A two-way homotopy maximum flux path planning method and device for unmanned ship formation

Abstract

The application provides a kind of unmanned ship formation's two-way homotopy maximum flux path planning method and device.The signed distance field is constructed, and the state space is upgraded to the volume sphere node sequence with adaptive safety radius, to decouple the directional guide vector of static obstacle repulsive force and the two-way volume expansion of adaptive step length is executed, the transition swept volume convex hull is extracted to execute non-interference verification, to establish the global homotopy equivalence of merging pipeline with volume level measurement;With the spatial gradient of signed distance field driving the initial topological skeleton converges to the local space axis, the maximum physical cross-section capacity is extracted;The capacity is mapped to the spatial compression factor to drive the cluster to execute lateral compression and longitudinal spacing compensation, finally generate the volume space pipeline with topological safety and maximum available cross-section capacity, solve the problem that the volume space pipeline of unmanned ship cluster passage path planning in restricted unstructured water area cannot simultaneously have topological safety and maximum available cross-section capacity.

Description

Technical Field

[0001] This invention relates to the field of multi-agent swarm cooperative control and autonomous navigation, and in particular to a bidirectional homotopy maximum flux path planning method and apparatus for unmanned vessel formations. Background Technology

[0002] This invention belongs to the field of multi-agent swarm collaborative control and autonomous navigation technology, and specifically relates to a path planning method, device and storage medium for unmanned vessel swarms in restricted unstructured waters.

[0003] With the development of the marine economy and offshore engineering, swarms of multiple Unmanned Surface Vehicles (USVs) are widely used in tasks such as inspection of cross-sea bridges, patrol of scattered islands and reefs, escort in narrow waterways, and emergency rescue in waterways. Unlike the navigation of a single unmanned vessel, when large-scale USV swarms perform tasks in restricted, unstructured waters such as cross-sea bridges, scattered islands and reefs, or narrow waterways, the system must construct a continuous volumetric spatial network for the swarm, rather than a zero-measure geometric path, to accommodate the dynamic reconfiguration of the swarm formation and suppress disturbances in the physical environment.

[0004] To generate the aforementioned paths, existing technologies mainly employ three types of planning architectures: the first type is graph search algorithms, such as... The first category consists of three types of algorithms: Dijkstra's algorithm, which discretizes the continuous space into a high-resolution grid and applies spatial expansion; the second category consists of heuristic potential field algorithms, such as Artificial Potential Field (APF) and Particle Swarm Optimization (PSO), which drive node expansion through the synthesis of gravitational and repulsive fields; and the third category consists of sampling-based planning algorithms, such as Rapid Exploratory Random Tree (RRT) and its bidirectional variant (Bi-RRT), Tube-RRT, etc., which avoid explicit spatial modeling through random sampling, determine bi-tree connections based on the Euclidean distance of the end nodes, and finally use geometric curves such as B-splines to smoothly interpolate the generated discrete node sequence.

[0005] However, when applying the aforementioned existing technologies to unmanned vessel swarms with limited physical width to perform long-distance crossing missions in restricted unstructured waters, the following objective technical phenomena were observed: Firstly, when bidirectional exploration trees attempt to merge in waters riddled with tiny reefs or narrow channels, even if the leading nodes at both ends meet the Euclidean distance threshold, the cluster still frequently encounters physical interference with obstacles while traveling along the merged nominal path. In some scenarios, the collision rate of the cluster is even close to 100%, and this phenomenon cannot be eliminated by increasing the sampling density or reducing the connection threshold.

[0006] Secondly, when the planner enters U-shaped traps, long straight narrow channels, or maze-like bottleneck waters, node expansion frequently experiences long-term stagnation and trajectory oscillations, the planning time increases several times compared to open waters, the success rate of solving the problem decreases significantly, and in some extremely narrow trap scenarios, the system cannot even output a feasible solution within a limited time.

[0007] Third, even if the planner eventually outputs a geometrically collision-free center trajectory, when a passageway with a physical width is generated along this trajectory according to the nominal width of the cluster, the lateral boundary of the passageway will still intersect or hug the obstacle, exhibiting a jagged and violent width fluctuation. This makes it impossible for the cluster to pass through the restricted area in the predetermined parallel wide formation, and it must be disbanded into a single column midway, resulting in a significant decrease in the overall throughput.

[0008] In view of the above, this application is hereby submitted. Summary of the Invention

[0009] This invention discloses a bidirectional homotopy maximum flux path planning method and apparatus for unmanned vessel formations, aiming to solve the problem that when planning the passage path of an unmanned vessel swarm with a limited physical width in restricted unstructured waters, the generated volumetric spatial pipeline is difficult to simultaneously possess topological safety and maximize the available cross-sectional capacity on a global scale.

[0010] The first embodiment of the present invention provides a bidirectional homotopy maximum flux path planning method for unmanned vessel formations, including: Obtain global environmental information of the restricted water area, construct a signed distance field of the workspace, and upgrade the state space to a sequence of volumetric sphere nodes with an adaptive safety radius based on the signed distance field; With the starting point and the ending point as the roots, an active tree and a target tree are initialized on the sequence of volume sphere nodes. A directional guidance vector decoupled from the static obstacle repulsion force is synthesized for each leading edge node. Bidirectional volume expansion is performed with an adaptive step size coupled to the adaptive safety radius to generate bidirectional directional topology branches. When the leading edge nodes of the active tree and the target tree attempt to intersect, the transition sweep volume convex hull of the source node sphere set and the target node sphere set is extracted. The interior of the convex hull and the obstacle space are subjected to non-interference verification. If the verification is successful, global homotopy equivalence is established and the initial topological skeleton is extracted by backtracking. Using the spatial gradient of the signed distance field as the evolutionary driving force, damped iterative gradient ascent deduction is performed on the internal nodes of the initial topological skeleton to drive them to converge toward the local spatial central axis, thereby obtaining the central axis node sequence, and extracting the maximum physical cross-sectional capacity under the confined water area along the central axis node sequence. The physical cross-sectional capacity is mapped along the path arc length to a dimensionless spatial compression factor, which is then output to the underlying formation controller to drive the unmanned vessel cluster to synchronously perform lateral formation compression and longitudinal following distance compensation.

