Oil immersed transformer inspection robot spectrum manifold modeling and control method

Abstract

The invention provides an oil immersed transformer inspection robot spectrum manifold modeling and control method, and relates to the field of data processing. The method comprises the following steps: acquiring an attenuation track of an oil immersed transformer inspection robot without control input, extracting a dominant singular vector to construct a spectrum manifold approximate tangent space, mapping a high-dimensional observation variable to a spectrum manifold dimensionality reduction coordinate system, and fitting an autonomous drift term and a control input influence term to construct a low-dimensional dynamic model; a control observation space is further constructed, a reverse re-parameter mapping function is established, a current observation variable is obtained in real time and mapped to spectrum manifold dimensionality reduction coordinates, a rolling time domain trajectory prediction optimization problem is constructed, a control input sequence is linearly solved through a sequence convex programming algorithm, and closed-loop control is completed. According to the technical scheme, the stability of the oil immersed transformer inspection robot can be improved conveniently.

Description

Technical Field

[0001] This application relates to the technical field of data processing, specifically to a method for spectral manifold modeling and control of an oil-immersed transformer inspection robot. Background Technology

[0002] With the continuous expansion of the State Grid infrastructure and the increasing service life, oil-immersed transformers, as core equipment in high-voltage power transmission, directly affect the reliability of the entire power system through their operational safety and internal structural stability. Currently, internal inspections of oil-immersed transformers primarily rely on manual disassembly and inspection. However, due to the high-viscosity insulating oil filling the interior, the limited space, and the complex electrical environment, manual inspections not only pose significant safety risks but also frequently lead to prolonged power outages, extended maintenance cycles, and system interruptions, severely restricting the timeliness of transformer condition monitoring and risk warning.

[0003] Therefore, developing an oil-immersed transformer inspection robot capable of stable operation in high-viscosity liquid environments has become an important direction for improving the intelligent operation and maintenance of transformers. However, due to the complex physical mechanisms introduced by the oil medium, such as strong nonlinear fluid damping, attitude disturbances, and propulsion coupling, traditional modeling methods, such as analytical models or higher-dimensional linear approximation methods based on the Koopman operator, are difficult to effectively capture the dominant dynamic behavior of the system in real operating environments, resulting in poor stability of the oil-immersed transformer inspection robot.

[0004] Therefore, there is an urgent need for a spectral manifold modeling and control method for oil-immersed transformer inspection robots. Summary of the Invention

[0005] This application provides a method for spectral manifold modeling and control of an oil-immersed transformer inspection robot, which facilitates the improvement of the stability of the oil-immersed transformer inspection robot.

[0006] The first aspect of this application provides a method for modeling and controlling the spectral manifold of an oil-immersed transformer inspection robot. The method includes: acquiring attenuation trajectory data of the oil-immersed transformer inspection robot under conditions without control input; extracting dominant singular vectors from the attenuation trajectory data based on singular value decomposition; constructing an approximate tangent space of the spectral manifold; and mapping the original high-dimensional observation variables to a dimensionality-reduced coordinate system of the spectral manifold based on the approximate tangent space. In the dimensionality-reduced coordinate system of the spectral manifold, autonomous drift terms and control input influence terms are fitted respectively based on polynomial basis functions to construct a low-dimensional model of the oil-immersed transformer inspection robot. A dynamic model is established; a control observation space is constructed based on the low-dimensional dynamic model, and the inverse reparameter mapping function from the control observation space to the spectral manifold is determined; the current observation variables of the oil-immersed transformer inspection robot are obtained, the inverse reparameter mapping function is input, the current dimensionality-reduced coordinates of the spectral manifold are obtained, and a trajectory prediction optimization problem in the rolling time domain is constructed through the dimensionality-reduced coordinates of the spectral manifold; the trajectory prediction optimization problem is solved linearly based on the sequential convex programming algorithm to obtain the control input sequence, and the oil-immersed transformer inspection robot is controlled through the control input sequence.

[0007] Optionally, the step of acquiring the attenuation trajectory data of the oil-immersed transformer inspection robot under no-control input conditions, extracting the dominant singular vectors from the attenuation trajectory data based on singular value decomposition, constructing an approximate tangent space of the spectral manifold, and mapping the original high-dimensional observation variables to the dimensionality-reduced coordinate system of the spectral manifold according to the approximate tangent space specifically includes: controlling the oil-immersed transformer inspection robot to perform natural attenuation motion under no-control input conditions, and collecting displacement, attitude, and acceleration observation variables through an inertial measurement unit and attitude position sensor to construct an attenuation trajectory data matrix; performing singular value decomposition on the attenuation trajectory data matrix to determine the left singular vector matrix, singular value matrix, and right singular vector matrix; constructing an approximate tangent space of the spectral manifold based on the right singular vectors corresponding to several dominant singular values ​​whose energy proportions in the singular value matrix satisfy a preset threshold; forming a linear projection matrix according to the approximate tangent space, and multiplying the original high-dimensional observation variables by the linear projection matrix to map them to the dimensionality-reduced coordinate system of the spectral manifold.

[0008] Optionally, the step of constructing a low-dimensional dynamic model of the oil-immersed transformer inspection robot by fitting autonomous drift terms and control input influence terms respectively based on polynomial basis functions in the spectral manifold reduced coordinate system specifically includes: calculating the time derivative of the spectral manifold reduced coordinate system based on the state time series in the spectral manifold reduced coordinate system through finite difference fitting, and constructing the target response quantity of the autonomous drift term; selecting the polynomial basis functions of a preset order, constructing the polynomial tensor product input vector of the spectral manifold reduced coordinate system, and fitting the mapping relationship between the reduced state and the time derivative using the least squares regression method to obtain... The coefficient matrix of the autonomous drift term is obtained; the observation trajectory data of the oil-immersed transformer inspection robot under the action of control input is obtained and mapped to the spectral manifold dimension-reduced coordinate system. Combined with the control input, a composite input vector is constructed consisting of the control input, the spectral manifold dimension-reduced coordinate system, and the tensor product term; based on the time derivative as the target response quantity, the linear term and nonlinear state modulation term of the control input influence are fitted by regression method to obtain the linear response matrix and nonlinear modulation coefficient tensor of the control input influence term, and a low-dimensional dynamic model containing the autonomous drift term and the control input influence term is constructed.

[0009] Optionally, the step of constructing a control observation space based on the low-dimensional dynamic model and determining the inverse reparameter mapping function from the control observation space to the spectral manifold specifically includes: constructing training data pairs based on the dimensionality-reduced coordinates of the spectral manifold and the original observation variables at the corresponding time; constructing a forward embedding mapping function from the dimensionality-reduced coordinates of the spectral manifold to the control observation space using polynomial basis functions to obtain an initial control observation space expression; constructing an inverse reparameter mapping function from the control observation space to the dimensionality-reduced coordinates of the spectral manifold based on the pairing relationship between the initial control observation space expression and the dimensionality-reduced coordinates of the spectral manifold; the inverse reparameter mapping function constructs a nonlinear regression expression through tensor product polynomial basis expansion.

[0010] Optionally, the step of obtaining the current observed variables of the oil-immersed transformer inspection robot, inputting them into the inverse reparameter mapping function to obtain the current spectral manifold reduced coordinates, and constructing a trajectory prediction optimization problem in the rolling time domain using the spectral manifold reduced coordinates specifically includes: obtaining the current observed variables of the oil-immersed transformer inspection robot at the current control moment; inputting the current observed variables into the inverse reparameter mapping function to obtain the current spectral manifold reduced coordinates; setting a fixed-length rolling time window and prediction steps; in the spectral manifold reduced coordinate system, using the current spectral manifold reduced coordinates as the initial state, and recursively generating a multi-step state evolution sequence in the prediction time domain in combination with the low-dimensional dynamic model; based on the multi-step state evolution sequence, constructing an objective function including a state deviation cost term, a control input penalty term, and a terminal state cost term, and applying state constraints and control input constraints to form a trajectory prediction optimization problem in the rolling time domain.

