A multi-audonomous underwater vehicle safety boundary formation control method and system

Abstract

The application discloses a kind of multi-autonomous underwater vehicle safety boundary formation control method and system, belong to underwater robot and multi-agent collaborative control technical field.Firstly, through online segmentation obstacle in underwater image, inside safety boundary is constructed using safety margin processing;Using arc length normalization resampling and truncated fourier series fitting, the parametric expression of boundary shape is realized;Based on parameter domain equidistant sampling, generate uniformly distributed target point set, and through graph laplacian consistency and boundary target attraction term design control law, make multi-autonomous underwater vehicle converge to safety boundary formation under limited communication conditions;Dynamic pretrigger and smooth interpolation mechanism are introduced to realize the continuous transition of multi-obstacle sequence formation;Finally, multi-objective optimization is used to balance tracking accuracy, safety spacing uniformity and control energy consumption, to obtain the parameter combination suitable for engineering.The application significantly improves the formation safety, adaptability and through efficiency in complex underwater environment.

Description

Technical Field

[0001] This invention relates to the field of underwater robot and multi-agent cooperative control technology, specifically to a method and system for safety boundary formation control of multiple autonomous underwater vehicles. Background Technology

[0002] Autonomous Underwater Vehicles (AUVs), with their autonomous navigation, exploration, and operational capabilities, are widely used in seabed resource exploration, environmental monitoring, and marine data acquisition. As mission scale and complexity increase, the limitations of single-vehicle operations in terms of coverage efficiency, endurance, and robustness are becoming increasingly apparent. Collaborative operations among multiple AUVs have become a crucial means to improve operational efficiency and reduce mission time and energy consumption. Formation control, as a key foundational technology for multi-AUV collaboration, is used to maintain the desired geometric configuration and achieve coordinated maneuvering. Especially in sea areas with complex obstacles such as reefs, buoys, and subsea pipelines, multi-AUV formations typically need to simultaneously meet requirements such as safe spacing within the formation, uniform formation distribution, and safe passage along obstacle boundaries, thus placing higher demands on formation control strategies.

[0003] In existing research on multi-agent formation control, various distributed consensus and formation tracking methods have been developed to achieve formation maintenance and trajectory tracking under conditions of disturbance and communication constraints. However, existing technologies still have shortcomings in safe formation in environments with unknown obstacles: a common approach pre-sets the desired formation or trajectory as a fixed template or predefined path, and often assumes that environmental geometry or obstacle boundaries can be obtained in advance; when obstacles are complex in shape, uncertain in location, or change over time, such methods have limited adaptability to online perception results.

[0004] To address obstacle avoidance and safety constraints, engineering often employs artificial potential fields and control obstacle functions as local obstacle avoidance mechanisms. However, these methods typically rely on specific assumptions about obstacle shape, formation topology, and communication connectivity. Under complex interference or input saturation conditions, they are prone to problems such as local minima, conservative maneuvering, and frequent topology reconfiguration, thus affecting formation stability and throughput efficiency. From a system integration perspective, many solutions still use environmental geometry and obstacle boundaries as known inputs, lacking a general technical approach that integrates the online construction of safety boundaries extracted from sensing data with formation generation and control design.

[0005] In addition, underwater visual perception is often affected by uneven illumination, scattering, attenuation, etc., resulting in strong intensity unevenness and blurred edge features in the image (or equivalent observation), which increases the difficulty of reliably extracting obstacle contours; if the extraction of safety boundaries is unstable, it will further affect the feasibility of formation reference shape generation and safety distance constraints.

[0006] Therefore, for multi-AUV formation operations in unknown or dynamically changing underwater obstacle environments, there is an urgent need for a safe formation control technology that can stably acquire and represent obstacle safety boundaries under limited perception and communication conditions, support online updates of formation references, and balance energy consumption and control smoothness while meeting safety distance and formation uniformity requirements.

[0007] To address this, a method and system for safety boundary formation control of multiple autonomous underwater vehicles is proposed. Summary of the Invention

[0008] The purpose of this invention is to provide a method and system for safe boundary formation control of multiple autonomous underwater vehicles (AUVs), which can solve the problem that existing technologies have difficulty in generating trackable safe boundary formations in real time based on online perception results in scenarios where underwater obstacles have complex shapes, unknown prior knowledge, or change over time. This enables safe, uniform, and smooth formation tracking of multiple AUVs along the safe boundary.

[0009] To achieve the above objectives, the present invention provides a multi-autonomous underwater vehicle safety boundary formation control method, comprising the following steps:

[0010] Step 1: Acquire underwater environment image data, segment the obstacle area to obtain an obstacle binary mask, and obtain the safe area and its safe boundary inside the obstacle through safety margin processing;

[0011] Step 2: Normalize and resample the safety boundary to obtain a sequence of boundary points with equal arc length distribution, and perform truncated Fourier series fitting on it to obtain the Fourier coefficient vector representing the boundary shape, thus realizing the parameterized representation of the boundary; transform the safety boundary contour point sequence in the image coordinate system to the formation control coordinate system through coordinate mapping.

[0012] Step 3: Select equally spaced parameter points corresponding to the number of autonomous underwater vehicles within the normalized parameter domain. Based on the parameterized expression of the safety boundary, map each parameter point to a set of target points on the safety boundary in the control coordinate system to achieve uniform distribution of autonomous underwater vehicles on the safety boundary.

[0013] Step 4: Construct a multi-autonomous underwater vehicle (AUV) interaction topology, and design a distributed control law based on the graph Laplace consistency term and the boundary target attraction term, so that each AUV can converge to the target point set while interacting with its neighbors, thereby achieving distributed safe formation control.

[0014] Step 5: When a boundary change is detected, the formation shape switching and transition mechanism is triggered. The interpolation function and spatiotemporal strategy are used to ensure that the formation is reconstructed before entering the safe distance of the obstacle.

[0015] Step 6: Tune the control and spatiotemporal parameters through multi-objective optimization, and comprehensively weigh the formation tracking error, safety distance and uniformity, as well as the control energy consumption and control input smoothness to obtain a parameter combination that meets engineering constraints.

[0016] Step 1 includes:

[0017] A grayscale image obtained after preprocessing underwater environment image data is acquired. A segmentation operator is constructed using a locally prefitted active contour model to obtain a binary obstacle mask. ,

[0018] in, This represents the preprocessed grayscale image. Represents the pixel coordinates of a grayscale image grayscale value; These are the pixel coordinates (column coordinates) in the horizontal direction of the image. These are the pixel coordinates (row coordinates) in the vertical direction of the image; Image width (number of pixel columns). Image height (number of pixel rows); This is a segmentation operator constructed based on a locally prefitted active contour model. To split the parameter set; This indicates that the pixel belongs to the obstacle area. This indicates that the pixel belongs to a non-obstacle area.

[0019] The set of segmentation parameters It must include at least the local neighborhood radius (window radius). The Used in Centered on, with radius Calculate local statistics within a local neighborhood.

[0020] This defines the obstacle area. and its boundaries : ,

[0021] in, To meet The set of all pixel coordinates; Represents boundary operators; Indicates the boundary line between the obstacle area and the non-obstacle area;

[0022] To provide an inner safety margin for the formation, a morphological erosion operator is used to obtain a safety mask. :

[0023] ,

[0024] in, For morphological erosion operators, Where is the corrosion radius; This indicates that the pixel belongs to the safe area. This indicates that the pixel does not belong to the safe area;

[0025] Define the security zone and security boundaries : ,

[0026] in, To meet The set of all pixel coordinates.