[0011] The second embodiment of the present invention provides a bidirectional homotopy maximum flux path planning device for unmanned vessel formations, comprising: The environment modeling module is configured to acquire global environmental information of the restricted water area, construct a signed distance field of the workspace, and upgrade the state space to a sequence of volumetric sphere nodes with an adaptive safety radius based on the signed distance field. The bidirectional volume expansion module is configured to initialize an active tree and a target tree on the volume sphere node sequence with the start and end points as roots, synthesize a directional guidance vector decoupled from the static obstacle repulsion force for each leading node, and perform bidirectional volume expansion with an adaptive step size coupled to the adaptive safety radius to generate bidirectional directional topology branches. The homotopy verification module is configured to extract the transition sweep volume convex hull of the source node sphere set and the target node sphere set when the leading edge nodes of the active tree and the target tree attempt to intersect. It performs non-interference verification on the interior of the convex hull and the obstacle space. If the verification is successful, global homotopy equivalence is established and the initial topological skeleton is extracted backtracking. The flux optimization module is configured to use the spatial gradient of the signed distance field as the evolutionary driving force to perform damped iterative gradient ascent deduction on the internal nodes of the initial topological skeleton, driving them to converge toward the local spatial central axis to obtain the central axis node sequence, and extract the maximum physical cross-sectional capacity under the confined water area along the central axis node sequence. The formation control module is configured to map the physical cross-sectional capacity along the path arc length into a dimensionless spatial compression factor, and output it to the underlying formation controller to drive the unmanned vessel cluster to synchronously perform lateral formation compression and longitudinal following distance compensation.

[0012] The third embodiment of the present invention provides a bidirectional homotopy maximum throughput path planning device for unmanned vessel formations, including a memory and a processor. The memory stores a computer program, which can be executed by the processor to implement the bidirectional homotopy maximum throughput path planning method for unmanned vessel formations as described in any of the above embodiments.

[0013] The fourth embodiment of the present invention provides a computer-readable storage medium, characterized in that it stores a computer program, which can be executed by the processor of the device where the computer-readable storage medium is located, to implement the bidirectional homotopy maximum throughput path planning method for unmanned vessel formations as described in any of the above claims.

[0014] Based on the bidirectional homotopy maximum flux path planning method and apparatus for unmanned surface vessel (USV) formations provided by this invention, a signed distance field is constructed and the state space is upgraded to a sequence of volumetric sphere nodes with an adaptive safety radius, providing a physical volume constraint basis for subsequent exploration. Bidirectional volume expansion is performed using a directional guidance vector decoupled from static obstacle repulsion and an adaptive step size coupled to the adaptive safety radius, avoiding local deadlocks while ensuring expansion safety. The transition sweep volume convex hull is extracted and its interaction with the obstacle space is verified without interference, thereby replacing zero-measure Euclidean distance determination with a volume-level metric, establishing the global homotopy equivalence of the merged pipelines. The spatial gradient of the symbolic distance field serves as the evolutionary driving force to perform iterative ascending deduction on the initial topological skeleton, driving it to converge toward the local spatial central axis and extracting the maximum physical cross-sectional capacity accordingly. This capacity is then mapped along the arc length as a spatial compression factor to drive the cluster to simultaneously perform lateral compression and longitudinal spacing compensation, ultimately generating a volumetric spatial pipeline that combines topological safety with maximum usable cross-sectional capacity. This fundamentally solves the problem that when planning the passage path of an unmanned vessel cluster with limited physical width in restricted unstructured waters, the generated volumetric spatial pipeline is difficult to simultaneously possess topological safety and maximize usable cross-sectional capacity globally. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating a bidirectional homotopy maximum throughput path planning method for unmanned vessel formations provided in the first embodiment of the present invention. Figure 2 This is a schematic diagram of continuous volume state space construction and adaptive safety radius mapping provided by the present invention; Figure 3 This is a schematic diagram of the volume-adaptive bidirectional tree exploration mechanism for static repulsion decoupling provided by the present invention; Figure 4 This is a comparison diagram of the global homotopy verification mechanism based on swept volume provided by the present invention and its trajectory search performance with that of the traditional zero-measure metric. Figure 5 This is a schematic diagram of the maximum throughput extraction mechanism of the passageway driven by the signed distance field (SDF) gradient provided by the present invention; Figure 6 This is a schematic diagram of the pipeline boundary synchronous mapping and cluster kinematic funnel deformation control mechanism provided by the present invention; Figure 7 This is a schematic diagram comparing the path generation tree of the method in this embodiment with the traditional dual-tree method, APF method, and volume sampling method under different impassable narrow gaps; Figure 8This is a bar chart comparing the statistical distribution of the search efficiency, path length, minimum channel width, and channel feasibility ratio of the method in this embodiment of the invention with traditional dual-tree method, APF method, and volume sampling method under different impassable narrow gaps. Figure 9 This is a schematic diagram comparing the spatial pipeline generation quality and central axis alignment mechanism of the method of this invention embodiment and the traditional volume sampling method under different obstacle densities; Figure 10 This is a comparison curve of the physical cross-sectional capacity and curvature smoothness of the spatial pipeline under different obstacle densities using the method of this invention and the traditional volume sampling method. Figure 11 This is a box plot comparing the search efficiency, path length, throughput capacity, and minimum channel width of the method in this embodiment of the invention with traditional planning methods under different obstacle densities. Figure 12 This is a measured trajectory verification diagram provided by the present invention for driving a large-scale (N=10) unmanned vessel swarm to perform continuous funnel deformation and dynamic reconstruction in real unstructured waters; Figure 13 This is a measured trajectory verification diagram provided by the present invention for driving a large-scale (N=15) unmanned vessel swarm to perform continuous funnel deformation and dynamic reconstruction in real unstructured waters; Figure 14 This is a schematic diagram of a module of a bidirectional homotopy maximum throughput path planning device for an unmanned vessel formation provided in the second embodiment of the present invention. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] To better understand the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0018] This invention discloses a bidirectional homotopy maximum flux path planning method and apparatus for unmanned vessel formations, aiming to solve the problem that when planning the passage path of an unmanned vessel swarm with a limited physical width in restricted unstructured waters, the generated volumetric spatial pipeline is difficult to simultaneously possess topological safety and maximize the available cross-sectional capacity on a global scale.

