AUV trajectory tracking method based on zeroing neural network

Abstract

The invention discloses an AUV trajectory tracking method based on a zeroing neural network. The method comprises the following steps: constructing an AUV kinematic model, and using a gradient descent method and a performance index to constrain the AUV kinematic model; restating the AUV trajectory tracking problem as a dynamic quadratic programming problem based on the AUV kinematic model; constructing a PEZNN model, wherein the PEZNN model represents a projection and ellipse zeroing neural network model; constructing an AUV-TTN network based on the PEZNN model and velocity and acceleration projection functions, wherein the AUV-TTN network represents an AUV path tracking neural network; solving the dynamic quadratic programming problem using the AUV-TTN network, tracking the AUV expected trajectory, and continuously iterating the predicted trajectory, thereby finally realizing the AUV trajectory tracking.

Description

Technical Field

[0001] The present invention relates to the technical field of AUV trajectory tracking, and in particular to an AUV trajectory tracking method based on a zeroing neural network. Background Art

[0002] In the field of marine engineering, autonomous underwater vehicles (AUVs) play a key role in marine operations by integrating autonomous perception, decision-making, and execution capabilities. Among various performance indicators, trajectory tracking has attracted extensive attention as a key indicator for evaluating AUV performance. However, existing AUV tracking methods have limitations in control accuracy and require a lot of computing resources and time, which limits their real-time application capabilities in dynamic environments. Summary of the invention

[0003] In view of the above-mentioned prior art, the present invention provides an AUV trajectory tracking method based on a zero-valued neural network, which mainly solves the technical problems existing in the above-mentioned background technology.

[0004] To achieve the above object, the technical solution of the embodiment of the present invention is implemented as follows: an AUV trajectory tracking method based on a zero-valued neural network, the method comprising the following steps:

[0005] Constructing an AUV kinematic model and constraining the AUV kinematic model using a gradient descent method and a performance indicator;

[0006] Based on the AUV kinematic model, the AUV trajectory tracking problem is restated as a dynamic quadratic programming problem;

[0007] Constructing a PEZNN model, wherein the PEZNN model represents a projection and elliptic zeroing neural network model;

[0008] An AUV-TTN network is constructed based on the PEZNN model and velocity and acceleration projection functions, wherein the AUV-TTN network represents an AUV path tracking neural network;

[0009] The AUV-TTN network is used to solve the dynamic quadratic programming problem, track the expected trajectory of the AUV, and continuously iterate the predicted trajectory to finally achieve AUV trajectory tracking.

[0010] Construct the AUV kinematic model, including:

[0011] In the local reference system of the earth, the six degrees of freedom of the AUV are expressed as:

[0012]

[0013] make , thus establishing the vector and vector The relationship between:

[0014]

[0015] By taking the derivative of both sides of the formula, the AUV kinematic model is as follows:

[0016]

[0017] in, represents the position coordinates of the AUV, represents the yaw of the AUV, represents the pitch of the AUV, represents the roll of the AUV, Indicates that the AUV is , and Linear velocity in direction, Indicates that the AUV is , and Angular velocity in direction, represents the initial position and rotation attitude of the AUV, represents the parameter matrix, The symbol represents the time t. T Represents the transpose of matrices and vectors.

[0018] The AUV kinematic model is constrained using a gradient descent method and performance indicators, including:

[0019] The following performance indicators are established to constrain the AUV drift caused by redundant degrees of freedom:

[0020]

[0021] Based on the design strategy of the gradient descent method, the above formula is modified as follows:

[0022]

[0023] Taking into account the physical limit constraints of AUV at the acceleration level, the above formula is further optimized into:

[0024]

[0025] in, represents the predicted trajectory, is the feedback gain coefficient, express The derivative of .

[0026] Based on the AUV kinematic model, the AUV trajectory tracking problem is restated as a dynamic quadratic programming problem, which specifically includes:

[0027] Based on the ZNN model, the error function of the AUV kinematic model is established:

[0028]

[0029] Will Map to six degrees of freedom and establish the following mapping relationship:

[0030]

[0031] in,

[0032]

[0033] According to the design idea of ​​the ZNN model, the error function is forced to drop to 0, and the following evolution formula is established:

[0034]

[0035] Considering the physical limit constraints of the underwater vehicle and based on the above formula, the AUV trajectory tracking problem is restated as the following dynamic quadratic programming problem:

[0036]

[0037] in, represents the expected trajectory, express The derivative of and are feedback gain coefficients, represents the maximum forward speed of the AUV in six degrees of freedom, represents the maximum backward speed of the AUV in six degrees of freedom, represents the maximum forward acceleration of the AUV in six degrees of freedom, It represents the maximum backward acceleration of the six degrees of freedom of the AUV.