[0011] Optionally, the linearization solution of the trajectory prediction optimization problem based on the sequential convex programming algorithm to obtain the control input sequence, and the control of the oil-immersed transformer inspection robot through the control input sequence, specifically includes: based on the current spectral manifold reduced coordinates, performing a first-order linear expansion along the autonomous drift term and control input influence term of the low-dimensional dynamic model to construct a linearized state transition model of the current spectral manifold reduced coordinates at the current prediction step; substituting the linearized state transition model into the objective function of the rolling time domain to reconstruct a convex quadratic programming problem with a quadratic cost term and linear constraints; iteratively solving the convex quadratic programming problem using the sequential convex programming algorithm to obtain the control input sequence that minimizes the cost function; extracting the first control input from the control input sequence and sending it to the oil-immersed transformer inspection robot to achieve closed-loop control of the current motion state.

[0012] Optionally, the reference trajectory is updated in real time during control execution; the predicted state of the oil-immersed transformer inspection robot in the spectral manifold reduced coordinate system is dynamically compared with the reference trajectory to obtain the degree of trajectory deviation; the optimization objective function in the rolling time domain is adjusted according to the degree of trajectory deviation to generate optimization results, which are used to correct the control input sequence for the next cycle to achieve adaptive tracking control of the non-static target trajectory.

[0013] A second aspect of this application provides a spectral manifold modeling and control device for an oil-immersed transformer inspection robot. The device includes an acquisition module and a processing module. The acquisition module acquires attenuation trajectory data of the oil-immersed transformer inspection robot under no-control-input conditions, extracts dominant singular vectors from the attenuation trajectory data based on singular value decomposition, constructs an approximate tangent space of the spectral manifold, and maps the original high-dimensional observation variables to a reduced-dimensional coordinate system of the spectral manifold based on the approximate tangent space. The processing module constructs a low-dimensional model of the oil-immersed transformer inspection robot in the reduced-dimensional coordinate system of the spectral manifold by fitting autonomous drift terms and control input influence terms respectively based on polynomial basis functions. The processing module is further configured to construct a control observation space based on the low-dimensional dynamic model and determine the inverse reparameter mapping function from the control observation space to the spectral manifold; the acquisition module is further configured to acquire the current observation variables of the oil-immersed transformer inspection robot, input the inverse reparameter mapping function, obtain the current dimensionality-reduced coordinates of the spectral manifold, and construct a trajectory prediction optimization problem in the rolling time domain using the dimensionality-reduced coordinates of the spectral manifold; the processing module is further configured to linearize and solve the trajectory prediction optimization problem based on the sequential convex programming algorithm to obtain the control input sequence, and control the oil-immersed transformer inspection robot using the control input sequence.

[0014] A third aspect of this application provides an electronic device including a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, and both the user interface and the network interface are used to communicate with other devices. The processor is used to execute the instructions stored in the memory to cause the electronic device to perform the method described above.

[0015] A fourth aspect of this application provides a computer-readable storage medium storing instructions that, when executed, perform the method described above.

[0016] In summary, one or more technical solutions provided in this application have at least the following technical effects or advantages: 1. By introducing a control architecture that combines spectral manifold modeling and model predictive control into the oil-immersed transformer inspection robot, it is possible to accurately describe nonlinear dynamic behavior in a low-dimensional state expression in a viscous fluid environment, which greatly reduces the control computation burden, improves trajectory tracking stability, real-time performance and control accuracy, and solves the technical bottleneck of high modeling dimensionality and poor control stability in the oil environment of traditional methods.

[0017] 2. By fitting the time derivatives and control response terms of the dimensionality-reduced coordinates of the spectral manifold, a complete low-dimensional dynamic model consisting of autonomous drift terms and control input influence terms was established. This modeling mechanism enables the system to model the nonlinear response to external control inputs while preserving the dominant dynamic characteristics. It is a key guarantee for control accuracy, predictability, and response stability, and directly determines the controllability and response quality of the entire control system.

[0018] 3. By transforming the nonlinear trajectory prediction optimization problem into a convex quadratic programming problem under linear constraints and solving it using a sequential convex programming algorithm, the controller can generate usable control input sequences in a highly efficient and low-latency manner. This step significantly improves the real-time response capability of the control and its deployment adaptability in embedded hardware environments, representing a key enhancement mechanism for the engineering feasibility of the control system. Attached Figure Description

[0019] Figure 1 A flowchart illustrating a spectral manifold modeling and control method for an oil-immersed transformer inspection robot provided in an embodiment of this application; Figure 2 A schematic diagram of a spectral manifold modeling and control device for an oil-immersed transformer inspection robot provided in an embodiment of this application; Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application.

[0020] Explanation of reference numerals in the attached figures: 21. Acquisition module; 22. Processing module; 31. Processor; 32. Communication bus; 33. User interface; 34. Network interface; 35. Memory. Detailed Implementation

[0021] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments.

[0022] In the description of the embodiments of this application, the words "for example" or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design that is described as "for example" or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design options. Rather, the use of the words "for example" or "for instance" is intended to present the relevant concepts in a specific manner.

[0023] In the description of the embodiments of this application, the term "multiple" means two or more. For example, multiple systems means two or more systems, and multiple screen terminals means two or more screen terminals. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the indicated technical features. Thus, a feature defined with "first" or "second" may explicitly or implicitly include one or more of that feature. The terms "comprising," "including," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0024] To address the aforementioned technical problems, this application provides a method for spectral manifold modeling and control of an oil-immersed transformer inspection robot, referring to... Figure 1 , Figure 1 This is a flowchart illustrating a spectral manifold modeling and control method for an oil-immersed transformer inspection robot, provided in an embodiment of this application. The method is applied to a server and includes steps S110 to S150, as follows: S110. Obtain the attenuation trajectory data of the oil-immersed transformer inspection robot under no control input conditions. Extract the dominant singular vector from the attenuation trajectory data based on singular value decomposition, construct the approximate tangent space of the spectral manifold, and map the original high-dimensional observation variables to the dimensionality-reduced coordinate system of the spectral manifold according to the approximate tangent space.

[0025] Specifically, the "no control input condition" refers to the practice during the modeling phase where, to accurately obtain the intrinsic dynamic characteristics of the system, no external control signals (such as propulsion voltage or attitude adjustment commands) are applied to the oil-immersed transformer inspection robot, allowing it to naturally decay back to a stable state under the initial disturbance. In this state, the motion is entirely determined by the system's own structure and the fluid environment, without any active intervention. For example, after releasing the initial displacement disturbance, the robot is allowed to freely decay its motion in the oil. The decay trajectory data refers to the multi-channel time-series data of the oil-immersed transformer inspection robot's position, attitude, velocity, and other states naturally decaying over time under the conditions of no control input, influenced by nonlinear factors such as fluid damping and inertial coupling. This data captures the system's intrinsic modal response process. For example, the entire record of the robot's asymmetric rotation after being subjected to a small impact, and its attitude angle slowly recovering to a stationary state over time, constitutes the decay trajectory data.

[0026] Singular Value Decomposition (SVD) is a matrix factorization method that decomposes the decay trajectory data matrix into three parts: a left singular vector matrix (representing the projection coefficients of each time step in the principal direction), a singular value matrix (representing the energy magnitude in the principal direction), and a right singular vector matrix (representing the principal direction of the observation channel). This method is used to extract the most representative dynamic patterns and reduce data dimensionality. For example, performing SVD on the robot's three-axis acceleration and attitude trajectory matrices can identify the dominant motion coupling patterns. The dominant singular vectors refer to the directions corresponding to the top few singular vectors with the highest energy proportion in the singular value matrix, representing the low-dimensional feature space with the greatest variation and best describing the dominant dynamic behavior of the system. In practice, the top few sets of singular vectors that account for more than 90% of the cumulative energy are usually retained. For example, the first three dominant singular vectors may correspond to the robot's main pitch, yaw, and fluid dragging directions with gradual changes.

