On-line multi-step prediction terrain tracking method for autonomous underwater vehicle

Abstract

The invention relates to the technical field of submarine topography tracking simulation, in particular to an on-line multi-step prediction topography tracking method for an autonomous underwater vehicle. Comprising the following steps that noise filtering is carried out on a depth value in the AUV navigation process and a height value relative to the seabed through a Kalman filtering algorithm, filtered water depth data are stored in a database, a water depth value at the k + 1 moment is predicted, terrain prediction fitting is carried out through data in the database, and a terrain curve is obtained; after the predicted terrain in front of the AUV is obtained, a correction point is generated based on a normal tracking strategy, the correction point is subjected to dynamic constraint, and a reasonable expected position point is output to the AUV; the motion of the AUV is guided by using the submarine topography, so that the tracking of the submarine topography is realized. According to the method, terrain tracking of the AUV under the unknown seabed condition is realized, and the stability of the AUV in the navigation process is ensured.

Description

Technical Field

[0001] This invention relates to the field of seabed terrain tracking simulation technology, and in particular to an online multi-step predictive terrain tracking method for autonomous underwater vehicles. Background Technology

[0002] An Autonomous Underwater Vehicle (AUV) is a self-propelled, tethered underwater robot capable of performing tasks in the ocean with little or no human supervision. In the military field, AUVs are primarily used for anti-submarine warfare, mine warfare, reconnaissance, and surveillance missions, requiring them to closely follow seabed topography to avoid detection by enemy equipment and enhance stealth and survivability. In the civilian field, AUVs are mainly used for seabed exploration, underwater rescue, seabed salvage, and marine scientific research, which also necessitates accurate terrain tracking to obtain high-quality data or perform specific tasks. Therefore, proposing an intelligent terrain-following method for autonomous underwater vehicles is essential.

[0003] Currently, methods for tracking seabed topography can be divided into two categories based on prior knowledge of topographic information: one is tracking under known seabed topographic environments, and the other is tracking under unknown seabed topographic environments.

[0004] In tracking scenarios based on known terrain, the following terrain tracking methods are commonly used: (1) A strategy combining pre-stored terrain matching and path planning is adopted. The commonly used method in engineering applications is terrain tracking based on PID control. This method adjusts the vertical motion of the AUV in real time through proportional, integral, and derivative links based on altimeter deviation. Its control structure is simple, the parameters are easy to tune, it is suitable for static or gradually changing terrain, and the amount of calculation is extremely small. It can achieve real-time control on low-computing-power hardware. However, it is lagging in response to sudden terrain changes such as steep slopes, which can easily cause overshoot or trajectory oscillations and lack the ability to predict terrain trends. (2) Based on optimal control theory and combined with global terrain information, an AUV's expected navigation trajectory similar to the seabed terrain trend is generated. The AUV will track the seabed terrain by tracking this trajectory. Although optimal control can generate vertical navigation paths, it requires global terrain information, has poor adaptability to sudden terrain changes such as steep slopes and cracks that are not modeled, and depends on accurate dynamic models, making it susceptible to external interference. (3) With the development of acoustic processing technology, a navigation method based on terrain feature matching has been proposed. This method achieves positioning and terrain tracking through real-time matching of multibeam sonar data with pre-stored maps. In unknown environments, the navigation method based on terrain feature matching can perform real-time matching and positioning, but it is easily affected by actual terrain deviations, has high computational overhead, and insufficient real-time performance. (4) Based on optical sensors, a vision / SLAM fusion method has been proposed to achieve seabed terrain tracking by combining real-time mapping with navigation. This method is limited by the turbidity interference of underwater optical sensors and the low resolution of acoustic imaging, and also requires high-performance computing units, resulting in high hardware costs.