[0038] Construct the PEZNN model, including:

[0039] Define a non-convex saturation function for:

[0040]

[0041] Based on the elliptic equation, the following formula is designed to smooth the convergence speed:

[0042]

[0043] The projection and ellipse activation functions are designed as:

[0044]

[0045] Therefore, the PEZNN model can be expressed as:

[0046]

[0047] in, represents the major axis of the ellipse, represents the minor axis of the ellipse, It also represents the feedback gain coefficient, ,

[0048] , .

[0049] Establish two projection functions of velocity and acceleration:

[0050]

[0051]

[0052] in, represents a sub-element in the input vector r, Representation vector The child elements of Representation vector The child elements of Representation vector The child elements of Representation vector The child elements of and denote velocity and acceleration projection functions respectively.

[0053] The AUV-TTN network is constructed based on the PEZNN model and the velocity and acceleration projection functions, including:

[0054] The AUV path tracking problem is reformulated as a general IE-DQP problem as follows:

[0055]

[0056] in, , , , It is a 6*6 identity matrix;

[0057] Use the Lagrange multiplier method to solve the above problem and establish the following Lagrange equation:

[0058]

[0059] minimize get:

[0060]

[0061] The solution to the above equation can be obtained by solving the following system of equations:

[0062]

[0063] The solution to the above equation can be obtained by solving the equation:

[0064]

[0065] Establish about The error function is:

[0066]

[0067] in:

[0068]

[0069]

[0070]

[0071] Use the PEZNN model to force the aforementioned error function to decrease:

[0072]

[0073] in:

[0074]

[0075]

[0076] in , , Both represent calculation matrices, express The derivative of express The derivative of

[0077] Based on the two projection functions of velocity and acceleration, the constructed AUV-TTN network is:

[0078]

[0079] Expand it to:

[0080]

[0081] in, Indicates interference.

[0082] The beneficial effects of the present invention are as follows: the AUV trajectory tracking method based on zeroing neural network proposed in the present application, in order to constrain the drift problem of redundant degrees of freedom of AUV, constructs a performance indicator to constrain redundant degrees of freedom, and at the same time, the performance indicator is extended to the acceleration level through the gradient descent method to better adapt to application requirements, and based on the performance limit of the AUV itself, the error between the expected trajectory and the predicted trajectory is simplified to a dynamic quadratic programming problem including one equality constraint and two inequality constraints, a non-convex saturation activation function is designed through the Frobieus norm, the convergence speed under small error conditions is smoothed through the elliptic equation, and a projection and elliptic zeroing neural network is proposed, and the aforementioned network model has a strong tolerance for various disturbances encountered in the AUV trajectory tracking task. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 It is a flow chart of the AUV trajectory tracking method based on the zeroing neural network in the embodiment of the present application;

[0084] Figure 2 In a noise-free environment, the AUV uses the AUV-TTN network to track the expected trajectory and predicted trajectory of the ideal curve.

[0085] Figure 3 The residual graph of the AUV tracking the ideal curve using the AUV-TTN network in a noise-free environment.

[0086] Figure 4 In a noise-free environment, the AUV uses the AUV-TTN network to track the expected trajectory and predicted trajectory for general smoothing.

[0087] Figure 5 Residual map of AUV tracking with general smoothing using the AUV-TTN network in a noise-free environment.

[0088] Figure 6 The expected and predicted trajectories of the AUV using the AUV-TTN network for general smoothing tracking in a constant noise environment.

[0089] Figure 7 This is the residual image of AUV tracking general smoothing using the AUV-TTN network in a constant noise environment.

[0090] Figure 8 The expected and predicted trajectories of the AUV using the AUV-TTN network to track general smoothness in a time-varying noise environment.

[0091] Fig. 9 This is the residual map of AUV tracking general smoothing using the AUV-TTN network in a time-varying noise environment.