[0027] In nonlinear dynamics, a spectral manifold is a low-dimensional invariant manifold spanned by a set of slow modes, capable of carrying the system's main evolutionary trends and decay behaviors. It is a subset of states that naturally converge under specific perturbations in a high-dimensional system, possessing attractiveness and structure fidelity. For example, after an inspection robot deviates from its stable posture in an oil-immersed environment, its trajectory will eventually converge to the spectral manifold composed of the main slow modes. The approximate tangent space is a first-order linear approximation space of the spectral manifold at its low-dimensional embedding point, composed of dominant singular vectors, representing the local linear spanning direction of the spectral manifold at the current state point. Constructing this tangent space facilitates subsequent linear projection and low-dimensional modeling. For example, if the dominant singular vectors are 3-dimensional, then the approximate tangent space is a 3-dimensional Euclidean space, which is the embedding surface in the original state space describing the main dynamic directions.

[0028] The original high-dimensional observation variables refer to the complete set of state variables collected by the robot at each time step. These typically include acceleration, angular velocity, attitude angles, position coordinates, and flow velocity feedback, and have high dimensionality, containing multi-source coupled information. For example, at a certain moment, the observation variables may include three axial acceleration values, three attitude angle values, and two depth flow velocity values, totaling eight dimensions. The spectral manifold-reduced coordinate system refers to the coordinate system obtained by reducing the original high-dimensional observation variables to a lower dimension through linear projection using the approximate tangent space of the spectral manifold. It is a simplified representation space of the system's dominant dynamic behavior. Each dimension in this coordinate system represents a dominant dynamic mode direction. For example, projecting eight-dimensional observation variables onto a spectral manifold-reduced coordinate system composed of three dominant singular vectors yields a three-dimensional state vector, which can be used as a simplified input state for the dynamic model.

[0029] In one possible implementation, the attenuation trajectory data of an oil-immersed transformer inspection robot under no-control input conditions is acquired. Dominant singular vectors are extracted from the attenuation trajectory data based on singular value decomposition (SVD), and an approximate tangent space of the spectral manifold is constructed. The original high-dimensional observation variables are then mapped to a reduced-dimensional coordinate system of the spectral manifold based on the approximate tangent space. Specifically, this includes: controlling the oil-immersed transformer inspection robot to perform natural attenuation motion under no-control input conditions, and collecting displacement, attitude, and acceleration observation variables through an inertial measurement unit and attitude position sensors to construct an attenuation trajectory data matrix; performing singular value decomposition on the attenuation trajectory data matrix to determine the left singular vector matrix, singular value matrix, and right singular vector matrix; constructing an approximate tangent space of the spectral manifold based on the right singular vectors corresponding to several dominant singular values ​​whose energy proportions satisfy a preset threshold in the singular value matrix; forming a linear projection matrix based on the approximate tangent space, and multiplying the original high-dimensional observation variables by the linear projection matrix to map them to a reduced-dimensional coordinate system of the spectral manifold.

[0030] Specifically, the first step involves controlling the oil-immersed transformer inspection robot to perform natural decay motion without any control input, and collecting observed variables to construct a decay trajectory data matrix. Specifically, while the robot is stationary inside the oil-immersed transformer, the controller is set to zero input, preventing the robot from receiving propulsion or attitude adjustment commands, and only subjecting it to limited initial disturbances (such as attitude disturbances or positional offsets). During this free decay process, an inertial measurement unit (IMU) and attitude position sensors are used to continuously observe the robot's state, collecting multi-dimensional time series data including three-axis displacement, attitude angles (such as pitch, yaw, and roll), and linear acceleration, to construct an observation variable matrix. ,in For the number of time steps, Given the dimensions of the observed variables, this matrix is ​​the decay trajectory data matrix.

[0031] The second step is to perform singular value decomposition on the decay trajectory data matrix. Singular value decomposition yields the following formula:

[0032] in: : Attenuation trajectory data matrix; : Left singular vector matrix, column vectors represent the projection direction of the active dynamics in the observation time dimension; : Singular value matrix, with non-negative real numbers on the main diagonal, representing the energy magnitude of each dominant direction; : Right singular vector matrix, column vectors represent the directions of the principal modes in the observation variable space.

[0033] The third step involves constructing an approximate tangent space for the spectral manifold based on the right singular vectors corresponding to the dominant singular values ​​in the singular value matrix whose energy proportions satisfy a preset threshold. Let the energy threshold be... Statistical outliers The item satisfies:

[0034] in Indicates the first A singular value. Before selection. The right singular vectors corresponding to the singular values ​​form a matrix. The column vectors of this matrix serve as orthogonal bases for the approximate tangent space of the spectral manifold, representing the linear embedding structure of the system in the dominant direction, also known as the spectral tangent space projection basis.

[0035] The fourth step involves forming a linear projection matrix based on the approximate tangent space of the spectral manifold, and mapping the original high-dimensional observation variables to the reduced-dimensional coordinate system of the spectral manifold. This is achieved using the approximate tangent space basis. Forming a linear projection matrix The definition is as follows:

[0036] Original observed variables Linear projection is performed at each time step to obtain the dimensionality-reduced coordinates of the spectral manifold. ,Right now:

[0037] in: : Dimensionally reduced coordinates of the spectral manifold; : Original observed variables; : an orthogonal basis for the approximate tangent space of a spectral manifold.

[0038] Through the above steps, the original complex observation variables are compressed into a dimensionality-reduced coordinate system of the spectral manifold in a low-dimensional space, realizing a structured representation of the dominant dynamic behavior and providing a low-dimensional controllable state foundation for subsequent fitting of dynamic models and predictive control strategies. This process can be repeatedly executed in batch processing or online sliding window mode in actual deployments to achieve dynamic updates of the spectral manifold and synchronization of state mapping.

[0039] S120. In the dimensionality-reduced coordinate system of the spectral manifold, a low-dimensional dynamic model of the oil-immersed transformer inspection robot is constructed by fitting autonomous drift terms and control input influence terms based on polynomial basis functions.

[0040] Specifically, polynomial basis functions refer to a set of polynomial functions used when fitting dynamic relationships to construct a nonlinear mapping between state variables and their time derivatives. These basis functions can flexibly express nonlinear characteristics. For example, if the motion of an oil-immersed transformer inspection robot in oil is affected by nonlinear fluid resistance, it is difficult to accurately describe the dynamic behavior using only linear functions, while polynomial basis functions can capture this nonlinear response. Autonomous drift terms refer to the natural evolution trend of a system's state over time when there is no external control input. Control input influence terms refer to the force terms generated by external control signals (such as the voltage of a micro-jet propulsion device or the duty cycle of a pump) on the system's state changes. Low-dimensional dynamic models refer to the system dynamic equations composed of autonomous drift terms and control input influence terms in a spectral manifold-reduced coordinate system, describing the main evolution laws of the original high-dimensional nonlinear dynamic system with low-dimensional state variables.

[0041] In one possible implementation, a low-dimensional dynamic model of the oil-immersed transformer inspection robot is constructed in the spectral manifold reduced-dimensional coordinate system by fitting autonomous drift terms and control input influence terms based on polynomial basis functions. Specifically, this includes: calculating the time derivative of the spectral manifold reduced-dimensional coordinate system using finite difference fitting based on the state-time series in the spectral manifold reduced-dimensional coordinate system to construct the target response of the autonomous drift term; selecting polynomial basis functions of a preset order to construct the polynomial tensor product input vector of the spectral manifold reduced-dimensional coordinate system; and using least squares regression to fit the relationship between the reduced-dimensional state and the time derivative. The mapping relationship is used to obtain the coefficient matrix of the autonomous drift term; the observation trajectory data of the oil-immersed transformer inspection robot under the action of control input is obtained and mapped to the spectral manifold dimension-reduced coordinate system. Combined with the control input, a composite input vector composed of the control input, the spectral manifold dimension-reduced coordinate system, and the tensor product term is constructed; based on the time derivative as the target response quantity, the linear term and nonlinear state modulation term of the control input influence are fitted by regression method to obtain the linear response matrix and nonlinear modulation coefficient tensor of the control input influence term, and a low-dimensional dynamic model containing the autonomous drift term and the control input influence term is constructed.