[0005] Tracking in unknown seabed terrain environments presents greater challenges. In scenarios lacking prior terrain information, research focuses on real-time perception and dynamic decision planning, typically employing the following methods: (1) Direct sensor feedback control, which adjusts the thruster directly using altimeter measurements. While simple and easy to implement, sensor noise can easily cause trajectory oscillations, and it lacks terrain prediction capabilities, making it prone to triggering emergency ascents in steep slope scenarios. (2) Based on direct sensor feedback, model predictive control algorithms are used to estimate unknown terrain ahead using short-term prediction techniques, improving the tracking capability of unknown seabed terrain to a certain extent. Although it can partially address unknown terrain, it heavily relies on high-precision dynamic models, and fuzzy rules depend on manual design. In complex terrain, rule blind spots or control conflicts are likely to occur, and model mismatch can easily lead to control failure. Furthermore, rolling optimization computation is computationally burdensome and difficult to run in real-time on low-computing-power platforms. (3) Behavior tree hierarchical control coordinates various scenarios through a manually designed rule library. Behavior tree hierarchical control requires a manually designed logic library, which is prone to conflicts in complex terrain and lacks global optimization capabilities, potentially leading to local suboptimal solutions. (4) In unknown environments, a terrain matching method based on grid maps has also been proposed, which divides the seabed terrain into regular grids and uses real-time sonar data to match and locate the grid cells, displaying the seabed terrain undulations in real time and assisting path planning to achieve terrain tracking. The terrain matching based on grid maps has a simple data structure, which is convenient for quick querying and matching and can intuitively display terrain undulations. However, the memory usage increases exponentially with the map size, making it difficult to store large-scale high-precision maps. The terrain update efficiency is low, and there is a contradiction between grid resolution and computational load. (5) With the development of artificial intelligence technology, data-driven methods are being used for terrain tracking. Deep learning is used to predict terrain features for terrain tracking in unknown seabed environments. However, current data-driven methods, which use deep learning to predict terrain features, require a large amount of labeled data. It is difficult to obtain actual sea area data, and the network inference latency is high, making it difficult to meet the needs of high-speed navigation.

[0006] When AUVs perform missions, they often face unknown marine environments, and the methods mentioned above mostly remain at the level of theoretical analysis, which still presents great difficulties in practical engineering applications. Summary of the Invention

[0007] The purpose of this invention is to overcome the above-mentioned defects in the existing technology and propose an online multi-step predictive terrain tracking method for autonomous underwater vehicles (AUVs). This method enables AUVs to perform terrain tracking in unknown seabed conditions, ensuring the autonomy and intelligence of AUVs during terrain tracking and guaranteeing the stability of AUVs during navigation.

[0008] The technical solution of this invention is: an online multi-step predictive terrain tracking method for autonomous underwater vehicles, comprising the following steps:

[0009] S1. Noise is filtered out from the depth and height relative to the seabed values ​​during AUV navigation using the Kalman filter algorithm, and the filtered water depth data is then processed. Store the data in the database and predict the water depth at time k+1.

[0010] S2. Using the data in the database, perform terrain prediction and fitting to obtain terrain curves;

[0011] S3. After obtaining the predicted terrain in front of the AUV, generate correction points based on the normal tracking strategy, apply dynamic constraints to the correction points, and output reasonable expected position points to the AUV.

[0012] The movement of the AUV is guided by the seabed topography, thereby enabling the tracking of the seabed topography.

[0013] In this invention, in step S1, the depth value during the navigation process is obtained in real time by the depth gauge mounted on the AUV, and the altitude value relative to the seabed during the navigation process is obtained in real time by the altimeter mounted on the AUV. The sum of the depth and height values ​​represents the water depth.

[0014] The Kalman filter algorithm is used to remove noise from the data, and the filtered data is then calculated. The data is stored in a database of size n. When the number of data entries exceeds n, new data is stored and the oldest data is deleted.

[0015] After filtering the data using the Kalman filter algorithm, the state vector at time k+1 is initially predicted based on the current state vector at time k.