[0092] Fig.10 This is the simulated trajectory diagram of AUV using AUV-TTN network to track general smoothness in a random noise environment.

[0093] Fig.11 This is the residual map of AUV tracking general smoothness using the AUV-TTN network in a random noise environment.

[0094] Fig.12 The expected and predicted trajectories of the AUV using the AUV-TTN network for general smooth tracking in an impulse noise environment.

[0095] Fig.13 This is the residual image of AUV tracking general smoothing using the AUV-TTN network in an impulse noise environment.

[0096] Fig.14 In a noise-free environment, the AUV uses the AUV-TTN network to track the expected trajectory and predicted trajectory of the non-smooth track.

[0097] Fig.15 The expected and predicted trajectories of the AUV using the AUV-TTN network for non-smoothing tracking in a constant noise environment.

[0098] Fig.16 The expected and predicted trajectories of the AUV using the AUV-TTN network for non-smoothing tracking in a time-varying noise environment.

[0099] Fig.17 This is the residual image of the AUV tracking the non-smoothness using the AUV-TTN network in a random noise environment.

[0100] Fig.18 The expected and predicted trajectories of the AUV using the AUV-TTN network for non-smooth tracking in an impulse noise environment.

[0101] Fig.19 In a noise-free environment, the AUV uses the AUV-TTN network to track the residual image of the non-smoothed environment.

[0102] Fig. 20 This is the residual image of the AUV tracking the unsmoothed object using the AUV-TTN network in a constant noise environment.

[0103] Fig.21 This is the residual image of the AUV tracking the unsmoothed state using the AUV-TTN network in a time-varying noise environment.

[0104] Fig. 22 This is the residual image of the AUV tracking the non-smoothness using the AUV-TTN network in a random noise environment.

[0105] Fig.23 This is the residual image of the AUV tracking the non-smoothed image using the AUV-TTN network in an impulse noise environment. DETAILED DESCRIPTION

[0106] The technical solution of the present invention is further elaborated in detail below in conjunction with the drawings and specific embodiments of the specification. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by technicians in the technical field of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention. In the following description, the expression "some embodiments" is related to a subset of all possible embodiments, but it should be understood that "some embodiments" can be the same subset or different subsets of all possible embodiments, and can be combined with each other without conflict.

[0107] In the following description, a large number of specific details are provided to provide a more thorough understanding of the present invention. However, it is apparent to those skilled in the art that the present invention can be implemented without one or more of these details. In other examples, in order to avoid confusion with the present invention, some technical features well known in the art are not described.

[0108] It should be understood that the present invention can be implemented in different forms and should not be interpreted as being limited to the embodiments proposed herein. On the contrary, providing these embodiments will make the disclosure thorough and complete, and the scope of the present invention will be fully conveyed to those skilled in the art. And the purpose of the terms used herein is only to describe specific embodiments and is not intended to be a limitation of the present invention. When used herein, the singular forms of "one", "one" and "said / the" are also intended to include plural forms, unless the context clearly indicates another way. It should also be understood that the terms "compose" and / or "include" when used in this specification determine the presence of the features, integers, steps, operations, elements and / or parts, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, parts and / or groups. When used herein, the term "and / or" includes any and all combinations of the relevant listed items.

[0109] It should also be noted that when an element is referred to as being "fixed to" another element, it may be directly on the other element or there may be a central element. When an element is considered to be "connected to" another element, it may be directly connected to the other element or there may be a central element at the same time. The terms "vertical", "horizontal", "inside", "outside", "left", "right" and similar expressions used herein are for illustrative purposes only and are not intended to be the only implementation method.

[0110] In order to fully understand the present invention, a detailed structure will be presented in the following description to illustrate the technical solution proposed by the present invention. The optional embodiments of the present invention are described in detail as follows, but in addition to these detailed descriptions, the present invention may also have other implementations.

[0111] Please refer to the attached Figure 1 The present application provides an AUV trajectory tracking method based on a zeroing neural network, the method comprising the following steps:

[0112] S1. Constructing an AUV kinematic model and using a gradient descent method and performance indicators to constrain the AUV kinematic model;

[0113] S2. Based on the AUV kinematic model, the AUV trajectory tracking problem is restated as a dynamic quadratic programming problem;

[0114] S3, constructing a PEZNN model, wherein the PEZNN model represents a projection and elliptic zeroing neural network model;

[0115] S4, constructing an AUV-TTN network based on the PEZNN model and the velocity and acceleration projection functions, wherein the AUV-TTN network represents an AUV path tracking neural network;

[0116] S5. Use the AUV-TTN network to solve the dynamic quadratic programming problem, track the desired trajectory of the AUV, continuously iterate the predicted trajectory, and finally achieve AUV trajectory tracking.

