Computational modeling method and system for action plans

Abstract

The present invention discloses a computational modeling method and system for action plans, which specifically relates to the field of simulated confrontation and is used to solve the problem of multi-platform collaborative path planning in a dynamic environment. It is based on a multi-constrained hierarchical hypergraph, abstracts the integration of space, time and resources, and significantly improves computing efficiency by relaxing the expansion of the convex hull and compressing the search domain with gradient sampling. At the same time, it dynamically adjusts the stability factor with the help of resource phase mapping and quantum taboo walk to ensure rapid approach to the global optimal solution; symplectic time window rearrangement and conjugate gradient sliding further realize fine timing correction, while confrontation prediction simulation verifies the survival potential and coverage confidence of the path, enhancing the reliability and safety of the plan under the disturbance of frequently changing three-dimensional geographic space, dynamic restricted areas and mobile obstacles; thereby effectively responding to the strict timing and resource requirements of multi-platform collaborative tasks and providing advanced computational modeling support for multi-platform collaborative tasks.

Description

Technical Field

[0001] The present invention relates to the field of simulated confrontation, and more particularly to a method and system for computationally modeling an action plan. Background Art

[0002] In a multi-role simulated confrontation environment, active entities need to perform collaborative tasks in a frequently changing three-dimensional geographic space. In this scenario, task execution faces multiple complex challenges: no-go zones are adjusted in real time as the scenario updates, mobile obstacles constantly interfere with the trajectory of active entities, and the task rhythm requires multiple platforms to arrive at collaborative positioning points synchronously and share limited energy. As the number of participating platforms increases and the scope of the task expands, cross-coupling occurs between variables such as path nodes, timing windows, and energy margins, causing the search space to expand exponentially with the dimension. Traditional traversal or heuristic path planning methods are prone to falling into local minima due to the limited search depth, and are unable to generate a globally feasible solution within the real-time scale of the simulation, ultimately leading to a deviation in the collaborative rhythm and reduced task completion.

[0003] In order to solve the above problems, a technical solution is now provided. Summary of the Invention

[0004] In order to overcome the above-mentioned defects of the prior art, an embodiment of the present invention provides a computational modeling method and system for action plans, which takes a multi-constrained hierarchical hypergraph as the core, integrates and abstracts space, time and resources, and compresses the search domain through convex hull relaxation expansion and gradient sampling, thereby significantly improving computational efficiency. At the same time, the stability factor is dynamically adjusted with the help of resource phase mapping and quantum taboo walk to ensure rapid approximation to the global optimal solution; symplectic time window rearrangement and conjugate gradient sliding further realize fine timing correction, while adversarial prediction simulation verifies the survival potential and coverage confidence of the path, enhancing the reliability and security of the plan under the disturbance of frequently changing three-dimensional geographic space, dynamic no-go zones and mobile obstacles; thereby effectively responding to the strict timing and resource requirements of multi-platform collaborative tasks, and providing advanced computational modeling support for multi-platform collaborative tasks to solve the problems raised in the above-mentioned background technology.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] The action plan can be computationally modeled, including the following steps:

[0007] S1: Construct a multi-constraint hierarchical hypergraph in a 3D dynamic map that integrates spatial area distribution, task timing windows, and platform resource status. Then, extract the anchor node set by traversing all constraint intersection areas and establish a cross-layer mapping table.

[0008] S2: Based on the anchor node set, the convex hull relaxation boundary expansion calculation is first performed to generate a hexahedral envelope grid, and then the resource margin gradient is used to guide the non-uniform grid sampling to form a candidate grid grid;

[0009] S3: For each candidate grid, the path phase dispersion and energy dissipation gradient are calculated. The global stability factor is obtained by combining the two. The tabu table weights are dynamically adjusted according to the factor, and then a phase-coded tabu roaming iteration is performed. During the iteration, the tabu table is recorded in real time to suppress loops and converge to the elite path cluster.

[0010] S4: Input the elite path cluster into the symplectic time window rearrangement operator, and correct the time coordinates of each path node through the conjugate gradient sliding strategy, so that the cross-platform coordination margin converges to the allowed interval and then outputs the timing path;

[0011] S5: Inject the timing path into the confrontation prediction simulation unit, perform cyclic calculations in the dynamic obstacle disturbance field, and test it with the survival probability threshold. When the requirements are met, solidify the timing path as the final command sequence.

[0012] In a preferred embodiment, step S1 includes the following contents:

[0013] First, the spatial range is divided into a set of spatial regions at multiple levels, where the bottom level is a high-resolution spatial grid representing specific geographic coordinate points, and the top level is a low-resolution macro-region representing a large-scale geographic partition.

[0014] Discretize the timeline into multiple time segments and assign each task a task timing window defined by the start time and end time;

[0015] Maintain resource status vectors for the platform and divide them into multiple resource levels;

[0016] Construct a hypergraph whose node set consists of sub-regions of a set of spatial regions, time slices, and resource levels, and whose hyperedges connect node sets that are compatible with each other in space, time, and resources;

[0017] Traverse the hypergraph by breadth-first search to identify the constraint intersection region that satisfies the space, time and resource constraints at the same time, and define the nodes in it as the anchor node set;

[0018] A cross-layer mapping table is established to record the hierarchical correspondence between anchor nodes in the spatial region set, time layer and resource layer.

[0019] In a preferred embodiment, step S2 includes the following:

[0020] First, the minimum convex polyhedron of the anchor node set in three-dimensional space is calculated, and the expanded convex polyhedron is generated by expanding it a fixed distance along the normal vector of the convex hull. The expanded convex polyhedron is then approximated as an axis-aligned hexahedral envelope lattice. Then, a resource margin function is defined within the hexahedral envelope lattice and its gradient is calculated. The sampling density is determined according to the gradient, so that the sampling density in areas with drastic resource changes is higher than that in areas with gentle resource changes. Finally, a non-uniformly distributed grid point set is generated within the hexahedral envelope lattice based on the sampling density to form a candidate grid point grid.

[0021] In a preferred embodiment, step S3 includes the following contents:

[0022] The taboo duration of paths in the taboo table is dynamically adjusted according to the global stability factor, where the global stability factor is generated by the comprehensive calculation of the path phase dispersion and the energy dissipation gradient. Subsequently, a phase-coded taboo walk iteration is performed. By encoding the paths as phase vectors and randomly walking in the phase space, paths or nodes not recorded in the taboo table are preferentially selected. The taboo table is updated in real time during the iterative process to suppress loops, and finally converges to an elite path cluster with a satisfactory global stability factor value.

[0023] In a preferred embodiment, step S3 includes the following contents:

[0024] For each node on the candidate path, the time difference and spatial difference between it and the next node are calculated. Then, the average of the time differences of all node pairs and the average of the spatial differences of all node pairs are calculated. Next, for each node pair, the absolute value of the difference between its time difference and the average of all time differences, as well as the absolute value of the difference between its spatial difference and the average of all spatial differences, are calculated and multiplied to obtain the product of each node pair. Finally, the products of all node pairs are accumulated to obtain the path phase dispersion, which quantifies the fluctuation of the path in time and space.

[0025] In a preferred embodiment, step S3 includes the following contents:

[0026] The energy dissipation gradient is calculated as follows: for each node on the candidate path, its resource consumption value is determined; then, for adjacent nodes, the absolute value of the difference in resource consumption between the two is calculated, and the maximum absolute value of resource consumption among all adjacent node pairs is found; then, the absolute value of the resource consumption difference of each adjacent node pair is multiplied by the maximum absolute value of resource consumption of all adjacent node pairs to obtain the product for each adjacent node pair; finally, the products of all adjacent node pairs are accumulated to obtain the energy dissipation gradient to quantify the change in resource utilization of the path.

