Path planning method based on fusion of zero neural network and resistance network

Abstract

The invention relates to the technical field of robot navigation, and discloses a path planning method based on fusion of a zero neural network and a resistance network. According to the method, a robot working area is dispersed into a grid map, the mapping relation between the grid map and a time-varying conical curved surface resistance network is established, obstacle grids correspond to disconnection resistors, and a starting point and an ending point correspond to a current injection point and a current outflow point respectively; constructing a fast zero neural network based on the resistance network mathematical model, and solving time-varying potential of each node; starting from the starting point by the robot, screening candidate nodes at the current grid position, determining the next step of moving the grid by combining the time-varying potential and the direction deviation of the candidate nodes, and repeating until the robot arrives at the terminal point. The real-time performance and the dynamic adaptability of path planning are improved, the local optimal solution is effectively avoided, the path planning is stable and reliable, and the method is suitable for various complex operation scenes.

Description

Technical Field

[0001] This application relates to the field of robot navigation technology, specifically to a path planning method based on the fusion of nullable neural networks and resistive networks. Background Technology

[0002] Robot path planning is a core technology for autonomous mobile robots to complete tasks, and it is widely used in various fields such as industrial production, outdoor operations, and logistics transportation. However, existing path planning methods still have many shortcomings in practical applications: some traditional algorithms struggle to respond quickly to environmental changes in large-scale work areas or dynamic environments, resulting in lengthy planning times and failing to meet the real-time operational needs of robots; some gradient-based planning methods are easily influenced by local information and get trapped in optimal solutions, leading to circuitous paths and low efficiency; simultaneously, most methods employ static modeling, making it difficult to adapt to dynamic scenarios such as changes in obstacle positions and adjustments to the work area, thus affecting the accuracy and stability of path planning. These problems limit the adaptability of autonomous mobile robots in complex dynamic environments, necessitating a path planning solution that balances real-time performance, stability, and dynamic adaptability. Summary of the Invention

[0003] To solve or at least partially solve the above-mentioned technical problems, embodiments of this application provide a path planning method based on the fusion of null neural networks and resistance networks.

[0004] This application provides a path planning method based on the fusion of nullable neural networks and resistance networks, including the following steps:

[0005] S1. Discretize the robot's working area into a grid map, and establish a mapping relationship between the grid map and the time-varying conic surface resistor network, wherein the obstacle grid in the grid map corresponds to the disconnection resistor in the time-varying conic surface resistor network, the starting point of the grid map corresponds to the current injection point of the time-varying conic surface resistor network, and the ending point of the grid map corresponds to the current outflow point of the time-varying conic surface resistor network.

[0006] S2. Based on the mathematical model of the time-varying conic surface resistance network, a fast nullification neural network is constructed, and the time-varying potential of each node in the time-varying conic surface resistance network is solved through the fast nullification neural network.

[0007] S3. Control the robot to start from the starting point, and at each current grid position, filter candidate nodes that meet the conditions. Based on the time-varying potential of the candidate nodes and the deviation between the forward direction and the destination direction, determine the grid to move to next. Repeat S3 until the robot reaches the destination.

[0008] Optionally, establishing the mapping relationship between the grid map and the time-varying conic surface resistance network in step S1 specifically includes the following steps:

[0009] S1.1 Construct a mathematical model of the time-varying conic surface resistive network based on the Laplace matrix method. The mathematical model is the admittance linear system equation of the time-varying conic surface resistive network.

[0010] S1.2. Each grid in the grid map corresponds to a node of the time-varying conic surface resistance network, wherein the resistance parameters of the time-varying conic surface resistance network have the characteristic of changing with time.

[0011] S1.3 Set the nodes of the time-varying conic surface resistor network corresponding to the obstacle mesh as disconnect resistors, set the nodes corresponding to the starting point as nodes for injecting current, and set the nodes corresponding to the ending point as nodes for flowing current.

[0012] Optionally, step S2 specifically includes the following steps:

[0013] S2.1 Based on the admittance linear system equation of the time-varying conic surface resistance network, a basic nullification neural network is constructed. The basic nullification neural network solves the time-varying potential by constructing an error function and driving the error function to converge to zero.

[0014] S2.2 Analyze the structural characteristics of the Laplace matrix of the time-varying conic surface resistive network. The Laplace matrix is ​​formed by combining a cyclic tridiagonal matrix and a tridiagonal quasi-Toeplitz matrix.

[0015] S2.3. Optimize the basic nullification neural network based on the structural characteristics to obtain the fast nullification neural network;

[0016] S2.4 Solve the time-varying potential of each node in the time-varying conic surface resistance network using the fast nulling neural network.

[0017] Optionally, step S2.3 specifically includes the following steps:

[0018] S2.3.1 Decompose the Laplace matrix to obtain a combination of the cyclic tridiagonal matrix and the tridiagonal quasi-Toeplitz matrix;

[0019] S2.3.2 Introduce Fast Fourier Transform and Discrete Sine Transform of the Fourth Kind, and design corresponding fast calculation algorithms for the cyclic tridiagonal matrix and the tridiagonal quasi-Toeplitz matrix, respectively;

[0020] S2.3.3 Integrate the fast calculation algorithm into the solution process of the basic nullification neural network, optimize the operation flow of the basic nullification neural network, and obtain the fast nullification neural network.

[0021] Optionally, S2.1 specifically includes the following steps:

[0022] S2.1.1 Based on the admittance linear system equations of the time-varying conic surface resistive network, construct the error function. The error function The difference between the actual output and the target output in the admittance linear system equations is expressed as follows: ,in The Laplace matrix of the time-varying conic surface resistive network is... Let be the nodal potential vector of the time-varying conic surface resistive network. It is a current vector;

[0023] S2.1.2 Design the time derivative of the error function, and drive the error function to converge to zero through the time derivative;

[0024] S2.1.3. Based on the error function and its time derivative, determine the dynamic equation of the basic null neural network and complete the construction of the basic null neural network.

[0025] Optionally, step S3 specifically includes the following steps:

[0026] S3.1 Obtain the robot's current grid position in the grid map, where the current grid position is initially the starting point;

[0027] S3.2. Based on the current grid position, determine the main direction pointing to the endpoint, filter the adjacent grids within the main direction and the preset angle range on both sides as initial candidate nodes, exclude obstacle grids and visited grids in the initial candidate nodes, and obtain the target candidate node.

[0028] S3.3 Calculate the normalized potential and direction deviation of each of the target candidate nodes, construct a composite scoring function based on the normalized potential and the direction deviation, and obtain the score value of each of the target candidate nodes through the composite scoring function;

[0029] S3.4 Select the target candidate node with the smallest score as the target grid position for the robot's next movement, and mark the grid position as the visited grid.

[0030] S3.5 Determine whether the target grid position for the next move is the endpoint. If not, update the target grid position for the next move to the new current grid position and return to S3.2. If yes, the path planning is complete.

[0031] Optionally, S3.3 specifically includes the following steps:

[0032] S3.3.1 Obtain the time-varying potential of all nodes in the time-varying conic surface resistive network, determine the maximum and minimum values ​​of the time-varying potential, and calculate the normalized potential of each target candidate node based on the maximum and minimum values. The expression for the normalized potential is as follows: ,in The time-varying potential of the target candidate node. The maximum value of the time-varying electromotive force at all nodes. This represents the minimum time-varying electromotive force at all nodes;

[0033] S3.3.2 Calculate the forward direction vector of the target candidate node relative to the current grid position, and the target direction vector pointing from the current grid position to the endpoint. Calculate the direction deviation by taking the dot product of the forward direction vector and the target direction vector. The expression for the direction deviation is: The main direction is the normalized result of the target direction vector, and the candidate direction is the normalized result of the forward direction vector.