[0019] The first embodiment of the present invention provides a bidirectional homotopy maximum flux path planning method for unmanned vessel formations, which is executed by a planning device (or system), specifically by one or more processors within the planning device, to at least implement the following steps: S101, Obtain global environmental information of the restricted water area, construct a signed distance field of the workspace, and upgrade the state space to a sequence of volumetric sphere nodes with an adaptive safety radius based on the signed distance field; In this embodiment, the system first acquires global environmental information of the confined water area. This global environmental information includes, but is not limited to, static obstacle contour data obtained from satellite remote sensing, electronic charts, lidar, or multi-source sensor fusion, and establishes the free space set of the workspace accordingly. With static obstacle space set The static obstacle space set This is the union of the spaces occupied by all static obstacles such as islands, reefs, bridge piers, submerged reefs, and coastlines within the restricted waters. Based on this, the system maps the entire workspace to a definition in free space. The continuous banded signed distance field S(·) on the free space is given by any coordinate point S(·). The scalar value of the signed distance field S(·) at that point Equal to the point to the set of static obstacles in space The minimum Euclidean distance to the boundary, i.e. ,in This represents any point on the boundary of a static obstacle; the signed distance field S(·) in Spatial gradient vector of a point S(q) through the Taking the spatial partial derivative, we get its direction. The direction of fastest increase, i.e., the direction pointing away from the nearest obstacle boundary, serves as the evolutionary driving force for subsequent gradient ascent inference. In engineering implementation, the signed distance field can be pre-calculated offline using a grid-based Fast Marching Method or Euclidean Distance Transform and stored in the planner's memory in the form of a lookup table to ensure accuracy during the online planning phase. and High-frequency access efficiency.

[0020] Please combine Figure 2 To transform the aforementioned zero-measure coordinate points into volumetric spatial elements with physical passage capability, the system upgrades the zero-measure path nodes in traditional path planning to volumetric sphere node tuples. ,in Let the coordinates of the sphere's center be the coordinates of this node. Let the adaptive safety radius of the node be [value], and let the adaptive safety radius be [value]. It is strictly equal to the scalar value of the signed distance field at the center of the sphere, i.e. The physical meaning of this constraint is: For the center of the ball, A solid sphere defined by its radius is always completely contained within free space. The internal structure avoids intersections with any static obstacles, fundamentally eliminating the possibility of tiny gaps that the cluster cannot traverse being included in the candidate nodes. In a preferred embodiment, exemplified by the waters of a cross-sea bridge, for each candidate sphere center... Online query for pre-calculated The corresponding entry will be obtained after the table entry. and tuple The node cache is written to the bidirectional volume exploration tree for subsequent steps, thereby providing a safe volume envelope with well-defined boundaries for dynamic array reconfiguration of the cluster in restricted unstructured waters.

[0021] S102, with the starting point and the ending point as the roots, initialize the active tree and the target tree on the volume sphere node sequence, synthesize the directional guidance vector decoupled from the static obstacle repulsion force for each leading edge node, and perform bidirectional volume expansion with an adaptive step size coupled to the adaptive safety radius to generate bidirectional directional topology branches; After completing the construction of the signed distance field and the dimensionality increase of the volume sphere nodes, the system enters the bidirectional volume adaptive tree exploration phase. The system initializes the active tree with the start and end points of the confined water area as roots. With target tree Each node in the tree uses the volume sphere node tuple. The tree is stored in a specific format, and in each round of expansion, one tree is alternately designated as the current active tree and the other as the opposing target tree to achieve bidirectional directional convergence.

[0022] Please combine Figure 3 In each round of expansion, the system retrieves the leading edge node from the current active tree that is closest to the current randomly sampled target point. and in free space The target point is obtained by random sampling according to a preset probability distribution. Simultaneously retrieve distances in the target tree Recent Frontier Nodes As an anchor point for cross-tree attraction, the system then synthesizes isotropic stochastic exploration forces according to the following formula. Dynamic cross-tree cross attraction pointing to the front edge node of the opposing target tree :

[0023]

[0024] Among them, the weighting coefficient and satisfy In a preferred embodiment of the present invention, it is possible to take , This approach aims to enhance directional convergence between the two trees while retaining necessary random exploration capabilities. Throughout the synthesis of the directional guidance vector, the system enforces the isolation of static obstacles from the leading nodes at the underlying mathematical model level. The generated repulsive force, and the forced isolation of this repulsive force, is a key technical feature that distinguishes this invention from traditional Artificial Potential Field (APF) and heuristic potential field algorithms such as Bi-APF-RRT*. Traditional algorithms synthesize static repulsive force and target attraction, inevitably leading to gradient cancellation and local minimum deadlock at restricted bottlenecks. In this embodiment, however, by completely delegating the physical obstacle avoidance responsibility to the sweep volume homotopy verification mechanism and the subsequent volume coupling step size constraint mechanism, the directional guiding vector synthesized in this step is:

[0025] It only performs the function of "topological attraction" and not the function of "obstacle avoidance and repulsion", thus obtaining a pure topological convergence direction; the composite vector is then arranged according to... After normalization, the volume expansion direction of the current node expansion is obtained. The underlying mechanical mechanism of this normalization operation lies in: restricting the extracted direction vector. Normalized to a unit modulus of 1, thus enabling subsequent volume adaptive step size. The scalar value can uniquely and deterministically control the physical extension span of the unmanned vessel, preventing the trajectory from undergoing kinematic divergence and jumps due to abnormal vector magnitude.

[0026] After determining the expansion direction, to prevent illegal node generation caused by the fixed step size exceeding the obstacle boundary, the system adjusts the physical extension step size as described above. The local maximum safety radius provided by the signed distance field =S( Strict coupling, with upper and lower bounds applied:

[0027] Where the scaling factor In a preferred embodiment of the present invention, Physical step size lower bound With the upper realm This is not an arbitrary, conventional engineering setting, but rather based on the physical length of a single unmanned vessel. Established nonholonomic kinematic boundaries. For example, take... The upper bound restricts the potential for missed topological transitions caused by infinitely amplified step sizes in open water.

[0028] Crucially, the lower bound threshold is The underlying mechanics lies in the fact that as the exploration tree approaches the obstacle boundary, the local safe radius shrinks drastically. If the step size is allowed to be smaller than the length of a single unmanned vessel, an extremely short polyline will be generated that is kinematically infeasible under underactuated tracking control, leading to the planner getting stuck in an "asymptotic sampling stagnation" deadlock at the obstacle edge. This physical lower bound, as a fundamental mathematical condition, eliminates the local deadlock phenomenon at its root. The system then proceeds accordingly. Generate new volumetric sphere nodes and assign them a radius according to the aforementioned adaptive safety radius mechanism. , complete tuple Write the corresponding bidirectional volume exploration tree. This mechanism enables the bidirectional exploration tree to automatically shrink proportionally when approaching narrow passes and to maintain efficient large-step expansion in open water. Together with the topological attraction properties of the directional guiding vector, it forms a stable bidirectional directional convergence process, providing safe candidate nodes for subsequent homotopy equivalence verification.