[0027] Step 2 includes:

[0028] Discrete security boundary Represented as a closed parametric curve: ,

[0029] in, Indicates curve parameters as The boundary point coordinate vector at that time; and The boundary points are respectively located in the image coordinate system. axial coordinate components and Axis coordinate components; symbols Indicates transpose; This indicates that the parametric curve is a closed curve;

[0030] Constructing new parameters by arc length normalization : ,

[0031] in The total arc length of the curve. From the starting point to the parameters The arc length is determined to achieve a uniform arc length distribution.

[0032] Approximating the safety boundary using a finite-term truncated Fourier series:

[0033] ,

[0034] in, This is the arc length normalization parameter; and These represent the safety boundaries in the parameters. place coordinates and Fourier fit values ​​of the coordinates; To truncate the harmonics of the Fourier series; Harmonic sequence number ; and These are the cosine and sine functions, respectively; for The coordinates corresponding to the first Coefficients of the cosine and sine terms for The coordinates corresponding to the first Coefficients of the cosine and sine terms; and They are respectively coordinates and Constant values ​​for coordinates;

[0035] And it is written in linear regression form, specifically: ,

[0036] in, The parameterized coordinate vector of the safety boundary under the arc length normalization parameter; For parameters The basis function matrix is ​​composed of truncated Fourier basis functions; This is the Fourier coefficient vector;

[0037] Stack the contour points after resampling with equal arc length: Construct block matrix : The Fourier coefficients are solved using least squares. : Furthermore, by using coordinate mapping, the sequence of safety boundary contour points in the image coordinate system is transformed to the cross-sectional plane used for formation control, thereby obtaining the parameterized expression of the safety boundary in the control coordinate system.

[0038] in, This represents the number of contour points after resampling with equal arc length; For the first The arc length normalization parameter corresponding to each resampling point; For safety boundaries in parameters The column vector of the contour points at the location, Give it its transpose row vector; This is a data vector obtained by stacking the coordinates of all contour points in order; For the regression matrix at parameter points The value at that location, Transpose it.

[0039] Step 4 includes:

[0040] Projecting the formation control of multiple autonomous underwater vehicles in three-dimensional space onto... Construct an undirected graph from a cross-sectional plane: Its Laplace matrix: and satisfy ;

[0041] in, It is a communication undirected graph; A set of nodes; Let be the set of edges used to represent the communication and interaction relationships between aircraft; It is an adjacency matrix. For weights; For degree matrix, For nodes The degree; The graph is a Laplace matrix;

[0042] No. An autonomous underwater vehicle in The pose of a plane is represented as: Stacking yields: ;

[0043] in, For time, For the first An autonomous underwater vehicle used in formation control Position state vector within the cross-sectional plane. and These respectively indicate that the aircraft is in in plane Axis coordinates and Axis coordinates For the number of autonomous underwater vehicles, To put all the aircraft in The global state vector is obtained by stacking the position vectors in the plane in order.

[0044] The model is constructed using single-integral kinematics, specifically as follows: And define the extended Laplace: ;

[0045] in, Indicates the first A spacecraft in The time derivative of the position in the plane. For the planar velocity control input of the i-th vehicle; To extend the Laplace matrix, Indicates the Kronecker product. for identity matrix;

[0046] The error is defined as follows:

[0047] Selected within the normalized parameter domain Construct a sampling matrix using equal-interval parameters. for:

[0048] Then the expected safe boundary formation for: ,

[0049] The goal is to achieve: Then the first Local tracking error of an autonomous underwater vehicle for:

[0050] Stacking error satisfy ;

[0051] Based on adjacency Design No. Control inputs of an autonomous underwater vehicle for:

[0052] ,

[0053] in, For nodes The set of neighbors of the i-th, representing the set of neighbors of the i-th. A set of indices of aircraft that have communication connections;

[0054] Get stacking control input for: , To mitigate the local tracking errors of each independent underwater vehicle The error vector obtained by stacking To control the gain and ensure all values ​​are greater than 0, the first term... The first term is a distributed consistency term based on graph Laplace, used to maintain formation consistency; the second term... Achieve attraction-convergence towards the target safety boundary.

[0055] Step 5 includes:

[0056] To ensure that the formation completes shape reconstruction before reaching obstacles, a dynamic pre-triggering mechanism is introduced:

[0057] Define formation in Average axial position in the direction for: ,

[0058] in, No. An autonomous underwater vehicle moves along in a three-dimensional coordinate system Position information along the axis;

[0059] Formation for expected safety boundaries instantaneous error Defined as: ,

[0060] Estimate the time required for shape convergence. for: ,

[0061] in, This refers to the safety margin factor. To control the upper limit of the input amplitude; Denotes the Euclidean norm;

[0062] The pre-trigger condition is selected as: ,

[0063] in, To trigger the reference position threshold, used to characterize the formation along The critical position of the action zone near the boundary switching point in the axial direction; The pre-trigger distance margin is used to reserve a distance for early switching before reaching the threshold position; For formation along The axial velocity of the direction;

[0064] The moment when the pre-trigger condition is first met is Then, smooth interpolation is used from the current shape. Transition to the next obstacle shape : ,

[0065] in, The stacked expected position vector of the reference trajectory in the control coordinate system, which varies with time, is used as the target for formation tracking; The smooth interpolation weight function is used at time 1000. Then the reference shape will be removed from the current shape. Smooth transition to the next obstacle shape ; This indicates taking the minimum value of the quantities within the parentheses, used to... Limited to Within the range; This is the transition time constant, used to adjust the rate of change of the smooth interpolation weight function;

[0066] And select the transition duration: , Thus, the reference trajectory that changes over time is obtained as follows: This allows for a smooth transition of the desired formation within a finite timeframe, while maintaining a safety margin. Complete the refactoring within the system;

[0067] in, The transition duration for shape switching; and These are the upper and lower limits of the transition duration, respectively. This is the duration scaling factor, satisfying... This is used to adjust the transition duration within the feasible range; The minimum available transition time, obtained based on the sailing propulsion distance constraint, is defined as follows: ; For triggering time Formation to threshold position The remaining axial distance; Triggering time The formation in The average axial position of the direction; To control the update cycle; This indicates taking the maximum value of the values ​​within the parentheses.

[0068] Step 6 includes:

[0069] Control and spatiotemporal parameter vectors Represented as: The parameter vector For subsequent multi-objective optimization and tuning.

[0070] At discrete sampling time Upper definition of formation tracking error for: ,

[0071] Construct the objective function for formation tracking error as follows: ,

[0072] The kth indicator for: ; For at any time The distance metric used to trigger the judgment is as follows. Distance threshold;

[0073] Safety distance and uniformity objective function for: ,

[0074] This represents the number of discrete time points within the statistical window. For the first Discrete control time; For a moment Next With the The actual Euclidean distance between the aircraft; The safety clearance penalty function; For a moment Next Local spacing between individual aircraft The sequence of spacing indicators that constitutes all aircraft; denoted as the variance of the spacing index sequence; These are the weighting coefficients;

[0075] in, , ;

[0076] and Representing time respectively Next The and the first The position and state vector of an autonomous underwater vehicle in the formation control coordinate system; This is the minimum safe distance threshold;

[0077] Control energy consumption and control input smoothness objective function for: ,

[0078] in, For a moment Stacking control input vectors, This is the stacking control input vector from the previous time step; These are the smoothness weighting coefficients;

[0079] The final solution is the following multi-objective optimization problem: The goal is to obtain a set of parameter solutions that meet the trade-offs between safety, accuracy, and energy consumption, and then select the compromise solution for actual control.

[0080] The present invention also provides a multi-autonomous underwater vehicle safety boundary formation control system implemented according to the method, comprising:

[0081] The perception and segmentation module is used to acquire underwater environment image data and segment the obstacle region to obtain a binary mask of the obstacle.

[0082] The safety boundary construction module is used to perform safety margin processing on the binary mask of the obstacle to obtain the safe region and its safety boundary located inside the obstacle.