[0117] In one embodiment, constructing an AUV kinematic model specifically includes:

[0118] In the local reference system of the earth, the six degrees of freedom of the AUV are expressed as:

[0119]

[0120] make , thus establishing the vector and vector The relationship between:

[0121]

[0122] in represents the initial position and rotation attitude of the AUV, and the other parameters are defined as:

[0123]

[0124]

[0125]

[0126]

[0127] in , , , , , , , , , .

[0128] Pair Vector and vector By taking the derivatives of the formula formed between the two sides, we get the AUV kinematic model as follows:

[0129]

[0130] in, represents the position coordinates of the AUV, represents the yaw of the AUV, represents the pitch of the AUV, represents the roll of the AUV, Indicates that the AUV is , and Linear velocity in direction, Indicates that the AUV is , and Angular velocity in direction, represents the initial position and rotation attitude of the AUV, represents the parameter matrix, The symbol represents the time t. T Represents the transpose of matrices and vectors.

[0131] Furthermore, in one embodiment of the present application, a gradient descent method and a performance index are used to constrain the AUV kinematic model, specifically including:

[0132] The following performance indicators are established to constrain the AUV drift caused by redundant degrees of freedom:

[0133]

[0134] Based on the design strategy of the gradient descent method, the above formula is modified as follows:

[0135]

[0136] By moving the terms, the above formula can be rearranged into:

[0137]

[0138] The solution set of the performance index can be calculated by the formula. However, considering the physical limit constraints of the AUV at the acceleration level, the performance of the AUV itself may make the speed change unable to meet the requirements of the formula, and the solution obtained by the above method is not always correct. Therefore, the above formula is further optimized to:

[0139]

[0140] in, represents the predicted trajectory, is the feedback gain coefficient, express The derivative of .

[0141] On the other hand, based on the AUV kinematic model, the AUV trajectory tracking problem is restated as a dynamic quadratic programming problem, which specifically includes:

[0142] Based on the ZNN model, the error function of the AUV kinematic model is established:

[0143]

[0144] in, represents the expected trajectory. As the expected trajectory, it is generally composed of three translation components:

[0145]

[0146] Will Map to six degrees of freedom and establish the following mapping relationship:

[0147]

[0148] in,

[0149]

[0150] According to the design idea of ​​the ZNN model, the error function is forced to drop to 0, and the following evolution formula is established:

[0151]

[0152] Considering the physical limit constraints of the underwater vehicle and based on the above formula, the AUV trajectory tracking problem is restated as the following dynamic quadratic programming problem:

[0153]

[0154] in, represents the expected trajectory, express The derivative of and are feedback gain coefficients, represents the maximum forward speed of the AUV in six degrees of freedom, represents the maximum backward speed of the AUV in six degrees of freedom, represents the maximum forward acceleration of the AUV in six degrees of freedom, It represents the maximum backward acceleration of the six degrees of freedom of the AUV.

[0155] Furthermore, in one embodiment of the present application, in the process of constructing the PEZNN model, a projection function defined based on the Frobenius norm is first introduced:

[0156]

[0157] Where J and L are two sets, projection Represents the projection from set L to set J, and defines the following set:

[0158]

[0159] Based on this, a new non-convex saturation function is proposed for:

[0160]

[0161] In order to ensure that the convergence speed of the ZNN model will not be too fast when the error function value is small, the following formula is designed based on the elliptic equation to smooth the convergence speed:

[0162]

[0163] The projection and ellipse activation functions are designed as:

[0164]

[0165] Therefore, the PEZNN model can be expressed as:

[0166]

[0167] in, represents the major axis of the ellipse, represents the minor axis of the ellipse, It also represents the feedback gain coefficient, , , .

[0168] In one embodiment, based on the inequality constraint, the following two projection functions of velocity and acceleration are established:

[0169]

[0170]

[0171] in, represents a sub-element in the input vector r, Representation vector The child elements of Representation vector The child elements of Representation vector The child elements of Representation vector The child elements of and denote velocity and acceleration projection functions respectively, , The above projection calculation is performed on each sub-element in the input vector r.