[0016] X k+1|k =F k X k ,

[0017] Among them, X k+1|k This represents the predicted state vector at time k+1. This represents the known state vector at the current moment. for The derivative of F represents the rate of change of water depth; k The state transition matrix is ​​represented as:

[0018]

[0019] Among them, F 11 Indicates the current For the next moment The influence of F 11 =1;

[0020] F 12 express For the next moment The impact, due to:

[0021]

[0022] Where Δt represents the time interval between two data acquisitions, therefore F 12 =Δt;

[0023] F 21 Indicates the current For the next moment The impact of F 21 =0;

[0024] F 22 express right The impact of F 22 =1; therefore:

[0025]

[0026] Covariance prediction:

[0027] P k+1|k =FP k F T +Q,

[0028] Among them, P k Let Q represent the covariance prediction matrix at time k; Q represents the prediction noise covariance matrix.

[0029] Calculate Kalman gain

[0030]

[0031] Where H represents the observation matrix and R represents the observation noise covariance matrix;

[0032] Update status:

[0033]

[0034] Among them, X k+1|k+1 This represents a posterior estimate of the system state;

[0035] Update covariance:

[0036]

[0037] Among them, P k+1|k+1 Let I represent the posterior estimate of the system covariance, and let I denote the identity matrix.

[0038] According to the revised X k+1|k Obtain the predicted water depth at time k+1

[0039] In step S2, the data in the database is represented as pairs. Where c n This represents the displacement of the AUV along the c direction at time n;

[0040] Using data from the database, terrain curves were analyzed using a cubic polynomial. To perform a fitting, let the objective function be:

[0041]

[0042] Among them, a m This represents the coefficient of the m-th power of the independent variable of the function. The function representing terrain curves is expressed as follows:

[0043]

[0044] To minimize Q, let it be the same for each coefficient a. m The partial derivatives for m = 0, 1, 2, 3 are zero:

[0045]

[0046] in, Represents the independent variable c f power of m;

[0047] After rearranging and simplifying, we obtain the system of linear equations:

[0048]

[0049] This system of equations can be represented in matrix form as follows:

[0050]

[0051] The values ​​of (a0, a1, a2, a3) are calculated from the above formula, and then the terrain curve is obtained.

[0052] Step S3 includes the following specific implementation steps:

[0053] S3.1 Based on the terrain curve obtained in step S2, the predicted value is... Substitute the values ​​and generate correction points based on the normal tracing strategy;

[0054] S3.2 Determine whether the correction points obtained in step S3.1 meet the dynamic constraints, and adjust the correction points that do not meet the dynamic constraints to obtain the correction adjustment points;

[0055] S3.3. Apply positional mutation restrictions to the correction and adjustment points obtained in step S3.2 to obtain the desired position point at the next moment.

[0056] In step S3.1,

[0057] Differentiate the terrain curve obtained in step S2 and convert the predicted value to the derivative. Substituting the values, we obtain the slope z of the tangent line to the terrain where the predicted point is located:

[0058]

[0059] The normal direction vector is (-z, 1), and the normalized unit normal vector is:

[0060]

[0061] Point The correction point is obtained by moving the object at a desired height distance d along the normal direction.

[0062]

[0063] Right now:

[0064]

[0065] Among them, c ′ k+1 h′ represents the lateral distance from the starting point to the correction point at time k+1. k+1 This represents the height of the correction point at time k+1 from the seabed.

[0066] In step S3.2,

[0067] When the correction point is at the current AUV location (c k ,h k When the correction point is to the lower left of the current AUV position (c), perform central symmetry on the correction point; when the correction point is at the current AUV position (c) k ,h k When the point is above and to the left of the correction point, perform horizontal symmetry; the correction formula is:

[0068]

[0069] In step S3.3, let the pitch constraint angle of the AUV be θ′, and the current pitch angle θ of the AUV be:

[0070]

[0071] Where, p l Indicates the AUV position point (c) at the previous moment. k-1 ,h k-1 ), pc Indicates the current AUV location (c k ,h k ), p n Indicates the adjustment point at the next moment. therefore,

[0072]

[0073] When θ > θ′, it means the angle of the location the AUV will travel to is too large, and it needs to be restricted to the dynamic constraint region. Let the desired height after the constraint be θ′. but

[0074] set up Then Δy is obtained from the following formula:

[0075]

[0076] When θ≤θ′, there is no restriction, that is...

