An efficient system dynamics modeling method for UAV swarm based on hadamard product

Abstract

This invention discloses an efficient system dynamics modeling method for UAV swarms based on the Hadamard product, belonging to the technical field of UAV swarm dynamics modeling. The method includes: constructing a Riemannian geometric computation system for the UAV swarm; establishing individual UAV interaction models; aggregating the individual interaction models into a unified tensor differential equation system; performing evolutionary solving of the tensor differential equation system; designing a humanoid intelligent hierarchical control architecture, embedding it into the swarm system dynamics model, and achieving intelligent control with autonomous adaptation and swarm collaboration capabilities. This invention significantly improves swarm operation capabilities in complex and denied environments, achieves efficient real-time simulation and control of ultra-large-scale swarms, and endows the swarm with humanoid intelligent collaboration and dynamic adaptation capabilities.

Description

Technical Field

[0001] This invention belongs to the technical field of UAV swarm dynamics modeling, specifically relating to an efficient UAV swarm system dynamics modeling method based on the Adama product. Background Technology

[0002] With the rapid development of UAV swarm technology and its expanding applications in complex environments, existing swarm cooperative control and dynamics modeling methods have gradually revealed the following key shortcomings: First, existing dynamic models have inherent limitations in complex geometric environments. Traditional UAV swarm dynamic models are generally based on the Euclidean space assumption and rely on vector operations in the Cartesian coordinate system. In real-world environments with significant curvature or complex topology, Euclidean distance and straight-line paths cannot accurately describe the true geometric relationships between entities, leading to directional and amplitude deviations in distance-based interaction force models. This can result in control failure, trajectory deviation, and even collision risks. Existing methods lack an inherent geometric framework to ensure the universality and consistency of motion laws in arbitrarily curved spaces.

[0003] Second, real-time computational efficiency and scalability are low in large-scale cluster simulation and control. As cluster size increases, traditional centralized or Euclidean-based distributed architectures face severe challenges in computational complexity. Existing numerical integration methods do not fully consider geometric constraints on manifolds, leading to accumulated errors during position and velocity updates, and making it difficult to achieve real-time simulation while maintaining accuracy. Furthermore, existing parallel computing schemes often lack in-depth optimization for specific operations on manifolds, failing to fully utilize the potential of modern heterogeneous computing hardware such as GPUs, thus limiting the feasibility of real-time control and simulation for ultra-large-scale clusters.

[0004] Third, swarm intelligence is limited, lacking adaptive collaboration and advanced decision-making capabilities. Existing collaborative control relies heavily on preset rules or simple local interactions, lacking human-like perception, understanding, contextual reasoning, role negotiation, and online learning abilities. In dynamic and unknown environments, the system cannot autonomously adjust interaction strategies, reallocate tasks, or optimize group behavior patterns based on real-time situations. Furthermore, traditional methods struggle to fuse and understand multi-source heterogeneous perceptual information within a unified geometric-semantic framework, resulting in delayed decision-making, poor adaptability, and an inability to meet the demands of intelligent collaboration in highly dynamic and adversarial scenarios. Summary of the Invention

[0005] The purpose of this invention is to address the above-mentioned shortcomings in the prior art by providing an efficient system dynamics modeling method for UAV swarms based on the Adama product, so as to solve the problems of inherent limitations of existing UAV dynamics models in complex geometric environments and low real-time computational efficiency in large-scale swarm simulation and control.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: An efficient system dynamics modeling method for unmanned aerial vehicle (UAV) swarms based on the Adama product includes the following steps: S1. Constructing the Riemannian geometric operation system for UAV swarms: Define the Riemannian manifold of UAV swarms, introduce exponential mapping, logarithmic mapping and geodesic distance as basic geometric operators, and extend the Hadamard product and shrinkage operator to the manifold tangent vector field; S2. Establish a single UAV interaction model: Define three types of interaction force models based on the geodesic distance, and establish a hierarchical force activation mechanism in combination with the Riemann indicator function, and introduce a random perturbation model on the manifold using covariant derivatives. S3. Construct a dynamic model of the bee colony system: Introduce a relative position tensor, and use the extended Adama product and shrinkage operator to aggregate the individual UAV interaction model into a unified set of tensor differential equations; S4. Distributed solution of the model: The Riemann numerical integration algorithm is used to solve the tensor differential equation system, and an evolutionary solution is performed by combining a distributed architecture and a heterogeneous hardware optimization strategy. S5. Based on the Riemannian geometric operation system, a humanoid intelligent hierarchical control architecture is designed and embedded into the dynamic model of the bee colony system to achieve intelligent control with autonomous adaptation and group cooperation capabilities.

[0007] Furthermore, step S1 includes the following sub-steps: S11. Define the Riemannian manifold in which the UAV swarm moves, and introduce exponential mapping, logarithmic mapping and geodesic distance as basic geometric operators; S12. Based on logarithmic mapping, construct the relative displacement matrix and geodesic distance matrix of unmanned pairs on the manifold; S13. Redefine the Hadamard product based on parallel translation to obtain the Riemann Hadamard product; S14. Extend the shrinking operator to the tangent vector field of the manifold to realize matrix-based batch operations on the manifold.

[0008] Furthermore, in S14, the shrinking operator unifies vectors distributed in different tangent spaces into a reference tangent space through parallel shifting.

[0009] Furthermore, step S2 includes the following sub-steps: S21. Based on covariant derivatives, establish a fundamental model of UAV dynamics on a Riemannian manifold: S22. Based on geodesic distance, three types of interaction force models are defined, including short-range repulsive force model, medium-range attractive force model, and long-range directional attractive force model; S23. Set the action distance threshold and activation conditions for various interactive forces, and establish a hierarchical force activation mechanism based on the Riemann indicator function; S24. Using covariant derivatives, a random perturbation model on a Riemannian manifold is introduced, and based on the parallel shift operator, the covariant derivative calculation equation for the random perturbation term is obtained.

[0010] Furthermore, in S23, the layered force activation mechanism is specifically as follows: when the geodesic distance between UAVs is less than the safe distance, only the near-range repulsive force is activated; when the geodesic distance between UAVs is within the attractive force range, the near-range repulsive force is turned off, and the mid-range attractive force is activated; when the geodesic distance between UAVs is within the directional force range, the mid-range attractive force is turned off, and the far-range directional force is activated.