[0029] S103, when the leading edge nodes of the active tree and the target tree attempt to intersect, extract the transition sweep volume convex hull of the source node sphere set and the target node sphere set, perform non-interference verification on the interior of the convex hull and the obstacle space, and if the verification is successful, establish global homotopy equivalence and backtrack to extract the initial topological skeleton. Please combine Figure 4 During the continuous expansion of the bidirectional volume exploration tree, the system immediately triggers a convergence judgment after each round of new node generation: using the newly generated volume sphere node in this round as the intersection. As the source node, it retrieves the distance in the opposing target tree. The most recent leading edge node is selected as the target node to be merged, and it is expanded into a target volume spherical node according to the aforementioned adaptive safety radius mechanism. ,in Therefore, the system performs strict two-level security verification on the transition area between the source node and the target node before merging.

[0030] The first level is spatial continuity verification, which requires that the volume spheres of the source node and the target node at least overlap geometrically, i.e., satisfy... This constraint ensures that there are no physically insurmountable geometric gaps between the two nodes, constituting a necessary condition for volume merging. The second level is homotopy equivalence verification, a key technical feature that distinguishes this embodiment from traditional Bi-RRT* and other zero-measure Euclidean distance determination methods. The system not only examines the scalar distance between the two endpoints, but also considers the scalar distance between them... For the center of the ball, A solid sphere with radius With For the center of the ball, A solid sphere with radius Take the union B_new ∪ B_target as input, and extract the transition sweep volume convex hull corresponding to this union. and the space combination between the interior of the convex hull and the static obstacle. Interference-free verification is performed to determine if there are overlapping regions:

[0031] In engineering implementation, the transition sweep volume convex hull can be extracted online in a two-dimensional water surface planning scenario by performing Graham scans or QuickHull algorithms on the discrete point sets of the two sphere boundaries. In three-dimensional scenarios or extended scenarios involving complex ship hull modeling, equivalent interference determination can also be performed using GJK collision detection algorithms or continuous collision detection (CCD) algorithms. The physical meaning of this two-level verification is that the first level ensures the endpoint connectivity of the two volume spheres, and the second level further extends the connectivity constraint from the zero-measure "straight line between two points" to the finite-measure "transition sweep volume between two spheres". Since the bounded convex hull has been verified to exclude all static obstacle interference, any continuous path deformation inside the convex hull will not cross the topological singularity formed by obstacles. Therefore, the merging pipeline between the source node and the target node has the homotopy equivalence class property in mathematics, fundamentally eliminating the topological collapse phenomenon caused by two search trees forcibly bridging around the same singularity in waters with dense small reefs.

[0032] The system determines that the bidirectional intersection passes verification only when both of the above-mentioned safety constraints are satisfied, establishing the global homotopy equivalence between the active tree and the target tree, and then... and To connect nodes, the system backtracks their respective bidirectional volume exploration trees, extracting an initial topological skeleton composed of a sequence of connected volume sphere nodes. This skeleton serves as the input for subsequent signed distance field gradient ascent derivation. If any constraint is not satisfied, the system rejects the current merge and returns to the directional guidance vector synthesis and adaptive step-size expansion process to continue generating new candidate nodes until the next intersection attempt passes verification. For typical confined waters with numerous small reefs, traditional zero-measure Euclidean distance determination may blindly bridge two search trees that bypass the same reef by only considering the endpoint distance, thus generating illegal connections that traverse obstacles. However, the swept volume convex hull verification in this step verifies the bounded outer envelope of the union of two spheres, enabling immediate identification and rejection of such topological inequivalence cases. This effectively ensures the physical security and global homotopy equivalence of the extracted initial topological skeleton.

[0033] To verify the actual technical effectiveness of the above-mentioned volume-adaptive bidirectional topology exploration mechanism based on signed distance field (S101), decoupling repulsion force (S102), and transition sweep volume verification mechanism (S103), please combine... Figure 7 and Figure 8 The data compares exploration efficiency and trajectory generation. Regarding topological connectivity and search efficiency, such as... Figure 7 and Figure 8 As shown, traditional methods, relying solely on zero-measure Euclidean distance and static repulsion, frequently fall into local minima or exhibit trajectory divergence. However, by employing the forced isolation of static repulsion and adaptive step-size expansion configured in this embodiment, not only is directional convergence achieved in various constrained scenarios, but the search time is also significantly reduced (e.g., in the C-shaped obstacle scenario, the average search time decreased from 28.9ms to 8.3ms), effectively suppressing asymptotic sampling stagnation from the underlying mathematical model. Furthermore, regarding the physical safety of the extracted topological skeleton, traditional methods are prone to blindly bridging physically impassable gaps in complex waters, leading to collisions. In contrast, the transition sweep volume convex hull verification mechanism configured in this embodiment achieves a 100% physical safety passability rate in all test scenarios (e.g., ...). Figure 8 As shown in the statistics of channel feasibility ratios, reliable global homotopy equivalence was established.

[0034] S104, convert the initial topological skeleton into one with nonholonomic kinematics. A continuous nominal trajectory is obtained, and the spatial gradient of the signed distance field is used as the evolutionary driving force to perform damped iterative gradient ascent deduction on the internal nodes of the nominal trajectory, driving it to converge toward the local spatial central axis to obtain the central axis node sequence, and extracting the maximum physical cross-sectional capacity under the confined water area along the central axis node sequence. After the bidirectional homotopy equivalence verification is passed and the initial topological skeleton is extracted, the system enters the flux maximization stage driven by the signed distance field gradient. Since the initial topological skeleton is composed of discrete piecewise linear segments, its derivatives are discontinuous and cannot satisfy the nonholonomic kinematic constraints of an underactuated unmanned surface vessel (USV). Therefore, the system is configured to first parameterize the initial topological skeleton using uniform B-splines to generate a system with nonholonomic kinematics. The nominal trajectory is continuous. However, conventional mathematical curve interpolation, in pursuing the minimization of path length, inevitably produces a "corner-cutting effect," which causes the curve to grow towards the interior corner of the obstacle, resulting in a sharp compression of the usable safe cross-sectional area. To neutralize this corner-cutting effect from the underlying mechanical mechanism, this step abandons the simple geometric interpolation smoothing approach and instead uses the spatial gradient of the signed distance field as the driving force for the skeleton evolution, performing a damped iterative ascending derivation on the initial topological skeleton.