[0077] This allows us to obtain the desired position of the AUV at the next moment.

[0078] The beneficial effects of this invention are:

[0079] (1) The multi-step predictive terrain tracking method proposed in this application enables AUVs to perform terrain tracking in unknown seabed conditions and ensures the autonomy and intelligence of AUVs in the terrain tracking process, providing a feasible solution for terrain tracking needs in the field of underwater robots, including but not limited to AUVs.

[0080] (2) This application does not use instantaneous data and data labeling, but uses local polynomial models of historical data in a pre-stored database to predict future terrain. This method is not limited to AUVs for seabed terrain prediction, but can be used for terrain prediction of robots such as drones and unmanned vehicles, which helps to achieve advanced decision-making.

[0081] (3) Compared with other methods, this application takes into account the motion limitations of AUV and proposes a normal strategy for terrain tracking. The pitch angle of AUV is dynamically adjusted by the normal direction correction amount, and its navigation axis is kept parallel to the terrain surface. This can ensure the stability of AUV during navigation and greatly reduce the sensor measurement error or failure caused by the large incident angle of sound waves on the seabed due to the changes in terrain. It is more suitable for engineering applications. Attached Figure Description

[0082] Figure 1 This is a flowchart of the method described in this invention;

[0083] Figure 2This is a diagram illustrating the process of obtaining the predicted terrain in front of the AUV and outputting a reasonable desired location point.

[0084] Figure 3 This is a schematic diagram showing the central symmetry of the correction point when it is located to the lower left of the current AUV position.

[0085] Figure 4 This is a schematic diagram showing the horizontal symmetry of the correction point when it is located to the upper left of the current AUV position.

[0086] Figure 5 This is a schematic diagram illustrating the abrupt limitation of the pitch angle of an AUV;

[0087] Figure 6 This is a terrain-following simulation diagram of an AUV performing constant-altitude navigation using the method described in this application. Detailed Implementation

[0088] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0089] Specific details are set forth in the following description to provide a full understanding of the invention. However, the invention can be practiced in many ways other than those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0090] In situations where seabed topography is unknown, this application proposes an online multi-step terrain prediction and tracking method for autonomous underwater vehicles (AUVs) based on the Kalman filtering (KF) algorithm and polynomial fitting. This application is the first to apply Kalman filtering for predicting the terrain ahead and proposes a normal tracking strategy. It corrects the position point based on the AUV's dynamic constraints to generate its desired navigation position. The specific implementation process is as follows: Figure 1 As shown. The specific implementation steps of this application are as follows.

[0091] The first step is that when the AUV begins its altitude-fixed navigation mission, it obtains the depth value during its navigation process in real time through its onboard depth gauge and the altitude value of the AUV relative to the seabed in real time through its onboard altimeter. The Kalman filter algorithm is used to filter out noise from the data, and the filtered water depth data is stored in the database.

[0092] Calculate the filtered result The data is stored in a database of size n. When the number of data entries exceeds n, new data is stored and the oldest data is deleted. This represents the sum of the depth count and the height count, i.e., the water depth.

[0093] After filtering the data using the Kalman filter algorithm, the state vector at time k+1 is initially predicted based on the current state vector at time k.

[0094] X k+1|k =F k X k ,

[0095] Among them, X k+1|k This represents the predicted state vector at time k+1. This represents the known state vector at the current moment. for The derivative of F represents the rate of change of water depth; k The state transition matrix is ​​represented as:

[0096]

[0097] Among them, F 11 Indicates the current For the next moment The effect of this is that, since the currently measured water depth value will be retained until the next moment, F 11 =1.