[0042] Specifically, the first step involves calculating the time derivative of the reduced-dimensional coordinates of the spectral manifold based on the state-time series in the reduced-dimensional coordinate system, thus constructing the target response of the autonomous drift term. The attenuation trajectory data collected by the oil-immersed transformer inspection robot under no-control-input conditions is then projected onto the reduced-dimensional coordinate system of the spectral manifold to obtain the reduced-dimensional state series. The state derivative at each time step is approximated using the finite difference method, specifically:

[0043] in: : No. Dimensionally reduced coordinates of the spectral manifold at time points; The corresponding time derivative is used as the target response of the autonomous drift term; Time step. This process generates... The sequence will be used as the target variable for subsequent regression fitting, reflecting the changing trend of the natural evolution state of the oil-immersed transformer inspection robot.

[0044] The second step involves selecting polynomial basis functions of a preset order, constructing the polynomial tensor product input vector of the spectral manifold's dimensionality-reduced coordinates, and fitting the autonomous drift term. The maximum order of the polynomial is set to [value missing]. Using all dimensionality-reduced coordinates Constructing a polynomial tensor product basis function vector ,in This represents the total number of terms in the polynomial. Each... With the corresponding Form regression pairs and fit the following relationships using least squares regression:

[0045] in: : The coefficient matrix of the autonomous drift term; The input vector is a polynomial tensor product composed of reduced-dimensional states. This regression model compresses the high-dimensional nonlinear mapping into a polynomial approximation structure on low-dimensional states, yielding the autonomous drift term. .

[0046] The third step involves acquiring the observed trajectory data under control inputs and mapping it to a spectral manifold reduced-dimensional coordinate system to construct a composite input vector. The oil-immersed transformer inspection robot is then run under open-loop control, and data is collected under different control inputs. Under certain conditions, the observed variables are mapped to a reduced-dimensional state sequence. To fit the control input influence term, the values ​​at each time step are... , Combined with its tensor product term, it forms a composite input vector:

[0047] in This represents the Kronecker product operation, which generates control-related nonlinear interaction terms; this vector describes how the control input modulates the system evolution as the state changes.

[0048] The fourth step involves fitting the linear and nonlinear state modulation terms that control the input's influence to construct a complete low-dimensional dynamic model, based on the time derivative as the target response. The resulting dynamic expression is as follows:

[0049] in: Autonomous drift term; The linear response matrix of the control input; : The coefficient tensor of the nonlinear modulation term; : Tensor product of state and control inputs.

[0050] In regression fitting, construct respectively and The input vector is solved using the joint least squares method. and Finally, a complete low-dimensional dynamic model containing autonomous drift terms and control input influence terms is obtained:

[0051] This model achieves unified modeling of the natural decay behavior and control response behavior of an oil-immersed transformer inspection robot in a spectral manifold reduced-dimensional coordinate system. It has advantages such as compact structure, high modeling accuracy, and ease of embedding into control frameworks. The model parameters can be fitted offline through batch processing or iteratively updated in actual deployment to adapt to dynamic environmental changes.

[0052] S130. Construct a control observation space based on a low-dimensional dynamic model, and determine the inverse reparameter mapping function from the control observation space to the spectral manifold.

[0053] Specifically, the control observation space refers to an intermediate state space that needs to be constructed to achieve state observation and feedback in the control closed loop of the oil-immersed transformer inspection robot. Its variables are observables that can be directly obtained from sensors or derived by combination. In this space, the controller can perform calculations based on actual observed variables (such as acceleration and attitude angles), thus replacing the spectral manifold reduced coordinates that are difficult to obtain directly. The purpose of the control observation space is to bridge the expression difference between the original high-dimensional observed variables and the spectral manifold reduced coordinates. For example, if the original observed variables are 8-dimensional, but the spectral manifold reduced coordinates are only 3-dimensional, then a 6-dimensional orthogonal control observation space can be constructed, making it both observable and adaptable to the modeling structure. The inverse reparameter mapping function from the control observation space to the spectral manifold refers to the function that nonlinearly maps the control observation space variable y(t) at the current moment to the spectral manifold reduced coordinate z(t), used for state reconstruction and model input initialization.

[0054] Therefore, based on the established low-dimensional dynamic model, a set of structured mapping mechanisms is introduced to achieve real-time control. The construction of the control observation space ensures that the observed variables effectively cover the spectral manifold state, while the inverse reparameter mapping function realizes the accurate recovery from observables to the dimensionality-reduced coordinates of the spectral manifold. This allows the controller to complete trajectory prediction and control input generation without directly obtaining the high-dimensional hidden state in actual deployment, thereby supporting the state estimation and closed-loop control objectives in the entire control loop of the oil-immersed transformer inspection robot.

[0055] In one possible implementation, a control observation space is constructed based on a low-dimensional dynamic model, and a reverse reparameter mapping function from the control observation space to the spectral manifold is determined. Specifically, this includes: constructing training data pairs based on the dimensionality-reduced coordinates of the spectral manifold and the original observation variables at corresponding times; constructing a forward embedding mapping function from the dimensionality-reduced coordinates of the spectral manifold to the control observation space using polynomial basis functions to obtain an initial control observation space expression; constructing a reverse reparameter mapping function from the control observation space to the dimensionality-reduced coordinates of the spectral manifold based on the pairing relationship between the initial control observation space expression and the dimensionality-reduced coordinates of the spectral manifold; and constructing a nonlinear regression expression for the reverse reparameter mapping function through tensor product polynomial basis expansion.

[0056] Specifically, the first step involves constructing training data pairs based on the spectral manifold dimensionality-reduced coordinates and the corresponding original observation variables, and then constructing a positive embedding mapping function from the spectral manifold dimensionality-reduced coordinates to the control observation space. After completing the spectral manifold dimensionality-reduction modeling, the spectral manifold dimensionality-reduced coordinates from the same time series are obtained. With the corresponding original observed variables This constitutes the training dataset. For input, To achieve this, a nonlinear mapping from the dimension-reduced coordinates of the spectral manifold to the observed variables is constructed using tensor product polynomial basis functions:

[0057] in: : Polynomial extended basis functions (such as those containing first-order, second-order, and cross terms); The positive embedding mapping matrix is ​​obtained by fitting using the least squares method. The original observed variables serve as the initial representation of the control observation space. Through this fitting operation, the dimensionality-reduced coordinates of the spectral manifold are embedded into the control observation space, achieving an initial reconstruction of the state in the dimension of the observed variables.

[0058] The second step involves constructing a reverse reparameter mapping function from the initial control observation space representation to the spectral manifold reduced coordinates, based on the pairing relationship between the initial control observation space representation and the spectral manifold reduced coordinates. After obtaining the observed variables under the spectral manifold reduced coordinates and their forward embedding mapping, the following steps are taken: For input, To achieve this goal, we reconstruct the nonlinear mapping using tensor product polynomial basis functions, establishing an inverse function from the control observation space to the dimension-reduced coordinates of the spectral manifold:

[0059] in: : Controlling the polynomial expansion of the observed variables; : Inverse reparameter mapping coefficient matrix; This function represents the nonlinear reconstruction of a low-dimensional state in the control observation space. It allows the controller to reconstruct the state at each time step using observed variables. Real-time estimation of spectral manifold dimensionality reduction coordinates This ensures a closed-loop online computation for status feedback.

[0060] The third step involves training constraints and orthogonalization of the inverse reparameter mapping function. To improve the stability and discriminability of the inverse reparameter mapping function, the initial fitting results are first subjected to Schmitt orthogonalization to ensure that the higher-order basis function terms... Satisfies orthogonality, that is:

[0061] Then retrain the mapping matrix in the orthogonal space. Finally, a mapping function that satisfies structural orthogonality and minimizes fitting error is constructed, specifically as follows:

[0062] in: For an identity matrix, the constraint is represented. The columns are orthogonal; the optimization objective is to minimize the mean square error between the dimensionality-reduced coordinates of the spectral manifold and their estimated values.