[0172] In one embodiment, an AUV-TTN network is constructed based on the PEZNN model and the velocity and acceleration projection functions, specifically including:

[0173] The AUV path tracking problem is reformulated as a general IE-DQP problem as follows:

[0174]

[0175] in, , , , is a 6*6 identity matrix, , which means is always non-negatively determined, and there is a unique global solution for this IE-DQP problem. When the two inequality constraints are not considered, the following E-DQP problem is:

[0176]

[0177] As a typical E-DQP problem, the Lagrange multiplier method is used to solve the above problem and the following Lagrange equation is established:

[0178]

[0179] in , in order to minimize get:

[0180]

[0181] The solution to the above equation can be obtained by solving the following system of equations:

[0182]

[0183] The solution to the above equation can be obtained by solving the equation:

[0184]

[0185] According to the design strategy of the ZNN model, The error function is:

[0186]

[0187] in:

[0188]

[0189]

[0190]

[0191] Use the PEZNN model to force the aforementioned error function to decrease:

[0192]

[0193] in:

[0194]

[0195]

[0196] in , , Both represent calculation matrices, express The derivative of express The derivative of

[0197] Then the independent variable The evolution formula of can be summarized as:

[0198]

[0199] Furthermore, based on the two projection functions of velocity and acceleration, the constructed AUV-TTN network is:

[0200]

[0201] Expand it to:

[0202]

[0203] in, Indicates the interference. In the AUV trajectory tracking task, it can be used to indicate disturbances such as ocean currents, sea currents, tides, and impact interference from organisms or floating objects.

[0204] In one embodiment, the AUV-TTN scheme is used to track the expected trajectory of the AUV in an ideal noise-free environment and a noise interference environment, and the predicted trajectory is continuously iterated to meet the accuracy requirements of the AUV path tracking task, and finally the predicted trajectory is obtained.

[0205] This application uses the AUV-TTN network to conduct tracking experiments on three different trajectories. The simulation results are as follows Figure 2-Figure 23 Specifically:

[0206] In a noise-free environment, the AUV uses the AUV-TTN network to track the ideal curve. The results are as follows: Figure 2 , Figure 3 shown. Figure 2 This is a simulated image of the predicted trajectory and the expected trajectory. It shows that even for an ideal trajectory, the AUV's tracking of it will be affected by the initial state. In addition, after the predicted trajectory and the expected trajectory overlap for the first time, the two trajectories always overlap. This proves that the AUV-TTN network can enable the AUV to complete this trajectory tracking task. Residual curve for Figure 3 As shown, the residual of this method can also converge to This can meet the actual needs of AUV trajectory tracking and further prove the effectiveness of this method.

[0207] In a noise-free environment, the AUV uses the AUV-TTN network to track a general smooth trajectory. The simulation results are as follows: Figure 4 , Figure 5 shown. Figure 4 It shows that the expected trajectory and the predicted trajectory deviate greatly at the beginning, but in the end, the predicted trajectory and the expected trajectory completely overlap. It is worth noting that from the residual trajectory Figure 5 It shows that its convergence time is slightly longer than the residual curve under the ideal trajectory, and the residual value in the steady state is less than , which shows that the AUV-TTN network is effective in solving the EI-DQP problem.

[0208] In a constant noise environment, the AUV tracks a generally smooth trajectory. The calculation results of the AUV-TTN network are as follows: Figure 6 , Figure 7 As shown. Figure 6 From the trajectory curve, it can be seen that the relationship between the predicted trajectory and the expected trajectory is similar to that in the noise-free case. This feature proves the robustness of the AUV-TTN network. In addition, Figure 7 The residual trajectory curve in can be found in Converges to a minimum value the following.

[0209] In a time-varying noise environment, the AUV tracks a generally smooth trajectory. The calculation results of the AUV-TTN network are as follows: Figure 8 , Fig. 9 As shown. In practical applications, complex waveforms are decomposed into the superposition of multiple simple harmonic waves, that is, most waves occurring in the ocean can be simplified into different sine waves or the sum of different sine waves, so a sine function is used as time-varying noise in this simulation. The results show that the AUV-TTN network can still enable the AUV to complete the trajectory tracking task.