[0083] The boundary parameterization module is used to resample the safety boundary by arc length normalization, and to perform truncated Fourier series fitting based on the boundary point sequence to obtain the Fourier coefficient vector; and to transform the safety boundary in the image coordinate system to the formation control coordinate system through coordinate mapping.

[0084] The target point uniform distribution module is used to select equally spaced parameter points corresponding to the number N of autonomous underwater vehicles within the normalized parameter domain. The target point set on the safety boundary is obtained by mapping according to the boundary parameterization expression. To achieve a uniform distribution of autonomous underwater vehicles on the safety boundary;

[0085] The distributed formation control module is used to construct the interactive topology of multiple autonomous underwater vehicles. Based on the graph Laplace consistency term and attraction term, a distributed control law is designed to enable each autonomous underwater vehicle to converge to the target point set while interacting with its neighbors.

[0086] The shape transition module is used to detect boundary changes and trigger shape switching and transition mechanisms. It uses interpolation functions and spatiotemporal strategies to ensure that the formation is reconstructed before entering the safe distance of the obstacle.

[0087] The multi-objective tuning module is used to tune the control and spatiotemporal parameters through multi-objective optimization, comprehensively balancing formation tracking error, safety and uniformity, and control energy consumption and smoothness to obtain a parameter combination that meets engineering constraints.

[0088] The constraint execution module is used to handle physical constraints and ensure that the control output meets the platform's feasibility requirements.

[0089] The present invention also provides an electronic device, including a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method.

[0090] The present invention also provides a storage medium storing a computer program or instructions that, when the computer program or instructions are run on a computer, execute the steps of the method described.

[0091] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0092] 1. Enhanced capability in constructing safe boundaries for complex underwater visual conditions. This invention preprocesses underwater environmental image data and segments obstacle regions, then performs morphological processing on the segmentation results based on safety margins to obtain safe regions and safe boundaries for formation control. This ensures that safe reference boundaries usable for navigation and formation can still be stably obtained under underwater imaging interference conditions such as uneven illumination, scattering attenuation, and edge blurring, improving environmental adaptability and robustness.

[0093] 2. The safety boundary representation is smoother and more compact, facilitating real-time sampling and control. This invention performs arc-length normalized resampling on the safety boundary and uses truncated Fourier series for parameterized fitting, transforming the discrete contour into a continuous, smooth curve representation with controllable parameter dimensions. This reduces the amount of boundary data and noise sensitivity, while also facilitating uniform sampling and generation of target points within the parameter domain, improving real-time performance and tracking stability.

[0094] 3. Achieving uniform distribution and distributed collaborative control along the safety boundary improves formation maintenance and safe passage capabilities. This invention selects equally spaced parameter points corresponding to the number of aircraft within the normalized parameter domain and maps them to a set of target points along the safety boundary, ensuring that each aircraft is uniformly distributed along the safety boundary. Combining a distributed control law with a consistency term and a boundary target attraction term, it can achieve formation shape maintenance and convergent tracking of the safety boundary under finite communication topology, reducing the risk of local congestion and collisions.

[0095] 4. The boundary switching process is continuous and controllable, suppressing error peaks caused by abrupt shape changes. To address multiple obstacles, this invention introduces pre-triggering conditions and a smooth interpolation mechanism, enabling the reference shape parameters to transition continuously over time. This avoids drastic changes in control input and increased transient errors caused by abrupt command changes during boundary switching, thereby improving the stability and continuity of the switching process.

[0096] 5. Parameters can be optimized and tuned through multi-objective optimization, taking into account safety distance, uniformity, and energy consumption. This invention constructs a multi-objective evaluation function that includes safety distance and uniformity indicators as well as control energy consumption and smoothness indicators. It optimizes and tunes the control gain and spatiotemporal parameters, achieving an adjustable trade-off between safety, formation uniformity, and control resource consumption, thereby enhancing engineering feasibility and adaptability to different task requirements. Attached Figure Description

[0097] Figure 1 This is a flowchart illustrating a safety boundary formation control method for multiple autonomous underwater vehicles according to the present invention.

[0098] Figure 2 This is a schematic diagram illustrating the mapping from the 3D coordinate system and the image plane to the YZ plane.

[0099] Figure 3 This is a schematic diagram showing the results of obstacle image segmentation and contour extraction.

[0100] Figure 4 A schematic diagram of the formation results of multiple AUVs on the plane boundary;

[0101] Figure 5 This is a schematic diagram of the error and heading change curves of multiple AUVs;

[0102] Figure 6 A schematic diagram of the formation results for fewer AUVs at the planar boundary;

[0103] Figure 7 A schematic diagram of the curves showing the relationship between AUV error and heading change;

[0104] Figure 8 A schematic diagram of the Pareto front and the compromise solution;

[0105] Figure 9 This is a schematic diagram of the three-dimensional multi-obstacle shape evolution;

[0106] Figure 10 A schematic diagram of the trajectory guided by the three-dimensional safety boundary;

[0107] Figure 11 A schematic diagram of planar boundary formation for the adaptive PID comparison method;

[0108] Figure 12 This is a schematic diagram comparing the 3D traversal methods of different algorithms. Detailed Implementation

[0109] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention above and in other aspects will become clearer.

[0110] This invention provides a method for safe boundary formation control of multiple autonomous underwater vehicles. Under conditions such as uneven intensity and weak edges due to scattering attenuation in underwater obstacle contour imaging, it achieves online extraction of obstacle safety boundaries and collaborative tracking of the formation along these boundaries. Furthermore, it performs smooth switching and 3D traversal verification in a multi-obstacle sequence environment. The flowchart of this method is shown below. Figure 1 As shown, the specific steps are as follows:

[0111] Step 1: Acquire underwater environment image data, segment the obstacle area to obtain an obstacle binary mask, and obtain the safe area and its safe boundary inside the obstacle through safety margin processing;

[0112] Underwater environment image data can be acquired in several ways: by acquiring underwater scene image sequences in real time using an underwater optical camera mounted on an autonomous underwater vehicle; or by acquiring data using external underwater camera equipment deployed in the sea trial environment. The acquired underwater environment image data can be a single frame image or continuous video frames, and can be accompanied by a timestamp to characterize the acquisition time, serving as input data for subsequent segmentation and safety boundary construction.

[0113] Step 1 includes:

[0114] Acquire grayscale images obtained after preprocessing underwater environment image data. A segmentation operator is constructed using a locally prefitted active contour model. A binary obstacle mask is obtained. :

[0115] ,

[0116] in, The preprocessed grayscale image in pixel coordinates The grayscale value at that location; These are the pixel coordinates (column coordinates) in the horizontal direction of the image. The vertical pixel coordinates (row coordinates) of the image; Image width (number of pixel columns). Image height (number of pixel rows); This indicates that the pixel belongs to the obstacle area. Indicates that a pixel belongs to a non-obstacle region; segmentation parameter set At least include the local neighborhood radius (window radius) of the locally prefitted active contour model, used to... Centered on, with radius Calculate local statistics within the neighborhood of .

[0117] This defines the obstacle region and its boundaries:

[0118] ,

[0119] in, This represents the obstacle region (set of obstacle pixels) defined by the binary obstacle mask, i.e., satisfying... The set of all pixel coordinates; Denotes the boundary operator, therefore Represents a set The boundary; Indicates obstacle area The boundary curve (obstacle profile) is the dividing line between the obstacle area and the non-obstacle area.

[0120] To provide an inner safety margin for the formation, a morphological erosion operator is employed. Obtain a security mask: ,

[0121] in, This is a morphological erosion operator used for shrinking binary masks; The erosion radius (the radius of the structuring element, in pixels) is used to characterize the pixel distance corresponding to the reserved inner safety margin in the image coordinate system. The security mask obtained through etched processing at pixel coordinates The value at that location, This indicates that the pixel belongs to the safe area. This indicates that the pixel does not belong to the safe area.