[0098] F 12 express For the next moment The impact, due to:

[0099]

[0100] Where Δt represents the time interval between two data acquisitions, therefore F 12 =Δt.

[0101] F 21 Indicates the current For the next moment The impact of F is not directly related to the other two factors. 21 =0.

[0102] F 22 express right Due to the influence of this, the rate of change of water depth from the previous moment will also be retained to the next moment, therefore F 22 =1. Therefore, the above formula can be written as:

[0103]

[0104] Covariance prediction:

[0105] P k+1|k =FP k F T +Q,

[0106] Among them, P k Let represent the covariance prediction matrix at time k; Q represents the prediction noise covariance matrix.

[0107] Calculate Kalman gain

[0108]

[0109] Where H represents the observation matrix and R represents the observation noise covariance matrix.

[0110] Update status:

[0111]

[0112] Among them, X k+1|k+1 This represents a posterior estimate of the system state.

[0113] Update covariance:

[0114]

[0115] Among them, P k+1|k+1 Let I represent the posterior estimate of the system covariance, and let I denote the identity matrix.

[0116] According to the revised X k+1|k Obtain the predicted water depth at time k+1

[0117] The second step involves using data from the database to predict and fit the terrain, thereby obtaining terrain curves.

[0118] Data pairs in a database are represented as Where c n This represents the displacement of the AUV along the c direction at time n. Using data from the database, a cubic polynomial is used to reconstruct the terrain curve. To perform a fitting, let the objective function be:

[0119]

[0120] Among them, a m This represents the coefficient of the m-th power of the independent variable of the function. The function representing terrain curves is expressed as follows:

[0121]

[0122] To minimize Q, let it be the same for each coefficient a. m The partial derivatives for m = 0, 1, 2, 3 are zero:

[0123]

[0124] Among them, c f m Represents the independent variable c f The power of m.

[0125] After rearranging and simplifying, we obtain the system of linear equations:

[0126]

[0127] This system of equations can be conveniently represented in matrix form as follows:

[0128]

[0129] Elements in the left-hand coefficient matrix (e.g.) ) and the elements in the right-hand vector (such as All are based on known probe data points. The calculation yielded the result.

[0130] The values ​​of (a0, a1, a2, a3) can be calculated from the above formula, and then the terrain curve can be obtained.

[0131] The third step involves obtaining the predicted terrain in front of the AUV and generating correction points based on the normal tracking strategy. The correction points directly generated by this strategy cannot meet the dynamic constraints of the AUV, so the correction points are adjusted, and finally a reasonable expected position point is output to the AUV.

[0132] Specifically, it includes the following steps.

[0133] First, based on the terrain curves obtained in the second step, correction points are generated according to the normal tracing strategy.

[0134] Differentiate the topographic curve obtained in the second step and convert the predicted value Substituting the values, we obtain the slope z of the tangent line to the terrain where the predicted point is located:

[0135]

[0136] The normal direction vector is (-z, 1), and the normalized unit normal vector is:

[0137]

[0138] Point The correction point is obtained by moving the object at a desired height distance d along the normal direction.

[0139]

[0140] Right now:

[0141]

[0142] Among them, c ′ k+1 h′ represents the lateral distance from the starting point to the correction point at time k+1. k+1 This represents the height of the correction point at time k+1 from the seabed.

[0143] Second, in order to maintain the continuity of the AUV's navigation direction and altitude changes, it is necessary to determine whether the correction point conforms to the dynamic constraints, and adjust the correction points that do not conform to the dynamic constraints to obtain the correction adjustment points.

[0144] Determine if the correction point is ahead of the current depth point. If the correction point is not ahead of the current depth point, its position needs to be adjusted. The specific adjustment method is as follows.

