the following formula:

[0056]

[0057] Due to the above technical solutions, the present invention has the following advantages:

[0058] The present invention can solve the trajectory tracking control problem of an unmanned underwater vehicle with unknown physical parameters under input saturation and model uncertainty conditions, thereby eliminating the dependence on the physical parameters of the unmanned underwater vehicle, enhancing the robustness to input saturation and model uncertainty, and achieving finite-time convergence of the tracking error. Brief Description of the Drawings

[0059] Figure 1 It is a schematic diagram of the flowchart of the model - free unmanned underwater vehicle trajectory tracking control method according to an embodiment of the present invention.

[0060] Figure 2 It is a schematic diagram of the model - free unmanned underwater vehicle trajectory tracking control system according to an embodiment of the present invention. Detailed implementation manners

[0061] In the drawings, the same or similar reference numerals are used to represent the same or similar elements or elements with the same or similar functions. The embodiments of the present invention will be described in detail below with reference to the drawings.

[0062] In the description of the present invention, the terms "center", "longitudinal", "lateral", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it should not be construed as limiting the protection scope of the present invention.

[0063] As Figure 1 shown, the model - free unmanned underwater vehicle trajectory tracking method provided by the embodiment of the present invention includes:

[0064] Step 1: Calculate the tracking error and the change rate of the tracking error according to the given desired trajectory and the measured pose of the unmanned underwater vehicle, and construct a nonlinear non - singular terminal sliding mode surface.

[0065] For example, in one embodiment, the nonlinear non - singular terminal sliding mode surface in Step 1 is expressed as S n :

[0066] S n = k 1 f 1 (e t ) + k 2 f 2 (e t ) + e tv (1)

[0067] Where:

[0068] e t represents the tracking error, e t = [e tx , e ty , e tz , e tφ , e tθ , e tψ T , (e​tx , e ty , e tz ), (e tφ , e tθ , e tψ ), respectively, represent the position tracking error and attitude tracking error in the three directions of the inertial coordinate system xyz, e t is obtained by calculating through Equation (2):

[0069] e t = η(t) - η d (t) (2)

[0070] In Equation (2), η(t) is the measured pose, and η d (t) is the given desired trajectory.

[0071] e tv represents the change rate of the tracking error, e tv = [e tvx , e tvy , e tvz , e tvφ , e tvθ , e tvψ T , (e tvx , e tvy , e tz ), (e tvφ , e tvθ , e tvψ ), respectively, represent the change rate of the position tracking error and the change rate of the attitude tracking error in the three directions of the inertial coordinate system xyz, e tv is obtained by calculating through Equation (3):

[0072]

[0073] In Equation (3), is the pose change rate, is the desired pose change rate.

[0074] k 1 and k 2 are preset values that satisfy k 1 ≥ 0.5, and k 2 ≥ 0 is sufficient, and they have no substantial physical meaning.

[0075] f 1 (e t ) and f 2 (e t ) are both intermediate / process parameters with no substantial physical meaning, and are respectively expressed as follows:

[0076] f 1 (e​t ) = [|e tx | sign(e tx ), |e ty | sign(e ty ), |e tz | sign(e tz ), |e tφ | sign(e tφ ), |e tθ | sign(e tθ ), |e tψ | sign(e tψ

[0077]

[0078] where, | | represents the absolute value, 0 < p i < 1, p i represents the exponent, having no substantial physical meaning, k 1 , k 1 and p i The value ranges of these parameter settings are beneficial to ensuring the convergence of the subsequent designed nonlinear adaptive law and the finite-time stability of the model-free robust adaptive control law. sign(x) is the sign function, which can be implemented by Equation (4):

[0079]

[0080] sign(x) can also be represented by the continuous saturation function f s (x) in Equation (5) to eliminate the jitter caused by the discontinuous function sign(x):

[0081]

[0082] In Equation (5), ρ 1 and ρ 2 are preset values, satisfying 0 < ρ 1 < 1, and ρ 2 > 0 is sufficient, having no substantial physical meaning.