[0035] Specifically, please combine Figure 5The system will distribute the components at preset arc length intervals. The continuous nominal trajectory is discretized into a nominal node sequence. Where N is the total number of discrete nodes, and the node spacing in a preferred embodiment of the present invention can be taken as 0.5 to 1.0 times the maximum longitudinal geometric length of a single unmanned vessel. ; starting with the first node of the sequence and the end node As a Dirichlet boundary condition, coordinate locking is performed, that is, let and In all subsequent iterations, the coordinates remain unchanged to ensure the physical constraints of the path's start and end points. Except for... and Nodes outside the gradient are defined as internal nodes and participate in gradient evolution. In the k-th iteration, the system reads each internal node. Spatial gradient vector in the signed range field And combined with the spatial displacement vector obtained from the previous iteration The spatial displacement vector of this round is calculated according to the following formula. :

[0036] Where the gradient ascent step size coefficient In a preferred embodiment of the present invention, η can be taken as 0.1, which is the spatial smoothing damping coefficient. μ can be set to 0.5; initial value of the displacement vector Let it be the zero vector, with initial position coordinates. The damping coefficient is taken from discrete nodes at the corresponding positions of the initial topological skeleton. The physical meaning is that the evolutionary inertia of the previous round is superimposed on the displacement of the current round in an exponentially decaying manner, thereby suppressing iterative oscillations and trajectory jitters that may be caused by simple gradient ascent in the local non-smooth region of SDF. The system further introduces a structural spatial decay factor. This factor is not an arbitrary constant, but is configured to respond to the number of smooth transition nodes at both ends of the start and end points. (i.e., the range of controlled nodes distributed at both ends of the nominal trajectory, used to perform smooth transition of spatial displacement force) constrained by Dirichlet piecewise boundary conditions. Its underlying logic is: when performing full-path spatial gradient extrapolation, it is essential to ensure that the coordinates of the initial topological skeleton at the start and end points are strictly locked to prevent path terminal drift. Simultaneously, the number of smooth transition nodes... The buffering mechanism prevents abrupt curvature changes in the trajectory near the start and end points, thus disrupting the kinematic smoothness of the underactuated unmanned vessel, and provides the middle nodes of the sequence with the maximum degree of freedom for central axis alignment.

[0037] Therefore, the constructed space decay factor The function definition is strictly limited to: If the current node index ,but If the current node index ,but In other cases (i.e., the node is in a completely free central space), The system updates the position coordinates of the internal nodes using the following formula:

[0038] The iteration continues until the magnitude of the current displacement vector of all internal nodes is lower than the preset convergence threshold, that is, all internal nodes converge and align with the ridge of the local SDF scalar value (i.e., the spatial central axis). The converged sequence of internal nodes, together with the first and last nodes, is denoted as the central axis node sequence. The physical essence of this gradient ascent derivation lies in the spatial gradient of the signed distance field. S(q) at any point in free space points away from the nearest obstacle boundary. Therefore, the iterative process driven by this gradient will inevitably drive each internal node to continuously move away from the restricted boundary and eventually stabilize at the maximum gap in the local water area, thus counteracting and neutralizing the inherent "corner contraction force" of the smooth geometric curve.

[0039] After obtaining the central axis node sequence, the system extracts the physical cross-sectional capacity at each central axis node location along the sequence using the following formula:

[0040] in The maximum safe radius at the central axis node position is given by the signed distance location. The physical meaning of factor 2 is the safe width obtained by extending symmetrically to both sides with this node as the center. This is the maximum nominal parallel width of the unmanned surface vessel swarm in unrestricted open water, which, in a preferred embodiment of the invention, is set according to the maximum lateral span of the swarm's nominal formation. The physical meaning of this min operator is: in confined bottleneck waters... At that time, the physical cross-sectional capacity is limited by the actual width of the environmental bottleneck; in open water... At this point, the physical cross-sectional capacity is truncated to the nominal parallel width limit of the cluster itself. Even if the water area at that location is wide enough, the cluster does not need to expand beyond the nominal array width. The system further extracts the data along the discrete central axis node sequence. By performing continuous interpolation representation based on the node arc length position, a continuous capacity function distributed along the path arc length s is obtained. This serves as the input for subsequent execution of spatial compression factor mapping and kinematic funnel deformation control.

[0041] To verify the actual physical effects of the signed distance field spatial gradient evolution mechanism (S104) configured in this step, please refer to [link / reference]. Figure 9 , Figure 10 as well as Figure 11 The data on the generation quality and statistical distribution of spatial pipes. Regarding the relationship between pipe generation quality and underlying mechanical smoothness, such as... Figure 9 and Figure 10 As shown, traditional unidirectional volume sampling methods rely on discrete string splicing, which inevitably results in a chamfering effect where the generated spatial pipe boundary grows towards the inner corner of the obstacle, mechanically inducing local bottlenecks and accompanied by severe curvature oscillations. However, after iterative gradient ascent derivation configured in this step, the nominal trajectory is actively and smoothly pushed towards the spatial central axis of the local maximum physical cross-section. Quantization curves confirm that the volume spatial pipe generated in this step has significantly improved curvature smoothness and smaller variance, thus effectively avoiding control chattering of the underactuated unmanned surface vessel during subsequent trajectory tracking from a geometric and mechanical perspective. Furthermore, regarding usable flux extraction and robustness under extreme constraints, such as… Figure 11 Statistical data confirms that in scenarios with obstacle densities as high as 60%, the minimum physical width of the channel extracted in this step is 31.2% higher than that of traditional methods. This quantitative data demonstrates that the spatial optimization mechanism in this step maximizes the extraction of the maximum usable passage cross-sectional capacity of the confined water area from the geometric level, thus providing crucial physical spatial support for the funnel deformation of the fluid structure in subsequent steps.

[0042] S105, the physical cross-sectional capacity is mapped along the path arc length to a dimensionless spatial compression factor, and output to the underlying formation controller to drive the unmanned vessel cluster to synchronously perform lateral formation compression and longitudinal following distance compensation.