[0034] S3.3.3. Construct a composite scoring function based on the normalized potential and the direction deviation. The expression of the composite scoring function is as follows: ,in The weighting coefficient for the directional deviation is used to calculate the score value of each target candidate node through the composite scoring function.

[0035] Optionally, the step S3.2 may be followed by the following steps:

[0036] S3.2.1 Determine whether the target candidate node has been obtained through filtering. If yes, proceed to S3.3; otherwise, proceed to S3.2.2.

[0037] S3.2.2 Return the robot's current grid position to the previous grid position and mark the current grid position as the obstacle grid;

[0038] S3.2.3. Using the previous grid position after the retreat as the new current grid position, S3.2 is executed again. After filtering to obtain new target candidate nodes, S3.3 is executed again.

[0039] Optionally, the execution of S3 further includes the following steps:

[0040] S3.3a. Real-time detection of environmental changes in the grid map using the robot's sensing devices, including changes in obstacle positions and changes in the work area;

[0041] S3.3b. When the environmental change is detected, the resistance parameters of the time-varying conic surface resistive network are updated synchronously, and the admittance linear system equation of the time-varying conic surface resistive network is adjusted based on the updated resistance parameters.

[0042] S3.3c. The adjusted admittance linear system equations are re-solved using the fast nullification neural network to obtain the updated time-varying potentials of each node.

[0043] S3.3d. Based on the updated time-varying potential, continue executing S3.2 to S3.5.

[0044] Optionally, the process of constructing the basic nullified neural network in step S2.1 further includes the following steps:

[0045] S2.1.4 Select a monotonically increasing odd function as the activation function of the basic nullified neural network. The activation function includes a linear activation function, a bipolar sigmoid activation function, a power sigmoid activation function, a smooth power sigmoid activation function, and a hyperbolic sine activation function.

[0046] S2.1.5. Based on the environmental complexity of the grid map and the robot's operational requirements, determine the appropriate target activation function from the activation functions;

[0047] S2.1.6 Integrate the target activation function into the dynamic equation of the basic null neural network to complete the construction of the basic null neural network.

[0048] The method provided in this application has the following beneficial effects:

[0049] This application discretizes the robot's working area into a grid map and establishes a mapping relationship with the time-varying conic surface resistance network. Obstacles, the starting point, and the ending point in the grid map correspond to the disconnected resistance, current injection point, and current outflow point in the resistance network, respectively. This transforms the complex path planning problem into a navigation problem based on potential gradients, ensuring that the robot naturally avoids obstacles during movement from a physical model perspective. A fast nullable neural network is used to solve for the time-varying potential of each node in the time-varying conic surface resistance network. This fully utilizes the time-varying characteristics of the resistance network and the efficient solution capability of the neural network, enabling rapid response to potential field fluctuations caused by environmental changes, providing real-time and accurate decision-making basis for path planning. Starting from the starting point, the robot selects candidate nodes at each current grid position and determines the next moving grid by combining the time-varying potential and direction deviation. This allows the robot to move towards the endpoint along the direction of natural potential decrease, while also considering the rationality of the forward direction, effectively reducing path detours and avoiding getting trapped in local optima. The entire method combines the physical characteristics of resistive networks with the computational advantages of nullable neural networks, improving the stability and adaptability of path planning. It can adapt to working environments of varying complexity and provide reliable path guidance for robots. Attached Figure Description

[0050] Figure 1 A schematic flowchart of a path planning method based on the fusion of a null neural network and a resistance network is provided for an embodiment of this application;

[0051] Figure 2 A schematic diagram of another path planning method based on the fusion of nullable neural network and resistance network provided in the embodiments of this application;

[0052] Figure 3 A schematic diagram of another path planning method based on the fusion of nullable neural network and resistance network provided in the embodiments of this application;

[0053] Figure 4 A schematic diagram of another path planning method based on the fusion of nullable neural network and resistance network provided in the embodiments of this application;

[0054] Figure 5 This is a partial structural diagram of a time-varying conical surface resistor network provided in an embodiment of this application. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this application clearer, specific embodiments of this application will be described in further detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely for explaining this application and not for limiting it. It should also be noted that, for ease of description, only the parts relevant to this application are shown in the drawings, not all of them. Before discussing exemplary embodiments in more detail, it should be mentioned that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe operations (or steps) as sequential processes, many of these operations can be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the operations can be rearranged. The process can be terminated when its operation is completed, but may also have additional steps not included in the drawings. The process can correspond to a method, function, procedure, subroutine, subprogram, etc.

[0056] The technical solutions of the embodiments of this application will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application are within the scope of protection of this application.

[0057] See Figures 1 to 5 This application provides a path planning method based on the fusion of a null neural network and a resistance network, including the following steps:

[0058] S1. Discretize the robot's working area into a grid map and establish a mapping relationship between the grid map and the time-varying conic surface resistance network. The obstacle grid in the grid map corresponds to the disconnection resistor in the time-varying conic surface resistance network. The starting point of the grid map corresponds to the current injection point of the time-varying conic surface resistance network, and the ending point of the grid map corresponds to the current outflow point of the time-varying conic surface resistance network.

[0059] S2. Based on the mathematical model of the time-varying conic surface resistance network, a fast nullification neural network is constructed, and the time-varying potential of each node in the time-varying conic surface resistance network is solved by the fast nullification neural network.

[0060] S3. Control the robot to start from the starting point. At each current grid position, select candidate nodes that meet the conditions. Based on the time-varying potential of the candidate nodes and the deviation between the forward direction and the destination direction, determine the grid to move to next. Repeat S3 until the robot reaches the destination.

[0061] Time-varying conic surface resistive networks (TFRs) are network structures formed by interweaving periodic ideal wires in the horizontal and vertical directions. The resistance between adjacent nodes in both the horizontal and vertical directions varies with time. This structure can adapt to the dynamic changes that may occur in the robot's working environment, providing a potential field basis that fits the actual scenario for path planning. The core requirement of robot path planning is to find a collision-free and efficient path from the starting point to the ending point. After current is injected, the TFR naturally forms a gradient distribution from high to low potential, which can provide clear movement guidance for the robot. Combined with the fast solution capability of nullable neural networks, accurate path planning in dynamic environments can be achieved.

[0062] In implementation, the robot's work area is first discretized into a regular grid map according to the spatial range of the actual work scenario and the robot's motion accuracy requirements. Each grid represents a unit area that the robot can move independently to. The size of the grid needs to be adapted to the robot's size and step length to ensure that the robot can move stably within the grid. Then, a mapping relationship is established between the grid map and the time-varying conic surface resistance network. Each grid in the grid map corresponds to a node in the time-varying conic surface resistance network, transforming the path planning problem in physical space into a problem of solving the potential distribution in the resistance network. This transformation method conforms to the core logic of resistance network modeling and can reflect the rationality of the path through the quantitative relationship of the potential. In this system, the obstacle grids in the grid map correspond to the disconnected resistors in the time-varying conic surface resistive network. This means that such nodes do not participate in current conduction in the resistive network, thus ensuring that the robot will not include the grid containing the obstacle in the candidate movement path during the path planning process. The starting point of the grid map corresponds to the current injection point of the time-varying conic surface resistive network, and the ending point of the grid map corresponds to the current outflow point of the time-varying conic surface resistive network. This setting enables the resistive network to form a natural potential gradient from the starting point to the ending point, providing basic guidance for the robot's movement.

[0063] Next, a fast nulling neural network is constructed based on the mathematical model of the time-varying conic surface resistive network. The mathematical model of the time-varying conic surface resistive network accurately describes the relationship between resistance parameters, nodal potentials, and currents within the network. The fast nulling neural network is specifically designed to address the solution requirements of this mathematical model, achieving efficient solution for the time-varying potentials of each node in the resistive network by dynamically adjusting the network state. During the solution process, the fast nulling neural network can respond in real-time to the time-varying characteristics of the resistive network, ensuring that the solved time-varying potentials reflect environmental changes promptly, providing accurate potential data support for path planning.