[0083] The nonlinear nonsingular terminal sliding mode surface constructed based on the tracking error and the rate of change of the tracking error is beneficial to eliminating the singular phenomenon caused by the traditional terminal sliding mode surface, can ensure the finite-time stability and robustness of the controller, and can reduce the chattering brought by the sliding mode control.

[0084] Step 2: Calculate the dynamic regression matrix according to the pose, velocity, and desired trajectory of the underwater vehicle.

[0085] According to Equations (1) and (3), the nonlinear nonsingular terminal sliding mode surface S nIt can be further expressed as Then Wherein χ represents an intermediate / process parameter used to simplify the formula and has no specific physical meaning.

[0086] According to The Euler - Lagrange motion model of the unmanned underwater vehicle in the inertial coordinate system is expressed as Equation (6):

[0087]

[0088] Wherein, τ d (t) represents the uncertainty parameter of the Euler - Lagrange motion model, and ISN(τ(t)) is the control input saturation function and is described as Equation (7):

[0089]

[0090] Wherein:

[0091] τ M 、τ m respectively represent the upper and lower bounds of the uncertainty τ(t). Both are unknown but are constants, satisfying τ M >0, and τ m <0.

[0092] M * (η(t)), C * (η(t), ξ(t)), D * (η(t), ξ(t)) represent intermediate / process parameters used to simplify the formula and have no specific physical meaning, and are respectively expressed as Equations (8), (9), (10):

[0093] M * (η(t)) = J -T (η(t))MJ -1 (η(t)) (8)

[0094]

[0095] D * (η(t), ξ(t)) = J -T (η(t))D(ξ(t))J -1 (η(t)) (10)

[0096] Wherein, J(η(t)), M, C(ξ(t)), D(ξ(t)) are the coordinate transformation matrix, the inertia matrix, the rigid - body centripetal force and Coriolis force matrix, and the hydrodynamic damping matrix respectively.

[0097] In this embodiment, an input saturation function is constructed by introducing a reverse scaling factor to handle the input saturation caused by the physical constraints of the thrusters and improve the smoothness of the control input.

[0098] According to the Euler-Lagrange motion model of the above-mentioned unmanned underwater vehicle, through parameter linearization, a dynamic regression matrix is obtained, as shown in Equation (11)

[0099]

[0100] In Equation (11), η(t) and ξ(t) are the measured pose and velocity respectively, is the desired pose change rate, η d (t) is the given desired trajectory, the superscript -1 represents the reciprocal, and the dot above the parameter represents the derivative of the parameter. It is composed of the physical parameters of the unmanned underwater vehicle, such as mass, moment of inertia, hydrodynamic coefficient, etc.

[0101] In the case where the physical parameters of the unmanned underwater vehicle are unknown, considering the adverse effects of input saturation and model uncertainty, first construct the motion model of the unmanned underwater vehicle in the body coordinate system, then transform it into the Euler-Lagrange motion model in the inertial coordinate system, and then combine the nonlinear nonsingular terminal sliding mode surface with the Euler-Lagrange motion model and through parameter linearization to obtain the dynamic regression matrix of the linear regression model.

[0102] Step 3, according to the sliding mode surface and the dynamic regression matrix, design a nonlinear adaptive law to obtain the estimated values of the unknown upper bound of the model uncertainty, the reciprocal of the lower bound of the input saturation reverse scaling factor, and the unknown physical parameters of the unmanned underwater vehicle.

[0103] In one embodiment, the nonlinear adaptive law is expressed as Equation (12) and is used to estimate the unknown upper bound τ of the model uncertainty dM , the reciprocal γ of the lower bound of the input saturation reverse scaling factor, and the vector of unknown physical parameters of the unmanned underwater vehicle

[0104]

[0105] In Equation (12), τ dM is the unknown upper bound of the model uncertainty, γ is the reciprocal of the lower bound of the input saturation reverse scaling factor, Γ is a set coefficient greater than 0, is a preset gain coefficient greater than 0, the hat above the parameter represents the estimated value of the parameter, and the dot above the parameter represents the derivative of the parameter. is the gain coefficient, expressed as Equation (13):

[0106]

[0107] Then, although the unmanned underwater vehicle with unknown physical parameters is affected by input saturation and model uncertainty, it can still be estimated by the designed non-linear adaptive law.