[0122] Define the security zone and security boundaries:

[0123] ,

[0124] in, Indicated by a safety mask A defined safe region (set of safe pixels) is one that satisfies... The set of all pixel coordinates; Indicates a safe area Safety boundary curves (safety profiles); The area is an obstacle zone, and This indicates that the safe area is located inside the obstacle area (retracted by morphological erosion), therefore the safe boundary is located inside the obstacle boundary.

[0125] In the discrete pixel domain, the security boundary By using the security mask The boundary is extracted; in one implementation, the boundary pixel set is determined using a morphological boundary extraction method, specifically as follows:

[0126]

[0127] in, Representing structural elements Perform an erosion operation on the binary security mask. Extract structural elements for the preset boundaries; This represents the set of boundary pixels extracted by the safety mask. Then... The boundary pixels are contour-tracked and sorted according to the 8-neighbor connectivity order to obtain the closed safe boundary curve. .

[0128] To stably extract obstacle contours under conditions of weak edges and uneven intensity, this implementation method employs an improved active contour model based on local prefitting energy (LPF-ACM) to segment the obstacle image, specifically as follows:

[0129] Construct the level set function, whose evolution equation is: ,

[0130] in, Level set function, The evolution time of the level set; The regularization Dirac function; The curvature of the curve at zero level set; For the Laplace operator; The weight of the curvature regularization term; The weights are for the distance regularization term; The weights of the energy-driven terms in the local prefitting; and These are the weighting coefficients for the local energy terms on the inner and outer sides of the contour, respectively.

[0131] Local energy term: ,

[0132] in, This is the preprocessed grayscale image; For Gaussian kernel function, This represents the convolution operation; and These are the locally fitted gray-scale mean values ​​estimated based on the regions inside and outside the current level set curve, respectively. and These represent the local fitting energy on the inner and outer sides of the contour, respectively.

[0133] After iteration until convergence, the segmentation mask is obtained: ,in, This is the termination iteration time at convergence. This is an indicator function, taking the value 1 when the condition within the parentheses is true, and 0 otherwise. After obtaining the binary obstacle mask, to obtain the safe region inside the obstacle, morphological erosion is further used to obtain the safe boundary, where the erosion structuring element is a disk-shaped structuring element with a radius of:

[0134] For each obstacle image, the level set function evolution iteration number NumIter is set to 80, and the parameters are taken as follows. Gaussian kernel standard deviation .

[0135] After obtaining the binary obstacle mask, morphological erosion is further used to obtain the safe region inside the obstacle to obtain the safe boundary, where the radius of the eroded structural element is taken as: Pixels

[0136] in, The radius of the corroded structural element; and These are the height and width of the current image, respectively, both in pixels; This represents the number of pixels on the shorter side of the image. This indicates that the larger value among the terms within the parentheses should be used. Therefore, the radius of the erosion structuring element should be at least 4 pixels and should be adaptively adjusted proportionally to the image size.

[0137] This yields the shrunken safe area and safe boundary, which are then used for subsequent formation tracking.

[0138] like Figure 3 As shown, the top row represents the original image, and the bottom row represents the segmentation results. The red closed curve represents the extracted outer boundary of the obstacle. This result demonstrates that even under conditions of uneven illumination, scattering and attenuation leading to uneven intensity, and weak lighting common in the seabed environment, this method can still accurately recover complex closed contours.

[0139] Step 2: Normalize and resample the safety boundary to obtain a sequence of boundary points with equal arc length distribution, and perform truncated Fourier series fitting on it to obtain the Fourier coefficient vector representing the boundary shape, thus realizing the parameterized representation of the boundary; transform the safety boundary contour point sequence in the image coordinate system to the formation control coordinate system through coordinate mapping.

[0140] Step 2 includes:

[0141] Discrete security boundary Represented as a closed parametric curve: ,

[0142] in, The parameterized curve representation of the safety boundary is given by the parameter being... The boundary point coordinate vector at that time; and The boundary points are respectively located in the image coordinate system. axial coordinate components and Axis coordinate components; symbols Indicates transpose, used to convert... Represented as a column vector; These are curve parameters (normalized parameters). Indicates the range of parameter values; This indicates that the parameter curve is a closed curve, meaning that the starting point and the ending point coincide.

[0143] Constructing new parameters by arc length normalization : , The total arc length of the curve. From the starting point to the parameters The arc length is determined to achieve a uniform arc length distribution.

[0144] Approximating the safety boundary using a finite-term truncated Fourier series:

[0145] ,

[0146] in, These are the curve parameters after arc length normalization; and These represent the safety boundaries in the parameters. place coordinates and Fourier fit values ​​of the coordinates; To truncate the order (harmonic number) of the Fourier series; Harmonic sequence number ; and These are the cosine and sine functions, respectively; for The coordinates corresponding to the first Coefficients of the cosine and sine terms for The coordinates corresponding to the first Coefficients of the cosine and sine terms; and They are respectively coordinates and The constant term (DC component) of the coordinates is used to characterize the overall translational offset of the curve.

[0147] And write it in linear regression form: ,

[0148] in, Arc length normalization parameter The parameterized coordinate vector of the lower safety boundary (can be written as) ; For parameters The basis function matrix is ​​composed of truncated Fourier basis functions (cosine and sine terms of each order and constant terms); Let be the Fourier coefficient vector. To facilitate writing the truncated Fourier fit in linear regression form, define the _th_... The basis function block matrix corresponding to the first harmonic is Its expression is:

[0149] ,

[0150] make Then there is ,in It is a second-order identity matrix. It can be further written in linear regression form. ,in .

[0151] Stack the contour points after resampling with equal arc length: Construct block matrix: The Fourier coefficients are solved using least squares: Furthermore, by transforming the sequence of safety boundary contour points in the image coordinate system to the cross-sectional plane used for formation control through coordinate mapping (including rotation, translation, and necessary scale normalization), a parameterized expression of the safety boundary in the control coordinate system is obtained.

[0152] in, This represents the number of contour points after resampling with equal arc length; For the first The arc length normalization parameter corresponding to each resampling point; For safety boundaries in parameters The column vector of the contour points at the location, Give it its transpose row vector; This is a data vector obtained by stacking the coordinates of all contour points in order; For the regression matrix at parameter points The value at that location, Transpose it; For each The block matrix is ​​used for least squares estimation. .

[0153] This implementation is first based on the safety boundary obtained in step 1. Extracting discrete boundary point sequences arranged in contour order Calculate the Euclidean distances between adjacent points and sum them to obtain the cumulative arc length. And let the total arc length Thus, the arc length normalization parameter is constructed. Then in the parameter domain Generate equally spaced sampling parameters (For example The corresponding boundary points are obtained through linear interpolation or spline interpolation. This yields a resampled boundary point sequence with equal arc length distribution. Based on this, the resampled boundary point sequences were respectively... and The coordinates are fitted with a truncated Fourier series to obtain the parameterized representation of the boundary and the Fourier coefficient vector.

[0154] Regarding parameter settings, the number of resampling points To balance boundary detail preservation and computational overhead, the following approach is recommended. ; Truncation of Fourier series order Used to control fitting smoothness and expressive power, typically taking... Fourier coefficients can be obtained through least squares fitting; when the boundary points are noisy, smoothing can be performed before fitting or regularization can be added in least squares to improve robustness.

[0155] like Figure 2 As shown, this embodiment is implemented in a three-dimensional coordinate system. The following obstacle sequence is traversed, in which The axis is the direction of formation movement; each obstacle is fixed. One corresponding to the position Cross-sectional safety boundaries. To facilitate formation control driven by image contours, the contour parameters in the image coordinate system are normalized and mapped to the formation control plane through rotation and translation. (plane), to obtain the Fourier coefficient vector used for control. .