[0027] In a preferred embodiment, step S4 includes the following contents:

[0028] By inputting the elite path cluster into the symplectic time window rearrangement operator for timing optimization, the time coordinates of the path nodes are adjusted to meet the task timing window requirements. Then, the conjugate gradient sliding strategy is used to gradually reduce the timing deviation between multiple platforms by calculating the sensitivity of the coordination margin to the time coordinate and iteratively adjusting the time coordinate along the conjugate direction until the coordination margin converges to the preset timing tolerance threshold. Finally, a timing path containing the corrected time coordinates is output to ensure that multiple platforms arrive at the coordinated positioning point synchronously.

[0029] In a preferred embodiment, step S4 includes the following contents:

[0030] After each iteration, the arrival time deviation of multiple platforms at the collaborative positioning point, i.e., the collaborative margin, is recalculated. When this deviation is less than or equal to the preset timing tolerance threshold, it is determined that the time coordinate adjustment has met the requirements and the iteration is stopped.

[0031] In a preferred embodiment, step S5 includes the following contents:

[0032] By inputting the timing path into the confrontation prediction simulation unit, multiple simulation calculations are performed in the dynamic obstacle disturbance field to calculate the survival probability, and then compare the survival probability with the preset survival probability threshold. When the survival probability is greater than or equal to the preset survival probability threshold, the timing path is solidified into the final command sequence.

[0033] The action plan computational modeling system includes: hypergraph modeling module, grid generation module, path optimization module, timing correction module and survival verification module;

[0034] Hypergraph modeling module: This module constructs a multi-constraint hierarchical hypergraph that integrates spatial area distribution, task timing windows, and platform resource status in a 3D dynamic map. It then extracts anchor node sets by traversing all constraint intersection areas and establishes a cross-layer mapping table.

[0035] Grid generation module: Based on the anchor node set, the convex hull relaxation boundary expansion calculation is first performed to generate a hexahedral envelope grid, and then the resource margin gradient is used to guide the non-uniform grid sampling to form a candidate grid grid;

[0036] Path Optimization Module: For each candidate grid, the path phase dispersion and energy dissipation gradient are calculated. The global stability factor is obtained by combining the two. The tabu table weights are dynamically adjusted according to the factor, and then a phase-coded tabu roaming iteration is performed. During the iteration, the tabu table is recorded in real time to suppress loops and converge to the elite path cluster.

[0037] Timing Correction Module: This module inputs the elite path cluster into the symplectic time window rearrangement operator and uses the conjugate gradient sliding strategy to correct the time coordinates of each path node. This module outputs the timing path after the cross-platform coordination margin converges to the allowed interval.

[0038] Survival verification module: Inject the timing path into the confrontation prediction simulation unit, cyclically calculate in the dynamic obstacle disturbance field and test it with the survival probability threshold. When the requirements are met, the timing path is solidified as the final command sequence.

[0039] The technical effects and advantages of the action plan computational modeling method and system of the present invention are as follows:

[0040] The present invention achieves the ability to efficiently generate reliable action plans in a multi-role simulated confrontation environment by constructing a multi-constrained hierarchical hypergraph, compressing the search space, optimizing path selection and timing correction, and conducting confrontation prediction simulation verification. This solution integrates spatial distribution, timing windows, and resource status into a unified abstract model, effectively compresses the search domain using convex hull relaxation expansion and gradient sampling, quickly approximates the global optimal path through phase mapping and taboo walks, and combines symplectic geometry timing optimization to ensure multi-platform collaborative consistency. Finally, the path survivability is verified in a dynamic obstacle disturbance field to generate a high-quality command sequence. The present invention breaks through the limitations of traditional methods that are prone to falling into local minima in complex dynamic scenarios, significantly improves the robustness, efficiency, and portability of path planning, and is suitable for frequently changing three-dimensional geographic spaces and resource-constrained confrontation tasks. The overall technical solution demonstrates outstanding innovation and practical value in terms of path quality, computational efficiency, and task success rate, providing advanced computational modeling support for multi-platform collaborative tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Schematic diagram of the flow of the computational modeling method of the action plan of the present invention.

[0042] Figure 2 This is a schematic diagram of the structure of the computational modeling system for the action plan of the present invention. DETAILED DESCRIPTION

[0043] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0044] Example 1: Figure 1 A computational modeling method for the action plan of the present invention is provided, including:

[0045] S1: Construct a multi-constraint hierarchical hypergraph in a 3D dynamic map that integrates spatial area distribution, task timing windows, and platform resource status. Extract the anchor node set by traversing all constraint intersection areas and establish a cross-layer mapping table.

[0046] S2: Based on the anchor node set, the convex hull relaxation boundary expansion calculation is first performed to generate a hexahedral envelope grid, and then the resource margin gradient is used to guide the non-uniform grid sampling to form a candidate grid.

[0047] S3: For the candidate grid, the path phase dispersion and energy dissipation gradient of each candidate path are first calculated. The global stability factor is obtained through exponential decay-hyperbolic tangent composite mapping. The taboo table weight is dynamically adjusted according to the factor size, and then a phase-coded taboo roaming iteration is performed. During the iteration process, the taboo table is recorded in real time to suppress loops and converge to the elite path cluster.

[0048] S4: Input the elite path cluster into the symplectic time window rearrangement operator, and correct the time coordinates of each path node through the conjugate gradient sliding strategy, so that the cross-platform coordination margin converges to the allowed interval and then outputs the timing path.

[0049] S5: Inject the timing path into the confrontation prediction simulation unit, perform cyclic calculations in the dynamic obstacle disturbance field, and test it with the survival probability threshold. When the threshold meets the requirements, the timing path is solidified as the final command sequence.

[0050] In a multi-role simulated confrontation environment, action entities need to perform collaborative tasks in a frequently changing three-dimensional geographic space. In this scenario, task execution faces multiple complex challenges: no-go zones are adjusted in real time as the scene is updated, mobile obstacles constantly interfere with the trajectory of action entities, and the task rhythm requires multiple platforms to arrive at collaborative positioning points synchronously and share limited energy. As the number of participating platforms increases and the scope of task coverage expands, cross-coupling occurs between variables such as path nodes, timing windows, and energy margins, causing the search space to expand exponentially with the dimension. Traditional traversal or heuristic path planning methods are prone to falling into local minima due to the limited search depth, and are unable to generate a global feasible solution within the real-time scale of the simulation, ultimately resulting in a deviation in the collaborative rhythm and reduced task completion. Therefore, a computational modeling method for action plans is needed that can effectively integrate spatial, temporal, and resource constraints, quickly converge to the global optimal solution, and improve the efficiency and robustness of task execution. The present invention provides a solid foundation for subsequent path planning and resource allocation by constructing a multi-constraint hierarchical hypergraph and extracting a set of anchor nodes, thereby addressing the limitations of traditional methods in complex dynamic environments.

[0051] The goal of step S1 is to construct a multi-constrained hierarchical hypergraph within the 3D dynamic map, integrating spatial region distribution, task timing windows, and platform resource status. This process extracts a set of anchor nodes by traversing all constraint intersections and simultaneously establishes a cross-layer mapping table. This process transforms complex spatial, temporal, and resource constraints into a unified abstract model, providing the data foundation and search framework for subsequent steps.

[0052] Step S1 includes the following contents:

[0053] S1-1. Constructing a multi-constrained hierarchical hypergraph:

[0054] The process of building a multi-constrained hierarchical hypergraph aims to integrate the spatial area distribution, task timing windows, and platform resource status in the three-dimensional dynamic map into a unified abstract model, forming a multi-dimensional network structure. The specific processing logic is as follows:

[0055] First, the spatial extent of the 3D dynamic map is divided into multiple levels of spatial region sets. The bottom level of the spatial region set consists of high-resolution spatial grids, each representing a specific geographic coordinate point; the top level of the spatial region set consists of low-resolution macro-regions, each representing a larger geographic partition. Each level of the spatial region set contains several sub-regions, and this layered approach enables multi-scale modeling of geographic space.