[0108] Designing a non-linear adaptive law to estimate the unknown upper bound of model uncertainty, the reciprocal of the lower bound of the input saturation inverse scaling factor, and the unknown physical parameters of the unmanned underwater vehicle according to the sliding mode surface and the dynamic regression matrix enables the design of the control law without the prior knowledge of the upper bound of the model uncertainty, the lower bound of the input saturation, and the physical parameters of the unmanned underwater vehicle, avoiding the dependence on these key parameters of the unmanned underwater vehicle.

[0109] Step 4: According to the estimated values obtained in Step 3, combined with the control law gain coefficient and the dynamic regression matrix, design a model-free robust adaptive finite-time control law.

[0110] In one embodiment, the model-free robust adaptive finite-time control law τ(t) is expressed as Equation (14):

[0111]

[0112] Based on the above model-free robust adaptive finite-time control law τ(t), the model-free robust adaptive finite-time trajectory tracking control of the unmanned underwater vehicle with unknown physical parameters under input saturation and model uncertainty conditions can be realized without the prior knowledge of the physical parameters of the unmanned underwater vehicle, which is beneficial to ensuring the tracking accuracy, robustness, and finite-time stability of the system.

[0113] As Figure 2 shown, the embodiment of the present invention also provides a model-free unmanned underwater vehicle trajectory tracking system, which includes an expected trajectory given module, a tracking control module, and an unmanned underwater vehicle, where:

[0114] The expected trajectory given module is used to give the expected trajectory that the unmanned underwater vehicle needs to track, and the unmanned underwater vehicle is the controlled object.

[0115] The tracking control module includes a non-linear non-singular terminal sliding mode surface construction unit, a dynamic regression matrix calculation unit, a non-linear adaptive law design unit, and a model-free robust adaptive finite-time control law design unit.

[0116] The non-linear non-singular terminal sliding mode surface construction unit is used to calculate the tracking error and the change rate of the tracking error according to the given expected trajectory and the measured pose of the unmanned underwater vehicle, and construct a non-linear non-singular terminal sliding mode surface.

[0117] The dynamic regression matrix calculation unit is used to calculate the dynamic regression matrix according to the pose, speed, and expected trajectory of the unmanned underwater vehicle.

[0118] The non - linear adaptive law design unit is used to design a non - linear adaptive law according to the sliding mode surface and the dynamic regression matrix, and obtain the upper bound of the unknown model uncertainty, the reciprocal of the lower bound of the input saturation inverse scaling factor, and the estimated values of the unknown physical parameters of the unmanned underwater vehicle.

[0119] The model - free robust adaptive finite - time control law design unit is used to design a model - free robust adaptive finite - time control law according to the estimated values of the non - linear adaptive law design unit, in combination with the control law gain coefficient and the dynamic regression matrix.

[0120] In one embodiment, the non - linear non - singular terminal sliding mode surface of the non - linear non - singular terminal sliding mode surface construction unit is represented by S in Equation (1). n .

[0121] In one embodiment, the dynamic regression matrix of the dynamic regression matrix calculation unit is represented by Equation (11).

[0122] In one embodiment, the non - linear adaptive law of the non - linear adaptive law design unit is represented by Equation (12).

[0123] In one embodiment, the model - free robust adaptive finite - time control law τ(t) is represented by Equation (14).