[0011] Furthermore, step S3 includes the following sub-steps: S31. Establish the state matrix and velocity state matrix of the UAV swarm, and construct the relative position tensor based on logarithmic mapping and parallel movement operator; S32. Construct a distance relationship matrix between UAVs based on geodesic distance; S33. Based on the relative position tensor and distance relationship matrix, the three types of interaction force models are expressed in matrix form, and the matrix-formed three types of interaction force models are aggregated by the Riemann-Hadamard product and the shrinking operator. S34. Construction of the overall dynamic equations: Integrating virtual viscous friction, external task control force, interactive resultant force and random disturbance to establish a unified set of tensor differential equations.

[0012] Furthermore, in step S33, the three types of interaction force models are expressed in a matrix format; For the near-range repulsive force model, the relative position tensor and distance relationship matrix are matrixed into a repulsive force interaction matrix. For the mid-range attraction model, based on the relative position tensor and the distance relationship matrix, it is matrixed into a gravitational interaction matrix; For the long-distance directional attraction model, based on the relative position tensor and the distance relationship matrix, it is matrixed into a directional force interaction matrix; The total repulsive force is calculated using the Riemann-Hadamard product, the contraction operator, and the repulsive force interaction matrix. The total attractive force is calculated using the Riemann-Hadamard product, the contraction operator, and the gravitational interaction matrix. The total directional force is calculated using the Riemann-Hadamard product, the contraction operator, and the interaction matrix of the directional force. The total repulsive force, total attractive force, and total directional force are superimposed to obtain the interactive resultant force.

[0013] Furthermore, step S4 includes the following sub-steps: S41. For the tensor differential equation system, design a Riemann numerical integration algorithm, including the Riemann-Euler method and the Riemann-Verlet method, to achieve the coordinated update of position and velocity on the manifold. S42. For parallel solving of tensor differential equations, a distributed computing architecture is developed, which groups and distributes the drone swarm to multiple computing nodes to optimize the computing performance of large-scale clusters. S43. To address the high computational load of tensor differential equation systems, a multi-hardware platform deployment strategy is adopted, including parallel computing optimization using single-core CPUs, multi-core CPUs, and GPUs. S44. Construct a simulation engine and process management system to drive the solution of tensor differential equations, drive the solver to run and manage the simulation process and data output.

[0014] Furthermore, step S5 includes the following sub-steps: S51. Design a humanoid intelligent hierarchical control architecture, construct a three-layer structure of perception and understanding, decision-making and reasoning and execution control, and achieve geometrically consistent integration with the single UAV interaction model and the swarm system dynamics model; S52. In the decision reasoning layer, attention mechanism and semantic rule base are integrated to generate decision commands based on the motion characteristics and scene semantics of the drone swarm, supporting real-time environment understanding and behavior selection. S53. Establish a group humanoid collaboration and role negotiation mechanism. Based on the parallel movement operator, dynamic task allocation and intention synchronization are achieved through role vectors on the manifold and parallel movement. S54. Develop an online learning and adaptive policy optimization module to parameterize the control policy as a mapping function on the parametric manifold; calculate the policy update direction based on the Riemann policy gradient theorem, use the parallel shift operator to correct the first and second moment estimates of the gradient, construct a Riemann adaptive moment estimator optimizer, and iteratively update the policy parameters on the parametric manifold through exponential mapping to achieve continuous adaptation to the environment.

[0015] The efficient system dynamics modeling method for UAV swarms based on the Adama product provided by this invention has the following beneficial effects: (1) This invention significantly improves swarm operation capabilities in complex and denied environments. In mountainous, canyon, or indoor environments, swarms based on this invention can maintain high-precision formation flight even in completely GPS denied environments, relying solely on relative ranging and inertial measurement. Compared to the formation divergence and collision accidents that occur with traditional Euclidean models in the same environment, this method solves the problem of missing absolute coordinates through manifold geometry, enabling swarms to have independent and reliable collaborative operation capabilities in key scenarios such as electronic warfare and underground rescue.

[0016] (2) This invention achieves efficient real-time simulation and control of ultra-large-scale clusters, breaking through the scale bottleneck. In simulation verification, the traditional method takes more than 5 seconds to calculate one step for 10,000 UAVs, while the distributed Riemann solver of this invention, combined with GPU acceleration, reduces the calculation time to less than 0.8 seconds at the same accuracy, meeting the real-time requirements. Actual test data shows that the system simulates 5,000 UAVs on 128 computing cores, and the strong scalability efficiency remains above 75%, demonstrating its excellent scalability and providing a computational foundation for the practical application of "swarm" tactics.

[0017] (3) It endows the cluster with human-like intelligent collaboration and dynamic adaptability. In multi-target dynamic encirclement scenarios, the cluster using the intelligent control module of this invention has a shorter average task completion time than the cluster based on fixed rules. The system can learn online and adapt to sudden situations such as sudden changes in wind speed and damage to some units. It can complete formation reconstruction and task redistribution within 30 seconds through role renegotiation, demonstrating strong autonomy and robustness.

[0018] (4) Provides accurate and consistent basis for spatial structure evaluation and closed-loop optimization. The configuration evaluation index based on Riemannian metric proposed in this invention realizes real-time quantitative feedback on the "orderliness" of the formation in the automatic aerial array assembly task. It does not change with the observation angle, overall formation rotation or translation, providing key technical support for the automated and high-precision construction of large-scale aerial physical structures.

[0019] (5) Reduce reliance on high-precision global infrastructure and enhance system deployment flexibility and resilience. This invention does not rely on an externally provided global absolute coordinate system; the cluster can establish a consistent geometric context through internal relative perception. This greatly reduces the system's dependence on vulnerable infrastructure such as satellites and ground base stations, and enhances its survivability and continuous combat capability in highly confrontational environments. Attached Figure Description

[0020] Figure 1 The flowchart illustrates an efficient system dynamics modeling method for unmanned aerial vehicle swarms based on the Adama product. Detailed Implementation