[0064] Finally, the robot is controlled to move from the starting point. At each current grid position, the robot first acquires the time-varying potential information corresponding to that position, and combines this with the position information of the destination to filter out candidate nodes that meet the movement conditions. The selection of candidate nodes needs to comprehensively consider the level of the time-varying potential and the deviation between the forward direction and the destination direction. The level of the time-varying potential directly reflects the proximity of the node to the destination, while the deviation between the forward direction and the destination direction ensures that the robot does not deviate too much from the target direction. That is, the candidate nodes that meet the conditions are adjacent grids that are not marked as obstacles, are not included in the visited record, have a relatively low time-varying potential that is closer to the potential level of the destination, and whose forward direction deviates from the main direction pointing to the destination within a reasonable range. After determining the grid for the next movement based on these two dimensions, the robot moves to that grid, and then repeats the above selection and movement process until the robot reaches the destination, completing the entire path planning.

[0065] This method transforms the path planning problem into a quantifiable potential calculation problem by mapping a resistor network to the robot's working environment. Leveraging the rapid solution capability of a nullable neural network, the real-time performance and accuracy of path planning are ensured. Furthermore, movement decisions based on potential gradients and directional deviations enable the robot's path to both avoid obstacles and conform to the target direction, reducing path detours and improving the efficiency and reliability of path planning. This method is applicable to robot path planning in various dynamic operational scenarios.

[0066] See Figure 2 In some implementations, establishing the mapping relationship between the grid map and the time-varying conic surface resistance network in S1 specifically includes the following steps:

[0067] S1.1. Construct a mathematical model of a time-varying conic surface resistive network based on the Laplace matrix method. The mathematical model is the admittance linear system equation of the time-varying conic surface resistive network.

[0068] S1.2. Each grid in the grid map corresponds to a node of the time-varying conic surface resistance network. The resistance parameters of the time-varying conic surface resistance network have the characteristic of changing with time.

[0069] S1.3 Set the nodes of the time-varying conic surface resistive network corresponding to the obstacle mesh as disconnect resistors, set the nodes corresponding to the starting point as nodes for injecting current, and set the nodes corresponding to the ending point as nodes for flowing current.

[0070] The mathematical model of time-varying conic resistive networks is the core foundation for establishing the mapping relationship between the mesh map and the resistive network. Only through accurate mathematical modeling can the physical characteristics of the robot's working environment be transformed into the electrical parameters of the resistive network, providing reliable theoretical support for subsequent potential calculation and path planning. The Laplace matrix method is an effective means of resistive network modeling, which can clearly describe the admittance correlation of each node in the network and is suitable for the structural characteristics of time-varying conic resistive networks.

[0071] In the implementation process, the first step is to construct the mathematical model of the time-varying conic surface resistive network. Based on the Laplace matrix method and combined with the structural characteristics of the time-varying conic surface resistive network, the admittance linear system equations of the network are constructed, and the equation expression is as follows: .in, For the time-varying conic surface resistive network, the Laplace matrix is ​​determined by the time-varying conductance between each node in the network, where the conductance is the reciprocal of the corresponding resistance. This is the time-varying potential vector of all nodes in the network, containing the potential value of each node as time changes; The current vector represents the injection and outflow of current in the network. This equation accurately reflects the dynamic relationship between potential, conductance, and current in a time-varying conic resistive network and is the core basis for subsequent potential calculations.

[0072] Subsequently, a one-to-one correspondence was established between the mesh map and the nodes of the resistance network. Based on the actual range and motion accuracy of the robot's working area, each independent mesh in the mesh map was mapped to a node of the time-varying conic surface resistance network, ensuring that every movable unit in the physical space could find a corresponding electrical representation in the resistance network. Simultaneously, the resistance parameters of the time-varying conic surface resistance network exhibit time-varying characteristics, and the resistance between adjacent nodes in the horizontal direction... Resistance between adjacent nodes in the longitudinal direction All follow time-varying patterns, and their expressions are as follows: , .in, and Initial time The resistance value, and The rate of change of resistance, As a time parameter, this time-varying characteristic can adapt to dynamic changes that may occur in the robot's working environment, such as the movement of temporary obstacles or adjustments to the work area. For example... Figure 5 The diagram shown is a partial structural schematic of a time-varying conical surface resistor network provided in an embodiment of this application. This represents the resistance between adjacent nodes in the horizontal direction. This represents the resistance between adjacent nodes in the longitudinal direction. It represents electric current.

[0073] Finally, the final settings for the mapping relationship are completed. For obstacle meshes in the mesh map, the corresponding time-varying conic surface resistive network nodes are set as disconnected resistors, meaning the conductance between this node and its adjacent nodes approaches zero. The corresponding element in the Laplace matrix is ​​set to zero, ensuring that current cannot be conducted through this node, thus eliminating the possibility of the robot moving towards the obstacle mesh in path planning. The resistive network node corresponding to the starting point of the mesh map is set as a current-injecting node, and the resistive network node corresponding to the ending point is set as a current-outflowing node. This allows current to be injected into the resistive network from the starting point, conducted through effective nodes, and flow out from the ending point, naturally forming a potential gradient from the starting point to the ending point. This provides clear movement guidance for the robot, ultimately completing the establishment of the complete mapping relationship between the mesh map and the time-varying conic surface resistive network.

[0074] This implementation method constructs a precise mathematical model using the Laplace matrix method, clearly defining the correspondence between the mesh and nodes. Combined with the time-varying characteristics of resistance and the targeted settings for obstacles and start / end points, the mapping relationship conforms to both the electrical theory of resistive networks and accurately reflects the actual working environment of the robot. This mapping method transforms the geometric constraints and dynamic changes of the physical environment into a quantitative representation of electrical parameters, providing a reliable input foundation for subsequent fast nullification neural network solutions to time-varying potentials, ensuring the accuracy and adaptability of path planning.

[0075] See Figure 3 In some implementations, S2 specifically includes the following steps:

[0076] S2.1 Based on the admittance linear system equations of the time-varying conic surface resistance network, a basic nullification neural network is constructed. The basic nullification neural network realizes the solution of time-varying potential by constructing an error function and driving the error function to converge to zero.

[0077] S2.2 Analyze the structural characteristics of the Laplace matrix of the time-varying conic surface resistive network. The Laplace matrix is ​​formed by combining a cyclic tridiagonal matrix and a tridiagonal quasi-Toeplitz matrix.

[0078] S2.3. Based on structural characteristics, the basic nullification neural network is optimized to obtain a fast nullification neural network;

[0079] S2.4 Solve the time-varying potential of each node in the time-varying conic surface resistive network using a fast nulling neural network.

[0080] The core of building a fast nullable neural network is to first establish a basic model adapted for solving time-varying potentials, and then optimize it by leveraging the structural advantages of the Laplace matrix of the resistor network. This improves computational efficiency while ensuring solution accuracy, meeting the real-time requirements of robot path planning. The admittance linear system equation of the time-varying conic surface resistor network is the core basis for solving the potential. The basic nullable neural network is specifically designed for the time-varying characteristics of this equation, while the special structure of the Laplace matrix provides a key entry point for model optimization.

[0081] In implementation, the first step is to construct a basic nullable neural network. Based on the admittance linear system equations of a time-varying conic surface resistive network, these equations accurately describe the dynamic relationship between time-varying resistance, nodal potential, and current, forming the theoretical foundation for potential calculation. The core design logic of the basic nullable neural network is to construct an error function and drive it to converge to zero, thereby achieving accurate tracking of the time-varying potential. The design of the error function must closely match the output characteristics of the admittance linear system equations, ensuring that the error directly reflects the deviation between the calculated potential value and the theoretical value. Through dynamic adjustment of the error, the output of the neural network continuously approximates the true time-varying potential, laying the foundation for subsequent optimization.