[0156] Step 3: Select equally spaced parameter points corresponding to the number of autonomous underwater vehicles within the normalized parameter domain, and map them to a set of target points on the safety boundary under the control coordinate system based on the parameterized expression of the safety boundary, so as to achieve uniform distribution of autonomous underwater vehicles on the safety boundary.

[0157] Assume the number of autonomous underwater vehicles in the formation is Based on the parameterized expression of the safety boundary obtained in step 2 (Already in formation control coordinate system), in the normalized parameter domain Select equally spaced parameter points corresponding to the number of aircraft. And use the boundary parameterization function to map it to the target point on the safety boundary.

[0158] Thus, the target point set is obtained. This is used to characterize the desired position of each vehicle on the safety boundary, achieving uniform distribution along the safety boundary; when When it is a closed curve, we can let and Equivalent, and the beginning and end are made continuous by using index loop.

[0159] To avoid the target point falling within the high curvature noise region of the boundary parameterized fitting, a phase offset can be added to the equally spaced parameter points. ,in This initial phase offset is used to adjust the overall starting position of the formation on the safety boundary; in dynamic scenarios, The parameters can be updated based on the parameters corresponding to the nearest boundary point of the formation to reduce initial transient errors. If the boundary parameterization in step 2 is still in the image coordinate system, then after obtaining... Then, the coordinates are transformed to the formation control coordinate system through coordinate mapping (rotation, translation, and necessary scale normalization); if coordinate mapping has been completed in step 2, then step 3 directly generates the formation in the control coordinate system. .

[0160] Step 4: Construct a multi-autonomous underwater vehicle (AUV) interaction topology, and design a distributed control law based on the graph Laplace consistency term and the boundary target attraction term, so that each AUV can converge to the target point set while interacting with its neighbors, thereby achieving distributed safe formation control.

[0161] Project formation control onto The cross-sectional plane is defined in the control coordinate system as follows: The position status of the autonomous underwater vehicle is as follows: A single-integral kinematic model is adopted. ,in The input is for planar velocity control. The communication topology is constructed as an undirected weighted graph. ,in Represents the set of aircraft nodes. Represents the set of communication edges. The adjacency matrix is; the corresponding graph Laplacian matrix is And define the extended Laplace as ; It is a diagonal matrix of degree. For nodes The degree.

[0162] No. An autonomous underwater vehicle in The pose of a plane is represented as: Stacking yields: ;

[0163] in, For time; For the first An autonomous underwater vehicle used in formation control Position state vector within the cross-sectional plane; and These respectively indicate that the spacecraft is in in plane Axis coordinates and Axis coordinates (units can be meters or normalized length, depending on the coordinate mapping); This indicates transpose. The number of autonomous underwater vehicles; To put all the aircraft in The global state vector is obtained by stacking the position vectors in the plane in order. Representing vectors The transpose (row vector), therefore The dimension is .

[0164] Using single-integral kinematics: And define the extended Laplace: ;

[0165] in, Indicates the first A spacecraft in The time derivative of the position in the plane; For the corresponding planar velocity control input (i.e., in) and (The desired velocity component in the direction). Single-integral kinematics is used to abstractly model the motion of the vehicle within the cross-sectional plane, facilitating the construction of distributed consistency and boundary tracking control laws and performing convergence analysis; in engineering implementation, coordinates can be further used to... Convert into speed, attitude, or thruster commands that the aircraft can execute (and may be combined with saturation to ensure feasibility).

[0166] Furthermore, let Then the global state satisfies . To extend the Laplace matrix, where Indicates the Kronecker product. for The identity matrix is ​​used to convert the Graph Laplace matrix. Extending scalar consistency to two-dimensional positional consistency allows the consistency terms in subsequent control laws to be written based on... It is in compact matrix form.

[0167] The error is defined as follows:

[0168] Based on the n equally spaced parameters selected in step 3 within the normalized parameter domain, the sampling matrix is ​​constructed as follows:

[0169] Then the expected safe boundary formation for: ,

[0170] The goal is to achieve: Then the first Local tracking error of an autonomous underwater vehicle for:

[0171] Stacking error satisfy ;

[0172] Based on adjacency Design No. Control inputs of an autonomous underwater vehicle for:

[0173] ,

[0174] in, For nodes The set of neighbors of the i-th, representing the set of neighbors of the i-th. The set of indices of aircraft that have communication connections.

[0175] Get stacking control input for: ,in, To mitigate the local tracking errors of each independent underwater vehicle The error vector obtained by stacking It is a distributed consistency item based on communication topology, used to maintain formation coherence. To control the gain and ensure that all terms are greater than 0, the first term in the above equation achieves error consistency and maintains formation continuity, while the second term achieves attraction and convergence to the target safety boundary.

[0176] Regarding parameter settings: the communication topology can adopt a ring topology or its extended form (e.g., each node communicates with its two nearest neighbors on the left and right sides). In this case, the following settings can be used: (Equal-weighted edges) are used for simplified implementation; different weights can also be set based on communication quality or distance. Control gain. The setting can be adjusted based on the convergence rate and control input amplitude constraints, and is usually taken as follows: It is a positive number; to balance fast convergence and smooth control, we can set it to... Alternatively, a set of parameters can be selected through simulation experiments to ensure error convergence and prevent input saturation under a given speed limit. The construction of the sampling matrix and the solution of the Fourier coefficients must satisfy the identifiable conditions of the number of sampling points and the truncation order; the number of resampling points should meet the following conditions. To avoid degeneracy in least squares solutions; when At this time, the truncation order can be reduced. Increase the number of boundary resampling points or introduce a regularization term to improve the stability of the fit.

[0177] In the planar formation experiment, each AUV in A single-integral model is used in the plane: ,

[0178] A circular topology is used: each AUV is connected to its two nearest neighbors on its left and right sides, thus each AUV has four neighbors. The edge weights are determined by... The corresponding Laplace matrix elements are: ,

[0179] Definition of the first Local tracking error of each AUV: ,

[0180] The control input takes the form of a superposition of consistency terms and attraction terms: ,

[0181] And can be stacked as: ,

[0182] The first term is used to maintain neighborhood consistency and suppress formation tearing, while the second term is used to guide each AUV to converge to its assigned safe boundary sampling point.

[0183] In the "multiple AUVs" scenario, take ,satisfy The AUVs start from the initial straight formation and converge to the target formation formed by the safety boundary under the action of the control law. Figure 4 The formation results for two types of boundaries, namely bilobal and circular, are presented.

[0184] Figure 5 The evolution of the coefficient error norm and the position error norm was recorded: the error decreased rapidly at the beginning of each segment; a brief peak appeared when the target boundary switched due to the change of reference; then the error converged rapidly again and remained small; the heading (attitude) adjustment was rapid and always bounded, thus verifying the effectiveness and stability of the control strategy in the "multi-AUV" scenario.

[0185] In the case of "few AUVs", take Due to the limited number of available AUVs and insufficient number of target points to allocate within the normalized parameter domain, the sampling matrix may exhibit rank deficiency. However, experimental results show that the system can still complete boundary formation and track and extract curve shapes, such as... Figure 6 As shown. Figure 6 (a) gives the formation process under a circular safety boundary: AUVs gradually move from an initial near-linear configuration toward the circular boundary and eventually form a near-uniform distribution along the circular boundary. Figure 6 (b) The formation process under a non-convex star-shaped safety boundary is presented: despite the sharp corners and large curvature changes of the boundary, each AUV can gradually converge to the vicinity of the target boundary and maintain a dispersed distribution along the boundary, indicating that the method still has good adaptability to different geometric boundary shapes under conditions with few AUVs. To characterize the error convergence characteristics under insufficient sampling conditions, an index is introduced. .