[0021] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0022] This embodiment presents an efficient system dynamics modeling method for UAV swarms based on the Adama product, referencing... Figure 1Specifically, it includes the following: S1. Constructing the Riemannian geometric computation system for UAV swarms: Define the Riemannian manifold of the UAV swarm, introduce exponential mapping, logarithmic mapping, and geodesic distance as basic geometric operators, and extend the Hadamard product and contraction operators to the tangent vector field of the manifold; specifically, it includes the following sub-steps: S11. Define the Riemannian manifold in which the UAV swarm moves, and introduce exponential mapping, logarithmic mapping and geodesic distance as basic geometric operators; Define the Riemannian manifold upon which the drone swarm motions reside, to describe the state of the drones at each point. Specifically, define the Riemannian manifold as a smooth manifold equipped with a Riemannian metric, that is, a positive definite symmetric bilinear form defined on each tangent space: In the formula, Represented as 3D smooth manifold, Represented as a point The tangent space at the point, Represented as at point Riemannian metric at that location It is a real number; Based on this, the state of the drone can be represented as: No. Location of the drone: ; No. The speed of the drone: , For point The tangent space at the point; Overall location status of the bee colony: , For the first The location of the drone; Number of drones; The core tools of exponential and logarithmic mappings are defined as the ensemble basis for modeling; In the representation of the exponential map for a point and drone speed ,index Defined as: In the formula, For definition in The exponential mapping function, For geodesics, Represent a unique geodesic that satisfies: , , This indicates that the initial velocity of the geodesic is defined as... ; In the representation of logarithms, for a point And at point There is a unique geodesic connection within its neighborhood. and Then the logarithmic mapping Defined as: In the formula, From point Time Direction mapping, ; tangent vector The Riemann norm, For the norm based on the Riemannian metric; point With point The geodesic distance between two points is: In the formula, Indicates geodesic distance.

[0023] S12. Based on logarithmic mapping, construct the relative displacement matrix and geodesic distance matrix of unmanned aerial vehicle pairs on a manifold; generalize the simple coordinate difference operation in Euclidean space to a geometric operation on a Riemannian manifold. Specifically, the relative displacement matrix is ​​constructed on the Riemannian manifold, assuming the position and state of the UAV swarm. Define the relative displacement matrix for: In the formula, For drones Pointing to drones The vector, which is located on the drone tangent space In this context, the length of the vector is equal to the geodesic distance. ; To be from point Time Direction mapping, manifold At point The tangent vector at the point; Let be the relative displacement matrix, which is a Matrix; From point Time Direction mapping, From point Time Direction mapping, From point Time Direction mapping, From point Time Direction mapping, From point Time Direction mapping, From point Time Direction mapping, From point Time Direction mapping, From point Time Direction mapping, From point Time Direction mapping; Geodesic distance matrix For one The matrix is ​​represented as: In the formula, For drones With drones Geodetic distance between them; For drones With drones Geodetic distance between them; The geodetic distance between UAV 2 and UAV 1. For drones Geodetic distance between UAV 1 and UAV 1 The geodetic distance between UAV 1 and UAV 2. For drones Geodetic distance between UAV 2 and UAV 2 For drone 1 and drone Geodetic distance between them For drone 2 and drone Geodetic distance between them; S13. Based on parallel translation, the Hadamard product is redefined to obtain the Riemann Hadamard product; this enables it to operate on vectors located in different tangent spaces, and parallel translation is introduced to ensure the geometric consistency of the operation. Introducing parallel translation ensures geometric consistency in computation: This operator moves the tangent vector along the geodesic from point […]. The tangent space moves to the point The tangent space, keeping the inner product unchanged: In the formula, From point Time Parallel translation operator, Let be a vector in the tangent space. For tangent space Any two vectors in the array; Three reference frame strategies are used: row reference frames are based on each row's reference point. As a baseline, the column reference frame uses the base point of each column. As a baseline, the global reference frame is fixed at a point. Based on; Based on this, for the tangent vector field matrix , ,in This leads to the definition of the Riemann Adama product: In the formula, The operator for the Riemann-Hadamard product. The matrix resulting from the Riemann-Hadamard product is the first... line, number Column elements; For located in tangent space The vector, For the Riemann tensor product; From point Time Parallel translation operator, For located in tangent space ; Verify covariance under isometric transformation: In the formula, For isometric transformations on a manifold, This corresponds to the forward mapping; Application of Riemann-Hadamard product in UAV interaction force calculation: In the formula, For the repulsive force matrix, The repulsive force coefficient, It is the -5th power pseudoinverse of the distance matrix. This is the repulsive force indicator function matrix based on the square of the geodesic distance.

[0024] S14. Extend the shrinking operator to the manifold tangent vector field to realize matrix-based batch operations on the manifold; Specifically, we define the Riemann contraction operator, which unifies vectors distributed in different tangent spaces to a reference tangent space through parallel translation: Line-wise indentation is represented as: In the formula, This is the column vector obtained by row-wise consolidation. For column number From 1 to Perform aggregation operations. From To the reference point Parallel translation operator, For matrix The first line, the Column elements, For matrix The line, number Column elements; Dimensions are matrices; In the shrinking operator, column shrinking is represented as: In the formula, This is the row vector obtained by column shrinking. For matrix The Row, first column element For matrix The line, number Column elements.

[0025] Applying the Riemannian contraction operator to calculate resultant force in UAV swarm dynamics: In the formula, , The total repulsion vector acting on each drone. , The interaction force matrix between unmanned aerial vehicles; Construct the overall dynamic equations for a single UAV: In the formula, For the quality of drones, For position vectors, For virtual viscous friction, For external task control, For interactive synergy, It is a random perturbation.

[0026] S2. Establish a single UAV interaction model: Define three types of interaction force models based on the geodesic distance, establish a hierarchical force activation mechanism in conjunction with the Riemann indicator function, and introduce a stochastic perturbation model on the manifold using covariant derivatives; specifically, it includes the following sub-steps: S21. Based on covariant derivatives, establish a fundamental model of UAV dynamics on a Riemannian manifold: In the formula, The covariant derivative of the velocity vector along its own direction; Define the forces in the dynamic equations: Virtual viscous friction: External task control: Interactive Synergy: Random perturbation: In the formula, The coefficient of friction, For velocity vectors, , To control the gain, , For the desired position and desired velocity, For the disturbance intensity, It is a close-range repulsive force. For mid-range attraction, For long-distance directional attraction; This is a white noise process.

[0027] Calculation of covariant derivatives based on the Levi-Civita connection: In the formula, For the actual acceleration of the manifold, For coordinate acceleration, coordinates speed, coordinates speed; Christoffel notation, derived from the Riemannian metric: In the formula, for The inverse matrix components, coordinates Partial derivatives, For coordinates The Riemann tensor under the current conditions coordinates Partial derivatives, For coordinates The Riemann tensor under the current conditions coordinates Partial derivatives, For coordinates The Riemann tensor below; This structure guarantees the geometric invariance of the dynamic equations on the manifold.