[0124] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them. Those of ordinary skill in the art should understand that the technical solutions recorded in the foregoing embodiments can be modified, or some of the technical features can be equivalently replaced; these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A model-free unmanned underwater vehicle trajectory tracking method, characterized in that: include: Step 1, according to the given expected trajectory and the measured posture of the unmanned underwater vehicle, the tracking error and the rate of change of the tracking error are calculated, and a nonlinear non-singular terminal sliding surface is constructed; Step 2, calculating the dynamic regression matrix according to the position, velocity and expected trajectory of the unmanned underwater vehicle; Step 3, according to the sliding surface and the dynamic regression matrix, a nonlinear adaptive law is designed to obtain the unknown upper bound of the model uncertainty, the inverse of the lower bound of the input saturation inverse scaling factor, and the estimated values ​​of the unknown physical parameters of the unmanned underwater vehicle; Step 4: Based on the estimated value obtained in step 3, the control law gain coefficient and the dynamic regression matrix are combined to design a model-free robust adaptive finite-time control law.

2. The model-free unmanned underwater vehicle trajectory tracking method according to claim 1, characterized in that: The nonlinear nonsingular terminal sliding surface of step 1 is denoted as S n : S n =k1f1(e t )+k2f2(e t )+e tv Among them, f1(e t ) and f2(e t ) are all intermediate parameters, which are represented as follows: f1(and t )=[|and tx |sign(e tx ),|and ty |sign(e ty ),|and tz |sign(e tz ),|and tφ |sign(e tφ ),|and tθ |sign(e tθ ),|and tψ |sign(e tψ )] T Among them, e t represents the tracking error, e t =[e tx ,e ty ,e tz ,e tφ ,e tθ ,e tψ ] T ,(e tx ,e ty ,e tz )、(e tφ ,e tθ ,e tψ ) are the position tracking error and attitude tracking error in the three directions of the inertial coordinate system xyz, e tv The tracking error is the tracking error change rate, e tv =[e tvx ,e tvy ,e tvz ,e tvφ ,e tvθ ,e tvψ ] T ,(e tvx ,e tvy ,e tz )、(e tvφ ,e tvθ ,e tvψ ) are the position tracking error change rate and attitude tracking error change rate in the three directions of the inertial coordinate system xyz, respectively, k1≥0.5, k2≥0, 0 <p i <1, || is the absolute value, sign() is the sign function.

3. The model-free unmanned underwater vehicle trajectory tracking method according to claim 1, characterized in that: The dynamic regression matrix of step 2 is expressed as Among them, η(t) and ξ(t) are the measured posture and velocity respectively, η d (t) is the given expected trajectory, is the expected posture change rate, It is composed of the physical parameters of the unmanned underwater vehicle. The superscript T represents the transpose, the superscript -1 represents the reciprocal, and the · above the parameter represents the derivative of the parameter. * (η(t)),C * (η(t),ξ(t)),D * (η(t),ξ(t)) are intermediate / process parameters used to simplify the formula, and are described as follows: M * (η(t))=J -T (η(t))MJ -1 (η(t)) D * (η(t),ξ(t))=J -T (η(t))D(ξ(t))J -1 (η(t)). Among them, J(η(t)), M, C(ξ(t)), and D(ξ(t)) are the coordinate transformation matrix, inertia matrix, rigid body centripetal force and Coriolis force matrix, and hydrodynamic damping matrix, respectively.

4. The model-free unmanned underwater vehicle trajectory tracking method according to any one of claims 1 to 3, characterized in that: The nonlinear adaptive law of step 3 is expressed as follows: Among them, τ dM is the unknown upper bound of model uncertainty, γ is the inverse lower bound of the input saturation inverse scaling factor, Γ is a setting coefficient greater than 0, is a preset gain coefficient greater than 0, the ∧ above the parameter head represents the estimated value of the parameter, and the · above the parameter head represents the derivative of the parameter. is the gain coefficient, expressed as follows:

5. The model-free unmanned underwater vehicle trajectory tracking method according to claim 4, characterized in that: The model-free robust adaptive finite-time control law τ(t) in step 4 is expressed as follows:

