A method, device and equipment for precise tracking control of unmanned aerial vehicles

Abstract

The present invention proposes a method, device and equipment for precise track tracking and control of unmanned aerial vehicles (UAVs). The method generates fused state data by fusing GPS track data and flight state information, and constructs a track-state phase space model using phase space reconstruction technology. Phase trajectory characteristic parameters are extracted based on dynamic trajectory analysis, and dynamic attractor characteristics are determined through attractor identification processing. The attractor center position and topological singularity position are identified using phase space topological analysis, and a composite potential field intensity distribution formed by the superposition of a conventional gravitational potential field and a repulsive-attractive bipolar potential field is constructed. The gradient of the composite potential field is calculated and adaptively modulated based on the relative relationship between the current position and the attractor center. In a local coordinate system with the singularity as the origin, the modulated gradient vector is decomposed into radial and circumferential components, and a spiral potential field is formed through selective curl enhancement. Finally, a tracking control instruction is generated and a signal modulation output is performed to achieve precise tracking and control of the UAV on a preset route.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle (UAV) navigation and control, and in particular to a method, device and equipment for precise track tracking and control of an UAV. Background Art

[0002] With the rapid development of drone technology, drones are increasingly being used in military reconnaissance, civilian monitoring, logistics distribution, emergency rescue, and other fields, placing increasing demands on the accuracy and reliability of track tracking control. Existing drone track tracking control methods primarily include classical PID control, linear quadratic regulator (LQR), model predictive control (MPC), sliding mode control, and adaptive control. These methods can achieve basic track tracking functions under ideal conditions.

[0003] However, existing technologies for handling the complex nonlinear dynamics of UAVs face the following key challenges: First, they lack an in-depth analysis of the essential characteristics of flight dynamics. Feedback control is based solely on instantaneous state errors, failing to reveal the system's inherent stability mechanisms and convergence characteristics, leading to a sharp decline in control performance under complex maneuvers or disturbances. Second, control strategy design lacks a systematic theoretical framework. Traditional methods either oversimplify and ignore nonlinear characteristics or are computationally complex and difficult to implement in real time. Parameter adjustment relies primarily on empirical trial and error, lacking adaptability to the system's dynamics. Third, overshoot and oscillation are common near the target. Existing methods typically employ fixed gains or simple switching strategies, failing to fine-tune according to flight state and environmental conditions, impacting tracking accuracy and stability. Fourth, they lack effective mechanisms for handling complex trajectories containing singularities. When the target trajectory contains special structures such as sharp turns and loops, traditional methods are prone to falling into local extremes or experiencing unstable behavior. Therefore, there is an urgent need to develop new track tracking methods based on dynamic analysis and intelligent control strategies. Summary of the Invention

[0004] This invention provides a method, device, and equipment for precise UAV trajectory tracking control, designed to achieve high-precision control of UAV trajectory tracking in complex environments. This method integrates key technologies such as phase space reconstruction, dynamics analysis, attractor identification, potential field construction, and gradient modulation. By extracting flight dynamics characteristics to construct a control strategy, it enables real-time correction of trajectory deviations and intelligent generation of control commands, resulting in a UAV trajectory tracking control system with high-precision tracking, rapid response, and strong robustness.

[0005] The first aspect of the present invention provides a method for precise tracking and control of an unmanned aerial vehicle, comprising the following steps:

[0006] Acquire GPS track data and flight status information of the UAV, perform data fusion processing on the GPS track data and the flight status information to generate fused status data, and perform phase space reconstruction on the fused status data to form a track-state phase space model;

[0007] Performing dynamic trajectory analysis on the track-state phase space model to obtain phase trajectory characteristic parameters, and performing attractor identification processing based on the phase trajectory characteristic parameters to determine dynamic attractor characteristics of track tracking;

[0008] Performing phase space topological analysis according to the characteristics of the dynamic attractor to identify the attractor center position and the topological singular point position, and generating a composite potential field intensity distribution based on the attractor center position and the topological singular point position;

[0009] Performing gradient calculation and direction analysis on the composite potential field intensity distribution to obtain potential field gradient information, and adaptively modulating the potential field gradient information based on a relative relationship between a current position and a center position of the attractor to obtain modulation gradient information;

[0010] constructing a local coordinate system based on the modulation gradient information and the topological singular point position, performing vector decomposition and selective enhancement processing on the modulation gradient information in the local coordinate system to generate tracking adjustment parameters, and generating tracking control instructions based on the tracking adjustment parameters;

[0011] The control signal is modulated and outputted according to the tracking control instruction, and a modulated flight control signal is outputted. The modulated flight control signal is outputted to the flight control system to realize accurate tracking control of the UAV on the preset route.

[0012] A second aspect of the present invention provides a precise track tracking control device for an unmanned aerial vehicle, comprising:

[0013] A data fusion module is used to obtain GPS track data and flight status information of the UAV, perform data fusion processing on the GPS track data and the flight status information to generate fused status data, and perform phase space reconstruction on the fused status data to form a track-state phase space model;

[0014] a trajectory analysis module, configured to perform dynamic trajectory analysis on the track-state phase space model to obtain phase trajectory characteristic parameters, and perform attractor identification processing based on the phase trajectory characteristic parameters to determine dynamic attractor characteristics of track tracking;

[0015] A potential field construction module is used to perform phase space topological analysis based on the characteristics of the dynamic attractor to identify the attractor center position and the topological singular point position, and generate a composite potential field intensity distribution based on the attractor center position and the topological singular point position;

[0016] a gradient modulation module, configured to perform gradient calculation and direction analysis on the composite potential field intensity distribution to obtain potential field gradient information, and adaptively modulate the potential field gradient information based on the relative relationship between the current position and the attractor center position to obtain modulation gradient information;

[0017] a control generation module, configured to construct a local coordinate system based on the modulation gradient information and the topological singular point position, perform vector decomposition and selective enhancement processing on the modulation gradient information in the local coordinate system to generate tracking adjustment parameters, and generate tracking control instructions based on the tracking adjustment parameters;

[0018] The signal output module is used to modulate and output the control signal according to the tracking control instruction, output the modulated flight control signal, and output the modulated flight control signal to the flight control system to achieve accurate tracking and control of the UAV on the preset route.

[0019] The third aspect of the present invention proposes a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of a method for precise trajectory tracking and control of an unmanned aerial vehicle disclosed in the first aspect are implemented.

[0020] The beneficial effects of the present invention are reflected in the following aspects: First, through the fusion processing of GPS track data and flight status information, phase space reconstruction, and dynamic trajectory analysis technology, it achieves accurate extraction of complex nonlinear dynamic characteristics and precise identification of attractor features during UAV flight. This method overcomes the technical difficulties of traditional control methods, such as insufficient utilization of flight data and unclear understanding of dynamic mechanisms. Through phase trajectory geometric feature analysis and convergence assessment, a complete dynamic feature description system is established, improving the track tracking system's ability to control flight stability and convergence characteristics. Second, through attractor center and topological singularity identification, composite potential field construction, and gradient adaptive modulation technology, a systematic control strategy generation mechanism is established. This method converts dynamic analysis results into executable control strategies. The gravitational potential field realizes the basic attraction effect, the bipolar potential field addresses the influence of singularities, and distance-dependent gradient modulation ensures rapid convergence over long distances and smooth convergence over short distances. This method overcomes the problem of traditional control methods' reliance on experience in parameter adjustment, realizes automatic generation and dynamic optimization of control strategies, and improves the control system's response speed and environmental adaptability. Third, through local coordinate system construction, vector decomposition, and selective enhancement technology, it achieves refined processing of complex trajectories and high-precision tracking control. This method decomposes the modulated gradient into radial and circumferential components in the local coordinate system of the singularity. By maintaining the radial component to ensure basic tracking performance, and enhancing the circumferential component to form a spiral potential field to achieve smooth orbiting, it effectively solves the control singularity and local extreme value problems that are prone to occur in traditional methods when dealing with complex trajectories such as sharp turns and loops, and improves the system's adaptability and tracking accuracy to various complex target trajectories.

[0021] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The accompanying drawings herein illustrate specific examples of the technical solutions described in the present invention, and together with the specific implementation methods constitute a part of the specification, and are used to explain the technical solutions, principles and effects of the present invention.

[0023] Unless otherwise specified or defined, the same reference numerals in different drawings represent the same or similar technical features, and the same or similar technical features may also be represented by different reference numerals.

[0024] Figure 1 The present invention is a flowchart of a method for accurately tracking and controlling a UAV.

[0025] Figure 2 This is a structural block diagram of a precise track tracking control device for an unmanned aerial vehicle of the present invention.

[0026] Figure 3It is a structural schematic diagram of a computer device of the present invention. DETAILED DESCRIPTION

[0027] In the following description, specific details such as specific system structures and techniques are provided for purposes of illustration rather than limitation to facilitate a thorough understanding of the embodiments of the present application. However, it will be apparent to those skilled in the art that the present application may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid obscuring the description of the present application with unnecessary detail.

[0028] It should be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of described features, integers, steps, operations, elements and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or collections thereof.

[0029] It will also be understood that the term "and / or" used in this specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.

[0030] As used in this specification and the appended claims, the term "if" can be interpreted as "when" or "upon" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrase "if it is determined" or "if [described condition or event] is detected" can be interpreted as meaning "upon determination" or "in response to determining" or "upon detection of [described condition or event]" or "in response to detecting [described condition or event]," depending on the context.

[0031] In addition, in the description of the present application specification and the appended claims, the terms "first", "second", "third", etc. are only used to distinguish the descriptions and cannot be understood as indicating or implying relative importance.

