A method for quickly reconstructing electromagnetic characteristics of a variable posture unmanned aerial vehicle group

Abstract

This invention discloses a method for rapidly reconstructing the electromagnetic characteristics of an unmanned aerial vehicle (UAV) swarm with variable attitude. The method treats each UAV in the swarm as an independently reusable electromagnetic module, constructing its spherical multi-port response model through a single full-wave simulation. It utilizes analytical spherical propagation operators to describe the free-space electromagnetic coupling between UAVs, and analytically characterizes the impact of UAV attitude and position changes on radiation patterns using spherical geometric transformation and translation operators. After assembling the swarm-level linear system in the spherical pattern space, the radiation and scattering electromagnetic characteristics of the UAV swarm under arbitrary attitude and formation conditions can be rapidly reconstructed without re-performing a full-wave simulation.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic field numerical analysis and aerospace electromagnetic engineering technology. Specifically, it relates to a method for rapidly reconstructing the electromagnetic radiation and scattering characteristics of UAV swarms during flight attitude, position and formation changes. It can be used in scenarios such as UAV swarm communication link evaluation, cooperative interference effectiveness analysis, stealth performance prediction and target observability assessment. Background Technology

[0002] With the development of unmanned aerial vehicle (UAV) technology, UAV swarms (UAV clusters) composed of multiple UAVs working together have received widespread attention in missions such as communication, reconnaissance, early warning, jamming, and strike. During mission execution, UAV swarms typically require real-time adjustments, specifically regarding the relative spatial positions and spacing between individual UAVs; the attitude parameters of individual UAVs, including roll, pitch, and yaw angles; and the overall formation structure and pointing direction of the swarm.

[0003] Because UAV platforms themselves possess a certain electromagnetic dimension, and their airframe structure, onboard antennas, and installation locations are relatively complex, the overall electromagnetic characteristics of a UAV swarm (including radiation pattern, gain distribution, mutual coupling characteristics, and radar cross-section) are highly sensitive to the aforementioned geometric states. Even small changes in attitude or position can cause significant alterations in the swarm's electromagnetic response. Existing electromagnetic analysis methods for UAV swarms mainly fall into two categories:

[0004] 1. Overall Full-Wave Simulation Method: This method involves modeling all UAVs and their onboard antennas uniformly and directly solving the group electromagnetic response using full-wave methods such as the method of moments (MoM) and the finite element method (FEM). While this method offers high accuracy, the computational scale increases rapidly with the number of UAVs, and remodeling and solving are required whenever the attitude or formation changes, resulting in enormous computational costs and making it difficult to meet the needs of dynamic analysis.

[0005] 2. Engineering approximation-based methods: These methods approximate the electromagnetic properties of a swarm through domain decomposition, empirical formulas, or simplified mutual coupling models. While computationally efficient, these methods have limited accuracy and applicability, making them unsuitable for high-precision electromagnetic analysis of complex UAV swarms.

[0006] However, in real-world missions, UAV swarms may need to examine a large number of different formations and attitude combinations within a short period of time. Traditional full-wave simulation methods struggle to complete such large-scale electromagnetic analysis within an acceptable timeframe. Therefore, a new method is urgently needed that satisfies the following conditions: each UAV is pre-calculated as an independently reusable electromagnetic module; the electromagnetic coupling relationships between different UAVs are given by an analytical free-space propagation model; changes in group attitude and position are achieved solely through analytical transformations, eliminating the need for re-solving the full-wave equations; and the electromagnetic characteristics of a large number of attitude combinations can be rapidly reconstructed and evaluated. Summary of the Invention

[0007] The purpose of this invention is to propose a rapid reconstruction method for the electromagnetic characteristics of an unmanned aerial vehicle (UAV) swarm with variable attitude. This method first treats each UAV as an independent electromagnetic region module, solving its electromagnetic response in one step and establishing a module model in a spherical pattern space. Second, it utilizes the analytical expression of free-space propagation to construct spherical propagation operators between UAVs, describing the incident radiation of a single UAV on other members. Third, it analytically describes the influence of UAV attitude and position changes on their radiation patterns using spherical geometric transformation and translation operators. Finally, it assembles and solves the swarm-level linear system in the spherical pattern space, achieving rapid reconstruction of the electromagnetic characteristics of the UAV swarm under arbitrary attitude and position combinations. Therefore, it eliminates the need for full-wave simulations for each swarm attitude and formation; the overall electromagnetic characteristics of the UAV swarm under arbitrary attitude and spatial distribution conditions can be rapidly reconstructed solely through matrix operations.