[0056] Secondly, the timeline is discretized into multiple time segments, each of which corresponds to a time layer in the hypergraph; a task timing window is assigned to each task, which is defined by the start and end time range of the task to ensure that the task is executed within the specified time.

[0057] Next, a resource state vector is maintained for each platform, which includes energy margin and load status. The resource status is divided into multiple resource levels, and each resource level corresponds to a resource layer in the hypergraph. For example, energy margin is divided into multiple levels from low to high.

[0058] Finally, the node set of the hypergraph is composed of sub-regions in the spatial region set, time segments in the time layer, and resource levels in the resource layer; the hyperedges of the hypergraph connect node sets that are compatible with each other in space, time, and resources. Compatibility is defined as the node combination that simultaneously meets the spatial location requirements of the task, the task timing window constraints, and the platform resource availability requirements.

[0059] The goal of constructing a multi-constrained hierarchical hypergraph is to integrate the complex distribution of spatial regions, task timing windows, and platform resource status constraints into a unified model, facilitating efficient path planning in a multidimensional search space. The hierarchical structure of spatial region collections supports problem processing at different levels of abstraction, with macro-regions used for coarse planning and spatial grids for fine-tuning, thereby reducing computational complexity while preserving critical details. The introduction of time and resource layers integrates time and resource constraints into the model, ensuring that path planning fully considers task requirements. The hypergraph naturally represents the relationships between multidimensional constraints through hyperedges, ensuring that the generated path satisfies all conditions and improving planning accuracy and reliability.

[0060] S1-2. Extracting anchor node set

[0061] The process of extracting the anchor node set aims to filter out the key nodes that meet the task constraints from the multi-constraint hierarchical hypergraph, providing a reference for subsequent path planning. The specific processing logic is as follows:

[0062] First, a set of nodes in a multi-constraint hierarchical hypergraph that simultaneously satisfies spatial, temporal, and resource constraints is identified to form a constraint intersection region. Nodes in the constraint intersection region are required to be spatially located in a non-restricted zone and avoid obstacles, temporally fall within the task timing window, and satisfy the platform's energy margin and payload requirements.

[0063] Next, starting from the starting node of the task, the breadth-first search method is used to traverse the multi-constraint hierarchical hypergraph, gradually marking all nodes that meet the constraints; the breadth-first search method explores the hypergraph according to the principle of shortest path first, and records each node in the constraint intersection area.

[0064] Finally, the node set in the constraint intersection region is defined as the anchor node set, which represents the key locations where tasks can be executed under specific time, place, and resource status.

[0065] The purpose of extracting anchor node sets is to narrow the search space for subsequent path planning by selecting nodes that satisfy all task constraints, thereby improving computational efficiency. Identifying constraint intersection regions ensures the feasibility of the anchor node set in terms of space, time, and resources, avoiding wasted computational resources in ineffective areas. A breadth-first search method prioritizes the exploration of the hypergraph with the optimal path, rapidly locating key nodes. The anchor node set serves as a benchmark for path planning, providing a clear direction for generating feasible paths and enhancing the practicality and targeted nature of the solution.

[0066] S1-3. Establish a cross-layer mapping table:

[0067] The process of establishing a cross-layer mapping table is intended to record the correspondence between different levels in a multi-constraint hierarchical hypergraph, supporting subsequent queries and dynamic adjustments. The specific processing logic is as follows: First, a mapping relationship is established between the spatial region set, time layer, and resource layer of the multi-constraint hierarchical hypergraph. The mapping relationship of the spatial region set corresponds the top-level macro region to the underlying spatial grid, the mapping relationship of the time layer corresponds the time segment to the specific time point, and the mapping relationship of the resource layer corresponds the resource level to the specific energy value and load status. Next, a cross-layer mapping table is created. The cross-layer mapping table is a multi-level index structure that records the hierarchical information of each anchor node in the spatial region set, time layer, and resource layer; the cross-layer mapping table stores the detailed correspondence of all anchor nodes in an indexed manner, facilitating quick access to data at different levels.

[0068] The purpose of establishing a cross-layer mapping table is to provide an efficient data structure that supports rapid navigation and data retrieval between different levels of a multi-constrained hierarchical hypergraph. The design of these mapping relationships allows the system to flexibly switch between macro-regions and spatial grids, time slices and specific time points, and resource levels and specific resource values, adapting to the varying granularity requirements of path planning. The multi-level index structure of the cross-layer mapping table optimizes query efficiency and ensures real-time generation of feasible paths in complex adversarial environments.

[0069] In a multi-role simulated confrontation environment, actors must navigate a dynamically changing geographic space, stringent mission timing requirements, and limited platform resource availability. Step S1 constructs a multi-constrained hierarchical hypergraph, transforming spatial regional distribution, mission timing windows, and platform resource status into a structured network model. It then extracts anchor node sets and establishes cross-layer mapping tables, laying the foundation for subsequent path planning and resource allocation. After step S1 is completed, the multi-constrained hierarchical hypergraph integrates the multidimensional constraints of the three-dimensional dynamic map. The anchor node sets provide key reference points, and the cross-layer mapping tables support efficient data access, ensuring the applicability and efficiency of computational modeling of action plans in complex environments.

[0070] Step S1 constructs a multi-constrained hierarchical hypergraph and extracts a set of anchor nodes, providing structured data support for action plan planning. However, relying solely on a set of anchor nodes cannot effectively address the exponential expansion of the search space and the need to find a global optimal solution, especially in dynamic scenarios with limited resources and high task complexity. Therefore, step S2 aims to further compress the search domain and generate an efficient set of candidate points based on the set of anchor nodes, laying the foundation for subsequent path planning.

[0071] Step S2 includes the following contents:

[0072] S2-1. Calculate the hexahedral envelope by performing convex hull relaxation and boundary expansion:

[0073] The process of implementing the convex hull relaxation boundary expansion calculation to generate the hexahedral envelope grid aims to build an extended and regular search area for the anchor node set to cope with the uncertainty in the dynamic environment. The specific processing logic is as follows:

[0074] First, based on the set of anchor nodes extracted in step S1, the minimum convex polyhedron in three-dimensional space is calculated. The minimum convex polyhedron is the minimum geometric boundary that contains all anchor nodes, ensuring that the search area covers all key locations.

[0075] Next, to accommodate dynamic obstacles and no-go zones, the minimum convex polyhedron is expanded with a relaxed boundary. This expansion is accomplished by translating each convex hull surface outward by a certain distance along its normal vector, generating the expanded convex polyhedron. The translation distance is determined by the dynamics of the scene, specifically the product of the average speed of the moving obstacles and the time step. This operation ensures that the search area has a certain buffer against dynamic disturbances.

[0076] Finally, the expanded convex polyhedron is approximated as an axis-aligned hexahedral envelope. The specific method involves calculating the projection range of the expanded convex polyhedron on the x, y, and z axes of space and determining the minimum and maximum values ​​on each axis, thereby constructing a regular hexahedral envelope. This hexahedral envelope covers the anchor node set and its relaxed boundaries, providing a standardized search area for subsequent grid point sampling.

[0077] The goal of implementing the convex hull relaxation boundary expansion to generate a hexahedral envelope lattice is to provide a search region that encompasses key nodes while providing a buffer margin for path planning in dynamic environments. The calculation of the minimum convex polyhedron ensures a compact search region that encompasses all anchor nodes, while the expansion operation allows for the movement of dynamic obstacles, enhancing the robustness of path planning. Approximating the hexahedral envelope lattice simplifies the spatial representation, facilitating efficient grid point sampling and computation on a regular grid structure, and reducing the complexity of subsequent processing.