[0032] References to "one embodiment" or "some embodiments" in this specification mean that a particular feature, structure, or characteristic described in conjunction with that embodiment is included in one or more embodiments of the present application. Thus, phrases such as "in one embodiment," "in some embodiments," "in other embodiments," and "in other embodiments" appearing in various places in this specification do not necessarily refer to the same embodiment, but rather mean "one or more but not all embodiments," unless otherwise specifically emphasized. The terms "including," "comprising," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0033] The technical solutions of the embodiments of this application are introduced below.

[0034] like Figure 1 As shown, an embodiment of the present invention provides a method for precise track tracking control of a UAV, comprising the following steps S110 to S160:

[0035] Step S110: Obtain the GPS track data and flight status information of the UAV, perform data fusion processing on the GPS track data and flight status information to generate fused status data, and perform phase space reconstruction on the fused status data to form a track-state phase space model.

[0036] Specifically, GPS track data collection relies on a high-precision GNSS receiver equipped with L1 / L2 dual-frequency reception, achieving sub-meter positioning accuracy. The receiver continuously records the drone's three-dimensional position coordinates, including longitude, latitude, and altitude, at a sampling rate of 10Hz, and also records the corresponding UTC timestamp to ensure data time accuracy. GPS track data also includes velocity vector information, using Doppler shift measurements to determine eastward, northward, and vertical velocity components, with velocity measurement accuracy reaching 0.1m / s. An integrated inertial navigation unit supplements and corrects track data in environments with GPS signal obstruction or interference, ensuring the integrity of the continuous track record. Flight status information is collected in real time via the integrated sensor network of the onboard flight management system. The attitude sensor, utilizing a combination of a three-axis gyroscope and accelerometer, measures the drone's pitch, roll, and yaw angles, achieving an angular accuracy of 0.1 degrees and an angular velocity accuracy of 0.05 degrees / s. A barometric altimeter provides redundant altitude measurement, cross-validating it with GPS altitude data. The pitot tube measures the drone's relative airspeed, covering the typical flight speed range of 5-50 m / s. The engine monitoring module collects thrust setpoints, speed parameters, and fuel consumption rate, reflecting the drone's power status. The control surface position sensors monitor the deflection angles of the ailerons, elevators, and rudders in real time, recording flight control surface status information. All sensor data is collected by the flight data recorder via the CAN bus network. Synchronous sampling is performed using a unified time base at a sampling frequency of 20 Hz to ensure temporal consistency of flight status information. The data recorder preprocesses the raw sensor signals, including noise filtering, range conversion, and unit normalization, to generate GPS track data and flight status information in a standard format. The Kalman filter fusion algorithm then deeply fuses the GPS track data with the flight status information. Using state estimation equations and observation equations, the GPS position and velocity information is combined with the IMU attitude and angular velocity data to generate fused state data containing position, velocity, attitude, and angular velocity.

[0037] In some embodiments, the phase space reconstruction of the fused state data to form a track-state phase space model includes: performing dimensional analysis on the fused state data to generate state vector dimensional information; determining the embedding dimension based on the state vector dimensional information to form phase space embedding parameters; performing coordinate transformation on the fused state data according to the phase space embedding parameters to generate a phase space coordinate sequence; and constructing a track-state phase space model based on the phase space coordinate sequence.

[0038] First, dimensional analysis is performed on the fused state data to generate state vector dimensional information. The GPS track data and flight state information in the fused state data are categorized and organized according to physical properties to identify the types and number of independent state variables contained in the data. Position dimensional information is extracted from the GPS track data, including spatial coordinate dimensions such as longitude, latitude, and altitude, as well as velocity dimensions such as easting velocity, northing velocity, and vertical velocity, to form the GPS state vector. Attitude dimensional information is extracted from the flight state information, including angular dimensions such as pitch, roll, and yaw, as well as the corresponding angular velocity dimensions, to form the attitude state vector. Dynamic state dimensional information, including dynamic-related dimensions such as thrust setpoint, airspeed, and pressure altitude, is integrated to form the dynamic state vector. Dimension counting and independence tests are used to determine the total dimensionality of the fused state data and the degree of correlation between the dimensions, generating state vector dimensional information describing the data structure. For example, in a complex maneuvering mission, when a UAV performs a spiral climb, dimensional analysis identifies multi-dimensional coupled features such as multi-dimensional changes in position coordinates, continuous changes in velocity vectors, and periodic changes in attitude angles, generating state vector dimensional information containing the primary control dimensions. By systematically identifying and classifying the fusion state data, the state vector dimension information is generated.

[0039] Next, the embedding dimension is determined based on the state vector dimensional information to form the phase space embedding parameters. Using the total dimension and correlation data for each dimension in the state vector dimensional information, the optimal embedding dimension for phase space reconstruction is determined using the correlation dimension calculation method D_corr = lim(r→0) log C(r) / log r, where C(r) is the correlation integral and r is the radius of the hypersphere. The dimension corresponding to the stabilization of D_corr is the optimal embedding dimension m. By analyzing the time delay correlation between the dimensions in the state vector dimensional information, the appropriate time delay parameter τ is calculated using the mutual information function I(τ) = ΣP(xi,xi+τ)log[P(xi,xi+τ) / (P(xi)P(xi+τ))] . The τ corresponding to the first local minimum of I(τ) is selected as the optimal delay to ensure that the reconstructed phase space fully reflects the original dynamic characteristics. The window length and sliding step size parameters required for phase space reconstruction are calculated based on the data sampling frequency and time span in the state vector dimensional information. Using the dimensional independence analysis results from the state vector dimensional information, the dominant dimension is selected as the baseline dimension for phase space reconstruction, and the mapping relationship between the other dimensions and the baseline dimension is determined. Combined with the data quality assessment results from the dimensional information, the fault tolerance and filtering parameters for phase space reconstruction are set to ensure the stability and accuracy of the reconstruction process. For example, in long-duration reconnaissance missions, when the state vector dimensional information indicates that the data contains multiple valid dimensions and there is a clear temporal correlation between the dimensions, the optimal embedding dimension is determined through correlation dimensionality analysis, the appropriate time delay parameter is set, and the appropriate window length is determined to form a complete phase space embedding parameter configuration. Phase space embedding parameters are formed through quantitative analysis of state vector dimensional information and parameter optimization.

[0040] The fused state data is then transformed according to the phase space embedding parameters to generate a phase space coordinate sequence. Using the optimal embedding dimension specified in the phase space embedding parameters, the fused state data is dimensionally selected and reduced to extract the primary state variables of the corresponding dimension. The time delay parameter specified in the phase space embedding parameters is then applied to the selected state variables for a time delay embedding transformation, constructing a sequence of delayed coordinate vectors. Based on the window length and sliding step specified in the phase space embedding parameters, a sliding window approach is used to segment the fused state data to generate continuous phase space coordinate points. Using the reference dimension mapping relationship specified in the phase space embedding parameters, the coordinates of the original state space are converted to standardized phase space coordinates to ensure consistency and comparability of the coordinate transformation. The filtering parameters specified in the phase space embedding parameters are then applied to smooth the transformed coordinate data and remove outliers, improving the quality and reliability of the phase space coordinates. By gradually applying all embedding parameters, the temporal structure of the fused state data is converted to a geometric structure in phase space, generating a phase space coordinate sequence containing complete dynamic information. For example, in target tracking, when the fused state data contains complex maneuvering trajectories, the original position-velocity-attitude data is transformed into a multidimensional coordinate sequence in phase space based on the determined embedding dimension and time delay parameters. Each coordinate point reflects the complete dynamic state of the drone at a specific moment. Through the systematic application of phase space embedding parameters and coordinate transformation processing, a phase space coordinate sequence is generated.

[0041] Finally, a trajectory-state phase space model is constructed based on the phase space coordinate sequence. The coordinate points in the phase space coordinate sequence are connected in chronological order to form a continuous trajectory curve in phase space, establishing the geometric topological structure of the trajectory. The spatial distribution of the phase space coordinate sequence is analyzed to identify clustered regions, sparse regions, and special structures of coordinate points, and to construct a regional partitioning and density distribution model for the phase space. Leveraging the temporal information of the phase space coordinate sequence, a dynamic description of the trajectory evolution is established, including the trajectory's convergence, periodicity, and stability characteristics. Based on the statistical properties of the phase space coordinate sequence, the geometric invariants of the trajectory are calculated: trajectory length L = Σ||Y(i+1) - Y(i)||, local curvature κ(t) = ||dY / dt × d²Y / dt²|| / ||dY / dt||³, torsion rate τ(t) = (dY / dt × d²Y / dt²)·d³Y / dt³ / ||dY / dt × d²Y / dt²||², and other geometric parameters. The trajectory geometry, spatial distribution, dynamic characteristics, and geometric invariants are integrated to form a complete trajectory-state phase space model. This model not only contains the spatial geometric information of the UAV trajectory but also incorporates the dynamic characteristics of the flight state, providing a unified mathematical description framework for subsequent trajectory analysis and control strategy design. For example, in formation flight missions, the trajectory-state phase space model constructed based on the multi-aircraft phase space coordinate sequence can simultaneously describe the individual trajectory characteristics of each aircraft and the coordinated motion pattern of the formation as a whole, providing a comprehensive state description for formation control. The trajectory-state phase space model is constructed through geometric analysis and dynamic modeling of the phase space coordinate sequence.

[0042] Step S120 , performing dynamic trajectory analysis on the track-state phase space model to obtain phase trajectory characteristic parameters, and performing attractor identification processing based on the phase trajectory characteristic parameters to determine the dynamic attractor characteristics of track tracking.

[0043] Specifically, the track tracking process of UAVs in complex flight environments often exhibits nonlinear dynamic characteristics. By analyzing the geometric properties and convergence characteristics of the phase space trajectory, the intrinsic stability mechanism and optimal control area of ​​track tracking can be revealed, thereby achieving more accurate and stable track tracking control.