[0028] S22. Based on geodesic distance, three types of interaction force models are defined, including short-range repulsive force model, medium-range attractive force model, and long-range directional attractive force model; The close-range repulsive force model is represented as: In the formula, The Riemann indicator function of the repulsive force. For drones and Geodetic distance between The square of; It is the repulsive force coefficient; The mid-range attraction model is represented as: In the formula, The attractiveness coefficient; For the Riemann indicator function of attraction; The long-distance directional attraction model is represented as: In the formula, For directional force coefficient, Let be the unit tangent vector along the geodesic line. The Riemann indicator function for the directional force; S23. Set the action distance threshold and activation conditions for various interactive forces, and establish a hierarchical force activation mechanism based on the Riemann indicator function; Three types of interactive forces are used to set action distance threshold parameters to establish a complete distance activation mechanism. First, the safe distance threshold for repulsive forces is set: in, The maximum safe distance for repulsive force is when the square of the geodesic distance between the two UAVs is less than 1. At this time, the repulsive force is activated. This parameter is determined based on the physical dimensions of the UAV and its safety margin.

[0029] Set the effective range of the attraction: in, and These distances constitute the lower and upper limits of the attraction's effect; within this range, the attraction is effective. It is usually set to slightly greater than , Determined based on desired cluster density and communication range.

[0030] Finally, the effective range of the directional force is set: In the formula, This is the maximum effective distance of the directional force, where drones outside the attractive force range but still within the perception range generate a directional attractive force between them. This parameter is determined by the maximum detection range of the drone's sensors.

[0031] After setting the threshold and activation conditions, a Riemann indicator function needs to be constructed and an activation mechanism set. The Riemann indicator function is constructed based on the square of the geodesic distance to ensure correct activation in curved space. For the repulsive force indicator function: For the attraction indicator function: For the directional force indication function: In the formula, This is an indicator function that takes the value 1 when the condition is met, and 0 otherwise; The layered force activation mechanism is as follows: when the geodesic distance between UAVs is less than the safe distance, only the near-range repulsive force is activated; when the geodesic distance between UAVs is within the attractive force range, the near-range repulsive force is turned off, and the mid-range attractive force is activated; when the geodesic distance between UAVs is within the directional force range, the mid-range attractive force is turned off, and the far-range directional force is activated. This layered mechanism avoids conflicts between different forces and ensures a smooth transition in the interaction between UAVs.

[0032] S24. A stochastic perturbation model on a Riemannian manifold is introduced using covariant derivatives, and based on the parallel shift operator, the covariant derivative calculation equation of the stochastic perturbation term is obtained to improve the stochastic factor description of the system dynamics equation. First, we define a perturbation model based on stochastic differential equations: In the formula, For random disturbance increments, The Brownian motion increment ensures the geometric consistency of random perturbations on the manifold.

[0033] The specific expression for the random perturbation force is: In the formula, The covariant derivative of a random perturbation process with respect to the population, and the perturbation strength. It can be represented as a time-varying function, where The attenuation coefficient is... Steady-state disturbance strength: In the formula, The initial disturbance intensity; After constructing the random perturbation model, we concretely realize the geometric properties of the random perturbation on the Riemannian manifold, and obtain the equation for calculating the covariant derivative of the random perturbation term: In the formula, for The total random disturbance at time t. For parallel translation operators along the trajectory, the geometric properties of random perturbations on the manifold are preserved; In order to be in The random disturbance that constantly acts on the drone For time step, It is standard Gaussian white noise.

[0034] S3. Construct a dynamic model of the bee colony system: Introduce a relative position tensor, and use the extended Adama product and shrinkage operator to aggregate the individual interaction model into a unified set of tensor differential equations. S31. Establish the state matrix and velocity state matrix of the UAV swarm, and construct the relative position tensor based on logarithmic mapping and parallel movement operator; First, the state matrix is ​​mathematically defined and constructed to establish a complete mathematical description system for the state matrix of the UAV swarm, defining the absolute position state matrix: In the formula, Indicates the location and status of the entire bee colony; Define the velocity state matrix: The state matrix is ​​constructed by stacking column vectors to ensure dimensional consistency in matrix operations.

[0035] The complete construction process of the relative position tensor includes: calculating the logarithmic mapping between all UAV pairs, forming The tangent vector field matrix; then the calculation process is optimized by using an all-one matrix E and transpose operations: In the formula, Represented as the extended Adama product, it ensures dimension matching.

[0036] To ensure the correctness of matrix operations on Riemannian manifolds, a geometric consistency guarantee mechanism needs to be established. This can be achieved by introducing a unified reference frame strategy to address the problem of operations on vectors in different tangent spaces. The first step is to unify all relative position vectors to the row frame of the row base point tangent space: In the formula, For observations from the UAV in the line reference frame Pointing to drones ; Secondly, all relative position vectors are unified to the column reference frame of the column base point tangent space: In the formula, For observations from the UAV in the reference frame Pointing to drones ; Integrating the above positions yields a result that unifies all relative position vectors to a global reference point. Unified global reference frame for tangent space: In the formula, For observations from a UAV in a fixed global reference frame Pointing to drones ; From point Time Parallel translation operator, For function coincidence operators, From point Time Parallel translation operator; This embodiment ensures the covariance of relative position descriptions under manifold transformations by leveraging the isometry and linearity of the parallel translation operator, providing a geometrically consistent framework for subsequent matrix operations.

[0037] S32. Construct a distance relationship matrix between UAVs based on geodesic distance; First, we establish a complete mathematical description system for the relative distance matrix, defining the geodesic distance square matrix: in, for A symmetric matrix, Indicates drone With drones The square of the geodesic distance between them For point Riemannian metric tensor at that location. It is a norm based on the Riemannian metric.

[0038] Define the geodesic distance matrix: in, For point With point The geodesic distance between them, the diagonal elements of the distance matrix satisfy =0 indicates that the distance between the drone and itself is zero, and the matrix has symmetry. This reflects the reciprocity of distance relationships.

[0039] Calculation of squared geodesic distance based on relative position tensor: In the formula, Riemannian metric tensor at a point The component at that location, The relative position vector of the th For each component, an optimized calculation process is adopted in the specific numerical calculation: In the formula, This indicates the extraction of diagonal elements from a matrix. The Riemannian metric tensor matrix is... The relative displacement matrix The transpose of .