[0078] S2-2. Using resource margin gradient to guide non-uniform grid sampling to form candidate grid grids:

[0079] The process of forming a candidate grid by guiding non-uniform grid sampling with resource margin gradients aims to generate a resource-sensitive candidate point set within the hexahedral envelope grid to optimize the resource utilization efficiency of path planning. The specific processing logic is as follows:

[0080] First, a resource margin function is defined within the hexahedral envelope lattice to represent the resource margin estimation at each spatial point. The resource margin comprehensively considers factors such as energy margin and load status.

[0081] Next, the gradient of the resource margin function in space is calculated. The gradient direction points to the direction of increasing resource margin, and the magnitude of the gradient indicates the severity of resource changes. exist The partial derivatives in the direction are calculated to obtain: .

[0082] Then, based on the resource margin gradient, non-uniform grid sampling is performed within the hexahedral envelope. The sampling density is proportional to the gradient size: higher in areas with drastic resource changes and lower in areas with more moderate changes. The sampling density is calculated by normalizing the gradient size to a value between the minimum and maximum sampling densities, ensuring more candidate points in resource-sensitive areas.

[0083] For example, based on the resource margin gradient , in the hexahedral envelope Non-uniform grid sampling is performed within. Sampling density With gradient mode The calculation formula is:

[0084]

[0085] in, is the minimum sampling density, is the maximum sampling density, Hexahedral envelope lattice The maximum value of the inner gradient modulus. This formula ensures that the sampling density is higher in areas where the resource changes sharply, and lower in areas where the change is gentle.

[0086] Finally, based on the sampling density, a non-uniformly distributed set of grid points is generated within the hexahedral envelope to form a candidate grid. The grid points in this candidate grid serve as candidate nodes for subsequent path planning, especially in resource-sensitive areas with higher density.

[0087] The goal of using resource margin gradients to guide non-uniform grid sampling to form a candidate grid is to optimize the distribution of the search space, making the candidate point set denser in resource-sensitive areas, thereby improving the resource adaptability of path planning. The calculation of resource margin gradients reveals key areas of resource variation. Non-uniform sampling ensures more candidate points in these areas, helping to generate paths with higher resource efficiency. Furthermore, reducing the number of candidate points in resource-stable areas reduces the computational burden and balances planning accuracy and efficiency.

[0088] Step S1 constructs a multi-constrained hierarchical hypergraph and extracts a set of anchor nodes, providing structured basic data support for action plan planning. Building on this foundation, step S2 utilizes the anchor node set to perform convex hull relaxation boundary expansion calculations to generate a hexahedral envelope lattice. This is then followed by a candidate grid point grid formed through resource margin gradient-guided non-uniform grid sampling. After step S2 is completed, the candidate grid point grid provides an efficient, resource-sensitive search space for subsequent path planning, ensuring rapid generation of high-quality path solutions within dynamic environments and resource constraints.

[0089] Step S2 generates a hexahedral envelope lattice and a candidate grid based on the anchor node set, providing an efficient and resource-sensitive set of candidate points for path planning. Building on this, step S3 calculates the path phase dispersion and energy dissipation gradient for each candidate path in the candidate grid, obtains a global stability factor through composite mapping, and performs phase-coded tabu walk iterations using dynamically adjusted tabu table weights. Ultimately, the algorithm converges to an elite path cluster, providing high-quality path candidates for timing correction in step S4.

[0090] Step S3 includes the following contents:

[0091] S3-1. Calculate the path phase dispersion and energy dissipation gradient of each candidate path:

[0092] The process of calculating the path phase dispersion and energy dissipation gradient of each candidate path aims to quantify the characteristics of the candidate path in terms of time, space, and resource utilization, providing basic data for subsequent path quality assessment. The specific processing logic is as follows:

[0093] First, multiple candidate paths are generated from the candidate grid. Each candidate path consists of a series of grid points connecting the start and end points of the task. Next, the path phase dispersion is calculated, which measures the degree of temporal and spatial fluctuation of the candidate path. This is calculated as follows: for each node on the candidate path, the time difference and spatial difference between it and the next node are determined. Then, the average of the time differences and the average of the spatial differences of all node pairs are calculated. Next, for each node pair, the absolute value of the difference between its time difference and the average of all time differences, as well as the absolute value of the difference between its spatial difference and the average of all spatial differences, are calculated. These two absolute values ​​are multiplied together to obtain the product for each node pair. Finally, the products of all node pairs are accumulated to obtain the path phase dispersion.

[0094] For example, the path phase dispersion of each candidate path can be calculated as follows:

[0095] 1). Candidate path generation:

[0096] In the candidate grid In the example, multiple candidate paths are generated by connecting adjacent grid points, which are recorded as path sets. Each path It consists of a series of grid points that meet the connection requirements of the starting point and the end point of the task. The grid points are recorded as ,in Indicates the path On the nodes.

[0097] 2). Path phase dispersion calculation:

[0098] Path phase dispersion is used to measure the degree of path fluctuation in time and space, reflecting the smoothness and continuity of the path. The calculation process is as follows:

[0099] On the path Each node on , calculate its relationship with the next node Time difference and spatial difference .in, is the time interval between two nodes, is the spatial distance between two nodes.

[0100] Defining path phase spread is the nonlinear accumulation of time and space differences between nodes, using the following formula:

[0101]

[0102] in, For path The total number of nodes, For path The average of all time differences, For path The average of all spatial differences.

[0103] Parameter explanation:

[0104] :node arrive time interval.

[0105] node arrive The three-dimensional space distance.

[0106] and : Represent the benchmark values ​​of time and space differences, respectively, used to measure local fluctuations.

[0107] This formula amplifies the joint fluctuations in time and space in the form of a product, avoiding the smoothing effect of linear addition and highlighting the local discontinuity of the path.

[0108] Calculate the energy dissipation gradient, which measures the rate of change in resource consumption along a candidate path. This is done by determining the resource consumption of each node on the candidate path. Then, for each adjacent node, calculate the absolute difference in resource consumption between them and find the maximum absolute value of resource consumption across all pairs of adjacent nodes. Then, multiply the absolute value of the resource consumption difference for each pair of adjacent nodes by the maximum absolute value of resource consumption across all pairs of adjacent nodes to obtain the product for each pair. Finally, accumulate these products across all pairs of adjacent nodes to obtain the energy dissipation gradient.

[0109] For example, the energy dissipation gradient of each candidate path can be calculated as follows:

[0110] The energy dissipation gradient is used to measure the rate of change in resource consumption along a path, reflecting the efficiency of resource utilization. The calculation process is as follows:

[0111] On the path Each node on , calculate its resource consumption ,Resource consumption comprehensively considers factors such as energy and load, and the unit is standardized resource unit.

[0112] Defining the energy dissipation gradient is the nonlinear cumulative amount of resource consumption difference between adjacent nodes, using the following formula:

[0113]

[0114] Parameter explanation:

[0115] :node The resource consumption value is calculated comprehensively based on factors such as energy and load.

[0116] : The absolute difference in resource consumption between adjacent nodes.

[0117] : The maximum absolute value of resource consumption of adjacent nodes, used to amplify the impact of local changes.

[0118] This formula amplifies local drastic changes in resource consumption by multiplying the maximum value, avoiding the smoothing of simple differences and highlighting the non-uniformity of resource utilization across paths.

[0119] The purpose of calculating path phase dispersion and energy dissipation gradient is to quantify the characteristics of candidate paths across multiple dimensions, providing a comprehensive basis for subsequent evaluation. Path phase dispersion amplifies local fluctuations in candidate paths by multiplying the time difference and spatial difference, highlighting joint discontinuities in time and space. The energy dissipation gradient amplifies local fluctuations by multiplying the resource consumption difference and the maximum value, highlighting heterogeneity in resource utilization across candidate paths. This calculation method ensures that the evaluation metrics accurately reflect the smoothness and resource efficiency of candidate paths.