[0186] Figure 7 The dynamic evolution of error and heading under conditions with few AUVs is presented. Among them, Figure 7 (a) Display indicators The brief peaks that appear at the initial time and near each boundary switch, and then rapidly decay to near zero, indicate that the fitting error under the undersampling condition can still be effectively suppressed; Figure 7 (b) Display the position error norm The transient increase during boundary switching, but then the error converges quickly and remains at a small steady-state value, indicating that the formation's tracking error of the target safety boundary can be recovered quickly after each switch. Figure 7 (c) Display the headings of each agent The bounded adjustment occurs only at the moment of switching, followed by a rapid return to a stable state without sustained oscillations or divergence, indicating that the control strategy maintains good controllability and smoothness even under conditions of low AUV coverage. In summary, the method can still achieve a relatively uniform boundary distribution and avoid excessive clustering even in under-sampling scenarios.

[0187] Step 5: When a boundary change is detected, the formation shape switching and transition mechanism is triggered. The interpolation function and spatiotemporal strategy are used to ensure that the formation is reconstructed before entering the safe distance of the obstacle.

[0188] When a change in the security boundary is detected (e.g., the currently tracked security boundary) Safety boundary corresponding to the next obstacle Upon completion of extraction and update, the shape switching and transition mechanism is activated. First, based on the formation... Average axial position in the direction Perform pre-trigger detection; when the pre-trigger condition is met... When the condition is first met, record the time when the condition is first met. It then begins a smooth interpolation transition of the reference shape parameters.

[0189] Specifically, let the current reference shape parameter be... The reference shape parameters corresponding to the next safety boundary are: The time-varying reference shape parameter during the transition period is defined as follows:

[0190] ,

[0191] This yields the reference trajectory (expected safety boundary formation) that varies over time. ,

[0192] This is used as the tracking target of the distributed control law in step 4, so that the formation can switch smoothly and continuously in the transition interval, avoiding error peaks and drastic changes in control input caused by sudden changes in reference instructions, thereby ensuring that the formation reconstruction is completed before entering the safe distance of the obstacle.

[0193] Regarding parameter settings: Pre-triggered position threshold (switch threshold position). For pre-trigger distance margin, For formation along Axial velocity in the direction; The estimated time required for one formation / shape convergence process can be obtained from the current error norm and control capability; The stacked expected position vector of the reference trajectory in the control coordinate system, which varies with time, is used as the target for formation tracking; The smooth interpolation weight function is used at time 1000. Then the reference shape will be removed from the current shape. Smooth transition to the next obstacle shape ; This indicates taking the minimum value of the quantities within the parentheses, used to... Limited to Within the range; This is the transition time constant, used to adjust the rate of change of the smooth interpolation weight function.

[0194] Transition duration Used to set the duration of smooth transition, can be pressed

[0195] ,

[0196] in and These are the lower and upper limits of the transition duration, respectively. This is the duration scaling factor. To control the update cycle / sampling cycle; the above settings enable Restricted to Within this range, the minimum transition time requirement given by the remaining distance and sampling period is simultaneously met, thereby improving the robustness and feasibility of the switching process.

[0197] Step 6: Tune the control and spatiotemporal parameters through multi-objective optimization, and comprehensively weigh the formation tracking error, safety distance and uniformity, as well as the control energy consumption and control input smoothness to obtain a parameter combination that meets engineering constraints.

[0198] Step 6 includes:

[0199] Control and spatiotemporal parameter vectors Represented as: ,

[0200] At discrete sampling time Upper definition of formation tracking error for: ,

[0201] Construct the objective function for formation tracking error as follows: ,

[0202] The kth indicator for: ; For at any time The distance metric used to trigger the decision can be defined as follows: ; This is a distance threshold used to determine whether the pre-triggering condition is met. Time-triggered indicator ,otherwise .

[0203] Safety distance and uniformity objective function for: ,

[0204] This represents the number of discrete time points within the statistical window. For the first Discrete detection; subscript Indicates the first in the formation With the An autonomous underwater vehicle, and This indicates that statistics are being compiled for all different aircraft pairs; For a moment Next With the The actual Euclidean distance between the aircraft; This is a safety distance penalty function used to soften distance constraints (e.g., when...). (A penalty is incurred when the distance is less than the safe distance threshold). For a moment Next Local spacing between individual aircraft The sequence of spacing indicators that constitutes all aircraft; The variance of the above sequence is used to measure the uniformity of the formation spacing distribution; , which are weighting coefficients used to balance the relative importance of the "safety distance penalty term" and the "uniformity (variance) term" in the objective function.

[0205] in, , ;

[0206] and Representing time respectively Next The and the first An autonomous underwater vehicle in a formation control coordinate system (such as...) Position state vector in the cross-sectional plane (e.g.) ), Describing the Euclidean norm, therefore This represents the actual Euclidean distance between the two spacecraft. The minimum safe distance threshold (the minimum permissible distance between members) is used to prevent collisions or dangerous proximity between formation members. Time through penalty function Apply spacing constraints.

[0207] Control energy consumption and control input smoothness objective function for: ,

[0208] in, For the first Discrete control time. This represents the number of discrete time points within the statistical window. For a moment The stacked control input vector (composed of the control inputs of all autonomous underwater vehicles). This is the stacking control input vector from the previous time step; Describing the Euclidean norm, Used to measure the amplitude of control input. Used to measure the change in control input between adjacent time steps (characterizing the smoothness of control input). This is a smoothness weighting coefficient used to balance the relative importance of the "control energy consumption term" and the "control input smoothness term".

[0209] The final solution is the following multi-objective optimization problem: The goal is to obtain a set of parameter solutions that meet the trade-offs between safety, accuracy, and energy consumption, and then select the compromise solution for actual control.

[0210] In the 3D traversal demonstration, five safety boundaries are placed sequentially along the axis: ,

[0211] in , Simultaneously, a multi-objective genetic algorithm is used to process the parameter vector. Pareto optimization is performed to balance formation tracking error, safe spacing and uniformity, and control energy consumption and control input smoothness, and box constraints are applied: Minimum allowable spacing .

[0212] Figure 8 The Pareto front projection distribution of the three-objective optimization results on the pairwise objective planes is shown. Blue dots represent Pareto non-dominated solutions, and red asterisks represent the final selected compromise solutions.

[0213] Specifically, Figure 8 The left figure shows the target of formation tracking error. Safety distance and uniformity target A compromise; Figure 8 The middle image shows the target of the formation tracking error. With control energy consumption and control input smoothness target A compromise; Figure 8 The right figure shows the safety distance and uniformity target. With control energy consumption and control input smoothness target A compromise.

[0214] Depend on Figure 8 As can be seen, due to the mutual constraints between different objectives, the Pareto solution set forms a clear compromise distribution on the three two-dimensional projection planes. The solution corresponding to the red asterisk is located in the region with relatively balanced overall performance, and therefore is selected as the actual control parameter. The final selected parameters are: ,

[0215] Under these parameters, a good overall balance is achieved among formation tracking error, safety distance and uniformity, and control cost. This results in a smoother trajectory, more stable boundary tracking, and lower control cost. Furthermore, it can maintain convergence even with small disturbances and inner loop constraints.

[0216] For each obstacle segment, four snapshots are displayed, showing the target boundary curve and the agent's position at interpolation rates of 0%, 33%, 67%, and 100%. Figure 9 (a) depicts the evolution of obstacle 1: starting with a linear formation, the agent gradually transforms into the safety boundary of the first obstacle; as it approaches the second obstacle, the formation transitions from the first boundary shape to the second, and so on, until it crosses the fifth obstacle. The corresponding processes for the remaining four obstacles are shown in... Figure 9 In (b)-(e), it was confirmed that the proposed method can effectively adapt to different boundary geometries.