[0008] The present invention provides a method for rapid reconstruction of the variable electromagnetic characteristics of an unmanned aerial vehicle (UAV) swarm, which mainly consists of the following steps:

[0009] 1. Construct the spherical domain pattern base and the group interface space:

[0010] Within the operating frequency band of the UAV swarm, the outer free space satisfies the homogeneous Helmholtz equation. To provide a unified characterization of the radiation and scattered fields in the angular direction, this invention selects two linearly independent spherical vector modes as basis functions, denoted as:

[0011]

[0012] Where p and q are pattern indicators used to distinguish different orders and different directional features.

[0013] Based on the finite-dimensional function set formed by these two types of modes, a spherical mode space is defined to uniformly describe: the radiation modes of each UAV; the incident modes of other UAVs or external sources on a particular UAV; and the distribution of radiation and scattering modes of the UAV swarm as a whole to the far field. In this mode space, the electromagnetic field is represented by mode coefficient vectors, which serve as the unified interface for subsequent module-level modeling and swarm-level reconstruction.

[0014] 2. Modeling of electromagnetic modules for a single UAV:

[0015] drones The device and its airborne antenna are considered as an independent electromagnetic region module, and a full-wave simulation is performed on this module. The simulation can employ the method of moments, the finite element method, or other appropriate full-wave methods to solve for the excitation u at a given port. i The surface current distribution and outer scattering field of the UAV.

[0016] Surrounding drones On the reference sphere, the radiation field is extracted and projected onto the spherical model basis to obtain the model coefficient vector. By linearly combining the excitations from different ports, the UAV module can be modeled as follows:

[0017]

[0018] in Let be the spherical multiport response matrix of the i-th UAV, where each column corresponds to the spherical radiation mode distribution under a standard port excitation. This matrix is ​​obtained through a one-time full-wave simulation and mode projection and can be reused in subsequent analyses.

[0019] 3. Sphere Propagation Operator in Free Space

[0020] For drones and The electromagnetic coupling between them is determined by free-space propagation. This invention introduces a spherical propagation operator in the spherical mode space. , used to describe radiation mode for The contribution relationship of the incident mode.

[0021] set up For drones The spherical model coefficient vector of outward radiation, then its... Equivalent incident mode coefficients on the reference sphere It can be written as:

[0022]

[0023] The elements are analytically calculated from the relative position vectors and coordinate system orientation relationships between the two UAVs. They are the result of the expansion of the free-space Green's function under the spherical mode basis, and have an analytical form, so no additional full-wave simulation is required.

[0024] By constructing a spherical propagation operator for all UAV pairs (i, j), a propagation matrix structure describing the electromagnetic coupling relationship within the entire UAV swarm can be obtained.

[0025] 4. Spherical Geometric Transformation Operator for UAV Attitude Changes

[0026] During flight, UAVs undergo attitude changes such as roll, pitch, and yaw, which alter the directionality of their radiation patterns in the global coordinate system. To avoid resimulating for each attitude, this invention introduces a spherical geometric transformation operator within the spherical pattern space.

[0027] For the i-th UAV, its attitude can be represented by a set of attitude parameters. Description: The linear operator constructed in this invention Its function is:

[0028]

[0029] in These are the spherical mode coefficients of the UAV module under a certain reference attitude. In posture The equivalent mode coefficients are calculated. This transformation operator is pre-constructed based on the analytical transformation formulas of the spherical mode in different coordinate directions, and only matrix and vector multiplication operations need to be performed during operation.

[0030] 5. Spherical translation operator for UAV position changes

[0031] The positional changes of a UAV in three-dimensional space also affect its relative phase and propagation path. To describe this change in mode space, this invention introduces a spherical translation operator. ,in Let be the position vector of the centroid or reference point of the i-th UAV in the global coordinate system. The function of this operator is:

[0032]

[0033] Mode coefficients after attitude transformation Mapped to spherical model coefficients based on a group reference coordinate system The spherical translation operator can also be calculated from the translation properties and phase factor of the spherical mode.

[0034] 6. Rapid reconfiguration of the overall electromagnetic response of UAV swarms

[0035] Suppose a swarm of drones contains N drones. Excite at a given port. Attitude parameters and position vector Under the given conditions, the self-radiation mode coefficients of the i-th UAV in the global coordinate system can be written as:

[0036]

[0037] Simultaneously, the i-th drone will also receive secondary radiation from other drones, with the incident mode coefficient being:

[0038]

[0039] in Let be the total radiation mode coefficient of the j-th UAV.

[0040] Establish linear combination relationships for UAV swarms in the spherical pattern space:

[0041]

[0042] Combine the total mode coefficients of all UAVs into a swarm mode vector:

[0043]

[0044] Define a group coupling matrix K, which is composed of each K ij If a block matrix is ​​formed, the above relationship can be written as:

[0045]

[0046] After sorting, we can obtain:

[0047] Where I is the identity matrix.