[0082] Subsequently, the structural characteristics of the Laplace matrix of the time-varying conic surface resistive network are analyzed. The Laplace matrix is ​​a core component of the admittance linear system equations, and its structure directly determines the solution complexity. Analysis of the element distribution and row-column correlation patterns of this matrix reveals that it is not a random structure, but rather a combination of a cyclic tridiagonal matrix and a tridiagonal quasi-Toeplitz matrix. The cyclic tridiagonal matrix exhibits a periodic distribution of non-zero elements, while the tridiagonal quasi-Toeplitz matrix displays an approximately diagonally symmetric structure. Both types of matrices possess structural advantages that simplify computation, providing crucial structural support for subsequent neural network optimization.

[0083] Based on the aforementioned structural characteristics, a fast nullification neural network is obtained by optimizing the basic nullification neural network. The core idea of ​​the optimization is to leverage the structural advantages of cyclic tridiagonal matrices and tridiagonal quasi-Toeplitz matrices to simplify the matrix operation process in the neural network. The basic nullification neural network needs to process the complete Laplacian matrix during the solution process, which involves a large amount of computation. However, by exploring the structural characteristics of the matrix, simplified operation rules can be designed to reduce unnecessary calculation steps and lower computational complexity. For example, by utilizing the periodicity and diagonal symmetry of the matrix, the repeated calculation of the same or approximately the same matrix elements can be avoided. Simultaneously, the multiplication logic between matrices and vectors can be optimized to make the operation process more compatible with the hardware computing characteristics, thereby improving the overall solution speed of the neural network.

[0084] Finally, a fast nullable neural network (FNN) is used to solve for the time-varying potentials of each node in the time-varying conic surface resistance network. The FNN inherits the convergence characteristics of the basic nullable neural network, ensuring the accuracy of the time-varying potential solution. Simultaneously, structural optimization significantly improves computational efficiency, enabling rapid response to parameter changes in the time-varying conic surface resistance network and timely output of updated node potentials. The obtained time-varying potentials are directly used for the robot's path decision-making, providing quantitative guidance for each grid position and ensuring that the robot can select the optimal movement path based on accurate potential information.

[0085] This implementation method, through a logical flow of "basic model construction - structural characteristic analysis - model optimization - potential solution," ensures both the theoretical rigor of time-varying potential solutions and improves solution efficiency through structural optimization. The fast nullification neural network not only maintains the accurate convergence characteristics of the basic nullification neural network but also fully utilizes the structural advantages of the Laplace matrix, effectively solving the problem of "difficulty in balancing accuracy and speed" in potential solutions under time-varying environments. This provides key technical support for the real-time performance and accuracy of robot path planning.

[0086] In some implementations, S2.3 specifically includes the following steps:

[0087] S2.3.1 Decompose the Laplace matrix to obtain a combination of a cyclic tridiagonal matrix and a tridiagonal quasi-Toeplitz matrix;

[0088] S2.3.2 Introducing the Fast Fourier Transform and the fourth type of Discrete Sine Transform, and designing corresponding fast calculation algorithms for cyclic tridiagonal matrices and tridiagonal quasi-Toeplitz matrices respectively;

[0089] S2.3.3 Integrate the fast computation algorithm into the solution process of the basic null neural network, optimize the operation process of the basic null neural network, and obtain the fast null neural network.

[0090] The core of this implementation method is to transform this structural advantage into improved computational efficiency through targeted matrix decomposition and fast transformation algorithms, thereby solving the problems of large matrix operation volume and slow solution speed in basic null neural networks, and ensuring that the solution of time-varying potential can meet the real-time requirements of robot path planning.

[0091] During implementation, the decomposition of the Laplace matrix is ​​performed first. Based on the structural characteristics of the time-varying conic surface resistive network, the combined form of its Laplace matrix can be explicitly characterized by the following formula:

[0092]

[0093] in, It is an n×n cyclic tridiagonal matrix that characterizes the periodic boundary properties of the resistor network in the horizontal direction; It is an m×m tridiagonal quasi-Toeplitz matrix, representing the Dirichlet-Neumann boundary properties in the longitudinal direction; , These are m-order and n-order identity matrices, respectively; , Let be the time-varying resistance parameters of the resistive network. This decomposition breaks down the complex Laplace matrix into a Kronecker product of two well-structured submatrices and the identity matrix, providing a clear computational object for subsequent fast algorithm design.

[0094] Next, for the two types of sub-matrices after decomposition, corresponding fast transformations are introduced and calculation algorithms are designed. For a cyclic tridiagonal matrix... Its periodic non-zero element distribution characteristic is highly compatible with the operational logic of the Fast Fourier Transform (FFT). Utilizing the properties of FFT, the multiplication of cyclic matrices and vectors can be transformed into element-wise multiplication in the frequency domain, significantly reducing computational complexity. This is specifically achieved through the process of "vector FFT transformation - frequency domain multiplication - inverse IFFT transformation". Fast multiplication with the potential vector. For a tridiagonal quasi-Toeplitz matrix. The fourth type of discrete sine transform (DST-IV) can efficiently achieve its diagonalization, and its diagonalization formula is as follows:

[0095]

[0096] in This is a DST-IV matrix. for The eigenvalues ​​of . Based on this diagonalization property, can be Vector multiplication is transformed into a simple operation in the transformation domain, and a corresponding fast calculation process is designed to avoid directly performing complex tridiagonal matrix multiplication.

[0097] Finally, the aforementioned fast computation algorithm is integrated into the solution process of the basic null neural network, thus optimizing the computational flow. The core operations of the basic null neural network include the multiplication of the Laplacian matrix and the potential vector, and matrix operations related to the error function; these are the key parts where the computational load is concentrated. The original direct matrix operations are replaced with the designed fast algorithm: in the calculation... When the FFT fast algorithm is enabled, in the calculation The DST-IV fast algorithm is employed, while the superposition logic of the two types of operation results is optimized. Through this targeted replacement and integration, the computational load of matrix operations is significantly reduced and the solution time of time-varying potentials is shortened without changing the convergence characteristics of the basic nullable neural network, ultimately forming a fast nullable neural network.

[0098] This implementation deeply integrates the characteristics of matrix structure with a dedicated fast transformation algorithm, realizing an optimized logic of "structure decomposition - algorithm adaptation - process integration". The fast nullification neural network, by accurately utilizing the computational advantages of cyclic tridiagonal matrices and tridiagonal quasi-Toeplitz matrices, avoids the inefficiency of indiscriminately processing complex matrices in traditional neural networks. While ensuring the accuracy of time-varying potential solutions, it significantly improves computational efficiency, providing core technical support for robots to rapidly adjust their paths in dynamic environments.

[0099] In some implementations, S2.1 specifically includes the following steps:

[0100] S2.1.1 Based on the admittance linear system equations of time-varying conic surface resistive networks, construct the error function. Error function The difference between the actual output and the target output in the admittance linear system equations is expressed as follows: ,in The Laplace matrix of the time-varying conic surface resistive network is... Let be the nodal potential vector of the time-varying conic surface resistive network. It is a current vector;

[0101] S2.1.2 Design the time derivative of the error function, and drive the error function to converge to zero through the time derivative;

[0102] S2.1.3. Based on the error function and its time derivative, determine the dynamic equation of the basic null neural network and complete the construction of the basic null neural network.

[0103] The core of the fundamental nullable neural network is to dynamically track the potential of nodes in a time-varying conic surface resistive network by constructing a precise error function and convergence mechanism. Its construction process must adhere to the time-varying characteristics of the admittance linear system equations to ensure that the network output continuously approximates the true potential value. The key to this process lies in the rational design of the error function, the clear definition of the convergence direction, and the rigorous derivation of the dynamic equations; these three elements together support the convergence performance of the fundamental nullable neural network.