[0063] Through the above three steps, a bidirectional invertible mapping relationship is established between the spectral manifold reduced coordinate system and the control observation space. The forward embedding function expresses the projection of the spectral structure onto observables, while the reverse reparameter mapping function enables state feedback estimation. This allows the oil-immersed transformer inspection robot to initialize trajectory prediction in real-time within the spectral manifold reduced coordinate system based on current observed variables, thus supporting the controller in performing rolling trajectory optimization and closed-loop control in the low-dimensional state space. This mapping mechanism possesses high fidelity, differentiability, and orthogonal decoupling capabilities, which are key guarantees for the real-time control response and the feasibility of modeling in this technical solution.

[0064] S140. Obtain the current observation variables of the oil-immersed transformer inspection robot, input the inverse reparameter mapping function, obtain the current spectral manifold dimension-reduced coordinates, and construct the trajectory prediction optimization problem in the rolling time domain through the spectral manifold dimension-reduced coordinates.

[0065] Specifically, the currently observed variable refers to the original multi-channel state variables of the oil-immersed transformer inspection robot collected by the inertial measurement unit, attitude position sensor, depth gauge, or other sensors at a certain control moment, including variables such as the robot's real-time position, attitude, velocity, and acceleration. The current spectral manifold reduced coordinates refer to the low-dimensional state expression obtained through spectral manifold approximation modeling. This state retains only the most dominant slow mode in the dynamics of the oil-immersed transformer inspection robot at the current moment, eliminating high-frequency disturbances and instantaneous excitation components; it is the mapping result of the high-dimensional system on the main dynamic structure. The rolling time domain refers to the future time period defined in model predictive control, within which the system state is predicted, optimized, and a control input sequence is generated. This time domain has a finite length and moves forward continuously with the control moment, typically set to an N-step prediction window. The trajectory prediction optimization problem refers to the joint optimization of the future N-step state trajectory and control input sequence based on the current state and a set reference trajectory in the spectral manifold reduced coordinate system. The goal is to minimize state deviation and control cost while satisfying system dynamics and constraints.

[0066] The core supporting mechanism for achieving a closed loop of perception-decision-execution in oil-immersed transformer inspection robots is to complete state estimation through an inverse reparameter mapping function, realize multi-step optimization planning through a rolling time domain, and generate control inputs through trajectory prediction optimization problems.

[0067] In one possible implementation, the current observed variables of the oil-immersed transformer inspection robot are obtained, and the inverse reparameter mapping function is input to obtain the current spectral manifold reduced coordinates. A trajectory prediction optimization problem in the rolling time domain is then constructed using these spectral manifold reduced coordinates. Specifically, this includes: obtaining the current observed variables of the oil-immersed transformer inspection robot at the current control moment; inputting the current observed variables into the inverse reparameter mapping function to obtain the current spectral manifold reduced coordinates; setting a fixed-length rolling time window and prediction steps; in the spectral manifold reduced coordinate system, using the current spectral manifold reduced coordinates as the initial state, and recursively generating a multi-step state evolution sequence in the prediction time domain using a low-dimensional dynamics model; based on the multi-step state evolution sequence, constructing an objective function containing a state deviation cost term, a control input penalty term, and a terminal state cost term, and applying state constraints and control input constraints to form a trajectory prediction optimization problem in the rolling time domain.

[0068] Specifically, the first step is to obtain the current observed variables of the oil-immersed transformer inspection robot at the current control moment, within the control cycle. Inside, the state variables of the oil-immersed transformer inspection robot are collected through inertial measurement units, attitude and position sensors, etc., forming the current observation variables. This includes high-dimensional observable measurements such as triaxial angles, velocities, accelerations, depths, and voltages. For example:

[0069] This variable belongs to the control observation space and is the input source for subsequent state estimation and control initialization.

[0070] The second step involves inputting the current observed variables into the inverse reparameter mapping function to obtain the dimensionality-reduced coordinates of the current spectral manifold. Then, the trained inverse reparameter mapping function is used to... Mapped to spectral manifold reduced coordinates The mapping formula is as follows:

[0071] in: : For observed variables Perform tensor product polynomial basis expansion; The mapping parameter matrix obtained during training; : Dimensionality-reduced coordinates of the spectral manifold are used for prediction initialization. This step enables real-time estimation from high-dimensional observed variables to low-dimensional states and serves as the starting point for trajectory optimization.

[0072] The third step involves setting a fixed-length rolling time window and the number of prediction steps. In the reduced-dimensional coordinate system of the spectral manifold, using the current reduced-dimensional coordinates as the initial state, a multi-step state evolution sequence is recursively generated within the prediction time domain using a low-dimensional dynamics model. The length of the rolling time window is set to... The prediction step size is a unit time step. From the current moment Constructing a state sequence by recursion to the future The future state is recursively generated based on the fitted low-dimensional dynamic model:

[0073] in: : No. Dimensionality reduction coordinates of the spectral manifold at each step; : Control input; Autonomous drift term; : Control input factors. As the initial state It iteratively generates state predictions for each future step, which are used for trajectory planning and cost function construction.

[0074] The fourth step involves constructing an objective function based on the multi-step state evolution sequence, including a state deviation cost term, a control input penalty term, and a terminal state cost term. State constraints and control input constraints are then applied, forming a trajectory prediction optimization problem in the rolling time domain. This problem is then solved based on the predicted state sequence. With the target reference trajectory Construct the following trajectory prediction optimization objective function:

[0075] in: : No. The reference state of the step; State error cost weight matrix; : Control input cost weight matrix; Terminal state error cost weight matrix.

[0076] And set constraints at the same time:

[0077] in and The state constraint domain and control input restriction domain are used to ensure that the oil-immersed transformer inspection robot operates within the physical safety boundary.

[0078] This process transforms the observed variables of the oil-immersed transformer inspection robot during actual operation into spectral manifold-reduced coordinates using an inverse reparameter mapping function. Then, it initializes and continuously constructs a future state prediction and control input optimization problem within this spectral manifold-reduced coordinate system. This optimization problem considers state deviation, input cost, terminal state penalty, and constraints, serving as the core computational structure for achieving high-precision trajectory tracking and robust response in model predictive control. This scheme ensures that the controller performs efficient and stable closed-loop control based on low-dimensional states, representing a concrete implementation of the deep integration of nonlinear modeling and optimization control.

[0079] S150. The trajectory prediction optimization problem is solved linearly based on the sequential convex programming algorithm to obtain the control input sequence, and the oil-immersed transformer inspection robot is controlled by the control input sequence.

[0080] Specifically, sequential convex programming algorithms are a class of approximation algorithms for solving nonlinear optimization problems. By linearizing or convexizing the nonconvex objective function and nonlinear constraints near the current state, the original nonconvex problem is transformed into a series of easily solvable convex optimization subproblems for iterative solution. The basic idea is that in each iteration, the nonlinear system is linearly approximated using the current estimated point to construct a convex optimization problem for solving the control input. The state is then updated before the next linearization round, continuing until convergence. Linearization refers to approximating the original nonlinear dynamic model linearly at the current operating point using first-order Taylor expansion or Jacobian matrix approximation, forming a linear state transition model, thus transforming the nonconvex trajectory optimization problem into a convex quadratic programming problem. This process is executed once in each rolling optimization, ensuring that each round of optimization is based on the linear structure near the current optimal solution point for prediction updates. The control input sequence refers to the set of control inputs over a future period obtained by solving the linearized trajectory prediction optimization problem in the rolling time domain.

[0081] By employing a sequential convex programming algorithm, the nonlinear optimization problem is transformed into a solvable convex structure. Within each rolling cycle, linearization modeling and optimization input generation are completed, and the output control input sequence is applied to achieve closed-loop execution. This method effectively improves the trajectory tracking accuracy, control stability, and real-time computation of oil-immersed transformer inspection robots in complex fluid environments, representing a key step in achieving dimensionality reduction control of high-dimensional nonlinear systems.

[0082] In one possible implementation, the trajectory prediction optimization problem is solved linearly based on a sequential convex programming algorithm to obtain a control input sequence. This control input sequence is then used to control the oil-immersed transformer inspection robot. Specifically, this involves: based on the current spectral manifold reduced coordinates, performing a first-order linear expansion along the autonomous drift term and control input influence term of the low-dimensional dynamics model to construct a linearized state transition model of the current spectral manifold reduced coordinates at the current prediction step; substituting the linearized state transition model into the objective function in the rolling time domain to reconstruct a convex quadratic programming problem with a quadratic cost term and linear constraints; iteratively solving the convex quadratic programming problem using a sequential convex programming algorithm to obtain a control input sequence that minimizes the cost function; and extracting the first control input from the control input sequence and sending it to the oil-immersed transformer inspection robot to achieve closed-loop control of the current motion state.