[0040] S33. Based on the relative position tensor and distance relationship matrix, the three types of interaction force models are expressed in matrix form, and the matrix-formed three types of interaction force models are aggregated by the Riemann-Hadamard product and the shrinking operator. The three types of interaction force models are represented in a matrix format. For the close-range repulsive force model, it is matrixed into a repulsive force interaction matrix: For the mid-range attraction model, it is matrixed into a gravitational interaction matrix: For long-distance directional attraction models, the matrix transformation is into a directional force interaction matrix: In the formula, The repulsive interaction matrix, It is the -5th power pseudoinverse of the distance matrix. The gravitational interaction matrix, It is the -3rd power pseudoinverse of the distance matrix. This is the attractive force indicator function matrix based on the square of the geodesic distance; For directional interaction matrix, The direction unit vector matrix, This is the orientation force exponential function matrix based on the square of the geodesic distance; The total repulsive force is calculated using the interaction matrix between the Riemann-Hadamard product and the repulsive force: The total attractive force is calculated using the Riemann-Hadamard product and the gravitational interaction matrix: The total directional force is calculated using the interaction matrix between the Riemann-Hadamard product and the directional force: The three types of interactive forces combine to form a combined interactive force: In the formula, The total number of drones in the cluster. For drones The repulsive force vector generated by UAV 1 For drones For the The repulsive force vector generated by the drone; In this embodiment, all force vectors lie in a unified tangent space. In M, the geometric correctness of vector addition is ensured.

[0041] S34. Construction of the overall dynamic equations: Integrating all force terms to establish a unified set of tensor differential equations, and completing the system-level dynamic model; Based on the generalization of Newton's second law to Riemannian manifolds, we construct the matrix-form dynamic equations: in, The second derivative of the position matrix represents the acceleration field, specifically the covariant acceleration; Within the Riemannian geometric framework, the acceleration term is expressed using covariant derivatives: This expression ensures the geometric invariance of the dynamic equations on the manifold.

[0042] After constructing the mathematical framework, it is necessary to present the specific expressions and integration methods of each force term in the dynamic equations. The friction term adopts a linear damping model. The control force term is designed based on state feedback: The interactive resultant term is: The random perturbation term is based on stochastic differential equations: in, The disturbance intensity matrix, Let be the random perturbation increment matrix.

[0043] The force terms are integrated through matrix addition to form a unified dynamic description: In the formula, This represents four types of force terms, specifically virtual viscous friction. External task control Interactive synergy and random disturbances .

[0044] S4. Distributed Solution of the Model: For the tensor differential equation system, the Riemann numerical integration algorithm is used, combined with a distributed architecture and heterogeneous hardware optimization strategy for evolutionary solution; it specifically includes the following sub-steps: S41. For the tensor differential equation system, design a Riemann numerical integration algorithm, including the Riemann-Euler method and the Riemann-Verlet method, to achieve the coordinated update of position and velocity on the manifold. Specifically, we will design and implement the Euler integral algorithm on Riemannian manifolds, and establish the complete mathematical framework of the Riemann-Euler method: in, for The velocity vector at time t, Let the velocity vector be the velocity vector at the current moment. For the total force, For time step, To determine the position of the drone on the Riemannian manifold at the next moment, Let this be the current position of the drone on the Riemannian manifold. For parallel translation operators along the trajectory, This is the index mapping for the current position.

[0045] Design a more accurate Riemann-Verlet integration algorithm and establish the mathematical expression of the Riemann-Verlet method: In the formula, The displacement term caused by the current velocity. This is a correction term for the second-order displacement caused by acceleration. This is the average acceleration term based on the trapezoidal law.

[0046] Implement an adaptive step size control mechanism and perform error analysis; establish a local truncation error. estimate: In the formula, This is the precise value of the drone's position at the next moment. This is an approximate value for the drone's position at the next moment. To approximate the trajectory numerically, the error is estimated by comparing results under different time steps. The adaptive step-size control strategy dynamically adjusts the time step based on the error estimate. in, To calibrate the time step, For the error time step, With a preset error tolerance, this strategy maximizes computational efficiency while ensuring computational accuracy, achieving the best balance between accuracy and efficiency.

[0047] S42. To address the need for large-scale parallel solutions to tensor differential equation systems, a distributed computing architecture was developed, which groups and distributes the drone swarm to multiple computing nodes to optimize the computing performance of large-scale clusters. Specifically, design a distributed computing task partitioning strategy and load balancing mechanism; establish a mathematical model for computing task partitioning: In the formula, Group the drones together. Indicates allocation to the first A subset of drones with computing nodes. To calculate the number of nodes, To indicate the allocation to the first A subset of drones with computing nodes. To indicate the allocation to the first A subset of drones with computing nodes. It is an empty set; Load balancing optimization objective function design: In the formula, For minimization functions, These are the weighting coefficients. This is the communication overhead function; Establish inter-node communication protocols and data synchronization mechanisms; design boundary UAV state exchange protocols: In the formula, No. A boundary drone ensemble of computing nodes. The communication threshold distance ensures necessary data exchange between adjacent packets.

[0048] Implementation of asynchronous communication mode based on MPI: in, and These are sending and receiving operations, respectively. For the neighbor set of border drones, Due to communication delay, To enable concurrent execution, this mechanism maximizes system parallel efficiency through overlapping computation and communication.

[0049] Data synchronization consistency guarantee: In the formula, For drones In time Data Node The information on For drones In time Data Node Information on; To ensure that the same drone is in the same state across different nodes, the consistency of the distributed system is maintained through timestamp verification and conflict resolution mechanisms.

[0050] S43. To address the high computational load of tensor differential equation systems, a multi-hardware platform deployment strategy is adopted, including parallel computing optimization using single-core CPUs, multi-core CPUs, and GPUs. Specifically, the first step is to design the mathematical model for the hardware abstraction layer: In the formula, As a collection of hardware platforms, It is a single-core central processing unit. It is a multi-core central processing unit. For hardware The estimated calculation time is as follows. These are hardware-related calculation coefficients. For hardware computing power, For communication overhead, This refers to the amount of communication data.

[0051] The single-core CPU optimization implementation employs instruction-level parallelism and cache optimization strategies: In the formula, Overall performance optimized for single-core processors To vectorize the concentration, For cache hit rate, This is an optimized computing kernel; it maximizes single-core computing throughput through manual loop unrolling, data prefetching, and SIMD instruction set optimization.

[0052] Multi-core CPU parallel computing is based on the OpenMP task allocation model: In the formula For multi-core parallel speedup, For single-core serial execution time, For use Parallel execution time per processor core, For the number of processor cores, For serial ratio, To reduce the communication synchronization overhead, a dynamic load balancing algorithm is adopted to distribute computing tasks to different cores according to UAV groups, and to reduce synchronization overhead through lock-free data structures and atomic operations.