[0120] S3-2. Obtain the global stability factor through the exponential decay-hyperbolic tangent composite mapping:

[0121] The process of obtaining the global stability factor through the exponential decay-hyperbolic tangent composite mapping aims to integrate the path phase dispersion and energy dissipation gradient to generate a unified candidate path quality index. The specific processing logic is as follows:

[0122] A composite mapping function is constructed to convert path phase dispersion and energy dissipation gradient into a global stability factor. The composite mapping function consists of two parts: the first is an exponential decay term, which takes path phase dispersion as input. As path phase dispersion increases, the output value decreases rapidly, imposing a greater penalty on candidate paths with large fluctuations. The second is a hyperbolic tangent term, which takes the energy dissipation gradient as input. As the energy dissipation gradient increases, the output value increases slowly, smoothing out changes in resource consumption. The global stability factor is the product of the output values ​​of the exponential decay term and the hyperbolic tangent term. Its value range is limited to 0 to 1, with larger values ​​indicating higher quality candidate paths.

[0123] For example, a composite mapping function can be constructed as follows:

[0124] To comprehensively evaluate the path phase dispersion and energy dissipation gradient , design composite mapping function , generating a global stability factor , the formula is as follows:

[0125]

[0126] Parameter explanation:

[0127] : adjustment coefficient of path phase dispersion, , controls the intensity of the penalty imposed by the discreteness on the stability factor.

[0128] : adjustment coefficient of energy dissipation gradient, , controls the influence of dissipation gradient on the stability factor.

[0129] : exponential decay term, when When it is small and close to 1, it means the path is smooth; when When it is larger and closer to 0, it means the penalty is greater.

[0130] : Hyperbolic tangent term, when When the value is small, it indicates high resource efficiency; when When it is large and approaches 1, it means that resource consumption fluctuates significantly.

[0131] Global stability factor The value range is [0,1), and the larger the value, the higher the path quality.

[0132] The purpose of obtaining the global stability factor through a composite exponential decay-hyperbolic tangent mapping is to combine multiple evaluation metrics into a single quality value, facilitating the comparison and screening of candidate paths. The exponential decay term's nonlinear penalty for path phase dispersion ensures strict smoothness requirements, emphasizing the continuity of candidate paths; the hyperbolic tangent term's gentle treatment of energy dissipation gradients balances resource efficiency assessments. This composite mapping approach balances candidate path smoothness with resource utilization stability, enhancing the comprehensiveness and accuracy of the global stability factor in quality assessment.

[0133] S3-3. Dynamically adjust the tabu table weights according to the factor size and then perform phase-coded tabu roaming iterations:

[0134] The process of dynamically adjusting the tabu table weights according to the factor size and then performing phase-coded tabu roaming iterations aims to optimize the search strategy using the global stability factor to improve the efficiency and quality of candidate path screening. The specific processing logic is as follows:

[0135] First, a tabu table is initialized. This table records recently visited candidate paths or nodes to prevent repeated searches. Next, the tabu duration of candidate paths in the tabu table is adjusted based on a global stability factor: for candidate paths with a larger global stability factor, a shorter tabu duration is set to allow more frequent exploration; for candidate paths with a smaller global stability factor, a longer tabu duration is set to limit repeated visits. Then, a phase-encoded tabu walk iteration is performed: each candidate path is encoded as a phase vector that incorporates temporal and spatial information about the candidate path nodes. A random walk is performed in the phase space, prioritizing candidate paths or nodes not recorded in the tabu table. After each iteration, the tabu table is updated to record newly visited candidate paths or nodes. The quality of the candidate paths is evaluated based on the global stability factor, and high-quality candidate paths are retained.

[0136] The purpose of performing phase-encoded tabu roaming iterations after dynamically adjusting the tabu table weights based on the factor size is to optimize the search process and improve the efficiency of generating high-quality candidate paths. Dynamically adjusting the tabu duration guides the search toward high-quality candidate paths based on the global stability factor, accelerating convergence. Phase encoding incorporates temporal and spatial information into the candidate path representation, enhancing the targeted search. Tabu roaming iterations ensure diversity and globality by limiting repeated visits.

[0137] S3-4. During the iteration process, the taboo table is recorded in real time to suppress loops and converge to the elite path cluster:

[0138] The process of recording the tabu table in real time during the iteration to suppress loops and converge to the elite path cluster aims to form a high-quality candidate path set through continuous optimization and recording. The specific processing logic is as follows:

[0139] During the phase-coded tabu roaming iterations, the tabu table records visited candidate paths or nodes in real time, preventing the search from repeatedly entering the same area and maintaining search diversity. As the iterations proceed, the search gradually converges to a set of candidate paths whose global stability factor values ​​meet the criteria, ultimately forming an elite path cluster. This elite path cluster serves as the output of step S3 and provides input for subsequent timing correction.

[0140] During the iteration process, the tabu table is recorded in real time to prevent loops and converge to an elite cluster of paths. The goal is to ensure a high-quality set of candidate paths through continuous optimization. Real-time updates to the tabu table effectively prevent loops during the search and enhance exploration capabilities. Convergence to an elite cluster of paths selects candidate paths with high global stability factors, providing high-quality input for subsequent timing corrections. This approach improves path planning efficiency and results quality, adapting to the needs of complex dynamic scenarios.

[0141] In a multi-role simulated adversarial environment, step S2 generates a candidate grid, providing an efficient and resource-sensitive search space for step S3. Based on this, step S3 sequentially calculates the path phase dispersion and energy dissipation gradient of the candidate paths to generate a global stability factor. This global stability factor is then used to dynamically adjust the tabu table weights and perform phase-coded tabu walk iterations, ultimately converging to an elite path cluster. After step S3 is completed, the elite path cluster serves as a set of high-quality candidate paths and is directly input into the subsequent timing correction step, ensuring rapid generation of high-quality action plans in complex dynamic scenarios.

[0142] Step S3 generates elite path clusters, providing a high-quality set of candidate paths for path planning. Each path consists of a sequence of nodes, each containing spatial coordinates and initial time coordinates. However, due to the strict timing requirements of multi-platform collaborative tasks, paths in the elite path cluster may deviate in the temporal dimension, resulting in inability to arrive at the collaborative location point synchronously. Based on this, step S4 uses the elite path cluster as input and corrects the time coordinates of each path node using the symplectic time window reordering operator and the conjugate gradient sliding strategy, so that the cross-platform coordination margin converges to the preset allowable range, ultimately outputting the time-matched path.

[0143] Step S4 includes the following contents:

[0144] S4-1. Input the elite path cluster into the symplectic time window rearrangement operator:

[0145] The process of inputting the elite path cluster into the symplectic time window rearrangement operator is to use the timing optimization method of symplectic geometry to adjust the time coordinates of the path nodes to meet the timing window requirements of multi-platform collaborative tasks. The specific processing logic is:

[0146] The symplectic time window reordering operator is an optimization technique based on symplectic geometry. It focuses on optimizing the timing characteristics of a path by adjusting the time coordinates of nodes while keeping the spatial structure of the path unchanged.

[0147] Each path in the elite path cluster consists of a series of nodes, each containing spatial coordinates and initial time coordinates. The symplectic time window reordering operator takes these paths as input and uses the task timing window as a constraint. The task timing window defines the time range of each co-location point within which all platforms must arrive. The symplectic time window reordering operator operates in phase space. By analyzing the coupling relationship between time and spatial coordinates, it adjusts the time coordinate of each node to achieve temporal and spatial consistency of the path while maintaining the overall structure and characteristics of the path.