[0210] In a random noise environment, the AUV uses the AUV-TTN network to track a general smooth trajectory. The simulation results are as follows: Fig.10 , Fig.11 As shown. In the simulation, Gaussian white noise with a mean of 0 and a variance of 0.1 is used as random noise. Simulation trajectory Fig.10 It shows that the expected trajectory and the predicted trajectory can coincide after the initial adjustment, and the effectiveness of the AUV-TTN network is once again proven. Fig.11 It shows that after the initial adaptation, the residual trajectory converges stably to a minimum value. Unlike time-varying noise and constant noise, the residual image here oscillates more frequently in the stable state. The oscillation here reflects that the AUV is affected by random noise, but these fluctuations are constrained within an acceptable range.

[0211] For practical and safety reasons, unpredictable impulse noise is applied to the simulation experiment. In the execution of AUV missions, in addition to considering issues such as bounded noise interference, accidental events such as collisions with marine organisms and obstacles need to be considered. If these events occur frequently, it indicates that the AUV is not suitable for working in this environment. However, if an accidental event occurs, this paper hopes that the AUV will not interrupt the mission. Therefore, this application considers a short-term high-intensity noise, called "impulse noise" to simulate this situation.

[0212] In this environment, the AUV uses the AUV-TTN network to track a general smooth trajectory. The simulation results are as follows: Fig.12 , Fig.13 As shown. From the trajectory image Fig.12 Analysis shows that during the period affected by impulse noise, there is a large deviation between the predicted trajectory and the expected trajectory, and the predicted trajectory quickly returns to the expected trajectory. At the same time, the predicted trajectory and the expected trajectory in other time periods coincide. Fig.13 This phenomenon is more intuitively shown. In the initial stage of the experiment, the residuals increased to a certain extent, and then the residuals decreased steadily for a short period of time. However, When , the residual suddenly increases, and this abnormal phenomenon lasts until After that, the residual converges steadily and finally stabilizes at the following.

[0213] Figure 14-Figure 23 is the tracking result of the AUV on the non-smooth trajectory in all the environments mentioned above. Figure 14-18 are the expected trajectory and predicted trajectory images, Figure 19-Figure 23 Is the corresponding residual trajectory image. Simulation trajectory Figure 14-18 It shows that in the whole experiment, the expected trajectory and the predicted trajectory are coincident most of the time, and the predicted trajectory deviates from the expected trajectory at the initial position and at the inflection point, but the deviation at the inflection point is small and disappears quickly. The predicted trajectory has a large deviation, which also shows that the experiment correctly simulates complex situations such as collisions encountered in the AUV trajectory tracking task.

[0214] from Figure 19-Figure 23 It can be seen that starting from the initial point that is a certain distance away from the expected trajectory, the residual trajectory quickly converges to Their sizes also meet the needs of practical applications. The residuals of the first four residual curves are within the acceptable residual range most of the time, while the fifth residual curve is When , a large residual is generated, which also corresponds to the impulse noise in the simulation experiment. In addition, all residual images have four large fluctuations, which also correspond to the turning points of the expected trajectory. At the same time, after this fluctuation, the residual quickly converges to This also proves that the AUV-TTN network has high convergence and robustness. These phenomena also show the effectiveness of the AUV-TTN network in tracking trajectories with limited inflection points. In summary, the predicted trajectory starts from a non-coincident origin and eventually overlaps with the expected trajectory, and inevitably produces residuals at the inflection points, which further illustrates the role of physical limit constraints and proves the integrity of the AUV-TTN network.