[0053] GPU-accelerated implementation of multi-level parallel architecture design: In the formula, For the network dimension, For thread block size, For the number of stream multiprocessors, For single Maximum number of threads that can be processed; This embodiment maximizes computational throughput by caching frequently accessed distance data in shared memory and reducing global memory accesses through register optimization.

[0054] Hybrid computing load distribution establishes an adaptive task scheduler: In the formula, for Calculate the load ratio. for Calculate the load ratio. for Effective computing power for Effective computing power; The computing load ratio between GPU and CPU is dynamically adjusted based on real-time performance monitoring to achieve optimal utilization of heterogeneous computing resources.

[0055] S44. Construct a simulation engine and process management system to drive the solution of tensor differential equations, drive the solver to run and manage the simulation process and data output; First, define the simulation state machine model: In the formula, It is a set of simulation states, including four basic states: initialization, running, paused, and stopped. For initialization state, In running state, It is in a paused state. It is in a stopped state; For a set of events, This is the state transition function, which triggers state transitions based on events. The simulation engine manages the simulation lifecycle using an event-driven finite state machine, ensuring the controllability and stability of the simulation.

[0056] Mathematical description and implementation of simulation loops: In the formula, For the next simulation time, For the current simulation time, The system state at the next moment. This represents the current system state. The system dynamics equations are presented; the simulation engine iteratively updates the system state through a numerical integrator and integrates a distributed computing architecture to achieve multi-node collaborative simulation. A real-time event handling mechanism allows for dynamic adjustment of parameters or response to external commands during simulation runtime.

[0057] Next, design the process manager and data output system; define the process control strategy: In the formula, It is a set of process operations, including initialization, single-step execution, data output, and checkpoint saving. For initialization operations, To perform the operation step by step, For data output operations, For checkpoint saving operations, The operation timestamp function ensures that each operation is executed according to the preset schedule. The process manager, based on a priority queue and event loop mechanism, coordinates simulation steps, data recording, and resource management, and supports the synchronization and mutual exclusion of parallel operations.

[0058] Data output and storage mechanisms: In the formula, For simulation datasets, For the position of time series, For the speed of time serialization, For time-series summation force, The total simulation time is calculated by the output system using a serialization function to convert the data into a specified format and supporting real-time streaming to the monitoring interface or subsequent analysis tools.

[0059] S5. Based on the Riemannian geometric operation system, design a humanoid intelligent hierarchical control architecture and embed it into the dynamic model of a bee colony system to achieve intelligent control with autonomous adaptation and group cooperation capabilities. This specifically includes the following sub-steps: S51. Design a humanoid intelligent hierarchical control architecture, construct a three-layer structure of perception and understanding, decision-making and reasoning and execution control, and achieve geometrically consistent integration with the single UAV interaction model and the swarm system dynamics model; This section constructs a humanoid intelligent hierarchical control architecture, designing a three-layer structure of perception and understanding, decision-making and reasoning, and execution control. This structure is seamlessly integrated into the Riemannian dynamics framework, ensuring the geometric consistency of the entire intelligent control process.

[0060] First, the mathematical framework of the hierarchical control architecture is defined as follows: In the formula, This represents a complete humanoid intelligent control architecture. This represents the perception and understanding layer. This represents the decision-making reasoning layer. Indicates the execution control layer. and These represent the information transfer and state transition operators from the perception layer to the decision layer and from the decision layer to the execution layer, respectively. These operators integrate Riemannian geometric operations such as exponential mapping, logarithmic mapping, and parallel shift, ensuring lossless information transfer on the manifold structure.

[0061] The geometric implementation of the three-layer structure is defined by the state manifold and the information mapping: In the formula, , Let these represent the manifolds containing the perceptual state and the decision state, respectively. This is the state tensor of the perception layer. For definition in Exponential mapping, The learnable humanoid decision weight matrix is ​​mapped through a fixed reference point. After performing a linear transformation in the tangent space, and then projecting back to the manifold through an exponential mapping, the modeling of human-like cognitive processes on the Riemannian manifold is realized.

[0062] A perception and understanding layer was constructed, which performs feature extraction and geometric encoding on the Riemannian manifold to form an environment understanding with geometric semantics. Its core processing flow is described by the following geometric feature extraction equation: In the formula, This represents the extracted Riemannian geometric vector. Representation based on manifold Feature extraction function, for, Indicates the current location of the drone With the One obstacle Geodetic distance between them This represents the current speed and direction of the drone. and the direction pointing to the obstacle The Riemann angle between them; This represents the number of obstacles within the perception range.

[0063] By fusing geometric features with semantic information, the final output state of the perceptual understanding layer is formed: In the formula, The final output state function of the perception and understanding layer. Encoding vectors for semantic information, This represents a multilayer perceptron implemented on a manifold, which preserves manifold constraints through affine transformations in the tangent space and exponential mappings.

[0064] Establish a geometric consistency integration mechanism between the three-layer control structure and the underlying Riemann dynamics model to ensure that the control commands generated by the humanoid intelligent decision-making can correctly and unambiguously drive the UAV's motion in curved space.

[0065] Define the output of the decision reasoning layer as the desired behavior instruction. The execution control layer is responsible for translating this into concrete control forces. The core of the integration mechanism is to establish a geometrically parallel instruction transmission and conversion link: In the formula, For the control force function, The instruction vector for the desired behavior. It is the decision point The instruction at the location is moved horizontally to the current actual position. Operators in the tangent space ensure that the geometric meaning of the command direction remains unchanged. To control the gain tensor; It is a geometric bias force used to compensate for the deviation between the desired trajectory and the actual geodesic due to the curvature of the manifold; This is the bias coefficient; Indicates the direction of current movement covariant derivative, From point Time Directional mapping.

[0066] S52. In the decision reasoning layer, attention mechanism and semantic rule base are integrated to generate decision commands based on the motion characteristics and scene semantics of the drone swarm, supporting real-time environment understanding and behavior selection. This section implements a human-like attention mechanism based on Riemannian manifolds. By quantifying the geometric correlation between different targets in the environment and the current decision, it simulates the human selective attention mechanism, providing dynamically weighted information input for intelligent behavior selection. Defined at time... drones Targets in the environment attention weights The calculation model is as follows: In the formula, Indicates drone At any moment For the target The normalized attention weight scalar, , They represent drones With the goal In the Riemannian manifold The position above; ) is from point Time The direction mapping is located in the tangent space. ; The unit tangent vector representing the direction of the UAV's current mission objective; Indicates at time drones The set of perceived neighbors; From point Time Direction mapping, For point With point Geodesic distance between two points For point With point The geodesic distance between two points; A human-like behavior selection mechanism based on a semantic rule base is established to transform high-level task instructions and geometric environmental perception into specific control behaviors, and to achieve real-time optimal decision-making through multi-objective optimization.