[0044] In some embodiments, the dynamic trajectory analysis of the track-state phase space model to obtain phase trajectory characteristic parameters includes: performing phase trajectory extraction on the track-state phase space model to obtain a phase trajectory curve; performing geometric feature analysis on the phase trajectory curve to generate curvature features and topological features; and performing parameter quantization processing based on the curvature features and the topological features to form phase trajectory characteristic parameters.

[0045] First, phase trajectory extraction is performed on the previously constructed trajectory-state phase space model to obtain phase trajectory curves. Based on phase space reconstruction theory and dynamical system theory, an adaptive step-size numerical integration method is used to extract continuous trajectory paths from the phase space model. The phase trajectory extraction process adheres to the mathematical foundation of Takens' embedding theorem, ensuring that the phase trajectory reconstructed from time series data maintains the geometric structure and topological properties of the original dynamical system. Trajectory extraction uses a modified Runge-Kutta algorithm. Starting from the starting point of the phase space coordinate sequence, each state point is connected point by point according to the temporal evolution sequence determined by the dynamic evolution equation, ensuring the physical rationality and mathematical consistency of the trajectory connection. During the extraction process, appropriate distance thresholds and time steps are set, cubic spline interpolation techniques are used to address gaps between trajectory points, and a Butterworth low-pass filter is used to eliminate high-frequency noise and measurement errors. This ensures that the phase trajectory curve maintains the original dynamic information while exhibiting good smoothness and continuity. Leveraging the velocity field information and phase flow characteristics in the phase space model, a trajectory segmentation algorithm and curvature change detection techniques are used to identify the main evolution paths and branching structures of the trajectory, thereby establishing a hierarchical trajectory description system that reflects the complexity of UAV flight dynamics. In low-altitude penetration missions in mountainous areas, when the UAV needs to perform complex maneuvers such as spiral climbs, emergency obstacle avoidance, and terrain following, the phase trajectory exhibits spiral structures, return patterns, and irregular annular geometric forms in the three-dimensional phase space. The trajectory extraction algorithm can accurately capture the geometric characteristics of these complex dynamic behaviors and generate a complete phase trajectory curve containing rich dynamic information.

[0046] The extracted phase trajectory curves are then subjected to geometric feature analysis to generate curvature and topological features. Based on the theory of differential geometry and algebraic topology, discrete geometric computational methods are used to analyze the intrinsic geometric properties and global topological properties of the trajectory curves. The geometric feature analysis process, based on the differential geometry theory of curves, obtains complete geometric information by calculating the first and second fundamental forms of the trajectory. Curvature analysis identifies the trajectory's geometric variation patterns and local shape characteristics by calculating the local curvature κ = ||r'(s) × r''(s)|| / ||r'(s)||³, the torsion τ = (r'×r'')·r''' / ||r'×r''||², and the geodesic curvature κ_g = ||∇_T T|| for each sampling point on the trajectory, where r(s) is the arc-length parameterized trajectory, T is the unit tangent vector, and ∇ is the covariant derivative. A multi-scale curvature calculation method is used to capture geometric variation at different scales. The probability distribution characteristics and spatial variation patterns of the trajectory curvature are statistically analyzed to quantify the trajectory's overall curvature, the severity of local variations, and the level of geometric complexity. Curvature calculation is based on a finite difference discretization method, using a multi-point difference scheme to improve numerical accuracy. An appropriate calculation window length is set to balance accuracy and noise robustness. Topological feature analysis, based on homological algebra and the theory of topological invariants, includes trajectory connectivity analysis, periodic structure identification, and topological classification. By calculating trajectory topological features such as connected components, fundamental groups, and homology groups, the global topological structure and topological equivalence classes of the trajectory are identified. A continuous homology method is used to analyze the changes in the trajectory's topological features at different scales, detecting closed loops, self-intersecting structures, and multiply connected regions in the trajectory. During maritime search and rescue patrol missions, when drones perform large-scale spiral searches and round-trip scanning flights, the phase trajectories exhibit distinct periodic and quasi-periodic topological features. Curvature analysis reveals that the trajectory has a concentrated curvature distribution in turning areas and near-zero curvature in straight segments. Topological analysis identifies the trajectory as having a torus or cylindrical topological structure, with multiple independent periodic components and quasi-periodic oscillation modes. These geometric and topological features accurately characterize the inherent geometric laws and dynamic periodicity of the search and rescue flight pattern.

[0047] Finally, parameters are quantified based on curvature and topological features to form phase trajectory characteristic parameters. Based on statistical theory and pattern recognition methods, qualitative geometric and topological features are converted into computable and comparable quantitative characteristic parameter representations through multidimensional feature extraction and data mining techniques. The parameter quantification process adheres to the basic principles of feature engineering to ensure that the extracted characteristic parameters have good discriminability, stability, and interpretability. The quantification process uses principal component analysis for feature dimensionality reduction and decorrelation. The distribution parameters of the geometric features are calculated using the statistical moment method. Fractal analysis is used to quantify the self-similarity and complexity of the trajectory. Information theory methods are used to calculate the information entropy and complexity index of the trajectory. The parameter set includes core characteristic parameters such as trajectory length, mean curvature, curvature variance, geometric complexity, topological characteristic number, periodicity index, and fractal dimension. Each parameter is standardized to ensure comparability and numerical stability across different dimensions. Sliding window statistics are used to calculate local characteristic parameters during the quantization process. Resampling methods are used to assess the statistical confidence of the parameters, establishing a quality assessment and reliability verification mechanism for the characteristic parameters. In formation collaborative flight missions, when multiple UAVs need to perform complex coordinated maneuvers and formation changes, the quantified trajectory characteristic parameters can accurately characterize the geometric similarity, topological consistency and dynamic coordination of each aircraft's flight trajectory, supporting the design of intelligent formation control strategies and real-time coordinated adjustments based on trajectory characteristics.

[0048] In some embodiments, the attractor identification processing is performed based on the phase trajectory characteristic parameters to determine the dynamic attractor characteristics of track tracking, including: performing convergence analysis on the phase trajectory characteristic parameters to generate convergence area information; performing attractor type judgment based on the convergence area information to generate an attractor type identifier; performing feature parameter extraction based on the attractor type identifier to establish an attractor stability parameter; and combining the attractor type identifier and the attractor stability parameter to form the dynamic attractor characteristics of track tracking.

[0049] Convergence analysis of the phase trajectory characteristic parameters is performed to generate convergence region information. This convergence analysis utilizes the Lyapunov stability theory V(x) = ∂V / ∂x · ẋ<0 and the trajectory convergence criterion ||X(t) - X*|| ≤ K·e^(-λt)||X(0) - X*||, where V(x) is the Lyapunov function, X* is the equilibrium point, λ is the convergence index, and K is a constant. The speed, direction, and region of convergence of the phase trajectory toward a stable state are calculated. Using the curvature and topological characteristics of the aforementioned phase trajectory characteristic parameters, the trajectory convergence index, convergence radius, and convergence time constant are determined numerically to assess the speed and stability of trajectory convergence. Phase space density analysis techniques are used to statistically analyze the distribution density of trajectory points in different regions, identifying high-density clusters as potential convergence regions. Trajectory terminal behavior analysis is used to calculate the asymptotic behavior of the trajectory after long-term evolution and determine the trajectory's final convergence target and convergence pattern. During a target tracking mission, when the drone tracked a rapidly maneuvering target, convergence analysis revealed that the phase trajectory formed a clear convergence region near the target's predicted location, with a convergence radius of approximately 45 meters, a convergence time constant of 6-10 seconds, and a convergence index of -0.8, demonstrating the tracking system's excellent convergence characteristics and stability. During a maritime search and rescue mission, when the drone searched for a missing vessel in complex sea conditions, convergence analysis identified multiple potential convergence regions corresponding to different search modes and flight strategies. This convergence region information enabled optimization of search paths and improved search efficiency.

[0050] Exemplarily, the attractor type judgment based on the convergence area information and the generation of the attractor type identification include: performing a geometric shape analysis on the convergence area information to generate a shape feature descriptor; performing attractor classification matching based on the shape feature descriptor to construct a classification result matrix; performing type coding analysis based on the classification result matrix to generate coding identification parameters; and generating an attractor type identification based on the coding identification parameters.

[0051] First, a geometric shape analysis is performed on the convergence region to generate a shape feature descriptor. Based on computational geometry and shape analysis theory, the essential shape features of the region are systematically extracted by calculating the geometric invariants and topological properties of the convergence region. The geometric shape analysis process must consider the shape stability and feature consistency requirements of the convergence region at different observation scales and analysis accuracies. The shape analysis utilizes a multi-level regional analysis approach, first extracting the region boundary and refining the contour. A gradient-based edge detection algorithm and improved contour tracking techniques are used to obtain a high-precision boundary description of the convergence region, eliminating noise interference and boundary blurring. The basic geometric parameters of the region are then systematically calculated, including key metrics such as region area, boundary perimeter, geometric center of mass position, principal axis directions, and boundary curvature distribution. Advanced shape description techniques are further employed to further calculate detailed geometric metrics such as the ratio of the major and minor axes, geometric eccentricity, shape compactness coefficient, boundary complexity index, and convexity measure. This multi-scale shape analysis method captures the multi-level information and scale dependence of shape features at different resolution levels. To ensure that the shape feature descriptor possesses good rotational, scale, and translation invariance, advanced Fourier descriptor technology is employed to convert complex boundary contour information into harmonic coefficient representations in the frequency domain, extracting low-frequency-dominated shape feature components while filtering out high-frequency noise. Geometric moment theory and invariant moment calculation methods are then used to generate high-order moment feature descriptors for the region. By organically combining multiple moment descriptors, such as Hu invariant moments, Zernike moments, and complex moments, a comprehensive shape feature vector with strong discriminative power and numerical stability is constructed. When a UAV performs complex mountain reconnaissance flights to avoid continuous mountain obstacles, the convergence region in phase space often exhibits distinct annular or horseshoe-shaped geometric features. In this case, the shape analysis algorithm, through precise geometric calculations, determines that the region exhibits a typical annular topological structure, with an eccentricity between approximately 0.15 and 0.25, an aspect ratio between 1.1 and 1.3, and a boundary complexity index indicating moderate complexity. These quantitative shape feature descriptors accurately characterize the geometric nature and topological properties of the annular convergence region.