[0148] The rationale for feeding elite path clusters into the symplectic time window reordering operator is that the properties of symplectic geometry maintain the spatial structural integrity of the path when adjusting the time coordinate, ensuring that the optimization process does not affect the physical feasibility of the path. By optimizing in phase space, the symplectic time window reordering operator effectively handles the interaction between time and space, improving the temporal coordination of the path. This approach provides high-quality initial input for the subsequent conjugate gradient sliding strategy, making timing correction more efficient and accurate, thereby meeting the strict timing requirements of multi-platform collaborative tasks.

[0149] S4-2. Correct the time coordinates of each path node using the conjugate gradient sliding strategy:

[0150] The process of correcting the time coordinates of each path node through the conjugate gradient sliding strategy aims to use iterative optimization methods to gradually reduce the timing deviation between multiple platforms until the timing requirements of the collaborative task are met. The specific processing logic is:

[0151] The conjugate gradient sliding strategy is an efficient iterative optimization technique that analyzes the sensitivity of the coordination margin to the time coordinate and adjusts the time coordinate along a specific direction to quickly reduce the timing deviation between multiple platforms.

[0152] The coordination margin is defined as the maximum deviation of the arrival time of multiple platforms at the coordinated positioning point, that is, the maximum difference between the arrival time of all platforms and the preset synchronous arrival time. The optimization goal is to make this deviation converge to the preset allowable range. The correction process includes the following steps:

[0153] First, the initial coordination margin is calculated with the initial time coordinate of the path as the starting point;

[0154] Then, the sensitivity of the coordination margin to the change of the time coordinate is analyzed to determine the adjustment direction. The sensitivity reflects the degree of influence of the time adjustment on the deviation.

[0155] Next, the new search direction is calculated by combining the current adjustment direction with the direction of the previous iteration. The new search direction is determined by integrating the information of the two directions to improve the search efficiency.

[0156] Subsequently, the time coordinates are updated along the new search direction, and the adjustment amplitude is determined by stepwise trial and error to maximize the reduction effect of the synergy margin;

[0157] Finally, the above steps are repeated until the coordination margin is less than or equal to a preset timing tolerance threshold.

[0158] The reason for using the conjugate gradient sliding strategy to correct time coordinates is that this method leverages the rapid convergence characteristics of iterative optimization to efficiently handle timing coordination issues across multiple platforms. Compared to traditional point-by-point adjustment methods, the conjugate gradient sliding strategy integrates historical directional information to avoid inefficient iterations during the adjustment process, improving convergence speed and stability. Using the coordination margin as an optimization objective directly quantifies the timing coordination requirements, ensuring that the adjustment process is clearly directional and measurable. This method can rapidly optimize time coordinates in complex dynamic scenarios, providing a reliable timing coordination path for subsequent adversarial prediction simulations.

[0159] S4-3. Output the timing path after the cross-platform coordination margin converges to the allowable range:

[0160] The process of outputting the timing path after the cross-platform coordination margin converges to the allowed range is intended to ensure the timing coordination of the path through iterative optimization and generate the final timing path. The specific processing logic is:

[0161] After each iteration, the arrival time deviation of multiple platforms at the co-location point, known as the coordination margin, is recalculated. When this deviation is less than or equal to the preset timing tolerance threshold, the time coordinate adjustment is deemed satisfactory and the iteration is terminated. At this point, the time coordinates of the nodes in the path have been optimized to ensure simultaneous arrival of multiple platforms at the co-location point. The adjusted paths are output as timing paths. Each timing path contains both the corrected time coordinates and the original spatial coordinates, providing input for subsequent adversarial prediction simulations.

[0162] The reason for outputting a timing path after the cross-platform coordination margin converges to the allowable range is that, through iterative optimization until the timing tolerance threshold is met, timing deviations between multiple platforms can be completely eliminated, ensuring the synchronization of task execution. The generation of a timing path marks the completion of path planning optimization in the time dimension, providing a high-quality input path for subsequent steps.

[0163] Step S3 generates an elite path cluster, providing a high-quality candidate path set for step S4. Step S4 receives the elite path cluster as input, first inputs it into the symplectic time window reordering operator for preliminary timing optimization, and then further corrects the time coordinates of each path node through the conjugate gradient sliding strategy, ultimately making the cross-platform coordination margin converge to the allowable interval, and outputs the timing path. After step S4 is completed, the timing path ensures that multiple platforms arrive at the coordinated positioning point synchronously in the frequently changing three-dimensional geographic space, meeting the strict timing requirements of the task. As the output of step S4, the timing path directly provides a reliable timing coordination path for the adversarial prediction simulation in step S5, thereby ensuring the consistency and efficiency of the entire task planning process.

[0164] In a multi-role simulated adversarial environment, action entities need to perform collaborative tasks in a frequently changing three-dimensional geographic space, facing dynamically adjusted no-go zones, disturbances from mobile obstacles, and the strict timing and resource requirements of multi-platform collaborative tasks. Steps S1 to S4 construct a multi-constrained hierarchical hypergraph, generate a candidate grid, optimize the path, and perform timing corrections to generate a timing path that meets the task requirements under spatial, temporal, and resource constraints. However, in actual adversarial environments, there are unpredictable dynamic obstacles and emergencies, and the execution of the timing path may be hindered due to insufficient survivability. To address this challenge, step S5 introduces an adversarial prediction simulation unit to perform survivability tests on the timing path to ensure its reliability and mission success rate in a dynamic environment.

[0165] Step S5 includes the following contents:

[0166] S5-1. Inject the timing path into the adversarial prediction simulation unit:

[0167] The process of injecting the timing path into the adversarial prediction simulation unit is to evaluate the execution performance of the timing path in a dynamic adversarial environment through the simulation module. The specific processing logic is as follows:

[0168] The Adversarial Prediction Simulation Unit is a specially designed simulation module used to test the survivability of timed paths in dynamic adversarial environments. A timed path consists of multiple paths, each containing a series of nodes. Each node is represented by spatial and temporal coordinates, guiding the movement and coordinated behavior of entities in three-dimensional geographic space. The Adversarial Prediction Simulation Unit constructs a disturbance field that approximates a real-world adversarial scenario by simulating the trajectory changes of moving obstacles and the dynamic adjustment of no-go zones. After the timed path is injected into the Adversarial Prediction Simulation Unit, the simulation module recreates the uncertainty factors in the dynamic environment and evaluates whether the timed path can successfully avoid moving obstacles and no-go zones during actual execution, ensuring the successful completion of the mission.

[0169] The rationale for injecting the scheduled path into the adversarial prediction simulation unit is that, by simulating a dynamic adversarial environment, we can pre-evaluate the scheduled path's survivability in the face of moving obstacles and no-go zones, ensuring path reliability and mission execution safety. This approach also offers the advantage of identifying potential path failure risks before actual execution, providing a basis for subsequent optimization and improving the robustness of the action plan and mission success rate in complex dynamic scenarios.

[0170] S5-2. Perform loop calculation in dynamic obstacle disturbance field:

[0171] The purpose of the cyclic calculation process in the dynamic obstacle disturbance field is to evaluate the survivability of the timing path in the dynamic environment through multiple simulations. The specific processing logic is as follows:

[0172] The dynamic obstacle perturbation field simulates the uncertainties inherent in an adversarial environment, including the random movement of mobile obstacles and the immediate adjustment of no-go zones. The movement trajectories of mobile obstacles are generated using a Markov chain model. The state transition model defines the probability of a mobile obstacle transitioning from one state to another, where each state includes its spatial position and velocity. Adjustments to no-go zones are driven by a random process, with the frequency of adjustments pre-set based on the dynamics of the adversarial scenario to reflect the random nature of no-go zone changes. Within the dynamic obstacle perturbation field, the timed path is simulated multiple times, with each calculation recording whether the timed path fails due to encountering a mobile obstacle or being blocked by a no-go zone. The number of calculations is set to a sufficiently high value to ensure the reliability of the survival probability statistics.