[0067] Define a single rule in the semantic rule base It is in the following form: In the formula, To identify the first Semantic rules, For conditional logic, For drones In carving The state of perception and understanding; For the first The conditional function of the rule, The conditional function is a Boolean function based on manifold geometry predicates. For the first The action function of the rule, This is a rule-based action function, which maps to a specific control behavior vector.

[0068] Based on attention weights and activation rules, the final behavioral decision is generated through weighted fusion and optimization selection: In the formula, drones At any moment The selected control vector for optimal behavior; This represents the set of candidate actions corresponding to all currently activated semantic rules; For candidate control behavior vectors Attention weights; Indicates neighboring drones The reference behavior vector. It is to transfer vectors from neighbors The tangent space is moved parallel to the current drone. Operators in the tangent space ensure vector additivity; ( ) represents the wind direction cost function. , These are non-negative scalar weighting coefficients.

[0069] S53. Establish a group humanoid collaboration and role negotiation mechanism. Based on the parallel movement operator, dynamic task allocation and intention synchronization are achieved through role vectors on the manifold and parallel movement. This embodiment establishes a role description and task allocation mechanism for UAV swarms on a Riemannian manifold. By defining geometric role vectors and matching them with task requirements, it achieves dynamic and reasonable task division in a human-like swarm. The role of an individual UAV is represented by a role vector located in its own tangent space, which encapsulates the type of task it is currently undertaking and its capability attributes. For the... The drone, its role vector The definition is as follows: In the formula, Indicates drone The normalized role vector, located at its current position. tangent space In the middle. The direction of this vector encodes specific role semantics in manifold geometry, norm constraints. This ensured the consistency of character representation.

[0070] Based on role vectors and task requirements, dynamic task allocation is modeled as a Riemann optimization problem. Assume there exists... Each task There is a global reference tangent space Demand vector defined in The goal is to assign a task to each drone, such that the roles of all drones match the requirements of their assigned tasks as closely as possible; this optimization problem is formulated as follows: In the formula, Denotes the set of decision variables for task allocation, where =1 indicates that the task will be completed. Assigned to drones Otherwise, it is 0; It involves moving the character vector from the individual tangent space to the global reference point in parallel. Operators for tangent spaces are used to make vectors in different tangent spaces comparable. Indicates in tangent space According to the Riemann metric Calculate geodetic distance; It is a task A fixed demand vector; It is a task The maximum number of drones that can be accommodated.

[0071] To achieve consensus on group intent, a consensus algorithm based on diffusion processes on a manifold is adopted; each drone updates its own role vector according to the role vectors of its neighbors, with the following update rules: In the formula, For drones The instantaneous rate of change For drones The role vector, drones Role vector; When the task environment or group state changes, a dynamic role switch needs to be triggered. The role switch condition is defined as a function based on local information: In the formula, It is an indicator function that triggers the drone when its value is 1. The role switching occurs between the drone and the dynamic target. The switching conditions consist of two parts: first, the drone and the dynamic target... The geodetic distance is less than the threshold. This indicates either the task has been accomplished or the goal has changed; secondly, it indicates any neighbor. Interactive force The range exceeds the threshold This indicates a significant change in the interaction conflicts or cooperation needs under the current role.

[0072] S54. Develop an online learning and adaptive policy optimization module to parameterize the control policy into a mapping function on the parametric manifold; calculate the policy update direction based on the Riemann policy gradient theorem, use the parallel shift operator to correct the first and second moment estimates of the gradient, construct a Riemann adaptive moment estimator optimizer, and iteratively update the policy parameters on the parametric manifold through exponential mapping to achieve continuous adaptation to the environment. First, define the parameterized strategy function. as follows: In the formula, The total number of learnable parameters of a policy exists in a parameter manifold. superior, For base point mapping neural network parameters, The parameters are linear parameter matrices; For parameterized strategy functions; For parameters The parameterized strategy function is set below; To perceive the state space; It is a neural network that maps states to base points on a manifold; It is a certain characteristic representation of a state; From the base point to feature point The logarithmic mapping results in a tangent vector; It is a parameterized linear transformation matrix; It is an exponential mapping that maps the tangent vector back to a point on the manifold; this is used here to correct and ensure the output geometric properties. Strategy performance is determined by expected cumulative reward. Measured by its Riemann gradient Located in parametric manifold tangent space Based on the Riemann generalization of the policy gradient theorem, the gradient calculation formula is as follows: In the formula, In the parametric manifold The above about The Riemann gradient operator; Representation Strategy Lower trajectory Expectations; This represents a trajectory from the initial state to the final state; At any moment parameters At this point, the Riemann gradient of the policy logarithmic probability; From time Initial discount cumulative rewards, As a discount factor, For instant rewards. It is to transfer the vector from The tangent space at the point is moved parallel to the point. Operators for tangent space.

[0073] To address the learning rate selection and ill-conditioned curvature issues in Riemann gradient descent, a Riemann adaptive moment estimation optimizer is constructed. This optimizer operates within the parameter manifold. Maintaining first-order moment estimates in the tangent space and second-order moment estimation In each iteration In the given parameters The tangent space is then used to calculate a weighted average with the current gradient. This ensures the geometric consistency of the moment estimate: In the formula, They represent the iterations respectively. The first and second moment estimation vectors at time. It is the attenuation rate hyperparameter. In iteration The first moment of time, From point Time Parallel translation operator, For iteration Second-order moment estimation vector, In iteration Riemannian measurement of time and place; The parameters are updated along the manifold using the corrected moment estimate: In the formula, These are the updated strategy parameters; It is at point Exponential mapping at the location; The initial learning rate; for, for; It is a very small positive number used to maintain numerical stability.

[0074] Although specific embodiments of the invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of this patent. Various modifications and variations that can be made by a person skilled in the art without inventive effort within the scope described in the claims still fall within the scope of protection of this patent.