[0048] For a given UAV swarm structure, the structure of K is related to the free-space propagation channel. Once constructed, it can be efficiently reused when attitude and port excitations change, and new A can be quickly obtained through matrix solving. tot .

[0049] 7. Calculation and rapid updating of electromagnetic performance indicators

[0050] By obtaining Atot, the field distribution of the group's external radiation or scattering can be reconstructed in the spherical model space, and the following can be further calculated: the group radiation pattern and main lobe direction; effective radiation gain and coverage area; group scattering cross-section under different incident directions; mutual coupling strength and energy distribution between individual units; and field strength variation in the specified observation direction.

[0051] The main advantage of this invention is that when the attitude, position, or port excitation of the UAV swarm changes during flight, this method only needs to update the corresponding geometric transformation operator and free radiation mode term. New A can be quickly obtained through matrix operations. tot It eliminates the need for full-wave simulation of individual drones or swarms, thus enabling rapid reconstruction of the electromagnetic characteristics of drone swarms. Attached Figure Description

[0052] Figure 1 This is a flowchart of a method for rapid reconstruction of the variable electromagnetic characteristics of an unmanned aerial vehicle (UAV) swarm, according to the present invention.

[0053] Figure 2 This is a top view of the initial layout of the UAV in an embodiment of the present invention.

[0054] Figure 3 This is a front view of the initial layout of the drone in an example of the present invention.

[0055] Figure 4This is a front view of the UAV after its attitude has changed in an example of the present invention.

[0056] Figure 5 This is a top view of the electric field distribution within a fixed field area corresponding to the UAV in this embodiment of the invention.

[0057] Figure 6 This is a normalized electric field distribution diagram within a fixed field area corresponding to the UAV in this embodiment of the invention.

[0058] Figure 7 This is a comparison chart of the rapid reconstruction method for the variable electromagnetic characteristics of UAV swarm attitude in this invention and the results of traditional full-wave simulation.

[0059] Figure 8 This is the far-field main beam pattern after the attitude change of the UAV in an example of the present invention. Detailed Implementation

[0060] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples.

[0061] in Figure 1 The following is an overall flowchart of a method for rapid reconstruction of the variable electromagnetic characteristics of an unmanned aerial vehicle (UAV) swarm, according to the present invention. Detailed supplementary descriptions are provided below for specific embodiments:

[0062] 1. Implementation Scenarios and Parameter Settings

[0063] First, a drone swarm consisting of four (N=4) identical drones is selected. Each drone is arranged in a predetermined fixed formation in three-dimensional space, as shown in the diagram. Figure 2 As shown, it presents a rhomboid structure, and the positions of its centroids are denoted as: .

[0064]

[0065] In this embodiment, the relative positions of the drones remain unchanged, that is... Throughout the analysis, the parameters remain constant, considering only the case where the UAV attitude parameters change. Each UAV includes an airframe structure and an onboard antenna, and its port excitation vector is denoted as: .

[0066] 2. Construction of a single-UAV spherical multi-port response matrix

[0067] For the i-th UAV, a one-time simulation calculation is performed using the full-wave electromagnetic numerical method under reference attitude conditions (e.g., zero roll, zero pitch, zero yaw). The radiated electromagnetic field is extracted on the reference sphere surrounding the UAV and projected onto the M-type and N-type vector mode bases in the spherical domain.

[0068]

[0069] Based on this, the corresponding spherical pattern coefficient vector is obtained: , where K is the total number of truncated spherical patterns. By linearly combining different port excitations, a linear mapping relationship can be established between the port excitations and the spherical pattern coefficients for the i-th UAV: ,in It can be obtained through a single full-wave simulation and remains unchanged in subsequent attitude change analyses.

[0070] 3. Spherical geometric transformation operators corresponding to attitude changes

[0071] Suppose that the i-th UAV undergoes attitude changes during flight, and its attitude parameters are expressed as: ,in These correspond to the roll angle, pitch angle, and yaw angle, respectively. Based on the analytical transformation relationship between different coordinate systems in the spherical model, a spherical geometric transformation operator is constructed: This operator is applied to the spherical mode coefficient vector under the reference attitude to obtain the equivalent mode coefficients after attitude change: The initial attitude change of the UAV can be referenced. Figure 3 The initial front view of the drone, and the drone's attitude after the roll are shown below. Figure 4 As shown, the drone's pitch angle is offset by 20° and its azimuth angle is offset by 45°.

[0072] 4. Spherical translation operator under fixed formation conditions

[0073] Since the drone swarm formation is fixed in this embodiment, the centroid position of each drone is... Since nothing changes, the corresponding spherical translation operator can be pre-constructed: This operator is used to map spherical model coefficients with the single-machine reference center as the origin to spherical model coefficients with the group reference coordinate system as the origin.