[0104] In implementation, the error function is constructed first. Based directly on the admittance linear system equations of the time-varying conic surface resistive network, which clearly define the relationship between potential, conductance, and current under ideal conditions, the error function must accurately reflect the deviation between the actual solution and the ideal state. The expression for the error function constructed accordingly is as follows: ,in It is the Laplace matrix of the time-varying conic surface resistive network, whose elements are dynamically adjusted over time to adapt to the time-varying characteristics of the resistance parameters; The potential vector of the network node is the core variable to be solved. The current vector represents the current distribution injected at the starting point and flowing out at the ending point. This error function directly quantifies the difference between the calculated potential value and the theoretical value, providing a clear target for subsequent convergence control.

[0105] Subsequently, the time derivative of the error function is designed to drive error convergence. To ensure that the error approaches zero quickly, a time derivative with a clear direction of convergence needs to be designed for the error function, expressed as:

[0106]

[0107] in, This is the derivative of the error function with respect to time. The convergence rate adjustment parameter is used to... For regularization parameters, These are integer powers of parameters, and the three together regulate the convergence speed and stability. It is an N-order identity matrix; This is a monotonically increasing odd function used to enhance the nonlinear adjustment capability of error convergence, ensuring stable convergence across different error ranges. This time derivative forces the error to converge to zero through a negative feedback mechanism, providing the core driving force for the dynamic adjustment of the neural network.

[0108] Finally, the dynamic equations of the fundamental nullified neural network are derived based on the error function and its time derivative. Regarding the error function... Taking the derivatives of both sides with respect to time, and considering the time-varying characteristics of the Laplace matrix in the circuit system, we can obtain:

[0109]

[0110] Substituting the time derivative of the designed error function into the above equation and rearranging, we obtain the dynamic equation of the basic null neural network:

[0111]

[0112] This equation clarifies the relationship between the time-varying rate of change of the potential vector and the error, the time-varying Laplace matrix, and its derivative, thus fully describing the dynamic evolution of the basic nullable neural network. By solving this dynamic equation, the state of the neural network can be continuously adjusted until the error function converges to zero, at which point the potential vector... This involves constructing a basic nullable neural network by representing the actual time-varying potentials of each node in the time-varying conic surface resistive network. This implementation constructs a basic nullable neural network adapted for solving time-varying potentials through a logical chain of "error quantization - convergence-driven - equation derivation." Its core advantage lies in fully utilizing the time-varying characteristics of the admittance linear system equations and the mathematical laws of error convergence, ensuring that the network can accurately track the dynamic changes in potential while possessing stable convergence performance. This provides a rigorous theoretical foundation and a complete model framework for subsequent optimization of fast nullable neural networks.

[0113] See Figure 4 In some implementations, S3 specifically includes the following steps:

[0114] S3.1 Obtain the robot's current grid position on the grid map, with the initial grid position being the starting point;

[0115] S3.2. Based on the current grid position, determine the main direction pointing to the endpoint, filter the adjacent grids within the preset angle range on both sides of the main direction as initial candidate nodes, exclude obstacle grids and visited grids in the initial candidate nodes, and obtain the target candidate node.

[0116] S3.3 Calculate the normalized potential and direction deviation of each target candidate node, construct a composite scoring function based on the normalized potential and direction deviation, and obtain the score value of each target candidate node through the composite scoring function;

[0117] S3.4 Select the candidate node with the smallest score as the target grid position for the robot's next move, and mark the grid position as a visited grid.

[0118] S3.5 Determine if the target grid position for the next move is the destination. If not, update the target grid position for the next move to the new current grid position and return to S3.2; if yes, the path planning is complete.

[0119] This implementation transforms the time-varying potential obtained from the fast nullification neural network into an executable movement path for the robot. Through standardized node selection, scoring, and movement logic, it ensures that the robot efficiently and without collisions reaches the destination from the starting point in a grid map. The entire process revolves around the logic of "real-time position perception - candidate node selection - optimal node decision - cyclic movement verification," making the path planning both aligned with potential gradient guidance and meeting the robot's actual motion requirements.

[0120] During implementation, the robot's current grid position on the grid map is first obtained. Using its own positioning device and the coordinate system of the grid map, the robot determines its current grid position. In the initial stage of path planning, this current grid position is directly set as the starting point, ensuring that the robot begins the path planning process from the preset starting point, providing a clear initial reference for subsequent movement.

[0121] Next, using the current grid position as a reference, the main direction pointing to the destination is determined. The main direction is determined based on the straight line connecting the current grid position and the destination, ensuring that this direction represents the shortest path from the current position to the destination, providing a core directional reference for robot movement. Subsequently, adjacent grids within the main direction and preset angle ranges on both sides are selected as initial candidate nodes. The preset angle range aims to balance path flexibility and directionality, preventing the robot from being confined to a single direction and unable to avoid obstacles, while also preventing overly dispersed directions from causing detours. During the selection process, the initial candidate nodes undergo a secondary selection, excluding obstacle grids and visited grids to obtain target candidate nodes. Excluding obstacle grids ensures that the robot does not collide during movement, while excluding visited grids prevents the robot from repeatedly circling within the same area, improving path planning efficiency.

[0122] Next, the normalized potential and orientation deviation of each target candidate node are calculated, and a composite scoring function is constructed based on these two indicators to obtain a score value for each target candidate node. The normalized potential unifies the potential differences between different nodes, intuitively reflecting the degree of proximity of the target candidate node to the endpoint; the orientation deviation measures the degree of deviation between the forward direction and the main direction corresponding to the target candidate node, ensuring that the robot's movement direction does not deviate too much from the endpoint. The composite scoring function integrates information from these two dimensions to achieve a comprehensive evaluation of the target candidate node, ensuring that the robot moves towards a lower potential (closer to the endpoint) while avoiding severe path detours caused by simply pursuing a lower potential.

[0123] Subsequently, the target candidate node with the lowest score is selected as the target grid position for the robot's next move, and this grid position is marked as a visited grid. The target candidate node with the lowest score is the optimal choice in the current situation, balancing "approaching the destination" and "correct direction." Marking it as a visited grid provides a basis for selecting subsequent candidate nodes and prevents repeated visits.

[0124] Finally, determine whether the target grid position for the next move is the destination. If the target grid position is not the destination, update the target grid position to the new current grid position, return to the step of filtering target candidate nodes, and continue to execute the subsequent filtering, scoring, and moving process; if the target grid position is the destination, it means that the robot has successfully reached the preset target, and the path planning process is completed.

[0125] This implementation method transforms abstract potential information into concrete robot movements through a standardized movement decision-making process. The entire process fully utilizes the gradient guidance effect of time-varying potentials and ensures collision-free and efficient paths through operations such as candidate node screening and visited grid marking. This enables the robot to stably complete path planning from the starting point to the destination in complex grid environments, combining practicality and reliability.

[0126] In some implementations, S3.3 specifically includes the following steps:

[0127] S3.3.1 Obtain the time-varying potential of all nodes in the time-varying conic surface resistive network, determine the maximum and minimum values ​​of the time-varying potential, and calculate the normalized potential of each target candidate node based on the maximum and minimum values. The expression for the normalized potential is as follows: ,in Let be the time-varying potential of the target candidate node. The maximum value of the time-varying electromotive force at all nodes. This represents the minimum time-varying electromotive force at all nodes;

[0128] S3.3.2 Calculate the forward direction vector of the target candidate node relative to the current grid position, and the target direction vector pointing from the current grid position to the endpoint. Calculate the direction deviation by taking the dot product of the forward direction vector and the target direction vector. The expression for the direction deviation is: The principal direction is the normalized result of the target direction vector, and the candidate direction is the normalized result of the forward direction vector.