[0145] When the correction point is at the current AUV location (c k ,h k When the point is located to the lower left of the correction point, perform central symmetry, such as... Figure 3 As shown. When the correction point is at the current AUV position (c k ,h k When the point is above and to the left of the correction point, perform horizontal symmetry, such as... Figure 4 As shown. No correction is needed for the remaining cases. The correction formula is shown below:

[0146]

[0147] Third, the positional mutation constraint is applied to the correction and adjustment points obtained in the above steps to obtain the expected position point at the next moment.

[0148] To address the dynamic constraints of the AUV, abrupt limitations are imposed on its pitch angle. This limitation is based on the AUV's position point (c) at the previous moment. k-1 ,h k-1 ) and the current position of the AUV (c k ,h k (This restricts the adjustment point at the next moment.)

[0149] like Figure 5 As shown, if the pitch constraint angle of the AUV is θ′, then the current pitch angle θ of the AUV can be expressed as:

[0150]

[0151] Where, p l p represents the AUV location at the previous moment. c p represents the current location of the AUV. n Indicates the adjustment point at the next moment. therefore,

[0152]

[0153] When θ > θ′, it means the angle of the location the AUV will travel to is too large and needs to be limited. Figure 5 The dynamic constraint region is shown. Let the desired height after constraint be [value missing]. but set up Then Δy can be obtained from the following formula:

[0154]

[0155] When θ≤θ′, there is no restriction, that is...

[0156] The above steps yield the desired position of the AUV at the next moment.

[0157] This application utilizes seabed topography to guide the movement of the AUV, thus enabling the tracking of seabed topography during the AUV's movement.

[0158] Based on the above method, we conducted simulations, setting up simulated seabed topography with noise, and performed topography tracking verification at heights of 10m and 15m above the seabed. The verification results are as follows. Figure 6 As shown, the shapes of the topographic tracking curves at a height of 10m and 15m above the seabed obtained by the method described in this application are similar to the actual original seabed topographic curves, thus demonstrating the effectiveness of the method described in this application.

[0159] The online multi-step predictive terrain tracking method for autonomous underwater vehicles provided by this invention has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from the principles of this invention, and these improvements and modifications also fall within the protection scope of the claims of this invention. The above description of the disclosed embodiments enables those skilled in the art to implement or use this invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of this invention. Therefore, this invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An online multi-step predictive terrain tracking method for an autonomous underwater vehicle, characterized in that, Includes the following steps: S1. Noise is filtered out from the depth and height relative to the seabed values ​​during AUV navigation using the Kalman filter algorithm, and the filtered water depth data is then processed. Store the data in the database and predict the water depth at time k+1. S2. Using the data in the database, perform terrain prediction and fitting to obtain terrain curves; S3. After obtaining the predicted terrain in front of the AUV, generate correction points based on the normal tracking strategy, apply dynamic constraints to the correction points, and output reasonable expected position points to the AUV. The movement of the AUV is guided by the seabed topography, thereby enabling the tracking of the seabed topography.

2. The online multi-step predictive terrain tracking method for autonomous underwater vehicles according to claim 1, characterized in that, In step S1, the depth value during the navigation process is obtained in real time by the depth gauge on the AUV, and the altitude value relative to the seabed during the navigation process is obtained in real time by the altimeter on the AUV. The sum of the depth and height values ​​represents the water depth. The Kalman filter algorithm is used to remove noise from the data, and the filtered data is then calculated. The data is stored in a database of size n. When the number of data entries exceeds n, new data is stored and the oldest data is deleted.