[0217] at last, Figure 10 (a) and (b) illustrate the 3D evolution of the agents guided by safety boundaries. As obstacles appear sequentially along the X-axis, the agent array translates forward, completing the transition of each shape within a preset safety margin before the corresponding obstacle. The formation closely matches the safety boundary at each stage, and the transitions between different shapes remain smooth. Throughout the multi-stage traversal, all three target metrics remain within the Pareto compromise region, without violating minimum spacing constraints or excessive control effort.

[0218] To verify the advantages of the method of the present invention, an adaptive PID controller was constructed as a comparison baseline, which is based on synchronization error. ,in ;

[0219] In the comparison method, the first The AUV control input is selected as follows: ,in Furthermore, robustness is enhanced by projecting constraints on the gain using an online adaptive law.

[0220] In the planar case, Figure 11 The process of forming a ring-shaped boundary formation by eight AUVs under an adaptive PID controller is demonstrated. Comparative analysis shows that both methods can form a boundary formation, but the method of this invention can achieve a more uniform spacing distribution and a more closely fitting shape in regions with high curvature or sharp geometric features; while the adaptive PID method is more sensitive to the initial gain and adaptive step size, and is more prone to oscillations in concave sections, which may lead to overshoot or slower convergence.

[0221] In the case of three-dimensional traversal, Figure 12The comparison results of five obstacle sequences are presented: the left figure shows the method of this invention, and the right figure shows the adaptive PID baseline. The method of this invention maintains the overall contour shape of each obstacle cross section, has a more uniform spacing distribution, and a smoother shape transition in the obstacle switching area; in contrast, the baseline method exhibits more obvious shape distortion and uneven distribution in the switching area.

[0222] The present invention also provides a multi-autonomous underwater vehicle safety boundary formation control system, including a perception and segmentation module, a safety boundary construction module, a boundary parameterization module, a target point uniform distribution module, a distributed formation control module, a shape transition module, a multi-target tuning module, and a constraint execution module;

[0223] In this embodiment, the perception and segmentation module is used to acquire underwater environment image data and segment the obstacle region to obtain an obstacle binary mask;

[0224] In this embodiment, the safety boundary construction module is used to perform safety margin processing on the binary mask of the obstacle to obtain the safe region and its safety boundary located inside the obstacle; and transforms the safety boundary in the image coordinate system to the formation control coordinate system through coordinate mapping.

[0225] In this embodiment, the boundary parameterization module is used to resample the safety boundary by arc length normalization and to perform truncated Fourier series fitting based on the boundary point sequence to obtain the Fourier coefficient vector.

[0226] In this embodiment, the target point uniform distribution module is used to select equally spaced parameter points within the normalized parameter domain, map them to a set of target points on the safety boundary, and perform coordinate mapping.

[0227] In this embodiment, the distributed formation control module is used to construct the interactive topology of multiple autonomous underwater vehicles (AUVs) and design a distributed control law based on the graph Laplace consistency term and attraction term, so that each AUV converges to the target point set while interacting with its neighbors.

[0228] In this embodiment, the shape transition module is used to trigger the shape switching and transition mechanism when the boundary changes are detected. The interpolation function and the spatiotemporal strategy are used to ensure that the formation is reconstructed before entering the safe distance of the obstacle.

[0229] In this embodiment, the multi-objective tuning module is used to tune the control and spatiotemporal parameters through multi-objective optimization, comprehensively balancing formation tracking error, safety and uniformity, and control energy consumption and smoothness to obtain a parameter combination that meets engineering constraints.

[0230] In this embodiment, the constraint execution module is used to process physical constraints so that the control output meets the platform's feasibility requirements.

[0231] The aforementioned system can implement the multi-autonomous underwater vehicle safety boundary formation control method described in this invention. However, the implementation device of the multi-autonomous underwater vehicle safety boundary formation control method described in this invention includes, but is not limited to, the multi-autonomous underwater vehicle safety boundary formation control system described in this invention.

[0232] This invention provides a method and system for safe boundary formation control of multiple autonomous underwater vehicles. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A method for safe boundary formation control of multiple autonomous underwater vehicles, characterized in that, Includes the following steps: Step 1: Acquire underwater environment image data, segment the obstacle area to obtain an obstacle binary mask, and obtain the safe area and its safe boundary inside the obstacle through safety margin processing; Step 2: Normalize and resample the safety boundary to obtain a sequence of boundary points with equal arc length distribution, and perform truncated Fourier series fitting on it to obtain the Fourier coefficient vector representing the boundary shape, thus realizing the parameterized representation of the boundary; transform the safety boundary contour point sequence in the image coordinate system to the formation control coordinate system through coordinate mapping. Step 3: Select equally spaced parameter points corresponding to the number of autonomous underwater vehicles within the normalized parameter domain. Based on the parameterized expression of the safety boundary, map each parameter point to a set of target points on the safety boundary in the control coordinate system to achieve uniform distribution of autonomous underwater vehicles on the safety boundary. Step 4: Construct a multi-autonomous underwater vehicle (AUV) interaction topology, and design a distributed control law based on the graph Laplace consistency term and the boundary target attraction term, so that each AUV can converge to the target point set while interacting with its neighbors, thereby achieving distributed safe formation control. Step 5: When a boundary change is detected, the formation shape switching and transition mechanism is triggered. The interpolation function and spatiotemporal strategy are used to ensure that the formation is reconstructed before entering the safe distance of the obstacle. Step 6: Tune the control and spatiotemporal parameters through multi-objective optimization, and comprehensively weigh the formation tracking error, safety distance and uniformity, as well as the control energy consumption and control input smoothness to obtain a parameter combination that meets engineering constraints.

2. The multi-autonomous underwater vehicle safety boundary formation control method according to claim 1, characterized in that, Step 1 includes: Acquire grayscale images obtained after preprocessing underwater environment image data. A segmentation operator is constructed using a locally prefitted active contour model to obtain a binary obstacle mask. : , in, These are the pixel coordinates in the horizontal direction of the image. The pixel coordinates in the vertical direction of the image; Image width, Image height; This is a segmentation operator constructed based on a locally prefitted active contour model. To split the parameter set, This indicates that the pixel belongs to the obstacle area. This indicates that the pixel belongs to a non-obstacle area; This defines the obstacle area. and its boundaries : , in, To meet The set of all pixel coordinates; Represents boundary operators; Indicates the boundary line between the obstacle area and the non-obstacle area; To provide an inner safety margin for the formation, a morphological erosion operator is used to obtain a safety mask. : ， in, For morphological erosion operators, Where is the corrosion radius; This indicates that the pixel belongs to the safe area. This indicates that the pixel does not belong to the safe area; Define the security zone and security boundaries : , in, To meet The set of all pixel coordinates.

3. The multi-autonomous underwater vehicle safety boundary formation control method according to claim 1, characterized in that, Step 2 includes: Discrete security boundary Represented as a closed parametric curve: , in, Indicates curve parameters as The boundary point coordinate vector at that time; and The boundary points are respectively located in the image coordinate system. axial coordinate components and Axis coordinate components; Indicates transpose; This indicates that the parametric curve is a closed curve; Constructing new parameters by arc length normalization : ,in The total arc length of the curve. From the starting point to the parameters The arc length is determined to achieve a uniform arc length distribution. Approximating the safety boundary using a finite-term truncated Fourier series: ， in, This is the arc length normalization parameter; and These represent the safety boundaries in the parameters. place coordinates and Fourier fit values ​​of the coordinates; To truncate the harmonics of the Fourier series; Harmonic sequence number ; and These are the cosine and sine functions, respectively; for The coordinates corresponding to the first Coefficients of the cosine and sine terms for The coordinates corresponding to the first Coefficients of the cosine and sine terms; and They are respectively coordinates and Constant values ​​for coordinates; And it is written in linear regression form, specifically: ,in The parameterized coordinate vector of the safety boundary under the arc length normalization parameter; For parameters The basis function matrix is ​​composed of truncated Fourier basis functions; This is the Fourier coefficient vector; Stack the contour points after resampling with equal arc length: Construct block matrix : The Fourier coefficients are solved using least squares. : Furthermore, by using coordinate mapping, the sequence of safety boundary contour points in the image coordinate system is transformed to the cross-sectional plane used for formation control, thereby obtaining the parameterized expression of the safety boundary in the control coordinate system. in, This represents the number of contour points after resampling with equal arc length; For the first The arc length normalization parameter corresponding to each resampling point; For safety boundaries in parameters The column vector of the contour points at the location, Give it its transpose row vector; This is a data vector obtained by stacking the coordinates of all contour points in order; For the regression matrix at parameter points The value at that location, Transpose it.