[0129] S3.3.3. Construct a composite scoring function based on normalized potential and direction deviation. The expression of the composite scoring function is as follows: ,in The weighting coefficient for directional deviation is used to calculate the score of each target candidate node through a composite scoring function.

[0130] This implementation method converts the potential and directional characteristics of the target candidate node into comparable score values ​​through quantitative calculation, providing a clear and unified basis for the robot's next movement decision, ensuring that the selected target candidate node not only conforms to the potential gradient guidance but also maintains the correct direction of movement, reducing path detours.

[0131] In implementation, the normalized potential of each target candidate node is first calculated. The fast nulling neural network has already solved for the time-varying potentials of all nodes in the time-varying conic surface resistive network. The numerical range of these potential values ​​varies depending on the network size and current settings, making direct comparison difficult to reflect the relative convergence between nodes. Therefore, it is necessary to first determine the maximum and minimum values ​​of the time-varying potentials of all nodes, and then normalize the time-varying potential of each target candidate node based on these two extreme values. The expression for the normalized potential is:

[0132]

[0133] in, The time-varying potential of a single target candidate node is directly taken from the solution result of the fast nullification neural network; This represents the maximum value of the time-varying electromotive force at all nodes, corresponding to nodes near the starting point of the grid map; This represents the minimum time-varying potential of all nodes, corresponding to nodes near the endpoint on the grid map. Calculation using this formula unifies the range of normalized potential values, providing a clear reflection of the relative distance between the target candidate node and the endpoint; a smaller value indicates closer proximity to the endpoint.

[0134] Next, the direction deviation of the target candidate node is calculated. First, the forward direction vector of the target candidate node relative to the current grid position is obtained; this vector consists of the coordinate difference between the target candidate node and the current grid position. Simultaneously, the target direction vector pointing from the current grid position to the endpoint is obtained; this vector consists of the coordinate difference between the endpoint and the current grid position. To eliminate the influence of coordinate scale on the calculation results, the forward direction vector and the target direction vector need to be normalized separately to obtain the candidate direction and the principal direction. Then, the direction deviation is calculated by the dot product of the two normalized vectors. The expression for the direction deviation is:

[0135]

[0136] Here, the principal direction is the normalized result of the target direction vector, and the candidate direction is the normalized result of the forward direction vector. The dot product operation is used to measure the angle between the two vectors. The value of the direction deviation ranges from 0 to 1. The smaller the value, the more consistent the forward direction is with the target direction, which can effectively prevent the robot from deviating from the destination direction due to simply pursuing a low potential.

[0137] Finally, a composite scoring function is constructed based on the normalized potential and direction deviation to calculate the score value of each target candidate node. The core of the composite scoring function is to weightedly fuse the quantitative indicators of the two dimensions, as expressed in the following expression:

[0138]

[0139] in, This is the weighting coefficient for directional deviation, used to adjust the degree of influence of directional deviation in the scoring, and can be flexibly set according to the needs of the robot's operation scenario; For normalized potential, This represents directional deviation. The score directly reflects the quality of the target candidate node; the smaller the score, the closer the node is to the endpoint and the better it is in maintaining the correct direction of movement, making it the optimal choice for the robot's next move.

[0140] This implementation method transforms abstract potential and direction information into specific numerical scores through a "single-index quantification - dual-dimensional fusion scoring" logic, providing clear quantitative basis for the robot's movement decisions. Its advantages lie in balancing path proximity and directionality, avoiding insufficient path optimization caused by relying solely on potential or direction. Furthermore, the calculation process is simple and efficient, adapting to the needs of real-time robot path planning and providing reliable technical support for the selection of target candidate nodes.

[0141] In some implementations, the following steps are included after S3.2:

[0142] S3.2.1 Determine whether the target candidate node has been obtained through filtering. If yes, proceed to S3.3; otherwise, proceed to S3.2.2.

[0143] S3.2.2 Return the robot's current grid position to the previous grid position and mark the current grid position as an obstacle grid;

[0144] S3.2.3. Using the previous grid position after retreating as the new current grid position, re-execute S3.2. After filtering to obtain new target candidate nodes, continue to execute S3.3.

[0145] This implementation provides a deadlock solution for path planning. When the robot cannot select a valid target candidate node at the current grid position, it breaks the stagnation state through backtracking correction, ensuring that path planning can continue to advance and improving the adaptability of the method in complex obstacle environments.

[0146] During implementation, after completing the screening of target candidate nodes, a validity judgment is first performed. The robot uses its own path decision module to check whether there are any target candidate nodes that meet the criteria in the screening results. If a target candidate node is found, it means that there is a feasible direction for the next move at the current position, and the subsequent scoring and decision steps are directly executed to maintain the normal process of path planning; if no target candidate node is found, it means that the current position is surrounded by obstacles or visited grids, resulting in a deadlock state with no feasible path. At this time, a backtracking correction process needs to be initiated to prevent the robot from stalling.

[0147] Then, a backtracking adjustment operation is performed. Based on its own movement record, the robot obtains the coordinates of the previous grid position and returns to that position via the motion control system. Simultaneously, the current grid position is marked as an obstacle grid. This operation aims to confirm that there is no feasible path to that grid, preventing it from being included in the candidate list again in subsequent planning and avoiding the robot repeatedly getting stuck in the same deadlock state. The marking process requires synchronously updating the grid map's state information to ensure accurate identification of the obstacle attributes of that grid during subsequent candidate node selection.

[0148] Finally, the candidate node selection process is restarted. Using the previous grid position after retreating as the new current grid position, the robot re-executes the target candidate node selection steps: first, it determines the main direction pointing from the new current grid position to the destination; then, it selects adjacent grids within the main direction and preset angle ranges on both sides as initial candidate nodes, excluding obstacle grids and already visited grids, resulting in new target candidate nodes. The selection process for new candidate nodes continues the original logic to ensure the consistency of path planning. After selection, subsequent scoring, decision-making, and movement steps are executed, allowing path planning to re-enter normal progress.

[0149] This implementation addresses the shortcomings of solely relying on forward selection of candidate nodes through a backtracking correction mechanism, effectively resolving deadlock issues that robots may encounter in complex environments. Without requiring additional complex computational logic, it quickly overcomes the predicament of no feasible paths through path backtracking and grid state marking, ensuring the continuity and integrity of path planning. Furthermore, this mechanism is adapted to the robot's motion control characteristics; the operation of returning to the previous grid is simple and easy to execute, without significantly increasing the system's computational burden, thus improving the reliability and practicality of the entire path planning method in real-world complex scenarios.

[0150] In some implementations, the S3 execution process also includes the following steps:

[0151] S3.3a. Real-time detection of environmental changes on the grid map using the robot's sensing devices, including changes in obstacle positions and changes in the work area.

[0152] S3.3b When an environmental change is detected, the resistance parameters of the time-varying conic surface resistive network are updated synchronously, and the admittance linear system equation of the time-varying conic surface resistive network is adjusted based on the updated resistance parameters.

[0153] S3.3c. The adjusted admittance linear system equations are re-solved using a fast nullification neural network to obtain the updated time-varying potentials of each node.

[0154] S3.3d: Based on the updated time-varying potential, continue executing S3.2 to S3.5.

[0155] This implementation method enables the path planning method to adapt to dynamic environments. By sensing environmental changes in real time and updating relevant parameters and potential information synchronously, it ensures that the robot can maintain the safety and effectiveness of the path in dynamic scenarios and avoid path failure or collision risks caused by environmental changes.