[0074] Therefore, the corresponding single-machine self-radiation mode coefficient can be obtained as follows:

[0075]

[0076] 5. Spherical Propagation Operator Between UAVs

[0077] For any two different drones Based on their relative positional relationships, a corresponding spherical propagation operator can be constructed: This operator is used to describe the equivalent incident mode formed by the radiation mode of the j-th UAV on the reference sphere of the i-th UAV:

[0078]

[0079] in Let be the total spherical pattern coefficients of the j-th UAV.

[0080] 6. Establishment and solution of group-level linear systems

[0081] Because for every drone, there is:

[0082]

[0083] By constructing a group vector from the total mode coefficients of the four drones, we can obtain:

[0084]

[0085] The corresponding group coupling matrix can also be obtained:

[0086]

[0087] At this point, the group relations can be written as: Solving this formula will yield the result. That is, to obtain the total spherical mode coefficients of the four machines under the current attitude combination.

[0088] 7. Radiation pattern reconstruction

[0089] In obtaining Afterwards, the total mode coefficient of the four drones can be disassembled. The spherical pattern basis functions are written in merged form:

[0090]

[0091] The reconstructed electric field of a certain drone in the far field can then be written as: ,

[0092] The total electric field of the four-machine group is: The reconstructed normalized electric field can be referenced. Figure 5 As shown, Figure 5 A top-view view showing the electric field distribution within a fixed field area is presented, while... Figure 6 This displays the normalized electric field distribution, where the X and Y axes range from... Figure 2 It is obtained after normalizing the spatial relative wavelengths corresponding to the X and Y axes.

[0093] By calculating the total electric field, the amplitude of the corresponding radiation pattern is obtained as follows: This leads to a further normalized direction pattern:

[0094]

[0095] For easier visual observation, Figure 7 First, it was given that Figure 2 and Figure 3 The comparison between the full-wave simulation results under the shown layout and the far-field results obtained by the method of this invention shows that the two curves are basically fitted, indicating that the method has good predictive ability. Meanwhile, in... Figure 8 The following is given Figure 4 The far-field main beam pattern after the offset is shown, and it is clear that the main beam has shifted with the change in attitude.

[0096] The above description is merely a specific example of the present invention. Obviously, those skilled in the art, after understanding the content and principles of the present invention, may make various modifications and changes in form and details without departing from the principles and structure of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A method for rapid reconstruction of the variable electromagnetic characteristics of an unmanned aerial vehicle (UAV) swarm, characterized in that, Includes the following steps: Step 1: Treat each UAV in the UAV swarm as an independent electromagnetic region module, perform a full-wave simulation on each module to obtain its electromagnetic field on the surrounding sphere, and project it onto the spherical mode basis to construct the spherical multi-port response matrix from port excitation to spherical mode coefficients. Step 2: In the spherical pattern space, construct a spherical propagation operator between any two UAVs based on the free space propagation characteristics, which is used to describe the contribution of the radiation pattern of one UAV to the incident pattern of another UAV. Step 3: Construct a spherical geometric transformation operator to describe the attitude change of the UAV, and transform the spherical mode coefficients under the reference attitude to the mode coefficients under the current attitude; Step 4: Construct a spherical translation operator to describe the changes in the UAV's position, mapping the mode coefficients in the local coordinate system to the mode coefficients in the group reference coordinate system; Step 5: In the spherical mode space, assemble the above response matrix, propagation operator, geometric transformation operator and translation operator into a swarm-level linear system, solve for the total radiation or scattering mode coefficients of the UAV swarm under a given combination of attitude and position, and then calculate electromagnetic performance indicators such as radiation pattern, gain or scattering cross section.

2. The method according to claim 1, characterized in that... The sphere propagation operator K ij The relative position and orientation parameters between the two UAVs are obtained through the analytical expansion of the free-space Green's function under the spherical mode basis.

3. The method according to claim 1, characterized in that... The spherical geometric transformation operator This is a linear transformation matrix acting on the coefficient vector of the spherical pattern, whose elements are calculated from the analytical transformation relationship between the spherical pattern and different directional coordinate systems.

4. The method according to claim 1, characterized in that... The spherical translation operator This is obtained by analytically solving the translation properties and phase factor of the spherical mode, and is used to map the mode coefficients with the single-machine reference center as the origin to the mode coefficients with the group reference center as the origin.

5. The method according to claim 1, characterized in that... The aforementioned group-level linear system can be represented as: ； in It is a group mode vector composed of the total mode coefficients of each individual machine. This represents the self-radiation mode coefficient vector for each individual unit. Let be the group coupling matrix composed of sphere propagation operators.

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