[0083] Specifically, firstly, the spectral manifold reduced coordinates of the oil-immersed transformer inspection robot in the current control cycle are obtained as the starting state for prediction optimization. Based on these reduced coordinates, the partial derivatives with respect to the state are calculated along the autonomous drift term and control input influence term of the low-dimensional dynamic model in the spectral manifold reduced coordinate system, forming a first-order Taylor expansion structure. Thus, a linearized state transition model is constructed in the current prediction step. This model uses the current spectral manifold reduced coordinates as the linearization point, approximating the nonlinear dynamic relationship in the low-dimensional dynamic model as a linear dynamic system.

[0084] Then, the linearized state transition model constructed above is substituted into the objective function of the previously constructed rolling time domain trajectory prediction optimization problem. The objective function includes a state deviation cost term, a control input penalty term, and a terminal state cost term. After introducing the linearized model, the original nonlinear dynamic constraints in the optimization problem are transformed into linear equality constraints, while keeping the constraint structure of the control variables unchanged. Thus, the original nonlinear optimization problem is reconstructed into a convex quadratic programming problem with a quadratic cost function and a set of linear constraints.

[0085] Next, the sequential convex programming algorithm is invoked to iteratively solve the convex quadratic programming problem in the rolling time domain based on the current linearized model. The algorithm updates the current control input estimate through multiple iterations until the objective function is minimized, thereby outputting a set of control input sequences that satisfy the optimal cost condition in the rolling time domain. This control input sequence represents the control input that needs to be applied at each future prediction time.

[0086] Finally, the system extracts the first control input from the control input sequence as the control signal that needs to be executed immediately in the current cycle. This control signal is then sent to the oil-immersed transformer inspection robot via the network communication module or actuator drive interface. This enables the robot to perform closed-loop attitude adjustment and propulsion control operations according to a linearized predicted trajectory in a high-viscosity oil environment, laying the foundation for a stable state for the next prediction cycle. This closed-loop control process is repeated in each control cycle, continuously optimizing trajectory tracking and dynamically correcting attitude.

[0087] In one possible implementation, the reference trajectory is updated in real time during control execution; the predicted state of the oil-immersed transformer inspection robot in the spectral manifold reduced coordinate system is dynamically compared with the reference trajectory to obtain the degree of trajectory deviation; the optimization objective function in the rolling time domain is adjusted according to the degree of trajectory deviation to generate optimization results, which are used to correct the control input sequence for the next cycle to achieve adaptive tracking control of the non-static target trajectory.

[0088] Specifically, firstly, the expected motion trajectory of the oil-immersed transformer inspection robot within the current time period is obtained. The expected trajectory is dynamically generated based on real-time task objectives or environmental changes, and updated in the time domain as a multi-step reference trajectory point sequence with clear time labels. This sequence is expressed in the spectral manifold dimensionality-reduced coordinate system and serves as the target trajectory benchmark in the rolling time domain.

[0089] Subsequently, the current predicted state evolution sequence in the spectral manifold reduced coordinate system, i.e. the trajectory sequence generated recursively based on the current reduced state and the low-dimensional dynamic model, is paired and compared with the reference trajectory point by point. The degree of deviation between the actual predicted state and the reference state is calculated at the same prediction step. The obtained trajectory deviation can include measures such as Euclidean distance, angle change or attitude deviation.

[0090] Next, the cost weight structure in the original optimization objective function in the rolling time domain is adjusted according to the degree of trajectory deviation at each step. Specifically, this can be manifested by increasing the cost weight of the offset state or increasing the weight ratio of the terminal error in the objective function, making the optimization objective function more sensitive to the local deviation between the current predicted trajectory and the reference trajectory, thereby enhancing its dynamic response capability and control and correction capability.

[0091] Finally, the objective function reconstructed by the deviation sensitivity is combined with the low-dimensional dynamic model to construct a new trajectory prediction optimization problem. Then, the sequential convex programming algorithm is called to solve the control input sequence for the next cycle. The optimization result is used as the control starting point after the end of the current control cycle, effectively realizing the dynamic adaptive tracking and rapid response control of the oil-immersed transformer inspection robot for the non-static reference trajectory.

[0092] This application also provides a spectral manifold modeling and control device for an oil-immersed transformer inspection robot, referring to... Figure 2 , Figure 2 This is a schematic diagram of a spectral manifold modeling and control device for an oil-immersed transformer inspection robot, provided in an embodiment of this application. The device is a server, comprising an acquisition module 21 and a processing module 22. The acquisition module 21 acquires attenuation trajectory data of the oil-immersed transformer inspection robot under conditions without control input, extracts dominant singular vectors from the attenuation trajectory data based on singular value decomposition, constructs an approximate tangent space of the spectral manifold, and maps the original high-dimensional observation variables to a reduced-dimensional coordinate system of the spectral manifold based on the approximate tangent space. The processing module 22, in the reduced-dimensional coordinate system of the spectral manifold, fits autonomous drift terms and control input influence terms respectively based on polynomial basis functions to construct a low-dimensional dynamic model of the oil-immersed transformer inspection robot. The processing module 22 constructs a control observation space based on a low-dimensional dynamic model and determines the inverse reparameter mapping function from the control observation space to the spectral manifold; the acquisition module 21 acquires the current observation variables of the oil-immersed transformer inspection robot, inputs the inverse reparameter mapping function, obtains the current dimensionality-reduced coordinates of the spectral manifold, and constructs a trajectory prediction optimization problem in the rolling time domain through the dimensionality-reduced coordinates of the spectral manifold; the processing module 22 solves the trajectory prediction optimization problem linearly based on the sequential convex programming algorithm to obtain the control input sequence, and controls the oil-immersed transformer inspection robot through the control input sequence.

[0093] In one possible implementation, the attenuation trajectory data of the oil-immersed transformer inspection robot under no-control input conditions is acquired. Dominant singular vectors are extracted from the attenuation trajectory data based on singular value decomposition (SVD), and an approximate tangent space of the spectral manifold is constructed. The original high-dimensional observation variables are then mapped to a reduced-dimensional coordinate system of the spectral manifold based on the approximate tangent space. Specifically, the processing module 22 controls the oil-immersed transformer inspection robot to perform natural attenuation motion under no-control input conditions, and collects displacement, attitude, and acceleration observation variables through an inertial measurement unit and attitude position sensor to construct an attenuation trajectory data matrix. The processing module 22 performs singular value decomposition on the attenuation trajectory data matrix to determine the left singular vector matrix, singular value matrix, and right singular vector matrix. Based on the right singular vectors corresponding to several dominant singular values ​​whose energy proportions in the singular value matrix satisfy a preset threshold, the processing module 22 constructs an approximate tangent space of the spectral manifold. The processing module 22 forms a linear projection matrix based on the approximate tangent space and multiplies the original high-dimensional observation variables by the linear projection matrix, mapping them to a reduced-dimensional coordinate system of the spectral manifold.

[0094] In one possible implementation, in the spectral manifold reduced coordinate system, an autonomous drift term and a control input influence term are fitted based on polynomial basis functions to construct a low-dimensional dynamic model of the oil-immersed transformer inspection robot. Specifically, this includes: processing module 22 calculating the time derivative of the spectral manifold reduced coordinate system based on the state-time series in the spectral manifold reduced coordinate system using finite difference fitting, and constructing the target response of the autonomous drift term; processing module 22 selecting polynomial basis functions of a preset order, constructing the polynomial tensor product input vector of the spectral manifold reduced coordinate system, and using least squares regression to fit the relationship between the reduced state and the time derivative. The mapping relationship is used to obtain the coefficient matrix of the autonomous drift term; the acquisition module 21 acquires the observation trajectory data of the oil-immersed transformer inspection robot under the action of control input, and maps it to the spectral manifold dimension-reduced coordinate system. Combined with the control input, a composite input vector composed of the control input, the spectral manifold dimension-reduced coordinate system, and the tensor product term is constructed; the processing module 22 uses the time derivative as the target response quantity, and fits the linear term and nonlinear state modulation term of the control input influence through regression method to obtain the linear response matrix and nonlinear modulation coefficient tensor of the control input influence term, and constructs a low-dimensional dynamic model containing the autonomous drift term and the control input influence term.