[0156] During implementation, continuous environmental change detection is performed during path planning. The robot's onboard sensors (such as LiDAR and vision cameras) scan the surrounding environment in real time, collecting dynamic information from the grid map. Two key types of environmental changes are detected: first, changes in obstacle positions, including unexpected movement of static obstacles and the appearance or disappearance of temporary obstacles; and second, changes in the work area, such as adjustments to work boundaries, the addition of new passable areas, or the designation of prohibited areas. The sensors transmit the collected environmental data to the robot's control module in real time, providing the initial basis for subsequent parameter updates.

[0157] When the control module detects an environmental change, it immediately initiates a parameter update process. Based on the specific environmental changes, the resistance parameters of the time-varying conic surface resistive network are updated synchronously: for mesh nodes corresponding to newly appearing obstacles, their resistance is set to an open state; for mesh nodes after obstacle removal, their original time-varying resistance characteristics are restored; for nodes involved in adjustments to the work area, their resistance parameters are adjusted accordingly to match the new area attributes. After the resistance parameters are updated, the admittance linear system equations of the time-varying conic surface resistive network are adjusted based on the updated resistance parameters to ensure that the equations accurately reflect the electrical characteristics of the resistive network under the current environment, making the subsequent potential solution highly compatible with the actual environment.

[0158] Subsequently, the adjusted admittance linear system equations are resolved using a fast nullification neural network. The high efficiency of the fast nullification neural network allows for rapid response to equation changes, enabling the recalculation of time-varying potentials at each node within a short time, resulting in an updated time-varying potential distribution. The re-solution process continues the original solution logic, ensuring the accuracy and reliability of the potential results. Simultaneously, its computational efficiency meets the requirements of real-time path adjustment in dynamic environments, preventing robot movement from stalling due to recalculation.

[0159] Finally, based on the updated time-varying electromotive force (TMF), steps S3.2 to S3.5 of the original path planning process are executed. Using the updated TMF as the new decision-making basis, the robot re-selects target candidate nodes at the current grid position, calculates the score, selects the next grid position to move to, and continues this process until the destination is reached. The updated TMF accurately reflects path guidance in a dynamic environment, ensuring that the robot can adjust its movement direction in a timely manner, avoid newly appearing obstacles, make full use of newly added passable areas, and maintain the safety and efficiency of the path.

[0160] This implementation method enables the path planning method to adapt to dynamic environments, capturing environmental changes in a timely manner and updating key parameters and potential information synchronously. This ensures that the robot's path planning is always based on the current real-world environmental state, effectively avoiding path failures, detours, or collisions caused by environmental changes. Simultaneously, this process fully utilizes the efficient solution capabilities of fast nullification neural networks and the logical consistency of the original path planning process, eliminating the need for additional complex decision-making mechanisms. It balances dynamic adaptability and execution efficiency, improving the method's practicality and reliability in real-world, complex, and dynamic scenarios.

[0161] In some implementations, the process of constructing the basic null neural network in S2.1 also includes the following steps:

[0162] S2.1.4 Select monotonically increasing odd functions as activation functions for the basic null neural network. Activation functions include linear activation functions, bipolar sigmoid activation functions, power sigmoid activation functions, smooth power sigmoid activation functions, and hyperbolic sine activation functions.

[0163] S2.1.5. Based on the environmental complexity of the grid map and the robot's operational requirements, determine the appropriate target activation function from the activation functions;

[0164] S2.1.6 Integrate the target activation function into the dynamic equation of the basic null neural network to complete the construction of the basic null neural network.

[0165] This implementation optimizes the convergence characteristics of the basic null neural network by selecting an appropriate activation function, enabling the neural network to adjust its computational performance according to the needs of different scenarios. This ensures that the time-varying potential can be solved stably and efficiently in various environments, providing reliable support for path planning.

[0166] In implementation, the first step is to determine the available activation function types during the construction of the basic nullable neural network. As a core component of the basic nullable neural network, the activation function directly affects the speed and stability of error convergence. Its selection must satisfy the property of a monotonically increasing odd function. This property ensures that the error function does not exhibit local fluctuations during convergence, guaranteeing consistency in the convergence direction. Available activation functions include linear activation functions, bipolar sigmoid activation functions, power sigmoid activation functions, smooth power sigmoid activation functions, and hyperbolic sine activation functions. These functions all meet the above requirements and possess different computational characteristics, adaptable to the solution needs of different scenarios.

[0167] Subsequently, based on the environmental complexity of the grid map and the robot's operational requirements, a suitable target activation function is determined from the available activation functions. The environmental complexity of the grid map is reflected in aspects such as obstacle distribution density and area size, while the robot's operational requirements include indicators such as movement speed and path accuracy. For example, in scenarios with simple environments, sparse obstacles, and high requirements for path planning speed, a linear activation function can be selected, as its computational logic is simple and can improve the solution speed of the neural network. In scenarios with complex environments, dense obstacles, and high requirements for solution stability, a smooth power sigmoid activation function or a hyperbolic sine activation function can be selected. These functions have stronger nonlinear characteristics and can better cope with complex error changes, ensuring the stability of the convergence process. In moderately complex scenarios that balance speed and stability, a bipolar sigmoid activation function or a power sigmoid activation function can be selected to achieve a balanced performance adaptation.

[0168] Finally, the determined target activation function is integrated into the dynamic equation of the basic null neural network. The dynamic equation of the basic null neural network is the core logic for potential calculation. The integration of the activation function requires precise replacement of the corresponding function terms in the equation to ensure that the overall structure and theoretical rigor of the equation are not altered. During the integration process, parameter configuration is needed to ensure that the activation function works synergistically with the error terms and matrix terms in the dynamic equation. This allows the neural network to reasonably adjust the error signal through the activation function during computation, further optimizing the speed and accuracy of error convergence. After integration, the basic null neural network possesses convergence characteristics adaptable to specific scenarios and can output accurate time-varying potential solutions according to actual needs, completing the full construction of the basic null neural network.

[0169] This implementation method, through flexible selection and integration of activation functions, enables the basic nullable neural network to adapt to various scenarios. It eliminates the need to reconstruct the overall neural network framework; performance optimization for different scenarios can be achieved simply by replacing activation functions. This ensures theoretical consistency while enhancing the method's practicality. Furthermore, the selected activation functions conform to the convergence theory of nullable neural networks, improving solution speed or stability without affecting the accuracy of potential calculation. This provides more flexible technical support for subsequent optimization of fast nullable neural networks and accurate calculation of time-varying potentials, enabling the entire path planning method to adapt to more diverse robot operation scenarios.

[0170] Additionally, considering that the current composite scoring function uses a fixed setting for the directional deviation weight coefficient, it is difficult to adapt to the dynamic changes in environmental complexity and robot operation requirements. This may lead to insufficient bias in path decision-making in some scenarios—for example, in complex obstacle environments, too small a directional deviation weight may cause path detours, while in simple open environments, too large a weight may limit path flexibility. To solve this problem, this improved implementation method can dynamically adjust the directional deviation weight coefficient, enabling the composite scoring function to adapt to scene changes in real time, further improving the accuracy and adaptability of path planning.

[0171] During implementation, the initial value of the directional deviation weighting coefficient is preset during the path planning initiation phase. The initial value is set based on a typical operating scenario, balancing the impact of normalized potential and directional deviation on the scoring results, ensuring that the path decision in the initial state has both approach and directionality, and providing a basic reference for subsequent dynamic adjustments.

[0172] Subsequently, during the continuous execution of path planning, two types of key information are collected in real time as the basis for weight adjustment. The first type is environmental complexity information, which is obtained by using the robot's sensors to count the density of obstacles, the complexity of obstacle shapes, and the width of feasible paths within the current working area. This information directly reflects the strength of the constraints imposed by the environment on the path direction. The second type is path status information, which is obtained by analyzing the robot's movement records to determine the detour of the planned path, the cumulative deviation between the current movement direction and the destination direction, and the number of candidate nodes selected. This information reflects the impact of the current weight settings on path decision-making.