3. The online multi-step predictive terrain tracking method for autonomous underwater vehicles according to claim 1, characterized in that, In step S1, after filtering the data using the Kalman filter algorithm, the state vector at time k+1 is initially predicted based on the current state vector at time k: X k+1|k =F k X k , Among them, X k+1|k This represents the predicted state vector at time k+1. This represents the known state vector at the current moment. for The derivative of F represents the rate of change of water depth; k The state transition matrix is ​​represented as: Among them, F 11 Indicates the current For the next moment The influence of F 11 =1; F 12 express For the next moment The impact, due to: Where Δt represents the time interval between two data acquisitions, therefore F 12 =Δt; F 21 Indicates the current For the next moment The impact of F 21 =0; F 22 express right The impact of F 22 =1; therefore: Covariance prediction: P k+1|k =FP k F T +Q, Among them, P k Let Q represent the covariance prediction matrix at time k; Q represents the prediction noise covariance matrix. Calculate Kalman gain Where H represents the observation matrix and R represents the observation noise covariance matrix; Update status: Among them, X k+1|k+1 This represents a posterior estimate of the system state; Update covariance: Among them, P k+1|k+1 Let I represent the posterior estimate of the system covariance, and let I denote the identity matrix. According to the revised X k+1|k Obtain the predicted water depth at time k+1 4. The online multi-step predictive terrain tracking method for autonomous underwater vehicles according to claim 1, characterized in that, In step S2, the data in the database is represented as pairs. Where c n This represents the displacement of the AUV along the c direction at time n; Using data from the database, terrain curves were analyzed using a cubic polynomial. To perform a fitting, let the objective function be: Among them, a m This represents the coefficient of the m-th power of the independent variable of the function. The function representing terrain curves is expressed as follows: To minimize Q, let it be the same for each coefficient a. m The partial derivatives for m = 0, 1, 2, 3 are zero: in, Represents the independent variable c f power of m; After rearranging and simplifying, we obtain the system of linear equations: This system of equations can be represented in matrix form as follows: The values ​​of (a0, a1, a2, a3) are calculated from the above formula, and then the terrain curve is obtained.

5. The online multi-step predictive terrain tracking method for autonomous underwater vehicles according to claim 1, characterized in that, Step S3 includes the following specific implementation steps: S3.1 Based on the terrain curve obtained in step S2, the predicted value is... Substitute the values ​​and generate correction points based on the normal tracing strategy; S3.2 Determine whether the correction points obtained in step S3.1 meet the dynamic constraints, and adjust the correction points that do not meet the dynamic constraints to obtain the correction adjustment points; S3.

3. Apply positional abrupt change restrictions to the correction and adjustment points obtained in step S3.2 to obtain the desired position point at the next moment.

6. The online multi-step predictive terrain tracking method for autonomous underwater vehicles according to claim 5, characterized in that, In step S3.1, Differentiate the terrain curve obtained in step S2 and convert the predicted value to the derivative. Substituting the values, we obtain the slope z of the tangent line to the terrain where the predicted point is located: The normal direction vector is (-z, 1), and the normalized unit normal vector is: Point The correction point is obtained by moving the object at a desired height distance d along the normal direction. Right now: Where, c′ k+1 h′ represents the lateral distance from the starting point to the correction point at time k+1. k+1 This represents the height of the correction point at time k+1 from the seabed.

7. The online multi-step predictive terrain tracking method for autonomous underwater vehicles according to claim 5, characterized in that, In step S3.2, When the correction point is at the current AUV location (c k ,h k When the correction point is to the lower left of the current AUV position (c), perform central symmetry on the correction point; when the correction point is at the current AUV position (c) k ,h k When the point is above and to the left of the correction point, perform horizontal symmetry; the correction formula is:

8. The online multi-step predictive terrain tracking method for autonomous underwater vehicles according to claim 5, characterized in that, In step S3.3, let the pitch constraint angle of the AUV be θ′, and the current pitch angle θ of the AUV be: Where, p l Indicates the AUV position point (c) at the previous moment. k-1 ,h k-1 ), p c Indicates the current AUV location (c k ,h k ), p n Indicates the adjustment point at the next moment. therefore, When θ > θ′, it means the angle of the location the AUV will travel to is too large, and it needs to be restricted to the dynamic constraint region. Let the desired height after the constraint be θ′. but set up Then Δy is obtained from the following formula: When θ≤θ′, there is no restriction, that is... This allows us to obtain the desired position of the AUV at the next moment.

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