[0052] Then, attractors are classified and matched based on shape feature descriptors to construct a classification result matrix. Based on modern pattern recognition theory and advanced machine learning methods, an intelligent pattern matching algorithm systematically compares the shape features of the current convergence region with a pre-established standard attractor type feature library and conducts a deep similarity assessment. The classification and matching process adopts a multi-level, multi-angle feature comparison strategy and a robustness verification mechanism to ensure the high accuracy and strong reliability of the classification results. A standard attractor feature library covering six basic types of attractors is established: point attractors, limit cycle attractors, torus attractors, spiral attractors, chaotic attractors, and strange attractors. Each basic type is further subdivided into multiple subtypes, each containing a large number of standard shape feature descriptor data for typical samples. This fully covers the shape variation range and statistical distribution characteristics of each type of attractor under different parameter conditions, different perturbation intensities, and different system states, forming a classification reference standard system with high statistical representativeness and wide applicability. The classification matching technology utilizes a variety of advanced distance metrics and similarity calculation methods, including weighted Euclidean distance, Mahalanobis distance, cosine similarity, kernel function similarity, and geodesic distance based on manifold learning. Through ensemble learning and multi-classifier fusion techniques, the results of various similarity metrics are integrated to significantly improve the robustness, accuracy, and generalization of the classification algorithm. Furthermore, state-of-the-art machine learning algorithms, such as support vector machines, random forests, gradient boosted decision trees, and deep neural networks, are employed to train high-precision, highly generalizable attractor-type classifiers. These classifiers are capable of effectively handling nonlinear classification boundaries, complex decision surfaces, and multi-category overlap in high-dimensional feature spaces. The classification matching results are organized and stored in a structured classification result matrix, with rows corresponding to candidate attractor types and columns corresponding to multi-dimensional evaluation metrics such as matching probability, confidence level, feature consistency index, classification stability, and historical statistical information. When the UAV performs a large-scale spiral search and rescue flight at sea to expand the search radius, the flight trajectory exhibits typical Archimedean spiral or logarithmic spiral characteristics. The shape feature matching analysis algorithm can accurately identify spiral attractors with significantly high matching probability and high confidence level, while the matching probability of limit cycle attractors is relatively low. The matching probabilities of other types of attractors are significantly lower than the set statistical threshold. The classification result matrix clearly and unambiguously reflects the classification certainty and identification reliability of spiral attractors.

[0053] Then, type coding analysis is performed based on the classification result matrix to generate coding identification parameters. Based on modern decision-making theory and uncertainty reasoning methods, a comprehensive analysis and intelligent decision-making process is conducted on the complex classification result matrix through multi-criteria decision-making algorithms, fuzzy logic reasoning, and probabilistic statistical reasoning techniques to determine the optimal attractor type classification result and confidence assessment. The type coding analysis process requires a comprehensive balance of multiple technical requirements such as classification accuracy, computational efficiency, system robustness, and real-time performance. Type coding analysis uses advanced weighted fusion decision-making methods and multi-attribute decision-making technology, comprehensively considering multiple key evaluation dimensions in the classification result matrix, including matching probability distribution, confidence level assessment, feature consistency index, classification boundary clarity, historical classification stability, and statistical significance. By scientifically setting the weight coefficients of each dimension and reasonably determining the decision threshold parameters, decision-making methods such as hierarchical analysis method, fuzzy comprehensive evaluation, and Bayesian reasoning are used to select the attractor type with the highest comprehensive score and optimal decision value as the final classification result. The coding and identification parameter design utilizes a hierarchical, multidimensional coding system and standardized coding specifications. This includes multiple coding elements, including main type coding for identifying basic attractor subcategories, subtype coding for refining classification granularity, confidence level coding for quantifying classification reliability, and special attribute tag coding for recording specific dynamic properties and geometric features. Each coding dimension has a clear physical meaning, a strict value range, and a standard coding format. A comprehensive quality control and consistency verification mechanism is integrated into the coding parameter generation process. Statistical verification methods such as cross-validation, bootstrap resampling, and repeated classification are used to comprehensively evaluate the numerical stability, statistical significance, and classification reproducibility of the coding results. Strict quality assessment standards and reliability assurance mechanisms are established to ensure that the generated coding and identification parameters possess excellent numerical reliability and engineering applicability. When a UAV performs a long-duration reconnaissance patrol flight along a predetermined route, its flight trajectory exhibits typical elliptical loop characteristics. The coding analysis algorithm comprehensively evaluates various indicators and determines that the main type code is "02," which clearly indicates the limit cycle attractor subcategory. The subtype code is "01," which specifically indicates a standard elliptical loop geometry. The confidence level code is "A," indicating a high-confidence classification result. The special attribute mark "STABLE" indicates stable periodic motion characteristics.

[0054] Finally, an attractor type identifier is generated based on the encoding identifier parameters. Based on the generated encoding identifier parameters, a unified attractor type identifier is generated strictly according to a predefined encoding rule system and standardized format specifications. This identifier utilizes an internationally accepted data format and standardized naming conventions, ensuring readability, parsability, and system compatibility. It can be directly recognized, parsed, and processed by the subsequent potential field construction module and control strategy generation module, enabling seamless data transfer and efficient information exchange between system modules. The attractor type identifier generation process includes several key steps: encoding validity verification, which uses a checksum algorithm to check the format correctness and numerical validity of the encoding parameters; format conversion, which converts the internal encoding format to a standard output format; and standardized output, which generates a final identifier in a unified format. Each step is equipped with corresponding quality checks and error handling mechanisms, ensuring the correctness, completeness, and consistency of the generated identifier through multi-level quality control. The identifier generation utilizes a structured data organization format, containing core information elements such as the attractor type name, standard encoding string, numerical confidence level, geometric attribute tags, and dynamic characteristic descriptions, forming a complete and detailed attractor type description document and data record. The generated identification document also automatically integrates important metadata such as timestamp information, data source identifiers, algorithm processing versions, and quality assessment results, fully supporting the system's data traceability, version management, and quality control requirements, establishing a comprehensive data management and version control system. When multiple UAVs need to execute complex formation coordinated flight, performing precise formation changes and highly coordinated maneuvers, the flight trajectories of each UAV are coupled to form complex dynamic characteristics. The type identification generation algorithm intelligently and comprehensively evaluates the convergence region characteristics and interaction patterns of each UAV within the formation, generating a composite attractor type identification that reflects the overall dynamic behavior of the formation. The main type code "05" explicitly indicates the composite attractor category, while the subtype code "03" specifically indicates a circular-spiral combined motion pattern. The confidence level code "A+" indicates a very high confidence classification result, and the special attribute code "MULTI" clearly identifies the characteristics of multi-UAV coordinated flight. This highly standardized and information-rich type identification provides an accurate and reliable dynamic description and control decision-making basis for the potential field construction algorithm and coordinated control strategy of the formation flying system.

[0055] Characteristic parameters are extracted based on the attractor type identifier, and attractor stability parameters are established. Based on dynamical system theory and stability analysis methods, and utilizing the detailed type information and precise geometric feature data contained in the previously generated attractor type identifier, a customized parameter extraction algorithm and corresponding mathematical analysis methods are employed for each attractor type to ensure the accuracy and comprehensiveness of characteristic parameter extraction. The parameter extraction process is categorized according to the attractor's dynamic characteristics and geometric structure. For point attractors, key parameters reflecting convergence performance are extracted, including core characteristic parameters such as the effective attraction domain radius, attraction strength coefficient, convergence rate constant, steady-state error bound, and convergence time estimate. For limit cycle attractors, key parameters describing periodic motion are systematically extracted, including the circular orbit radius, main oscillation frequency, phase drift characteristics, amplitude stability, and periodic stability index. For torus attractors, complex parameters describing quasi-periodic motion are comprehensively extracted, including high-dimensional characteristic parameters such as the torus geometric dimension, fundamental frequency combination, quasi-periodicity measure, frequency locking characteristics, and topological invariants. The attractor's stability parameters are precisely calculated using a variety of dynamic analysis methods. These include Lyapunov exponent spectrum λᵢ = lim(t→∞) (1 / t)ln(||δxᵢ(t)|| / ||δxᵢ(0)||), where δxᵢ represents the i-th orthogonal perturbation direction, which is used to quantify the system's exponential stability (λ_max<0) and chaotic characteristics (λ_max>0). Power spectral density analysis and frequency domain analysis techniques are used to identify the system's frequency response characteristics and harmonic components. Linearized perturbation response analysis is used to assess the system's sensitivity and recovery characteristics to small perturbations. Global stability analysis is used to determine the system's stability region boundaries and robustness margins. A systematic linearization analysis method is used to calculate the attractor's local linearization characteristics and local stability criteria near the equilibrium point. Lyapunov direct and indirect methods are used to evaluate the system's asymptotic and exponential stability. Large-scale global analysis techniques are used to assess the attractor's global stability, robustness margin, and adaptability to parameter changes.In complex formation flight missions, when multiple UAVs perform tight formation maintenance tasks in a complex airflow environment and the system identifies typical limit cycle attractor characteristics, the characteristic parameter extraction algorithm can accurately obtain the key stability parameters required for formation maintenance, including the standard radius range of formation circular flight, the main oscillation frequency characteristics of formation periodic maneuvers, the time constant of phase coordination, and the Lyapunov exponent showing a stable negative range, indicating that the formation system has good exponential convergence characteristics. The comprehensive stability index is close to the theoretical optimal value, indicating that the formation dynamics system has excellent stability performance and coordinated flight capabilities. Even in the face of complex environmental challenges such as smoke interference in forest fire monitoring, strong updraft disturbances or electromagnetic interference and other adverse factors, the extracted attractor stability parameters can still clearly show that the system has strong robustness and anti-interference capabilities, and can maintain flight stability under various external interference and environmental disturbance conditions and quickly recover to the desired coordinated flight state.