[0173] The rationale for performing loop calculations within a dynamic obstacle disturbance field is that, through multiple simulations, we can comprehensively assess the survivability of the timing path under different dynamic scenarios, ensuring the accuracy and reliability of the assessment results. This approach also offers the advantage of simulating a variety of possible dynamic environmental changes, identifying potential risks of the timing path in the face of uncertainty in advance, and providing a solid data foundation for subsequent survival probability calculations.

[0174] S5-3. Test with survival probability threshold:

[0175] The purpose of the survival probability threshold test is to determine whether the timing path meets the task requirements by calculating the survival probability of the timing path and comparing it with the preset threshold. The specific processing logic is as follows:

[0176] The survival probability is defined as the probability that a timing path is successfully executed across multiple runs. It is calculated as the ratio of the number of successful runs to the total number of runs. The number of successful runs represents the number of runs in which the timing path is not interrupted by moving obstacles or blocked by no-go zones. The total number of runs is the total number of simulated runs. The preset survival probability threshold is determined by the mission requirements and reflects the specific survivability requirements of the mission. If the survival probability is greater than or equal to the preset survival probability threshold, the timing path is considered sufficiently survivable in a dynamic environment. If the survival probability is less than the preset survival probability threshold, the process returns to the previous steps to re-optimize the candidate path or adjust the timing parameters.

[0177] The reason for testing with the survival probability threshold is that by comparing the survival probability with the preset survival probability threshold, it is possible to intuitively determine whether the timing path meets the survivability requirements of the task, ensuring the reliability of the path in a dynamic environment and the safety of task execution.

[0178] S5-4. When the threshold meets the requirements, the timing path is solidified as the final command sequence:

[0179] The process of solidifying the timing path into the final command sequence when the threshold meets the requirements is to convert the timing path that has passed the survivability test into the actual execution command. The specific processing logic is:

[0180] When the survival probability is greater than or equal to the preset survival probability threshold, the timing path is deemed sufficiently survivable in a dynamic environment and is solidified into the final command sequence. The final command sequence contains specific instructions for the action entities, namely the spatial coordinates, time coordinates, and resource allocation plan for each path, which guides the actual execution of the task.

[0181] The rationale for solidifying the timing path as the final command sequence when the thresholds are met is to ensure the reliability of the timing path in a dynamic environment and the safety of mission execution through survivability testing, thereby providing high-quality action plans for the acting entity. This approach offers the advantage of enabling comprehensive evaluation and optimization of the timing path before actual execution, ensuring successful mission completion and the survivability of the acting entity.

[0182] In a multi-role simulated adversarial environment, the aforementioned step S4 generates a timing path through the symplectic time window rearrangement operator and the conjugate gradient sliding strategy, providing a high-quality candidate path set for path planning. Step S5 receives the timing path as input, first injects it into the adversarial prediction simulation unit for survivability testing, then performs a loop calculation in the dynamic obstacle disturbance field, calculates the survival probability and compares it with the preset survival probability threshold, and finally solidifies the timing path that passes the survivability test into the final command sequence. After step S5 is completed, the final command sequence provides the action entity with a high-quality action plan for dealing with mobile obstacles and no-go zone adjustments in the frequently changing three-dimensional geographic space, ensuring the smooth completion of the mission and the survivability of the action entity.

[0183] Example 2: Figure 2 The present invention provides a computational modeling system for action plans, including: a hypergraph modeling module, a grid generation module, a path optimization module, a timing correction module, and a survival verification module;

[0184] Hypergraph modeling module: Constructs a multi-constraint hierarchical hypergraph that integrates spatial area distribution, task timing windows, and platform resource status in a three-dimensional dynamic map, extracts anchor node sets by traversing all constraint intersection areas, and establishes a cross-layer mapping table.

[0185] Grid generation module: Based on the anchor node set, the convex hull relaxation boundary expansion calculation is first performed to generate a hexahedral envelope grid, and then the resource margin gradient is used to guide the non-uniform grid sampling to form a candidate grid grid.

[0186] Path optimization module: For the candidate grid, the path phase dispersion and energy dissipation gradient of each candidate path are first calculated, and the global stability factor is obtained by comprehensive calculation of the two. The taboo table weight is dynamically adjusted according to the size of the factor, and then the phase-coded taboo roaming iteration is performed. During the iteration process, the taboo table is recorded in real time to suppress loops and converge to the elite path cluster.

[0187] Timing correction module: The elite path cluster is input into the symplectic time window rearrangement operator, and the time coordinates of each path node are corrected through the conjugate gradient sliding strategy, so that the cross-platform coordination margin converges to the allowed interval and then the timing path is output.

[0188] Survival verification module: Inject the timing path into the confrontation prediction simulation unit, cyclically calculate in the dynamic obstacle disturbance field and test it with the survival probability threshold. When the requirements are met, the timing path is solidified as the final command sequence.

[0189] The above formulas are all dimensionless and numerical calculations. The formulas are obtained by collecting a large amount of data and performing software simulation to obtain the most recent real situation. The preset parameters in the formulas are set by technicians in this field according to actual conditions.

[0190] It should be noted that the system of the present invention can be deployed on the device itself to realize embedded applications, and can also be run on a PC or other terminal with a user interface, thereby meeting a variety of hardware environments and usage requirements.

[0191] The above description is merely illustrative of certain exemplary embodiments of the present invention. It goes without saying that those skilled in the art will be able to modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the above drawings and description are illustrative in nature and should not be construed as limiting the scope of protection of the claims.

[0192] It should be noted that, in this document, if there are relational terms such as first and second, etc., they are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprises", "includes" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device that includes a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article or device. In the absence of further limitations, an element defined by the phrase "comprises a ..." does not exclude the presence of other identical elements in the process, method, article or device that includes the element.

[0193] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of this application. Therefore, the scope of protection of this application should be based on the scope of protection of the claims.

Claims

1. The action plan can be calculated and modeled, characterized by: Including steps: S1: Construct a multi-constraint hierarchical hypergraph in a 3D dynamic map that integrates spatial area distribution, task timing windows, and platform resource status. Then, extract the anchor node set by traversing all constraint intersection areas and establish a cross-layer mapping table. The task timing window is a task execution time range defined by the start time and end time, which is used to ensure that each task is completed within the specified time; The constraint intersection region is the node set region in the multi-constraint hierarchical hypergraph that satisfies the space, time and resource constraints at the same time, and is identified by traversing the hypergraph through breadth-first search; The cross-layer mapping table is an index structure that records the hierarchical correspondence between anchor nodes in spatial region sets, time layers, and resource layers. It is used to support fast navigation and data retrieval between different layers. S2: Based on the anchor node set, the convex hull relaxation boundary expansion calculation is first performed to generate a hexahedral envelope grid, and then the resource margin gradient is used to guide the non-uniform grid sampling to form a candidate grid grid; The resource margin gradient is the gradient of the resource margin function in space. The sampling density is determined based on its size, so that the sampling density in areas with drastic resource changes is higher than that in areas with gentle changes. This is used to guide the non-uniform grid sampling within the hexahedral envelope. S3: For each candidate grid, the path phase dispersion and energy dissipation gradient are calculated. The global stability factor is obtained by combining the two. The tabu table weights are dynamically adjusted according to the factor, and then a phase-coded tabu roaming iteration is performed. During the iteration, the tabu table is recorded in real time to suppress loops and converge to the elite path cluster. Path phase dispersion is calculated by multiplying the absolute deviations of the time and space differences of adjacent nodes on a candidate path with their respective averages, and then summing the products of all node pairs. It is used to quantify the degree of path fluctuation in time and space dimensions. The energy dissipation gradient is calculated by multiplying the absolute value of the resource consumption difference between adjacent nodes on the candidate path and the absolute value of the maximum resource consumption difference, and then accumulating the product of all adjacent node pairs. It is used to quantify the change in resource utilization of the path. S4: Input the elite path cluster into the symplectic time window rearrangement operator, and correct the time coordinates of each path node through the conjugate gradient sliding strategy, so that the cross-platform coordination margin converges to the allowed interval and then outputs the timing path; Phase-encoded tabu walk iteration is an optimization algorithm that encodes paths into phase vectors and performs random walks in phase space, while dynamically adjusting the tabu table weights to suppress loops and converge to an elite path cluster. The coordination margin refers to the maximum deviation of the arrival time of multiple platforms at the co-location point. It is used to quantify the margin of cross-platform timing coordination and ensure that it converges to the allowable range. The sliding strategy is an iterative correction method based on conjugate gradients. It calculates the sensitivity of the coordination margin to the time coordinate and adjusts the node time coordinate along the conjugate direction to gradually reduce the timing deviation. S5: Inject the timing path into the confrontation prediction simulation unit, perform cyclic calculations in the dynamic obstacle disturbance field, and test it with the survival probability threshold. When the requirements are met, solidify the timing path as the final command sequence.