[0215] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. The protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. AUV trajectory tracking method based on zeroing neural network, characterized in that: The method comprises the following steps: Constructing an AUV kinematic model and constraining the AUV kinematic model using a gradient descent method and a performance indicator; Based on the AUV kinematic model, the AUV trajectory tracking problem is restated as a dynamic quadratic programming problem; Constructing a PEZNN model, wherein the PEZNN model represents a Projection and Elliptic Zeroing Neural Network model; An AUV-TTN network is constructed based on the PEZNN model and velocity and acceleration projection functions, wherein the AUV-TTN network represents an AUV path tracking neural network; The AUV-TTN network is used to solve the dynamic quadratic programming problem, track the AUV's expected trajectory, and continuously iterate the predicted trajectory to ultimately achieve AUV trajectory tracking. Construct the AUV kinematic model, including: In the local reference system of the earth, the six degrees of freedom of the AUV are expressed as: s(t)=[s x (t),s y (t),s z (t),θ x (t),θ y (t),θ z (t)] T Let v(t) = [v x (t), v y (t), v z (t),ω x (t),ω y (t),ω z (t)], thus establishing the relationship between vector v and vector s: By taking the derivative of both sides of the formula, we get the AUV kinematic model as follows: Among them, s x (t), s y (t), s z (t) represents the position coordinate of AUV, θ x (t) represents the yaw of AUV, θ y (t) represents the pitch of the AUV, θ z (t) represents the roll of the AUV, v x (t), v y (t), v z (t) represents the AUV and Linear velocity in the direction, ω x (t),ω y (t),ω z (t) represents the AUV and The angular velocity in the direction, s0 represents the initial position and rotation attitude of the AUV, y(τ) represents the parameter matrix, τ represents the substitution of time t, and the symbol T represents the transposition of the matrix and vector; The AUV kinematic model is constrained using a gradient descent method and performance indicators, including: The following performance indicators are established to constrain the AUV drift caused by redundant degrees of freedom: Based on the design strategy of the gradient descent method, the above formula is modified as follows: Taking into account the physical limit constraints of AUV at the acceleration level, the above formula is further optimized into: Among them, s pl (t) represents the predicted trajectory, ζ is the feedback gain coefficient, Indicates pl The derivative of (t); Based on the AUV kinematic model, the AUV trajectory tracking problem is restated as a dynamic quadratic programming problem, which specifically includes: Based on the ZNN model, the error function of the AUV kinematic model is established: E1(t)=s pl (t)-s dl (t) Will s dl (t) is mapped to six degrees of freedom, and the following mapping relationship is established: in, According to the design idea of ​​the ZNN model, the error function is forced to drop to 0, and the following evolution formula is established: Considering the physical limit constraints of the underwater vehicle and based on the above formula, the AUV trajectory tracking problem is restated as the following dynamic quadratic programming problem: Among them, s dl represents the expected trajectory, Indicates dl The derivative of ζ and μ are both feedback gain coefficients, v min represents the maximum forward speed of the AUV in six degrees of freedom, v max represents the maximum backward speed of the AUV in six degrees of freedom, a min represents the maximum forward acceleration of the AUV in six degrees of freedom, a max It represents the maximum backward acceleration of the six degrees of freedom of the AUV; Construct the PEZNN model, including: Define a non-convex saturation function P h (x) is: Based on the elliptic equation, the following formula is designed to smooth the convergence speed: The projection and ellipse activation functions are designed as: Therefore, the PEZNN model can be expressed as: Among them, p represents the length of the major axis of the ellipse, q represents the length of the minor axis of the ellipse, λ also represents the feedback gain coefficient, ξ1>0, ξ2>ξ1>0, ξ3<-ξ1<0; Establish two projection functions of velocity and acceleration: Among them, r i represents the sub-element in the input vector r, v mini Represents vector v min The child element in v maxi Represents vector v max The child element in a mini Represents vector a min The child element in a maxi Represents vector a max The child element in P v With P a denote velocity and acceleration projection functions respectively; The AUV-TTN network is constructed based on the PEZNN model and the velocity and acceleration projection functions, including: The AUV path tracking problem is reformulated as a general IE-DQP problem as follows: Among them, x(t)=v(t), p(t)=ζ(s pl (t)-s0), c(t)=s dl (t)+μ(s dl (t)-s pl (t)), W(t) = I0 is a 6×6 identity matrix; Use the Lagrange multiplier method to solve the above problem and establish the following Lagrange equation: minimize get: The solution to the above equation can be obtained by solving the following system of equations: The solution to the above equation can be obtained by solving the equation: f(y(t),t)=H(t)y(t)+b(t)=0 The error function about f(t) is established as: E(f(t))=H(t)y(t)+b(t) in: Use the PEZNN model to force the aforementioned error function to decrease: in: Where H(t), y(t), and b(t) all represent calculation matrices. represents the derivative of y(t), represents the derivative of (t); Based on the two projection functions of velocity and acceleration, the constructed AUV-TTN network is: Expand it to: Among them, η(t) represents the interference.

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