[0056] The attractor type identifier and attractor stability parameter are combined to form the track tracking dynamic attractor signature. Based on multi-source information fusion theory and knowledge representation methods, advanced data fusion and information integration techniques are used to organically combine and deeply integrate the previously generated attractor type identifier and attractor stability parameter to establish a unified and standardized attractor signature representation system and a complete dynamic signature description framework. The data fusion process utilizes a multi-level fusion architecture, encompassing information integration at different abstraction levels: data-level fusion, feature-level fusion, and decision-level fusion. Weighted fusion algorithms, Bayesian fusion methods, and fuzzy fusion techniques are used to effectively integrate and coordinate feature information from different sources, types, and accuracies. The dynamic attractor signature is organized and stored in a multi-level, multi-dimensional data structure, forming a hierarchical signature description framework and a standardized data representation format. The data structure design utilizes an object-oriented hierarchical organization approach, with the top layer representing the attractor type identifier, the middle layer representing the stability parameter, and the bottom layer representing detailed geometric features and topological properties. This supports multi-dimensional feature querying, association analysis, and inference computation. During the feature combination process, the intrinsic correlation, numerical consistency and logical compatibility between different parameters are systematically considered. The accuracy, completeness and reliability of the feature data are ensured through strict parameter verification and multiple cross-validation mechanisms. The correlation analysis adopts statistical methods such as correlation analysis, principal component analysis and factor analysis to identify the linear correlation, nonlinear dependence and causal relationship between different feature parameters. The consistency test adopts a multi-level verification mechanism such as numerical consistency check, logical consistency verification and semantic consistency check, and finally obtains the attractor characteristics that fully describe the dynamic characteristics of track tracking.

[0057] Step S130 , performing phase space topological analysis according to the dynamic attractor characteristics to identify the attractor center position and the topological singular point position, and generating a composite potential field intensity distribution based on the attractor center position and the topological singular point position.

[0058] Specifically, the attractor type identification and stability parameters from the previously generated trajectory tracking dynamic attractor features are used to determine the attractor's geometric center and singular point distribution through phase space topological analysis. Topological analysis employs homology theory and differential topology methods, determining the corresponding topological structure analysis strategy based on the attractor type identification. For point attractors, the attractor center is determined by calculating the centroid of the phase trajectory density distribution using the formula X_c = ∫ρ(x)·x·dx / ∫ρ(x)dx, where ρ(x) is the phase space density function. For limit cycle attractors, the ring geometric center algorithm is used to calculate the loop's geometric center and principal axis orientation. For chaotic attractors, unstable fixed points are identified as topological singularities by calculating Poincare sections and regression mapping. The singularity identification algorithm is based on phase flow analysis. Equilibrium points are identified by solving the vector field zero-point equation f(x) = 0. The singularity type is determined by calculating the eigenvalues ​​of the Jacobian matrix J = ∂f / ∂x. Real eigenvalues ​​correspond to saddle points, while complex eigenvalues ​​correspond to foci or centers. Singularity stability is determined through linearization analysis. A negative real part of the eigenvalue indicates a stable singularity (attractive), a positive real part indicates an unstable singularity (repulsive), and a zero real part corresponds to a neutral singularity. During a complex flight mission, when a drone tracks a spiraling target, topological analysis identifies the spiral axis as the attractor center and the spiral's starting and ending points as topological singularities, providing precise spatial anchors for subsequent potential field construction. Through systematic analysis of the phase space topology and identification of key points, the locations of the attractor center and topological singularities were determined.

[0059] In some embodiments, the generation of a composite potential field strength distribution based on the center position of the attractor and the position of the topological singularity includes: constructing a conventional gravitational potential field based on the center position of the attractor; constructing a repulsion-attraction bipolar potential field based on the position of the topological singularity; and superimposing the conventional gravitational potential field and the repulsion-attraction bipolar potential field to form a composite potential field strength distribution.

[0060] A conventional gravitational potential field is constructed based on the identified attractor center position, using a Newtonian-like gravitational field model to achieve basic attraction on the flight trajectory. The gravitational potential field is constructed using the potential function U_a(x) = -k_a / ||x - x_c||^α, where x is the phase space position, x_c is the attractor center position, k_a is the gravitational strength coefficient, and α is the distance decay exponent. The gravitational strength coefficient k_a is dynamically determined based on the attractor radius and convergence rate constant in the attractor stability parameters: k_a = λ·R_a·v_c, where λ is the absolute value of the Lyapunov exponent, R_a is the attractor radius, and v_c is the convergence rate. The choice of the distance decay exponent α affects the potential field's range and gradient characteristics. For strong short-range attraction, α=2 simulates the inverse square law, while for weak long-range attraction, α=1 achieves linear decay. The potential field gradient calculation, ∇U_a = α·k_a·(x - x_c) / ||x - x_c||^(α+1), provides the gravitational direction and strength information required for flight control. To avoid central singularities, a regularization process is introduced near the attractor center: U_a(x) = -k_a / (||x - x_c||^α + ε), where ε is a small positive number to prevent the denominator from reaching zero. For multiple attractors, a weighted superposition approach is used to construct a combined gravitational field: U_total = Σwi·U_ai. The weights w_i are determined based on the stability index of each attractor and the current mission priority. In formation flight missions, the desired position of each UAV forms an attractor center, and the gravitational potential field is used to maintain formation and stabilize the formation. A conventional gravitational potential field is constructed based on gravitational modeling of the attractor center and potential field distribution calculation.

[0061] Based on the identified topological singularity, a repulsive-attractive bipolar potential field is constructed to achieve precise control of the flight trajectory and obstacle avoidance. This bipolar potential field employs the combined potential function U_s(x) = k_r·exp(-||x - x_s||² / σ_r²) - k_a·exp(-||x - x_s||² / σ_a²), where x_s is the singularity location, k_r and k_a are the repulsive and attractive strength coefficients, respectively, and σ_r and σ_a are the range parameters. The potential field parameters are determined based on the singularity type. For saddle points, repulsion dominates (k_r>k_a), resulting in a trajectory diversion effect. For focal singularities, attraction is enhanced (k_a ≈ k_r), producing a spiral motion trend. For neutral singularities, the bipolar effects are balanced (k_r = k_a), resulting in a circular motion pattern. The range parameters are determined by the singularity's influence domain: σ_r = β_r·√|λ_max|, σ_a = β_a·√|λ_min|, where λ_max and λ_min are the maximum and minimum eigenvalues ​​of the Jacobian matrix at the singularity, and β_r and β_a are adjustment coefficients. The spatial distribution of the potential field exhibits a bipolar characteristic, with a strong repulsive region near the singularity, an attractive potential well in the midfield, and the potential energy tending to zero in the far field. The gradient field calculation, ∇U_s = 2(x - x_s)[k_r / σ_r²·exp(-||x - x_s||² / σ_r²) - k_a / σ_a²·exp(-||x - x_s||² / σ_a²)], provides a complex force field distribution. Multi-singularity superposition employs a vector synthesis method, accounting for interactions and shielding effects between singularities. During obstacle avoidance flight, singular points at the obstacle's boundary generate a repulsive potential field, guiding the flight trajectory around the obstacle. Simultaneously, attractive singular points are set behind the obstacle to create a smooth detour path. By modeling and optimizing the bipolar potential field at the singular point location, a repulsive-attractive bipolar potential field is constructed.

[0062] A conventional gravitational potential field is superimposed with a repulsive-attractive bipolar potential field to generate a composite potential field intensity distribution suitable for complex flight missions. This potential field superposition employs a weighted linear combination, U_composite(x) = w_a·U_a(x) + w_s·U_s(x) + U_coupling(x), where w_a and w_s are weight coefficients and U_coupling is a coupling correction term. The weight coefficients are determined by an optimization algorithm whose objective function encompasses multiple metrics, including trajectory tracking accuracy, energy consumption, and stability margin. Genetic algorithms or particle swarm optimization are used to find the optimal weights. The coupling correction term, U_coupling = γ·U_a·U_s / (U_a² + U_s² + δ), accounts for the nonlinear interaction between the two potential fields, where γ is the coupling strength and δ is the regularization parameter. Analysis of the equipotential surfaces of the composite potential field reveals a rich topological structure, including key features such as stable equilibrium points, unstable saddle points, potential wells, and potential barriers. The local properties of each point are determined by calculating the Hessian matrix H = ∂²U_composite / ∂x². Positive definite indicates a local minimum (stable point), indefinite indicates a saddle point, and negative definite indicates a local maximum (unstable point). The potential field intensity distribution is visualized using contour plots and vector field plots, intuitively displaying the potential energy landscape and gradient flow. An adaptive adjustment mechanism dynamically adjusts the potential field parameters based on the flight state, enhancing the gravitational force when approaching the target and increasing the repulsive force when encountering a threat. During flight in complex urban environments, buildings generate a repulsive potential field, while the target generates an attractive potential field. This composite potential field guides the drone safely through the building complex and accurately reaches its target. The composite potential field intensity distribution is formed through the scientific superposition of potential fields and parameter optimization.

[0063] Step S140 , performing gradient calculation and direction analysis on the composite potential field intensity distribution to obtain potential field gradient information, and adaptively modulating the potential field gradient information based on the relative relationship between the current position and the attractor center position to obtain modulation gradient information.