[0043] Please combine Figure 6 After completing the central axis node sequence Convergence Alignment and Continuous Capacity Function After extraction, the system enters the kinematic funnel deformation control stage, establishing a deterministic bijective closed loop from geometric capacity to underlying multi-agent kinematic commands. The core idea of ​​this stage is: Although the maximum available cross-sectional capacity distributed along the path arc length has been characterized, its dimension is physical length unit and its value varies drastically with the geometry of the water area, making it difficult to directly use as an adjustment parameter for each unmanned vessel to track the target. Therefore, the system normalizes this dimensional capacity function into a dimensionless scalar field that strictly falls within the closed interval [0,1], as a unified scalar control variable to drive the deformation of the cluster formation.

[0044] Specifically, the system will obtain the continuous capacity function Mapped to a dimensionless spatial compressibility factor using the following formula :

[0045] in This is the maximum nominal parallel width of the unmanned vessel swarm in unrestricted open water. The minimum physical width required for unmanned surface vessels to pass in a single file is described. The maximum lateral geometry of a single unmanned surface vessel is determined by the sum of the maximum lateral geometry of the vessel and the preset safety redundancy distance between adjacent vessels in a single column, and satisfies 0 < < In a preferred embodiment of the present invention, it is possible to take The maximum lateral geometry of a single unmanned surface vessel; Preset non-zero positive constants are used in and To prevent numerical singularities caused by the denominator of the above expression approaching zero when the values ​​are close, the aforementioned... The physical meaning of the operator lies in strictly truncating the normalization result within the closed interval [0.0, 1.0]: when the arc length position is in an unconstrained open water area. Approaching and The corresponding cluster does not require any array compression; when the arc length position is in a physically narrow bottleneck area. Approaching W_min The corresponding cluster needs to perform maximum array compression; in the intermediate transition region The values ​​are then taken continuously in proportion to quantify the intensity of environmental bottleneck constraints in a dimensionless manner.

[0046] After obtaining the spatial compression factor distributed along the arc length, the system broadcasts it directly to the underlying formation controller as a unified scalar control variable, driving each unmanned surface vessel to synchronously update two types of kinematic tracking targets online. One is the lateral formation compression command, which updates the lateral tracking target offset of the i-th unmanned surface vessel according to the following formula. :

[0047] in The first is the lateral offset reference value of the i-th unmanned surface vessel relative to the geometric centerline of the formation in the nominal formation in open water. This reference value is determined by the preset wide formation geometry of the cluster (such as a side-by-side formation or a wedge formation). The second is the longitudinal following distance compensation command, which updates the longitudinal following distance of the i-th unmanned surface vessel relative to its preceding followed object using the following formula. :

[0048] in The nominal longitudinal spacing between adjacent unmanned vessels in open water. This refers to the longitudinal safety distance required to meet the safe braking distance requirements of the fore and aft vessels in a single-file convoy mode, and typically... This is to compensate for the increased vertical space requirements when the cluster shrinks from a wide formation to a narrow formation. The cooperative physical meaning of the two types of instructions is that when Each unmanned boat and The cluster maintains a wide-formation parallel formation in open waters; when Each unmanned boat 0 and The cluster shrinks into a single column; in the intermediate transition area, it is based on... The real-time values ​​are executed synchronously and proportionally to achieve horizontal array contraction and vertical spacing expansion, forming a continuous and smooth fluid structure funnel deformation.

[0049] like Figure 12 and Figure 13 In the actual satellite-deployed test in the waters shown, when a formation of 15 unmanned surface vessels (USVs) approached a 23.5-meter-wide bridge opening, the extracted physical cross-sectional capacity decreased to 20.21 meters. Based on this, the system accurately output a spatial compression factor of α(s)≈0.43. Directly driven by this scalar, the swarm spontaneously performed a proportional lateral contraction of approximately 43% and corresponding longitudinal spacing compensation the instant it approached the bridge opening. The entire USV formation smoothly passed through the bridge opening with a continuous, smooth funnel-shaped deformation attitude. After leaving the restricted area, as α(s) returned to 0 along the arc length, the USVs autonomously restored their parallel wide formation in open water. This deterministic mapping mechanism allows the swarm to complete a closed loop from the geometric capacity of the planning layer to the kinematic commands of the execution layer without relying on any discrete state machine switching or passive obstacle avoidance rules. It does so solely with a unified dimensionless scalar field, maximizing the number of available parallel units and the overall throughput of the swarm in restricted waters.

[0050] Please see Figure 14 The second embodiment of the present invention provides a bidirectional homotopy maximum flux path planning device for unmanned vessel formations, comprising: The environmental modeling module 201 is configured to acquire global environmental information of the restricted water area, construct a signed distance field of the workspace, and upgrade the state space to a sequence of volumetric sphere nodes with an adaptive safety radius based on the signed distance field. The bidirectional volume expansion module 202 is configured to initialize an active tree and a target tree on the volume sphere node sequence with the start point and the end point as the roots, synthesize a directional guidance vector decoupled from the static obstacle repulsion force for each leading node, and perform bidirectional volume expansion with an adaptive step size coupled to the adaptive safety radius to generate bidirectional directional topology branches. The homotopy verification module 203 is configured to extract the transition sweep volume convex hull of the source node sphere set and the target node sphere set when the leading edge nodes of the active tree and the target tree attempt to intersect, perform non-interference verification on the interior of the convex hull and the obstacle space, and establish global homotopy equivalence and backtrack to extract the initial topological skeleton when the verification is successful. The flux optimization module 204 is configured to use the spatial gradient of the signed distance field as the evolutionary driving force to perform damped iterative gradient ascent deduction on the internal nodes of the initial topological skeleton, driving them to converge toward the local spatial central axis to obtain the central axis node sequence, and extract the maximum physical cross-sectional capacity under the confined water area along the central axis node sequence. The formation control module 205 is configured to map the physical cross-sectional capacity along the path arc length into a dimensionless spatial compression factor and output it to the underlying formation controller to drive the unmanned vessel cluster to synchronously perform lateral formation compression and longitudinal following distance compensation.

[0051] The third embodiment of the present invention provides a bidirectional homotopy maximum throughput path planning device for unmanned vessel formations, including a memory and a processor. The memory stores a computer program, which can be executed by the processor to implement the bidirectional homotopy maximum throughput path planning method for unmanned vessel formations as described in any of the above embodiments.

[0052] The fourth embodiment of the present invention provides a computer-readable storage medium, characterized in that it stores a computer program, which can be executed by the processor of the device where the computer-readable storage medium is located, to implement the bidirectional homotopy maximum throughput path planning method for unmanned vessel formations as described in any of the above claims.