Claims

1. A method for efficient system dynamics modeling of UAV swarm based on Hadamard product, characterized in that, Includes the following steps: S1. Constructing the Riemannian geometric operation system for UAV swarms: Define the Riemannian manifold of UAV swarms, introduce exponential mapping, logarithmic mapping and geodesic distance as basic geometric operators, and extend the Hadamard product and shrinkage operator to the manifold tangent vector field; S2. Establish a single UAV interaction model: Define three types of interaction force models based on the geodesic distance, and establish a hierarchical force activation mechanism in combination with the Riemann indicator function, and introduce a random perturbation model on the manifold using covariant derivatives. S3. Construct a dynamic model of the bee colony system: Introduce a relative position tensor, and use the extended Adama product and shrinkage operator to aggregate the individual UAV interaction model into a unified set of tensor differential equations; S4. Distributed solution of the model: The Riemann numerical integration algorithm is used to solve the tensor differential equation system, and an evolutionary solution is performed by combining a distributed architecture and a heterogeneous hardware optimization strategy. S5. Based on the Riemannian geometric operation system, a humanoid intelligent hierarchical control architecture is designed and embedded into the dynamic model of the bee colony system to achieve intelligent control with autonomous adaptation and group cooperation capabilities.

2. The Hadamard product based swarm of UAVs efficient system dynamics modeling method of claim 1, wherein, S1 includes the following sub-steps: S11. Define the Riemannian manifold in which the UAV swarm moves, and introduce exponential mapping, logarithmic mapping and geodesic distance as basic geometric operators; S12. Based on logarithmic mapping, construct the relative displacement matrix and geodesic distance matrix of unmanned pairs on the manifold; S13. Redefine the Hadamard product based on parallel translation to obtain the Riemann Hadamard product; S14. Extend the shrinking operator to the tangent vector field of the manifold to realize matrix-based batch operations on the manifold.

3. The Hadamard product based swarm of UAVs efficient system dynamics modeling method of claim 2, wherein, In S14, the shrinking operator unifies vectors distributed in different tangent spaces into a reference tangent space through parallel shifting.

4. The Hadamard product based swarm of UAVs efficient system dynamics modeling method of claim 1, wherein, S2 includes the following sub-steps: S21. Based on covariant derivatives, establish a fundamental model of UAV dynamics on a Riemannian manifold: S22. Based on geodesic distance, three types of interaction force models are defined, including short-range repulsive force model, medium-range attractive force model, and long-range directional attractive force model; S23. Set the action distance threshold and activation conditions for various interactive forces, and establish a hierarchical force activation mechanism based on the Riemann indicator function; S24. Using covariant derivatives, a random perturbation model on a Riemannian manifold is introduced, and based on the parallel shift operator, the covariant derivative calculation equation for the random perturbation term is obtained.

5. The efficient system dynamics modeling method for UAV swarms based on Adama product according to claim 4, characterized in that, In S23, the layered force activation mechanism is as follows: when the geodesic distance between UAVs is less than the safe distance, only the near-range repulsive force is activated; when the geodesic distance between UAVs is within the attractive force range, the near-range repulsive force is turned off and the mid-range attractive force is activated; when the geodesic distance between UAVs is within the directional force range, the mid-range attractive force is turned off and the far-range directional force is activated.

6. The Hadamard product based swarm of UAVs efficient system dynamics modeling method of claim 1, wherein, S3 includes the following sub-steps: S31. Establish the state matrix and velocity state matrix of the UAV swarm, and construct the relative position tensor based on logarithmic mapping and parallel movement operator; S32. Construct a distance relationship matrix between UAVs based on geodesic distance; S33. Based on the relative position tensor and distance relationship matrix, the three types of interaction force models are expressed in matrix form, and the matrix-formed three types of interaction force models are aggregated by the Riemann-Hadamard product and the shrinking operator. S34. Construction of the overall dynamic equations: Integrating virtual viscous friction, external task control force, interactive resultant force and random disturbance to establish a unified set of tensor differential equations.

7. The Hadamard product based swarm of UAVs efficient system dynamics modeling method of claim 6, wherein, In S33, the three types of interaction force models are expressed in a matrix format. For the near-range repulsive force model, the relative position tensor and distance relationship matrix are matrixed into a repulsive force interaction matrix. For the mid-range attraction model, based on the relative position tensor and the distance relationship matrix, it is matrixed into a gravitational interaction matrix; For the long-distance directional attraction model, based on the relative position tensor and the distance relationship matrix, it is matrixed into a directional force interaction matrix; The total repulsive force is calculated using the Riemann-Hadamard product, the contraction operator, and the repulsive force interaction matrix. The total attractive force is calculated using the Riemann-Hadamard product, the contraction operator, and the gravitational interaction matrix. The total directional force is calculated using the Riemann-Hadamard product, the contraction operator, and the interaction matrix of the directional force. The total repulsive force, total attractive force, and total directional force are superimposed to obtain the interactive resultant force.

8. The Hadamard product based swarm of UAVs efficient system dynamics modeling method of claim 7, wherein, S4 includes the following sub-steps: S41. For the tensor differential equation system, design a Riemann numerical integration algorithm, including the Riemann-Euler method and the Riemann-Verlet method, to achieve the coordinated update of position and velocity on the manifold. S42. For parallel solving of tensor differential equations, a distributed computing architecture is developed, which groups and distributes the drone swarm to multiple computing nodes to optimize the computing performance of large-scale clusters. S43. To address the high computational load of tensor differential equation systems, a multi-hardware platform deployment strategy is adopted, including parallel computing optimization using single-core CPUs, multi-core CPUs, and GPUs. S44. Construct a simulation engine and process management system to drive the solution of tensor differential equations, drive the solver to run and manage the simulation process and data output.

9. The Hadamard product based swarm of UAVs efficient system dynamics modeling method of claim 1, wherein, S5 includes the following sub-steps: S51. Design a humanoid intelligent hierarchical control architecture, construct a three-layer structure of perception and understanding, decision-making and reasoning and execution control, and achieve geometrically consistent integration with the single UAV interaction model and the swarm system dynamics model; S52. In the decision reasoning layer, attention mechanism and semantic rule base are integrated to generate decision commands based on the motion characteristics and scene semantics of the drone swarm, supporting real-time environment understanding and behavior selection. S53. Establish a group humanoid collaboration and role negotiation mechanism. Based on the parallel movement operator, dynamic task allocation and intention synchronization are achieved through role vectors on the manifold and parallel movement. S54. Develop an online learning and adaptive policy optimization module to parameterize the control policy as a mapping function on the parametric manifold; calculate the policy update direction based on the Riemann policy gradient theorem, use the parallel shift operator to correct the first and second moment estimates of the gradient, construct a Riemann adaptive moment estimator optimizer, and iteratively update the policy parameters on the parametric manifold through exponential mapping to achieve continuous adaptation to the environment.

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