[0095] In one possible implementation, a control observation space is constructed based on a low-dimensional dynamic model, and a reverse reparameter mapping function from the control observation space to the spectral manifold is determined. Specifically, the processing module 22 constructs training data pairs based on the dimensionality-reduced coordinates of the spectral manifold and the original observation variables at the corresponding time, and constructs a forward embedding mapping function from the dimensionality-reduced coordinates of the spectral manifold to the control observation space using polynomial basis functions to obtain the initial control observation space expression; the processing module 22 constructs a reverse reparameter mapping function from the control observation space to the dimensionality-reduced coordinates of the spectral manifold based on the pairing relationship between the initial control observation space expression and the dimensionality-reduced coordinates of the spectral manifold, and the reverse reparameter mapping function constructs a nonlinear regression expression through tensor product polynomial basis expansion.

[0096] In one possible implementation, the current observed variables of the oil-immersed transformer inspection robot are obtained, and the inverse reparameter mapping function is input to obtain the current spectral manifold reduced coordinates. A trajectory prediction optimization problem in the rolling time domain is then constructed using these spectral manifold reduced coordinates. Specifically, this includes: an acquisition module 21 acquiring the current observed variables of the oil-immersed transformer inspection robot at the current control moment; a processing module 22 inputting the current observed variables into the inverse reparameter mapping function to obtain the current spectral manifold reduced coordinates; the processing module 22 setting a fixed-length rolling time window and prediction steps, and using the current spectral manifold reduced coordinates as the initial state, recursively generating a multi-step state evolution sequence in the prediction time domain using a low-dimensional dynamics model; and the processing module 22 constructing an objective function containing a state deviation cost term, a control input penalty term, and a terminal state cost term based on the multi-step state evolution sequence, and applying state constraints and control input constraints to form a trajectory prediction optimization problem in the rolling time domain.

[0097] In one possible implementation, the trajectory prediction optimization problem is solved linearly based on a sequential convex programming algorithm to obtain a control input sequence. The control input sequence is then used to control the oil-immersed transformer inspection robot. Specifically, the processing module 22 performs a first-order linear expansion along the autonomous drift term and control input influence term of the low-dimensional dynamic model based on the current spectral manifold reduced coordinates to construct a linearized state transition model of the current spectral manifold reduced coordinates at the current prediction step. The processing module 22 substitutes the linearized state transition model into the objective function in the rolling time domain to reconstruct a convex quadratic programming problem with a quadratic cost term and linear constraints. The processing module 22 iteratively solves the convex quadratic programming problem using a sequential convex programming algorithm to obtain a control input sequence that minimizes the cost function. The processing module 22 extracts the first control input from the control input sequence and sends it to the oil-immersed transformer inspection robot to achieve closed-loop control of the current motion state.

[0098] In one possible implementation, the processing module 22 updates the reference trajectory in real time during the control execution process; the processing module 22 dynamically compares the predicted state of the oil-immersed transformer inspection robot in the spectral manifold reduced coordinate system with the reference trajectory to obtain the degree of trajectory deviation; the processing module 22 adjusts the optimization objective function in the rolling time domain according to the degree of trajectory deviation, generates optimization results, and uses the optimization results to correct the control input sequence of the next cycle to achieve adaptive tracking control of the non-static target trajectory.

[0099] It should be noted that the above embodiments of the apparatus are only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the apparatus and method embodiments provided in the above embodiments belong to the same concept, and the specific implementation process can be found in the method embodiments, which will not be repeated here.

[0100] This application also provides an electronic device, with reference to... Figure 3 , Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include: at least one processor 31, at least one network interface 34, a user interface 33, a memory 35, and at least one communication bus 32.

[0101] The communication bus 32 is used to enable communication between these components.

[0102] The user interface 33 may include a display screen and a camera. Optionally, the user interface 33 may also include a standard wired interface and a wireless interface.

[0103] The network interface 34 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface).

[0104] The processor 31 may include one or more processing cores. The processor 31 connects to various parts of the server via various interfaces and lines, executing instructions, programs, code sets, or instruction sets stored in the memory 35, and calling data stored in the memory 35 to perform various server functions and process data. Optionally, the processor 31 may be implemented using at least one hardware form of Digital Signal Processing (DSP), Field-Programmable Gate Array (FPGA), or Programmable Logic Array (PLA). The processor 31 may integrate one or a combination of several of the following: Central Processing Unit (CPU), Graphics Processing Unit (GPU), and modem. The CPU primarily handles the operating system, user interface, and applications; the GPU is responsible for rendering and drawing the content to be displayed on the screen; and the modem handles wireless communication. It is understood that the modem may also not be integrated into the processor 31 and may be implemented as a separate chip.

[0105] The memory 35 may include random access memory (RAM) or read-only memory. Optionally, the memory 35 may include a non-transitory computer-readable storage medium. The memory 35 can be used to store instructions, programs, code, code sets, or instruction sets. The memory 35 may include a program storage area and a data storage area, wherein the program storage area may store instructions for implementing an operating system, instructions for at least one function (such as touch function, sound playback function, image playback function, etc.), instructions for implementing the above-described method embodiments, etc.; the data storage area may store data involved in the above-described method embodiments, etc. Optionally, the memory 35 may also be at least one storage device located remotely from the aforementioned processor 31. Figure 3 As shown, the memory 35, which serves as a computer storage medium, may include an operating system, a network communication module, a user interface module, and an application program for a spectrum manifold modeling and control method for an oil-immersed transformer inspection robot.

[0106] exist Figure 3In the electronic device shown, the user interface 33 is mainly used to provide an input interface for the user and to obtain the user input data; while the processor 31 can be used to call the application program stored in the memory 35, which is a method for modeling and controlling the spectrum manifold of an oil-immersed transformer inspection robot. When executed by one or more processors, the electronic device executes one or more methods as described in the above embodiments.

[0107] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0108] This application also provides a computer-readable storage medium storing instructions. When executed by one or more processors, these instructions cause an electronic device to perform one or more of the methods described in the above embodiments.

[0109] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0110] In the several embodiments provided in this application, it should be understood that the disclosed apparatus can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the shown or discussed mutual couplings or direct couplings or communication connections may be through some service interfaces; indirect couplings or communication connections between apparatuses or units may be electrical or other forms.

[0111] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0112] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0113] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage device (CMD). Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned memory includes various media capable of storing program code, such as USB flash drives, portable hard drives, magnetic disks, or optical disks.

[0114] The foregoing description is merely an exemplary embodiment of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure. Those skilled in the art will readily conceive of other embodiments of this disclosure upon considering the specification and the disclosure of practical truth. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure. The specification and embodiments are considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

Claims

1. A method for spectral manifold modeling and control of an oil-immersed transformer inspection robot, characterized in that, The method includes: Acquire attenuation trajectory data of oil-immersed transformer inspection robot under no control input conditions, extract dominant singular vectors from the attenuation trajectory data based on singular value decomposition, construct an approximate tangent space of the spectral manifold, and map the original high-dimensional observation variables to the dimensionality-reduced coordinate system of the spectral manifold according to the approximate tangent space. In the reduced-dimensional coordinate system of the spectral manifold, a low-dimensional dynamic model of the oil-immersed transformer inspection robot is constructed by fitting autonomous drift terms and control input influence terms based on polynomial basis functions. Based on the low-dimensional dynamic model, a control observation space is constructed, and the inverse reparameter mapping function from the control observation space to the spectral manifold is determined. The current observation variables of the oil-immersed transformer inspection robot are obtained, the reverse reparameter mapping function is input, the current spectral manifold dimension-reduced coordinates are obtained, and the trajectory prediction optimization problem in the rolling time domain is constructed through the spectral manifold dimension-reduced coordinates. The trajectory prediction optimization problem is solved linearly using a sequential convex programming algorithm to obtain a control input sequence, which is then used to control the oil-immersed transformer inspection robot.