[0053] Based on the bidirectional homotopy maximum flux path planning method and apparatus for unmanned surface vessel (USV) formations provided by this invention, a signed distance field is constructed and the state space is upgraded to a sequence of volumetric sphere nodes with an adaptive safety radius, providing a physical volume constraint basis for subsequent exploration. Bidirectional volume expansion is performed using a directional guidance vector decoupled from static obstacle repulsion and an adaptive step size coupled to the adaptive safety radius, avoiding local deadlocks while ensuring expansion safety. The transition sweep volume convex hull is extracted and its interaction with the obstacle space is verified without interference, thereby replacing zero-measure Euclidean distance determination with a volume-level metric, establishing the global homotopy equivalence of the merged pipelines. The spatial gradient of the symbolic distance field serves as the evolutionary driving force to perform iterative ascending deduction on the initial topological skeleton, driving it to converge toward the local spatial central axis and extracting the maximum physical cross-sectional capacity accordingly. This capacity is then mapped along the arc length as a spatial compression factor to drive the cluster to simultaneously perform lateral compression and longitudinal spacing compensation, ultimately generating a volumetric spatial pipeline that combines topological safety with maximum usable cross-sectional capacity. This fundamentally solves the problem that when planning the passage path of an unmanned vessel cluster with limited physical width in restricted unstructured waters, the generated volumetric spatial pipeline is difficult to simultaneously possess topological safety and maximize usable cross-sectional capacity globally.

[0054] Exemplary examples show that the computer program described in the third and fourth embodiments of the present invention can be divided into one or more modules, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules can be a series of computer program instruction segments capable of performing specific functions, which describe the execution process of the computer program in the device for implementing a bidirectional homotopy maximum flux path planning system for unmanned vessel formations. For example, the apparatus described in the second embodiment of the present invention.

[0055] The processor referred to can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor. This processor is the control center of the bidirectional homotopy maximum throughput path planning method for unmanned surface vessel (USV) formations, connecting various parts of the method through various interfaces and lines.

[0056] The memory can be used to store the computer program and / or modules. The processor, by running or executing the computer program and / or modules stored in the memory, and by calling the data stored in the memory, implements various functions of a bidirectional homotopy maximum flux path planning method for unmanned vessel formations. The memory may mainly include a program storage area and a data storage area. The program storage area may store the operating system, at least one application program required for a function (such as sound playback function, text conversion function, etc.), etc.; the data storage area may store data created based on the use of the mobile phone (such as audio data, text message data, etc.). In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0057] If the implemented module is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0058] It should be noted that the device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, in the accompanying drawings of the device embodiments provided by this invention, the connection relationships between modules indicate that they have communication connections, which can be specifically implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.

[0059] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A bidirectional homotopy maximum flux path planning method for unmanned surface vessel (USV) formations, characterized in that, include: Obtain global environmental information of the restricted water area, construct a signed distance field of the workspace, and upgrade the state space to a sequence of volumetric sphere nodes with an adaptive safety radius based on the signed distance field; With the starting point and the ending point as the roots, an active tree and a target tree are initialized on the sequence of volume sphere nodes. A directional guidance vector decoupled from the static obstacle repulsion force is synthesized for each leading edge node. Bidirectional volume expansion is performed with an adaptive step size coupled to the adaptive safety radius to generate bidirectional directional topology branches. When the leading edge nodes of the active tree and the target tree attempt to intersect, the transition sweep volume convex hull of the source node sphere set and the target node sphere set is extracted. The interior of the convex hull and the obstacle space are subjected to non-interference verification. If the verification is successful, global homotopy equivalence is established and the initial topological skeleton is extracted by backtracking. The initial topological skeleton is converted into a nominal trajectory with nonholonomic kinematic continuity. The spatial gradient of the signed distance field is used as the evolutionary driving force to perform damped iterative gradient ascent deduction on the internal nodes of the nominal trajectory, driving it to converge toward the local spatial central axis to obtain the central axis node sequence. The maximum physical cross-sectional capacity under confined water area is extracted along the central axis node sequence. The physical cross-sectional capacity is mapped along the path arc length to a dimensionless spatial compression factor, which is then output to the underlying formation controller to drive the unmanned vessel cluster to synchronously perform lateral formation compression and longitudinal following distance compensation.

2. The bidirectional homotopy maximum flux path planning method for unmanned vessel formations according to claim 1, characterized in that, The construction of the signed distance field of the workspace, and the subsequent dimensionality upgrade of the state space into a sequence of volumetric sphere nodes with an adaptive safety radius based on the signed distance field, specifically involves: For any coordinate point in free space The minimum Euclidean distance to the nearest static obstacle boundary is defined as the scalar distance value of that point. With spatial gradient vector The scalar distance value of this point satisfies: in, Represents the set of static obstacles in space. Let be any point on the boundary of the obstacle; Upgrade traditional zero-measure path nodes to volume spheres. and let the adaptive safety radius The signed distance field scalar value is strictly equal to the node location, ensuring that all said volume spherical nodes are strictly inside free space and do not enter impassable tiny gaps.

3. The bidirectional homotopy maximum flux path planning method for unmanned vessel formations according to claim 1, characterized in that, The synthesis of directional guidance vectors that decouple the static obstacle repulsion force for each leading node is specifically as follows: For the nearest front node of the active tree Calculate the isotropic stochastic exploration force respectively. With the nearest front node pointing to the target tree Dynamic cross-tree attraction : in, Both represent vectors. Norm operations for Randomly sample target points within the area. and These are the random bias weights and the cross-tree gravity bias weights, respectively, and satisfy the following conditions: ; During the synthesis of the directional guidance vector, the repulsive force exerted by static obstacles on the leading edge node is forcibly isolated; the final synthesized directional guidance vector is: Its normalization direction is the volume expansion direction of the leading edge node, and its expression is: .

4. The bidirectional homotopy maximum flux path planning method for unmanned vessel formations according to claim 3, characterized in that, The bidirectional volume expansion performed with an adaptive step size coupled to the adaptive safety radius specifically refers to: The leading edge node Physical extension step size The local maximum safety radius provided by the signed distance field Couple and apply upper and lower bound cutoffs: in, This is the scaling factor. and Based on the physical size of the unmanned vessel The set lower and upper limits of the physical step size, where This allows the minimum expansion step size to exceed the nonholonomic minimum turning capability of the underactuated unmanned vessel, thereby eliminating the asymptotic sampling stagnation deadlock phenomenon when approaching the obstacle boundary from the underlying mathematical conditions. Based on the normalization direction u and the adaptive step size Generate new volume sphere nodes using the following formula: The new volume sphere node is then incorporated into the corresponding bidirectional volume exploration tree.