[0064] Specifically, a gradient calculation is performed on the composite potential field intensity distribution U_composite(x) generated above to extract the spatial rate of change and force field direction information of the potential field. The gradient calculation uses a combination of analytical differentiation and numerical differentiation. The gradient vector ∇U_composite = ∂U_composite / ∂x = w_a·∇U_a + w_s·∇U_s + ∇U_coupling, where the gradients of each component have been derived during the potential field construction. The gravitational potential field gradient ∇U_a = α·k_a·(x - x_c) / ||x -x_c||^(α+2) points to the center of the attractor and its intensity decreases with increasing distance. The bipolar potential field gradient ∇U_s contains the vector composite of two components, repulsive and attractive, and exhibits complex directional changes near the singularity. Gradient direction analysis determines the direction of steepest descent by calculating the unit gradient vector n = -∇U_composite / ||∇U_composite||, which is the desired flight control direction. The gradient strength ||∇U_composite|| reflects the strength of the control action, and isogradient analysis identifies areas of gradient concentration and flattening. The curl of the gradient field, ∇×∇U_composite, verifies the conservatism of the potential field. Theoretically, it should be zero; nonzero values ​​indicate numerical errors or potential field singularities. Divergence analysis, ∇·∇U_composite = ∇²U_composite, provides Laplace information about the potential field. Positive values ​​indicate potential energy minima (stable equilibrium points), while negative values ​​indicate potential energy maxima (instability points). Singular points in the gradient field are identified by solving for ∇U_composite = 0. These points correspond to critical points in the potential field and require special treatment to prevent control failure. During complex terrain tracking flight, gradient information accurately reflects the impact of terrain undulations on the flight path: ridges produce repulsive gradients, while valleys form attractive gradients. Potential field gradient information is obtained through systematic calculation of the spatial gradient field and analysis of its directional characteristics.

[0065] In some embodiments, the adaptive modulation of the potential field gradient information based on the relative relationship between the current position and the center position of the attractor includes: calculating the distance value from the current position to the center position of the attractor; nonlinearly modulating the potential field gradient information based on the distance value to obtain modulation gradient information, wherein, when the distance value is greater than a preset distance threshold, a gradient amplification function is used to enhance the control response; when the distance value is less than the preset distance threshold, a gradient attenuation function is used to avoid overshoot.

[0066] The Euclidean distance to the center of the attractor is calculated using the current position information from real-time flight status data. The current position x_current is extracted from the fused status data and contains 3D coordinates and attitude information. This information is then mapped to phase space through coordinate transformation. Distance calculations use the standard Euclidean norm d = ||x_current - x_c||, where x_c is the attractor center position determined by S130. To improve computational efficiency, the squared distance d² = (x_current - x_c)ᵀ(x_current - x_c) can be used directly in subsequent judgments, avoiding square root operations. The relative position vector r = x_current - x_c provides directional information, which is used to determine the drone's orientation relative to the attractor. The rate of change of distance ḋ = rᵀ·v / ||r|| is calculated using the projected velocity vector v. Positive values ​​indicate movement away from the attractor, while negative values ​​indicate movement toward it. Statistical analysis of the historical distance series {d(t-τ),..., d(t)} identifies distance change trends, which are used to predict future motion trends. The distance normalization d_norm = d / R_a (R_a is the radius of the attraction domain) converts the absolute distance into a relative distance, which facilitates the unified processing of systems of different scales. In the case of multiple attractors, the distance vector D = [d1, d2, ..., d n ], identifying the nearest attractor as the dominant control target. During cooperative formation flight, each drone calculates the distance to the formation center and adjacent drones for formation-maintaining control. Based on accurate real-time distance calculation and dynamic tracking, the distance value from the current position to the attractor center is generated.

[0067] Based on the calculated distance value, a non-linear modulation strategy is adopted to adaptively adjust the potential field gradient information. This piecewise modulation strategy stems from the idea of variable gain control in control theory. When far from the target, a large control gain is required to achieve rapid approach, while when close to the target, a small control gain is needed to ensure stable convergence and avoid overshoot oscillation caused by inertia. The modulation function is designed as a piecewise non-linear form G_mod = M(d)·∇U_composite, where M(d) is the distance-dependent modulation coefficient. When the distance d > d_threshold, the gradient amplification function M_far(d) = 1 + β_amp·(d / d_threshold - 1)^γ_amp is used, where β_amp is the amplification intensity coefficient and γ_amp is the non-linear exponent. Typical values are β_amp = 2.0 and γ_amp = 1.5 to achieve rapid approach at long distances. When the distance d < d_threshold, the gradient attenuation function M_near(d) = α_decay·(d / d_threshold)^γ_decay + (1 - α_decay)·exp(-λ_decay·(1 - d / d_threshold)) is used, where α_decay is the minimum attenuation coefficient, γ_decay is the attenuation exponent, and λ_decay is the exponential decay rate. Typical parameters are α_decay = 0.3, γ_decay = 2.0, and λ_decay = 5.0 to ensure smooth convergence at short distances. The transition region [0.8d_threshold, 1.2d_threshold] uses cubic spline interpolation to ensure the continuity and differentiability of the modulation function. The upper and lower bounds of the modulation coefficient M(d) ∈ [M_min, M_max] prevent over-modulation, with a typical range of [0.2, 3.0]. Directional selectivity modulation considers the angle θ = arccos(v·∇U / ||v||||∇U||) between the velocity direction and the gradient direction. The modulation is enhanced during reverse motion M_dir = 1 + κ·(1 - cos(θ)) and weakened during forward motion. The dynamic threshold adjustment mechanism adjusts d_threshold = d_base·(1 + ξ_env) in real time according to the flight mission and environmental conditions, where ξ_env is the environmental correction factor. In a precision landing mission, the distance threshold decreases with the decrease in altitude to ensure precise control in the final stage. Based on gradient-based non-linear modulation and parameter adaptation, the modulated gradient information is finally obtained.

[0068] Step S150, construct a local coordinate system based on the modulated gradient information and the topological singularity position, decompose the modulated gradient information vectorially and perform selective enhancement processing in the local coordinate system to generate tracking adjustment parameters, and generate a tracking control command based on the tracking adjustment parameters.

[0069] Specifically, using the modulation gradient information G_mod and the topological singular point location x_s, a local coordinate system with the singular point as its origin is constructed for fine control analysis. This local coordinate system is constructed using the principal axis decomposition method, with the nearest topological singular point x_s as the coordinate origin, and the characteristic directions of the flow field at the singular point are calculated. The principal axis directions of the local coordinate system are determined by performing eigendecomposition J = QΛQ^T on the vector field near the singular point, where J is the Jacobian matrix, Q is the eigenvector matrix, and Λ is the eigenvalue diagonal matrix. The first principal axis e1, along the eigenvector corresponding to the maximum eigenvalue, represents the primary evolution direction of the flow field. The second principal axis e2 is perpendicular to e1 and lies in the phase plane. The third principal axis e3 = e1 × e2 completes the right-handed coordinate system. The coordinate transformation matrix T = [e1, e2, e3]^T converts global coordinates to local coordinates, where x_local = T(x_global - x_s). For saddle-point singularities, the coordinate axes lie along the stable and unstable manifolds; for focal-point singularities, the coordinate axes lie along the radial and tangential directions of the spiral motion. The dynamic adjustment of the local coordinate system takes into account the movement and deformation of the singularity. The Kalman filter is used to track the changes in the position of the singularity, and the update cycle is synchronized with the control cycle. In the case of multiple singularities, the dominant singularity with the greatest influence is selected to construct the coordinate system. The degree of influence is determined by distance weighting and field strength evaluation. When flying in a vortex environment, a local coordinate system with the vortex center as the origin can accurately describe the characteristics of the spiral motion. The local coordinate system is established based on the extraction of singularity features and the construction of the coordinate transformation matrix.

[0070] In some embodiments, the vector decomposition and selective enhancement processing of the modulated gradient information in the local coordinate system to generate tracking adjustment parameters includes: extracting a gradient vector from the modulated gradient information; decomposing the gradient vector into a radial component and a circumferential component; retaining the radial component for basic track tracking, applying curl enhancement to the circumferential component to form a spiral potential field surrounding a singular point; and resynthesizing the enhanced circumferential component with the radial component to generate tracking adjustment parameters.

[0071] The complete gradient vector representation is extracted from the modulated gradient information G_mod, ensuring that both the vector's direction and magnitude are fully preserved. The gradient vector is expressed in the local coordinate system as G_local = T·G_mod, where T is the coordinate transformation matrix constructed above. Numerical stability checks are performed during the vector extraction process. When ||G_local|| < ε_min (ε_min is the minimum gradient threshold), the exponentially weighted average of historical gradients, G_local = α·G_current + (1-α)·G_history, is used to avoid numerical instability. The time derivative of the gradient vector, ∂G_local / ∂t, is calculated using finite differences to predict gradient trends. The local properties of the vector field are obtained by calculating the gradient of the gradient, ∇G_local, to identify regions of gradient concentration and divergence. Singular value decomposition G_local = UΣV^T separates the main and minor components of the gradient, retaining the main component for enhanced robustness. Vector normalization, ĝ = G_local / ||G_local||, and the modulus, ||G_local||, are stored separately to facilitate subsequent direction control and intensity adjustment. In a strong wind interference environment, the filtering of the gradient vector can effectively suppress high-frequency disturbances and maintain the stability of the control direction. The gradient vector is extracted based on the coordinate transformation and numerical processing of the gradient information.