4. The multi-autonomous underwater vehicle safety boundary formation control method according to claim 1, characterized in that, Step 4 includes: Projecting the formation control of multiple autonomous underwater vehicles in three-dimensional space onto... Construct an undirected graph from a cross-sectional plane: Its Laplace matrix: and satisfy ; in, It is a communication undirected graph; A set of nodes; Let be the set of edges used to represent the communication and interaction relationships between aircraft; It is an adjacency matrix. For weights; It is a diagonal matrix of degree. For nodes The degree; The graph is a Laplace matrix; No. An autonomous underwater vehicle in The pose of a plane is represented as: Stacking yields: ; in, For time, For the first An autonomous underwater vehicle used in formation control Position state vector within the cross-sectional plane. and These respectively indicate that the aircraft is in in plane Axis coordinates and Axis coordinates For the number of autonomous underwater vehicles, To put all the aircraft in The global state vector is obtained by stacking the position vectors in the plane in order. The model is constructed using single-integral kinematics, specifically as follows: And define the extended Laplace: ; in, Indicates the first A spacecraft in The time derivative of the position in the plane. For the planar velocity control input of the i-th vehicle; To extend the Laplace matrix, Indicates the Kronecker product. for identity matrix; The error is defined as follows: Selected within the normalized parameter domain Construct a sampling matrix using equal-interval parameters. for: Then the expected safe boundary formation for: , The goal is to achieve: Then the first Local tracking error of an autonomous underwater vehicle for: Stacking error satisfy ; Based on adjacency Design No. Control inputs of an autonomous underwater vehicle for: ， in, For nodes The set of neighbors of the i-th, representing the set of neighbors of the i-th. A set of indices of aircraft that have communication connections; Get stacking control input for: ,in, To mitigate the local tracking errors of each independent underwater vehicle The error vector obtained by stacking To control the gain and ensure all values ​​are greater than 0, the first term... The first term is a distributed consistency term based on graph Laplace, used to maintain formation consistency; the second term... Achieve attraction-convergence towards the target safety boundary.

5. The multi-autonomous underwater vehicle safety boundary formation control method according to claim 1, characterized in that, Step 5 includes: To ensure that the formation completes shape reconstruction before reaching obstacles, a dynamic pre-triggering mechanism is introduced: Define formation in Average axial position in the direction for: , in, No. An autonomous underwater vehicle moves along in a three-dimensional coordinate system Position information along the axis; Formation for expected safety boundaries instantaneous error Defined as: , Estimate the time required for shape convergence. for: , in, This refers to the safety margin factor. To control the upper limit of the input amplitude; Denotes the Euclidean norm; The pre-trigger condition is selected as: , in, To trigger the reference position threshold, used to characterize the formation along The critical position of the action zone near the boundary switching point in the axial direction; The pre-trigger distance margin is used to reserve a distance for early switching before reaching the threshold position; For formation along The axial velocity of the direction; The moment when the pre-trigger condition is first met is Then, smooth interpolation is used from the current shape. Transition to the next obstacle shape : , in, The stacked expected position vector of the reference trajectory in the control coordinate system, which varies with time, is used as the target for formation tracking; The smooth interpolation weight function is used at time 1000. Then the reference shape will be removed from the current shape. Smooth transition to the next obstacle shape ; This indicates taking the minimum value of the quantities within the parentheses, used to... Limited to Within the range; This is the transition time constant, used to adjust the rate of change of the smooth interpolation weight function; And select the transition duration: , Thus, the reference trajectory that changes over time is obtained as follows: This enables a smooth transition of the desired formation with a safety margin. Complete the refactoring within the system; in, The transition duration for shape switching; and These are the upper and lower limits of the transition duration, respectively. This is the duration scaling factor; The minimum available transition time, obtained based on the sailing propulsion distance constraint, is defined as follows: , Triggering time Formation to threshold position The remaining axial distance, Triggering time The formation in The average axial position of the direction, To control the update cycle; This indicates taking the maximum value of the values ​​within the parentheses.

6. The multi-autonomous underwater vehicle safety boundary formation control method according to claim 1, characterized in that, Step 6 includes: Control and spatiotemporal parameter vectors Represented as: At discrete sampling time Upper definition of formation tracking error for: , Construct the objective function for formation tracking error as follows: , The kth indicator for: ; For at any time The distance metric used to trigger the judgment is as follows. Distance threshold; Safety distance and uniformity objective function for: , This represents the number of discrete time points within the statistical window. For the first Discrete control time; For a moment Next With the The actual Euclidean distance between the aircraft; The safety clearance penalty function; For a moment Next Local spacing between individual aircraft The sequence of spacing indicators that constitutes all aircraft; denoted as the variance of the spacing index sequence; These are the weighting coefficients; Control energy consumption and control input smoothness objective function for: , in, For a moment Stacking control input vectors, This is the stacking control input vector from the previous time step; These are the smoothness weighting coefficients; The final solution is the following multi-objective optimization problem: The goal is to obtain a set of parameter solutions that meet the trade-offs between safety, accuracy, and energy consumption, and then select the compromise solution for actual control.

7. A multi-autonomous underwater vehicle safety boundary formation control system implemented using the method described in any one of claims 1 to 6, characterized in that, include: The perception and segmentation module is used to acquire underwater environment image data and segment the obstacle region to obtain a binary mask of the obstacle. The safety boundary construction module is used to perform safety margin processing on the binary mask of the obstacle to obtain the safe region and its safety boundary located inside the obstacle. The boundary parameterization module is used to resample the safety boundary by arc length normalization, and to perform truncated Fourier series fitting based on the boundary point sequence to obtain the Fourier coefficient vector; and to transform the safety boundary in the image coordinate system to the formation control coordinate system through coordinate mapping. The target point uniform distribution module is used to select equally spaced parameter points within the normalized parameter domain, map them to a set of target points on the safety boundary, and perform coordinate mapping. The distributed formation control module is used to construct the interactive topology of multiple autonomous underwater vehicles. Based on the graph Laplace consistency term and attraction term, a distributed control law is designed to enable each autonomous underwater vehicle to converge to the target point set while interacting with its neighbors. The shape transition module is used to detect boundary changes and trigger shape switching and transition mechanisms. It uses interpolation functions and spatiotemporal strategies to ensure that the formation is reconstructed before entering the safe distance of the obstacle. The multi-objective tuning module is used to tune the control and spatiotemporal parameters through multi-objective optimization, comprehensively balancing formation tracking error, safety and uniformity, and control energy consumption and smoothness to obtain a parameter combination that meets engineering constraints. The constraint execution module is used to handle physical constraints and ensure that the control output meets the platform's feasibility requirements.

8. An electronic device, characterized in that, It includes a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the multi-autonomous underwater vehicle safety boundary formation control method as described in any one of claims 1 to 6.

9. A storage medium, characterized in that, The system stores a computer program or instructions that, when executed on a computer, perform the steps of the multi-autonomous underwater vehicle safety boundary formation control method as described in any one of claims 1 to 6.

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