2. The method for spectral manifold modeling and control of an oil-immersed transformer inspection robot according to claim 1, characterized in that, The process of acquiring attenuation trajectory data of an oil-immersed transformer inspection robot under no-control-input conditions, extracting dominant singular vectors from the attenuation trajectory data based on singular value decomposition, constructing an approximate tangent space of the spectral manifold, and mapping the original high-dimensional observation variables to the dimensionality-reduced coordinate system of the spectral manifold according to the approximate tangent space, specifically includes: The oil-immersed transformer inspection robot is controlled to perform natural decay motion without control input, and displacement, attitude and acceleration observation variables are collected by inertial measurement unit and attitude position sensor to construct decay trajectory data matrix; Perform singular value decomposition on the decay trajectory data matrix to determine the left singular vector matrix, singular value matrix, and right singular vector matrix; Based on the right singular vectors corresponding to several dominant singular values ​​whose energy proportions satisfy a preset threshold in the singular value matrix, an approximate tangent space of the spectral manifold is constructed. A linear projection matrix is ​​formed based on the approximate tangent space, and the original high-dimensional observation variables are multiplied by the linear projection matrix and mapped to the spectral manifold reduced coordinate system.

3. The method for spectral manifold modeling and control of an oil-immersed transformer inspection robot according to claim 1, characterized in that, In the reduced-dimensional coordinate system of the spectral manifold, a low-dimensional dynamic model of the oil-immersed transformer inspection robot is constructed by fitting autonomous drift terms and control input influence terms based on polynomial basis functions, specifically including: Based on the state-time series in the reduced-dimensional coordinate system of the spectral manifold, the time derivative of the reduced-dimensional coordinates of the spectral manifold is calculated by finite difference fitting, and the target response of the autonomous drift term is constructed. Select the polynomial basis functions of a preset order, construct the polynomial tensor product input vector of the dimensionality-reduced coordinates of the spectral manifold, and use the least squares regression method to fit the mapping relationship between the dimensionality-reduced state and the time derivative to obtain the coefficient matrix of the autonomous drift term. The observation trajectory data of the oil-immersed transformer inspection robot under the action of control input is obtained and mapped to the spectral manifold dimension-reduced coordinate system. Combined with the control input, a composite input vector is constructed consisting of the control input, the spectral manifold dimension-reduced coordinate system, and the tensor product term. Based on the time derivative as the target response, the linear term and nonlinear state modulation term of the control input influence are fitted by regression method to obtain the linear response matrix and nonlinear modulation coefficient tensor of the control input influence term, and a low-dimensional dynamic model containing the autonomous drift term and the control input influence term is constructed.

4. The method for spectral manifold modeling and control of an oil-immersed transformer inspection robot according to claim 1, characterized in that, The construction of the control observation space based on the low-dimensional dynamic model and the determination of the inverse reparameter mapping function from the control observation space to the spectral manifold specifically include: Training data pairs are constructed based on the reduced-dimensional coordinates of the spectral manifold and the original observation variables at the corresponding time. A positive embedding mapping function from the reduced-dimensional coordinates of the spectral manifold to the control observation space is constructed using polynomial basis functions to obtain the initial control observation space representation. Based on the pairing relationship between the initial control observation space representation and the dimensionality-reduced coordinates of the spectral manifold, an inverse reparameter mapping function from the control observation space to the dimensionality-reduced coordinates of the spectral manifold is constructed. The inverse reparameter mapping function is used to construct a nonlinear regression representation through tensor product polynomial basis expansion.

5. The method for spectral manifold modeling and control of an oil-immersed transformer inspection robot according to claim 1, characterized in that, The process of obtaining the current observed variables of the oil-immersed transformer inspection robot, inputting the inverse reparameter mapping function to obtain the current spectral manifold dimensionality-reduced coordinates, and constructing a trajectory prediction optimization problem in the rolling time domain using the spectral manifold dimensionality-reduced coordinates specifically includes: Obtain the current observed variables of the oil-immersed transformer inspection robot at the current control moment; The current observed variable is input into the inverse reparameter mapping function to obtain the current spectral manifold reduced coordinates; A fixed-length rolling time window and prediction steps are set. Under the reduced-dimensional coordinate system of the spectral manifold, the current reduced-dimensional coordinates of the spectral manifold are used as the initial state. The low-dimensional dynamic model is combined to recursively generate a multi-step state evolution sequence in the prediction time domain. Based on the multi-step state evolution sequence, an objective function is constructed that includes a state deviation cost term, a control input penalty term, and a terminal state cost term. State constraints and control input constraints are then applied to form a trajectory prediction optimization problem in the rolling time domain.

6. The method for spectral manifold modeling and control of an oil-immersed transformer inspection robot according to claim 1, characterized in that, The linear solution of the trajectory prediction optimization problem based on the sequential convex programming algorithm yields a control input sequence, which is then used to control the oil-immersed transformer inspection robot. Specifically, this includes: Based on the current spectral manifold reduced coordinates, a first-order linear expansion is performed along the autonomous drift term and control input influence term of the low-dimensional dynamics model to construct a linearized state transition model of the current spectral manifold reduced coordinates at the current prediction step; Substituting the linearized state transition model into the objective function of the rolling time domain, it is reconstructed into a convex quadratic programming problem with a quadratic cost term and linear constraints; The sequential convex programming algorithm is used to iteratively solve the convex quadratic programming problem to obtain the control input sequence that minimizes the cost function; The first control input in the control input sequence is extracted and sent to the oil-immersed transformer inspection robot to achieve closed-loop control of the current motion state.

7. The method for spectral manifold modeling and control of an oil-immersed transformer inspection robot according to claim 1, characterized in that, The method further includes: The reference trajectory is updated in real time during control execution; The predicted state of the oil-immersed transformer inspection robot in the reduced-dimensional coordinate system of the spectral manifold is dynamically compared with the reference trajectory to obtain the degree of trajectory deviation. The optimization objective function in the rolling time domain is adjusted according to the degree of trajectory deviation to generate optimization results. The optimization results are used to correct the control input sequence for the next cycle to achieve adaptive tracking control of non-static target trajectories.

8. A spectral manifold modeling and control device for an oil-immersed transformer inspection robot, characterized in that, The device includes an acquisition module (21) and a processing module (22), wherein, The acquisition module (21) is used to acquire the attenuation trajectory data of the oil-immersed transformer inspection robot under no control input conditions, extract the dominant singular vector from the attenuation trajectory data based on singular value decomposition, construct the approximate tangent space of the spectral manifold, and map the original high-dimensional observation variables to the dimensionality-reduced coordinate system of the spectral manifold according to the approximate tangent space. The processing module (22) is used to fit autonomous drift terms and control input influence terms respectively based on polynomial basis functions in the spectral manifold reduced coordinate system to construct a low-dimensional dynamic model of the oil-immersed transformer inspection robot. The processing module (22) is also used to construct a control observation space based on the low-dimensional dynamic model and determine the inverse reparameter mapping function from the control observation space to the spectral manifold; The acquisition module (21) is also used to acquire the current observation variables of the oil-immersed transformer inspection robot, input the reverse reparameter mapping function, obtain the current spectral manifold dimension-reduced coordinates, and construct a trajectory prediction optimization problem in the rolling time domain through the spectral manifold dimension-reduced coordinates; The processing module (22) is also used to linearize the trajectory prediction optimization problem based on the sequential convex programming algorithm to obtain the control input sequence, and to control the oil-immersed transformer inspection robot through the control input sequence.

9. An electronic device, characterized in that, The electronic device includes a processor (31), a memory (35), a user interface (33), and a network interface (34). The memory (35) is used to store instructions. The user interface (33) and the network interface (34) are both used to communicate with other devices. The processor (31) is used to execute the instructions stored in the memory (35) to cause the electronic device to perform the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores instructions that, when executed, perform the method as described in any one of claims 1 to 7.

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