[0072] The extracted gradient vector is decomposed into radial and circumferential components relative to the singularity, achieving decoupled control of the motion mode. The radial unit vector e_r = r / ||r||, where r = x_current - x_s, is the position vector from the current position to the singularity. The circumferential unit vector e_θ = e_z × e_r / ||e_z × e_r||, where e_z is a unit vector perpendicular to the plane of motion. The radial component G_r = (G_local·e_r)e_r represents the tendency of motion toward or away from the singularity, while the circumferential component G_θ = (G_local·e_θ)e_θ represents tangential motion around the singularity. The completeness of the decomposition is verified by G_local = G_r +G_θ + G_z, ensuring no information loss, where G_z is the perpendicular component. The sign of the radial component provides information about the direction of motion: G_r·e_r>0 indicates movement away from the singularity, while G_r·e_r<0 indicates movement toward the singularity. The rotational direction of the circumferential component is determined by e_θ·(∇×G_local), with positive values ​​indicating counterclockwise and negative values ​​indicating clockwise. The component ratio |G_θ| / |G_r| reflects the spiral nature of the motion; a large ratio indicates predominantly rotational, while a small ratio indicates predominantly radial motion. Dynamic decomposition considers the influence of singularity type, emphasizing the radial component for source and sink points and the circumferential component for vortex points. In target-circling reconnaissance missions, the decomposed circumferential component dominates the achievement of stable circular flight trajectories. Through orthogonal gradient decomposition and component characteristic analysis, the separation of radial and circumferential components is achieved.

[0073] The radial component G_r is maintained as the basis for tracking control, while the circumferential component G_θ is selectively enhanced. The radial component retention strategy G_r_keep = η_r·G_r, where the retention coefficient η_r ∈ [0.8, 1.0] is adjusted based on the tracking accuracy requirements to ensure basic approach or avoidance functions. The circumferential component's curl is enhanced using the eddy current enhancement algorithm G_θ_enhanced = G_θ + Γ·K(r)·e_θ, where Γ is the circulation intensity, K(r) = (1 - exp(-r² / σ²)) / r is the radial distribution function, and σ controls the eddy current influence range. The circulation intensity Γ is determined based on the singularity type and mission requirements. For focal singularities, Γ = 2π·ω·r², where ω is the desired angular velocity; for saddle point singularities, Γ = Γ0·tanh(r / r0) to achieve a gradual transition. Curl enhancement creates an artificial eddy field near a singularity, guiding the trajectory into a spiral motion pattern, helping to avoid control singularities caused by directly crossing the singularity. The enhancement function is designed to ensure that ▽×G_θ_enhanced ≠ 0, breaking the conservative constraints of the potential field and introducing active rotational motion. Selective enhancement switches based on the mission mode: in reconnaissance mode, curl is enhanced to achieve regional coverage, while in tracking mode, curl is weakened to achieve rapid approach. The enhancement parameter is adaptively adjusted to Γ = Γ0(1 +λ·σ_trajectory), where σ_trajectory is a measure of trajectory complexity. In mountain search and rescue missions, the spiral search pattern generated by curl enhancement can effectively expand the search coverage. Through selective component processing and the superposition of the curl field, an enhanced circumferential component is formed.

[0074] The retained radial component G_r_keep is vector-synthesized with the enhanced circumferential component G_θ_enhanced to generate the final tracking control parameters. This vector synthesis employs weighted superposition G_composite = w_r·G_r_keep + w_θ·G_θ_enhanced + G_coupling. The weight coefficients w_r and w_θ are dynamically adjusted based on the flight mode, and the coupling term G_coupling = μ·(G_r × G_θ) / ||G_r||||G_θ|| accounts for the interaction between the components. The weight configuration strategy adaptively switches based on the mission phase. During the approach phase, w_r = 0.7 and w_θ = 0.3 emphasize radial motion, while during the orbit phase, w_r = 0.3 and w_θ = 0.7 emphasize circumferential motion. A sigmoid function is used to smooth the transition phase. The amplitude of the composite vector, ||G_composite|| = min(||G_composite||, G_max), is adjusted to prevent control saturation. Direction optimization is achieved by constraining the angle with the desired trajectory. Tracking control parameters include the composite gradient vector G_composite, the control gain matrix K_control = diag(k_x, k_y, k_z), the time constant τ_response, and a saturation limit parameter. Parameter integrity checks ensure the inclusion of necessary information, such as position control, velocity feedforward, and acceleration constraints. The parameter format utilizes a standardized control parameter data structure, facilitating direct parsing and execution by the controller. In complex formation maneuvers, the synthesized tracking control parameters can simultaneously meet the dual requirements of formation maintenance and trajectory tracking. Based on the optimized synthesis of vectors and the structured organization of parameters, the tracking control parameters are ultimately generated.

[0075] Based on the tracking control parameters, executable tracking control commands are generated through a control allocation algorithm and command mapping mechanism. These tracking control parameters include key information such as the composite gradient vector G_composite, the control gain matrix K_control, and the time constant τ_response. These abstract control parameters must be converted into thrust and attitude control commands that can be directly executed by the UAV. Control command generation employs a hierarchical decoupling strategy. First, the required total control force F_total = K_force·||G_composite|| is calculated based on the modulus of the composite gradient vector ||G_composite||. K_force is the force-to-gradient conversion coefficient, determined based on the UAV's mass and dynamic characteristics. The total control force is decomposed in the body coordinate system into a thrust component, T_cmd = F_total·cos(α), and a lateral force component, F_lateral = F_total·sin(α), where α is the angle between the composite gradient vector and the vertical. The attitude control command is determined based on the directional information of the gradient vector, and the desired attitude angle is calculated using inverse kinematics. The pitch angle command θ_cmd = atan2(G_composite_x, G_composite_z) controls forward and backward motion. The roll angle command φ_cmd = atan2(G_composite_y, sqrt(G_composite_x² + G_composite_z²)) controls left and right motion. The yaw angle command ψ_cmd is determined by the heading hold requirement or the horizontal projection direction of the gradient vector. Attitude angle commands are saturated to ensure |φ_cmd| ≤ φ_max = 30° and |θ_cmd| ≤ θ_max = 20° to prevent instability caused by excessive attitude angles. Angular rate commands are calculated using attitude error and control gains. The roll rate command is p_cmd = K_p (φ_cmd - φ_current) / τ_response, the pitch rate command is q_cmd = K_q (θ_cmd - θ_current) / τ_response, and the yaw rate command is r_cmd = K_r (ψ_cmd - ψ_current) / τ_response. Angular rate commands are also subject to clipping, typically to |p_cmd|, |q_cmd|, and |r_cmd| ≤ 60° / s. Control commands are timestamped using the system clock: t_cmd = t_current + Δt_pred, where Δt_pred is the predicted time offset to compensate for control delay.The tracking control instructions are encapsulated into a standardized data structure, including the thrust instruction T_cmd, the attitude angle instructions [φ_cmd, θ_cmd, ψ_cmd], the angular rate instructions [p_cmd, q_cmd, r_cmd], the control mode flag, and the timestamp information. The instruction priority setting is dynamically adjusted according to the flight phase. The altitude control has the highest priority during takeoff and landing phases, the trajectory tracking has the highest priority during the cruise phase, and the safety control during emergency obstacle avoidance overrides all other instructions. The instruction validity check includes numerical range verification, timing consistency check, and dynamic feasibility assessment to ensure that the generated control instructions meet the tracking requirements and are within the execution capabilities of the UAV. Through the systematic conversion of the tracking adjustment parameters to the control instructions, the generation of the tracking control instructions is completed.

[0076] Step S160, perform control signal modulation and output processing according to the tracking control instructions, output the modulated flight control signal, and output the modulated flight control signal to the flight control system through the modulated flight control signal to achieve precise tracking control of the UAV for the preset route.

[0077] Specifically, perform signal modulation processing based on the tracking control instructions to convert the discrete control instructions into continuous control signals. The control signal modulation uses multi-rate sampling and interpolation techniques to convert the discrete instructions with the control period Tc into continuous signals with the execution period Te, where Te << Tc to ensure control smoothness. The thrust signal modulation converts the thrust instruction T_cmd into a continuous thrust curve through second-order Bessel interpolation T(t) = T_cmd(k) + (T_cmd(k+1) - T_cmd(k))·B(t / Tc), where B(τ) = 3τ² - 2τ³ is the Bessel basis function. The attitude signal modulation considers the quaternion representation of the attitude to avoid Euler angle singularities, converts the attitude instructions [φ_cmd, θ_cmd, ψ_cmd] into the quaternion q_cmd, and achieves smooth transition through spherical linear interpolation SLERP. The modulation of the angular rate signal introduces dynamic constraints, ω(t) = ω_cmd·(1 - exp(-t / τ_response)) to ensure angular acceleration limits. The time-varying modulation of the control gain K(t) = K_control·σ(t), where σ(t) is a scheduling function related to the mission phase. The signal integrity protection is achieved through redundant coding and verification mechanisms, and each control signal is appended with a timestamp, a sequence number, and a CRC check code. In high-dynamic maneuvering tasks, the signal modulation algorithm adaptively adjusts the interpolation density and smoothing parameters to ensure control responsiveness during sharp turns and stability during straight flights. According to the continuous processing of the control instructions and the imposition of dynamic constraints, the modulated flight control signal is output.

[0078] The modulated flight control signal is transmitted to the flight control system via a standard control interface, driving the actuators for precise trajectory tracking. Signal outputs utilize a synchronous transmission mechanism, with the thrust control signal u_T(t), attitude control signal u_att(t), and angular rate control signal u_ω(t) output on a unified time base to ensure coordinated control actions. After receiving the modulated signal, the flight control system uses an inner-loop controller to track the attitude command, while an outer-loop controller maintains trajectory accuracy. The control error e(t) = x_desired(t) - x_actual(t) is fed back to the modulation module in real time, forming a closed-loop control structure. The error convergence characteristic satisfies ||e(t)|| ≤ ||e(0)||·exp(-λt), where λ>0 is the convergence rate, determined by system stability analysis. The anti-disturbance mechanism estimates the external disturbance d(t) through a disturbance observer and adds a compensation term u_comp = -d(t) to the control signal to offset effects such as wind disturbances. The performance monitoring module evaluates tracking accuracy metrics in real time, including RMS position error, peak attitude error, and control energy consumption, automatically adjusting control parameters when performance degrades. Even in complex flight environments, the system maintains centimeter-level trajectory tracking accuracy, even when encountering wind gusts or sensor noise. Precise execution of modulation signals and closed-loop feedback control ultimately enable the drone to precisely track its pre-set route.