5. The bidirectional homotopy maximum flux path planning method for unmanned vessel formations according to claim 4, characterized in that, The process of extracting the transition sweep volume convex hull of the source node sphere set and the target node sphere set, and performing interference-free verification on the interior of the convex hull and the obstacle space, specifically involves: New node The adaptive safety radius mechanism is extended to volumetric spherical nodes. ,in, Let be the radius of the volume sphere node. Define the coordinates of the center of the volume sphere node; define the front edge nodes of the target tree to be merged as volume sphere nodes. ,in Let the coordinates of the center of the sphere be the target node. The adaptive safety radius for the target node; Source nodes to be merged With the target node Two levels of safety constraints are executed sequentially: Level 1: Verification of geometric overlap of endpoint volume spheres, requiring compliance with... Second level: using the source node sphere set With the target node sphere set The union of the inputs is used to extract the transition sweep volume convex hull. And verify: in, A collection of static obstacles in space. If the set is empty, global homotopy equivalence between the active tree and the target tree is established only when both levels of constraints are satisfied, and backtracking connections are made to form the initial topological skeleton; if any constraint is not satisfied, the current merge is rejected and the synthesis of the directional guiding vector is returned to continue expansion.

6. The bidirectional homotopy maximum flux path planning method for unmanned vessel formations according to claim 5, characterized in that, The process involves using the spatial gradient of the signed distance field as the evolutionary driving force to perform damped iterative gradient ascent deduction on the internal nodes of the initial topological skeleton, driving them to converge toward the local spatial central axis, thereby obtaining the central axis node sequence, specifically: The initial topological skeleton is parameterized using a uniform B-spline to extract a discrete nominal node sequence with nonholonomic kinematic continuity. and with and Locking in the Dirichlet boundary conditions; In the k-th iteration, read each internal node. Spatial gradient vector in the signed range field Calculate the spatial displacement vector using the following formula. : in, This is the gradient ascent step size. The spatial smoothing damping coefficient, Let be the spatial displacement vector of the i-th internal node in the k-th iteration; Introducing a space attenuation factor fixed at both ends Perform coordinate updates on the internal nodes: Wherein, the spatial attenuation factor The number of smooth transition nodes at both ends of the start and end points. Constrained Dirichlet piecewise boundary conditions are used to maintain the local trajectory while preventing terminal coordinate drift. Continuity, its function definition is strictly limited to: if ,but ;like ,but In other cases, ;in The total number of nodes in the discrete nominal node sequence; Iterate until the internal nodes converge to the ridge with the maximum local SDF scalar value, to obtain the central axis node sequence. , Let be the position of the i-th internal node in the k-th iteration.

7. The bidirectional homotopy maximum flux path planning method for unmanned vessel formations according to claim 6, characterized in that, Extracting the maximum physical cross-sectional capacity of the confined water area along the central axis node sequence, specifically: Along the central axis node sequence Extract the physical cross-sectional capacity at this location using the following formula. : in, The signed distance field scalar value for the central axis node. The maximum nominal parallel width of the unmanned vessel swarm in unrestricted open waters; The capacity of the physical cross-section is represented as a continuous function along the path arc length s to obtain the capacity function. , as input for spatial compression factor mapping.

8. The bidirectional homotopy maximum flux path planning method for unmanned vessel formations according to claim 7, characterized in that, The physical cross-sectional capacity is mapped along the path arc length to a dimensionless spatial compressibility factor, specifically as follows: The capacity function Mapped to a dimensionless spatial compressibility factor using the following formula : in, The minimum physical width required for unmanned surface vessel swarms to pass in a single column. This represents the maximum nominal parallel width of the cluster in unconstrained open water. To prevent the denominator from being a singular non-zero positive number; The space compressibility factor The configuration is as follows: when the current arc length position is in unrestricted open water, When in a region with an extremely narrow physical bottleneck, This allows for the explicit truncation of the physical constraints of environmental bottlenecks into an equivalent quantification. Dimensionless scalar factor within the interval.

9. The bidirectional homotopy maximum flux path planning method for unmanned vessel formations according to claim 7, characterized in that, The output to the underlying formation controller drives the unmanned surface vessel swarm to synchronously perform lateral formation compression and longitudinal following distance compensation, specifically: The space compressibility factor Directly drives each unmanned surface vessel to synchronously update two types of kinematic tracking targets, including the lateral formation compression command: Longitudinal following spacing compensation command: in, Let the nominal lateral formation offset be the i-th unmanned vessel. and These refer to the nominal longitudinal spacing in open water and the safe spacing for a single-column formation, respectively. This enables the unmanned vessel cluster to... Maintaining a parallel, wide formation in open waters, It contracts into a single column, and at the intermediate value, it performs lateral contraction and longitudinal spacing expansion in a proportional manner, forming a continuous fluid structure funnel deformation.

10. A bidirectional homotopy maximum flux path planning device for unmanned vessel formations, characterized in that, include: The environment modeling module is configured to acquire global environmental information of the restricted water area, construct a signed distance field of the workspace, and upgrade the state space to a sequence of volumetric sphere nodes with an adaptive safety radius based on the signed distance field. The bidirectional volume expansion module is configured to initialize an active tree and a target tree on the volume sphere node sequence with the start and end points as roots, synthesize a directional guidance vector decoupled from the static obstacle repulsion force for each leading node, and perform bidirectional volume expansion with an adaptive step size coupled to the adaptive safety radius to generate bidirectional directional topology branches. The homotopy verification module is configured to extract the transition sweep volume convex hull of the source node sphere set and the target node sphere set when the leading edge nodes of the active tree and the target tree attempt to intersect. It performs non-interference verification on the interior of the convex hull and the obstacle space. If the verification is successful, global homotopy equivalence is established and the initial topological skeleton is extracted backtracking. The flux optimization module is configured to use the spatial gradient of the signed distance field as the evolutionary driving force to perform damped iterative gradient ascent deduction on the internal nodes of the initial topological skeleton, driving them to converge toward the local spatial central axis to obtain the central axis node sequence, and extract the maximum physical cross-sectional capacity under the confined water area along the central axis node sequence. The formation control module is configured to map the physical cross-sectional capacity along the path arc length into a dimensionless spatial compression factor, and output it to the underlying formation controller to drive the unmanned vessel cluster to synchronously perform lateral formation compression and longitudinal following distance compensation.

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