6. A model-free unmanned underwater vehicle trajectory tracking system, characterized in that: It includes a desired trajectory setting module, a tracking control module and an unmanned underwater vehicle, wherein the unmanned underwater vehicle specifically includes: A nonlinear non-singular terminal sliding surface construction unit, which is used to calculate the tracking error and the tracking error change rate according to the given expected trajectory and the measured unmanned underwater vehicle posture, and construct a nonlinear non-singular terminal sliding surface; A dynamic regression matrix calculation unit, which is used to calculate the dynamic regression matrix according to the position, velocity and expected trajectory of the unmanned underwater vehicle; A nonlinear adaptive law design unit, which is used to design a nonlinear adaptive law according to a sliding surface and a dynamic regression matrix, and obtain an unknown upper bound of model uncertainty, an inverse lower bound of an input saturation inverse scaling factor, and an estimated value of an unknown physical parameter of the unmanned underwater vehicle; The model-free robust adaptive finite-time control law design unit is used to design a model-free robust adaptive finite-time control law according to the estimated value of the nonlinear adaptive law design unit, combined with the control law gain coefficient and the dynamic regression matrix.

7. The model-free unmanned underwater vehicle trajectory tracking system according to claim 6, characterized in that: The nonlinear non-singular terminal sliding surface of the construction unit is represented by S n : S n =k1f1(e t )+k2f2(e t )+e tv Among them, f1(e t ) and f2(e t ) are all intermediate parameters, which are represented as follows: f1(and t )=[|and tx |sign(e tx ),|and ty |sign(e ty ),|and tz |sign(e tz ),|and tφ |sign(e tφ ),|and tθ |sign(e tθ ),|and tψ |sign(e tψ )] T Among them, e t represents the tracking error, e t =[e tx ,e ty ,e tz ,e tφ ,e tθ ,e tψ ] T ,(e tx ,e ty ,e tz )、(e tφ ,e tθ ,e tψ ) are the position tracking error and attitude tracking error in the three directions of the inertial coordinate system xyz, e tv The tracking error is the tracking error change rate, e tv =[e tvx ,e tvy ,e tvz ,e tvφ ,e tvθ ,e tvψ ] T ,(e tvx ,e tvy ,e tz )、(e tvφ ,e tvθ ,e tvψ ) are the position tracking error change rate and attitude tracking error change rate in the three directions of the inertial coordinate system xyz, respectively, k1≥0.5, k2≥0, 0 <p i <1, || is the absolute value, sign() is the sign function.

8. The model-free unmanned underwater vehicle trajectory tracking system according to claim 6, characterized in that: The dynamic regression matrix of the dynamic regression matrix calculation unit is expressed as Among them, η(t) and ξ(t) are the measured posture and velocity respectively, η d (t) is the given expected trajectory, is the expected posture change rate, It is composed of the physical parameters of the unmanned underwater vehicle. The superscript T represents the transpose, the superscript -1 represents the reciprocal, and the · above the parameter represents the derivative of the parameter. * (η(t), C * (η(t),ξ(t)),D * (η(t),ξ(t)) are intermediate / process parameters used to simplify the formula, and are described as follows: M * (η(t))=J -T (η(t))MJ -1 (η(t)) D * (η(t),ξ(t))=J -T (η(t))D(ξ(t))J -1 (η(t)). Among them, J(η(t)), M, C(ξ(t)), and D(ξ(t)) are the coordinate transformation matrix, inertia matrix, rigid body centripetal force and Coriolis force matrix, and hydrodynamic damping matrix, respectively.

9. The model-free unmanned underwater vehicle trajectory tracking system according to any one of claims 6 to 8, characterized in that: The nonlinear adaptive law of the design unit is expressed as follows: Among them, τ dM is the unknown upper bound of model uncertainty, γ is the inverse lower bound of the input saturation inverse scaling factor, Γ is a setting coefficient greater than 0, is a preset gain coefficient greater than 0, the ∧ above the parameter head represents the estimated value of the parameter, and the · above the parameter head represents the derivative of the parameter. is the gain coefficient, expressed as follows:

10. The model-free unmanned underwater vehicle trajectory tracking system according to claim 9, characterized in that: The model-free robust adaptive finite-time control law τ(t) is expressed as follows:

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