[0079] In order to implement the UAV precise trajectory tracking control method corresponding to the above method embodiment, to achieve the corresponding functions and technical effects. Figure 2 , Figure 2 The following is a block diagram of a precise trajectory tracking control device 200 for a drone provided in an embodiment of the present application. For ease of explanation, only the parts related to this embodiment are shown. The precise trajectory tracking control device 200 for a drone provided in an embodiment of the present application includes:

[0080] The data fusion module 201 is used to obtain GPS track data and flight status information of the UAV, perform data fusion processing on the GPS track data and the flight status information to generate fused status data, and perform phase space reconstruction on the fused status data to form a track-state phase space model;

[0081] A trajectory analysis module 202 is configured to perform dynamic trajectory analysis on the track-state phase space model to obtain phase trajectory characteristic parameters, and perform attractor identification processing based on the phase trajectory characteristic parameters to determine dynamic attractor characteristics of track tracking;

[0082] A potential field construction module 203 is configured to perform phase space topological analysis based on the dynamic attractor characteristics to identify the attractor center position and the topological singular point position, and generate a composite potential field intensity distribution based on the attractor center position and the topological singular point position;

[0083] a gradient modulation module 204 for performing gradient calculation and direction analysis on the composite potential field intensity distribution to obtain potential field gradient information, and adaptively modulating the potential field gradient information based on the relative relationship between the current position and the attractor center position to obtain modulation gradient information;

[0084] a control generation module 205 configured to construct a local coordinate system based on the modulation gradient information and the topological singular point position, perform vector decomposition and selective enhancement processing on the modulation gradient information in the local coordinate system to generate tracking adjustment parameters, and generate tracking control instructions based on the tracking adjustment parameters;

[0085] The signal output module 206 is used to modulate and output the control signal according to the tracking control instruction, output the modulated flight control signal, and output the modulated flight control signal to the flight control system to achieve accurate tracking and control of the UAV on the preset route.

[0086] The above-mentioned drone precise track tracking control device 200 can implement the drone precise track tracking control method of the above-mentioned method embodiment. The optional options in the above-mentioned method embodiment also apply to this embodiment and will not be described in detail here. The remaining contents of the embodiment of this application can be referred to the contents of the above-mentioned method embodiment and will not be repeated in this embodiment.

[0087] like Figure 3 As shown, the third embodiment of the present invention further provides a computer device, including a memory 301, a processor 302, and a computer program stored in the memory 301 and executable on the processor 302, characterized in that when the processor 302 executes the program, the steps of the method for precise trajectory tracking and control of a drone described in the first embodiment of the present invention are implemented.

[0088] The purpose of the above embodiments is to exemplify and deduce the technical solution of the present invention, and to fully describe the technical solution, purpose and effect of the present invention. Its purpose is to enable the public to have a more thorough and comprehensive understanding of the disclosed content of the present invention, and it does not limit the scope of protection of the present invention.

[0089] The above embodiments are not exhaustive and may include many other embodiments not listed above. Any replacements and improvements made without violating the concept of the present invention are within the scope of protection of the present invention.

Claims

1. A method for precise tracking and control of an unmanned aerial vehicle, characterized in that: include: Acquire GPS track data and flight status information of the UAV, perform data fusion processing on the GPS track data and the flight status information to generate fused status data, and perform phase space reconstruction on the fused status data to form a track-state phase space model; Performing dynamic trajectory analysis on the track-state phase space model to obtain phase trajectory characteristic parameters, and performing attractor identification processing based on the phase trajectory characteristic parameters to determine dynamic attractor characteristics of track tracking; Performing phase space topological analysis according to the characteristics of the dynamic attractor to identify the attractor center position and the topological singular point position, and generating a composite potential field intensity distribution based on the attractor center position and the topological singular point position; Performing gradient calculation and direction analysis on the composite potential field intensity distribution to obtain potential field gradient information, and adaptively modulating the potential field gradient information based on a relative relationship between a current position and a center position of the attractor to obtain modulation gradient information; constructing a local coordinate system based on the modulation gradient information and the topological singular point position, performing vector decomposition and selective enhancement processing on the modulation gradient information in the local coordinate system to generate tracking adjustment parameters, and generating tracking control instructions based on the tracking adjustment parameters; The control signal is modulated and outputted according to the tracking control instruction, and a modulated flight control signal is outputted. The modulated flight control signal is outputted to the flight control system to realize accurate tracking control of the UAV on the preset route.

2. The method for precise tracking of unmanned aerial vehicles according to claim 1, wherein: The performing phase space reconstruction on the fused state data to form a track-state phase space model includes: Performing dimensional analysis on the fusion state data to generate state vector dimensional information; Determine the embedding dimension based on the state vector dimensional information to form a phase space embedding parameter; Performing coordinate transformation on the fusion state data according to the phase space embedding parameters to generate a phase space coordinate sequence; A track-state phase space model is constructed based on the phase space coordinate sequence.

3. The method for precise tracking of a UAV according to claim 1, wherein: The performing dynamic trajectory analysis on the track-state phase space model to obtain phase trajectory characteristic parameters includes: performing phase trajectory extraction on the track-state phase space model to obtain a phase trajectory curve; Performing geometric feature analysis on the phase trajectory curve to generate curvature features and topological features; Parameter quantization processing is performed based on the curvature feature and the topological feature to form phase trajectory characteristic parameters.

4. The method for precise tracking and controlling of a UAV according to claim 1, wherein: The attractor identification process based on the phase trajectory characteristic parameters is performed to determine the dynamic attractor characteristics of the track tracking, including: performing convergence analysis on the phase trajectory characteristic parameters to generate convergence region information; Performing attractor type judgment based on the convergence region information and generating an attractor type identifier; Extract characteristic parameters according to the attractor type identifier and establish attractor stability parameters; The attractor type identifier and the attractor stability parameter are combined to form a dynamic attractor feature for track tracking.

5. The method for precise tracking and controlling an unmanned aerial vehicle according to claim 1, wherein: The generating of a composite potential field intensity distribution based on the attractor center position and the topological singular point position includes: Constructing a conventional gravitational potential field based on the center position of the attractor; constructing a repulsive-attractive bipolar potential field based on the position of the topological singular point; The conventional gravitational potential field and the repulsion-attraction bipolar potential field are superimposed to form a composite potential field intensity distribution.

6. The method for precise tracking and controlling an unmanned aerial vehicle according to claim 1, wherein: Adaptively modulating the potential field gradient information based on the relative relationship between the current position and the attractor center position includes: Calculate the distance from the current position to the center of the attractor; The potential field gradient information is nonlinearly modulated based on the distance value to obtain modulation gradient information, wherein when the distance value is greater than a preset distance threshold, a gradient amplification function is used to enhance the control response; when the distance value is less than the preset distance threshold, a gradient attenuation function is used to avoid overshoot.

7. The method for precise tracking and controlling an unmanned aerial vehicle according to claim 1, wherein: The performing vector decomposition and selective enhancement processing on the modulation gradient information in the local coordinate system to generate tracking adjustment parameters includes: extracting a gradient vector from the modulation gradient information; Decomposing the gradient vector into a radial component and a circumferential component; The radial component is kept for basic track tracking, and the curl enhancement is applied to the circumferential component to form a spiral potential field around the singular point; The enhanced circumferential component and the radial component are resynthesized to generate tracking adjustment parameters.

8. The method for precise tracking and controlling an unmanned aerial vehicle according to claim 4, wherein: The determining the attractor type based on the convergence region information and generating an attractor type identifier includes: Performing geometric shape analysis on the convergence region information to generate a shape feature descriptor; Perform attractor classification matching based on the shape feature descriptors and construct a classification result matrix; Performing type coding analysis based on the classification result matrix to generate coding identification parameters; An attractor type identifier is generated according to the encoding identifier parameter.

9. A precise track tracking control device for an unmanned aerial vehicle, characterized in that: include: A data fusion module is used to obtain GPS track data and flight status information of the UAV, perform data fusion processing on the GPS track data and the flight status information to generate fused status data, and perform phase space reconstruction on the fused status data to form a track-state phase space model; a trajectory analysis module, configured to perform dynamic trajectory analysis on the track-state phase space model to obtain phase trajectory characteristic parameters, and perform attractor identification processing based on the phase trajectory characteristic parameters to determine dynamic attractor characteristics of track tracking; A potential field construction module is used to perform phase space topological analysis based on the characteristics of the dynamic attractor to identify the attractor center position and the topological singular point position, and generate a composite potential field intensity distribution based on the attractor center position and the topological singular point position; a gradient modulation module, configured to perform gradient calculation and direction analysis on the composite potential field intensity distribution to obtain potential field gradient information, and adaptively modulate the potential field gradient information based on the relative relationship between the current position and the attractor center position to obtain modulation gradient information; a control generation module, configured to construct a local coordinate system based on the modulation gradient information and the topological singular point position, perform vector decomposition and selective enhancement processing on the modulation gradient information in the local coordinate system to generate tracking adjustment parameters, and generate tracking control instructions based on the tracking adjustment parameters; The signal output module is used to modulate and output the control signal according to the tracking control instruction, output the modulated flight control signal, and output the modulated flight control signal to the flight control system to achieve accurate tracking and control of the UAV on the preset route.

10. A computer device, characterized in that: The method comprises a memory and a processor; the memory is used to store a computer program; the processor is used to execute the computer program and implement the method according to any one of claims 1 to 8 when executing the computer program.

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