2. The method for computational modeling of an action plan according to claim 1, characterized in that: Step S1 includes the following contents: First, the spatial range is divided into a set of spatial regions at multiple levels, where the bottom level is a high-resolution spatial grid representing specific geographic coordinate points, and the top level is a low-resolution macro-region representing a large-scale geographic partition. Discretize the timeline into multiple time segments and assign each task a task timing window defined by the start time and end time; Maintain resource status vectors for the platform and divide them into multiple resource levels; Construct a hypergraph whose node set consists of sub-regions of a set of spatial regions, time slices, and resource levels, and whose hyperedges connect node sets that are compatible with each other in space, time, and resources; Traverse the hypergraph through breadth-first search to identify the constraint intersection area that satisfies space, time and resource constraints at the same time, and define the nodes in it as the anchor node set; A cross-layer mapping table is established to record the hierarchical correspondence between anchor nodes in the spatial region set, time layer and resource layer.

3. The method for computational modeling of action plans according to claim 2, characterized in that: Step S2 includes the following contents: First, the minimum convex polyhedron of the anchor node set in three-dimensional space is calculated, and the expanded convex polyhedron is generated by expanding it a fixed distance along the normal vector of the convex hull. The expanded convex polyhedron is then approximated as an axis-aligned hexahedral envelope lattice. Then, a resource margin function is defined within the hexahedral envelope lattice and its gradient is calculated. The sampling density is determined according to the gradient, so that the sampling density in areas with drastic resource changes is higher than that in areas with gentle resource changes. Finally, a non-uniformly distributed grid point set is generated within the hexahedral envelope lattice based on the sampling density to form a candidate grid point grid.

4. The method for computational modeling of action plans according to claim 3, characterized in that: Step S3 includes the following contents: The taboo duration of paths in the taboo table is dynamically adjusted according to the global stability factor, where the global stability factor is generated by the comprehensive calculation of the path phase dispersion and the energy dissipation gradient. Subsequently, a phase-coded taboo walk iteration is performed. By encoding the paths as phase vectors and randomly walking in the phase space, paths or nodes not recorded in the taboo table are preferentially selected. The taboo table is updated in real time during the iterative process to suppress loops, and finally converges to an elite path cluster with a satisfactory global stability factor value.

5. The method for computational modeling of action plans according to claim 3, characterized in that: Step S3 includes the following contents: For each node on the candidate path, the time difference and spatial difference between it and the next node are calculated. Then, the average of the time differences of all node pairs and the average of the spatial differences of all node pairs are calculated. Next, for each node pair, the absolute value of the difference between its time difference and the average of all time differences, as well as the absolute value of the difference between its spatial difference and the average of all spatial differences, are calculated and multiplied to obtain the product of each node pair. Finally, the products of all node pairs are accumulated to obtain the path phase dispersion, which quantifies the fluctuation of the path in time and space.

6. The method for computational modeling of action plans according to claim 3, characterized in that: Step S3 includes the following contents: The energy dissipation gradient is calculated as follows: for each node on the candidate path, its resource consumption value is determined; then, for adjacent nodes, the absolute value of the difference in resource consumption between the two is calculated, and the maximum absolute value of resource consumption among all adjacent node pairs is found; then, the absolute value of the resource consumption difference of each adjacent node pair is multiplied by the maximum absolute value of resource consumption of all adjacent node pairs to obtain the product for each adjacent node pair; finally, the products of all adjacent node pairs are accumulated to obtain the energy dissipation gradient to quantify the change in resource utilization of the path.

7. The method for computational modeling of action plans according to claim 4, characterized in that: Step S4 includes the following contents: By inputting the elite path cluster into the symplectic time window rearrangement operator for timing optimization, the time coordinates of the path nodes are adjusted to meet the task timing window requirements. Then, the conjugate gradient sliding strategy is used to gradually reduce the timing deviation between multiple platforms by calculating the sensitivity of the coordination margin to the time coordinate and iteratively adjusting the time coordinate along the conjugate direction until the coordination margin converges to the preset timing tolerance threshold. Finally, a timing path containing the corrected time coordinates is output to ensure that multiple platforms arrive at the coordinated positioning point synchronously.

8. The method for computational modeling of action plans according to claim 7, characterized in that: Step S4 includes the following contents: After each iteration, the arrival time deviation of multiple platforms at the collaborative positioning point, i.e., the collaborative margin, is recalculated. When this deviation is less than or equal to the preset timing tolerance threshold, it is determined that the time coordinate adjustment has met the requirements and the iteration is stopped.

9. The method for computational modeling of action plans according to claim 8, characterized in that: Step S5 includes the following contents: By inputting the timing path into the confrontation prediction simulation unit, multiple simulation calculations are performed in the dynamic obstacle disturbance field to calculate the survival probability, and then compare the survival probability with the preset survival probability threshold. When the survival probability is greater than or equal to the preset survival probability threshold, the timing path is solidified into the final command sequence.

10. A computerized modeling system for an action plan, for implementing the computerized modeling method for an action plan according to any one of claims 1 to 9, characterized in that: include: Hypergraph modeling module, grid generation module, path optimization module, timing correction module and survival verification module; Hypergraph modeling module: This module constructs a multi-constraint hierarchical hypergraph that integrates spatial area distribution, task timing windows, and platform resource status in a 3D dynamic map. It then extracts anchor node sets by traversing all constraint intersection areas and establishes a cross-layer mapping table. Grid generation module: Based on the anchor node set, the convex hull relaxation boundary expansion calculation is first performed to generate a hexahedral envelope grid, and then the resource margin gradient is used to guide the non-uniform grid sampling to form a candidate grid grid; Path Optimization Module: For each candidate grid, the path phase dispersion and energy dissipation gradient are calculated. The global stability factor is obtained by combining the two. The tabu table weights are dynamically adjusted according to the factor, and then a phase-coded tabu roaming iteration is performed. During the iteration, the tabu table is recorded in real time to suppress loops and converge to the elite path cluster. Timing Correction Module: This module inputs the elite path cluster into the symplectic time window rearrangement operator and uses the conjugate gradient sliding strategy to correct the time coordinates of each path node. This module outputs the timing path after the cross-platform coordination margin converges to the allowed interval. Survival verification module: Inject the timing path into the confrontation prediction simulation unit, cyclically calculate in the dynamic obstacle disturbance field and test it with the survival probability threshold. When the requirements are met, the timing path is solidified as the final command sequence.

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