[0173] Based on the information collected above, a dynamic adjustment logic is designed. When high environmental complexity is detected (e.g., dense obstacles, narrow feasible paths), the directional deviation weight coefficient is appropriately increased to strengthen the weight of directional accuracy in the score, preventing the robot from getting stuck in a circuitous path surrounded by obstacles due to excessive pursuit of low potential. When low environmental complexity is detected (e.g., sparse obstacles, open and unconstrained), the directional deviation weight coefficient is appropriately decreased to enhance the guiding role of the potential gradient in path decision-making, enabling the robot to choose a shorter path to quickly approach the destination. Simultaneously, if the detour of the planned path exceeds a preset threshold, or the cumulative deviation between the current movement direction and the destination direction continues to increase, the directional deviation weight coefficient is automatically increased to correct the path direction in a timely manner. If the number of target candidate nodes is too small, resulting in insufficient path flexibility, the directional deviation weight coefficient is appropriately decreased to expand the range of effective candidate nodes.

[0174] After each weight coefficient adjustment, the updated weight coefficients are dynamically input into the composite scoring function, replacing the original fixed weight values ​​in the target candidate node scoring calculation. The weight adjustment process adopts a gradual update method, with the adjustment range dynamically set according to the severity of environmental changes and the magnitude of path state deviations, avoiding excessive fluctuations in scoring results due to sudden weight changes, and ensuring the continuity and stability of path decisions.

[0175] Furthermore, after the robot reaches its destination or completes a path planning step, it records the environmental characteristics of the task scenario, the adjustment trajectory of the weight coefficients, and the performance indicators of the final path (such as path length, movement time, and collision-free rate), forming a scenario-weight adaptation database. When encountering similar scenarios again, the historical adaptation weights in the database can be directly called as initial values, shortening the adaptation cycle of weight adjustments and improving the quality of initial decisions in path planning.

[0176] This improved implementation achieves real-time adaptation of the directional deviation weight coefficients to scene changes. It eliminates the need to reconstruct the overall framework of the composite scoring function; dynamic optimization of the weights alone enhances the scene adaptability of path decision-making. This maintains compatibility with existing methods while overcoming the limitations of fixed weights. The adjusted composite scoring function can optimize decision-making tendencies in real time based on environmental constraints and path status, reducing path detours in complex obstacle environments and improving mobility in simple, open environments. This further enhances the practicality and reliability of the entire path planning method in diverse scenarios.

[0177] Additionally, existing path planning methods, when selecting target candidate nodes and deciding on movement paths, do not fully consider the robot's physical motion constraints, relying solely on potential and directional deviations for decision-making. This may lead to planned paths exceeding the robot's actual motion capabilities—for example, the robot has physical characteristics such as minimum turning radius and limited step length. If the position of a candidate node exceeds these constraints, the planned path will be unexecutable, potentially even causing mechanical damage or loss of control. To address this issue, this improved implementation incorporates the robot's physical motion constraint assessment into the path decision-making process, ensuring that the planned path not only meets potential guidance and directional requirements but also possesses practical feasibility.

[0178] During implementation, the robot's physical motion constraints are preset before path planning begins. Based on the robot's model, mechanical structure design, and motion control system characteristics, two types of core constraints are defined: first, steering constraints, such as the minimum turning radius, which defines the maximum turning angle the robot can achieve when moving from its current grid position to an adjacent grid, avoiding the planning of sharp turns beyond its steering capabilities; second, movement constraints, such as the maximum step size and grid adaptation size, ensuring the robot can stably enter the grid corresponding to the target candidate node without colliding with grid boundaries or surrounding obstacles during movement. These constraints will serve as crucial criteria for subsequent candidate node selection, forming the decision-making standard together with potential and orientation conditions.

[0179] Subsequently, motion constraint judgment is added to the target candidate node screening process. After excluding obstacle meshes and visited meshes, a constraint verification step is added: based on preset steering constraint parameters, the steering angle from the current mesh position to each initial candidate node is calculated, and meshes whose steering angle exceeds the angle range corresponding to the minimum turning radius are excluded; combined with the motion constraint parameters, it is determined whether the mesh size corresponding to each initial candidate node is adapted to the robot's movement step size, and meshes that are too small or whose position exceeds the maximum movement step size are excluded. The candidate nodes after constraint verification not only meet the basic requirements of no collision and no repetition, but also conform to the robot's physical motion capabilities, forming the final target candidate nodes.

[0180] In the path decision-making and movement execution process, path feasibility verification is further incorporated. After selecting the target candidate node with the lowest score, the robot does not directly execute the movement. Instead, it simulates the movement process from the current grid position to the target candidate node through the motion simulation module to verify whether the turning action and movement distance conform to the preset motion constraint parameters. If the simulation results show that the path is executable, the movement operation is executed and the visited grid is marked; if the simulation results show that there is a constraint conflict (such as insufficient turning angle or mismatched step size), the target candidate node is temporarily stored as an "inexecutable node," and the node with the second lowest score is selected from the remaining target candidate nodes for verification again until an executable node that simultaneously satisfies the potential, direction, and motion constraints is found.

[0181] Furthermore, a constraint adaptation mechanism is designed to address the need for adjusting constraint parameters in dynamic environments. If the robot's motion constraint parameters change dynamically during operation due to load variations or terrain differences (such as climbing slopes or overcoming obstacles), the robot's motion state monitoring module collects data such as mechanical structure load and power output in real time, dynamically updating the preset steering and movement constraint parameters. The updated parameters are immediately synchronized to the candidate node selection process, ensuring that subsequent path decisions are adapted to the robot's current motion capabilities and preventing path unexecutability due to outdated constraint parameters.

[0182] This improved implementation addresses the gap between planned paths and actual execution capabilities by incorporating physical motion constraints into path decision-making. Its advantage lies in the fact that it does not require altering the core logic of the original potential calculation and direction determination. By simply adding constraint parameter presetting, screening and verification, and dynamic adaptation steps, the planned path becomes practically executable, maintaining compatibility with the original method while improving its reliability in real-world applications. Furthermore, the constraint parameter presetting and dynamic update mechanism adapts to the needs of different robot models and operating scenarios, enabling the path planning method to be flexibly applied to various robots with physical motion constraints, further broadening its applicability.

[0183] Additionally, considering that existing path planning methods rely on fast nullification neural networks to solve for time-varying potentials, always covering all nodes in the entire grid map, significant computational redundancy occurs in large-scale operation scenarios. The robot only needs local potential information about its current surroundings and direction of travel to make decisions; solving for potentials in distant, irrelevant areas not only consumes additional computational power but also prolongs the overall response time. Especially in dynamic environments, computational resource consumption may cause delays in updating potentials in critical areas. Furthermore, the potential solution does not consider the robot's energy consumption characteristics, potentially leading to frequent turns and rapid accelerations in the planned path, increasing the robot's energy costs. This improved implementation method achieves dual-dimensional optimization through "local potential focused solution + energy-conscious path optimization," reducing computational consumption while improving the energy economy of the path.

[0184] In implementation, a hierarchical "core-edge" grid model is first constructed to define the focus area for potential calculation. Based on the robot's sensing radius, step length, and operational objective, the grid map is divided into core and edge regions: the core region is a rectangular area centered on the current robot position, extending outwards within a preset range, covering all grids the robot might move from its next step to the next three steps; this region is crucial for path decision-making. The edge region consists of the remaining grids outside the core region, affecting only long-term path trends rather than immediate decisions. The size of the preset range can be dynamically adjusted according to environmental complexity; in complex environments, the range is reduced to focus on key areas, while in open environments, the range is appropriately expanded to maintain path continuity.

[0185] A differentiated potential calculation strategy is designed based on a hierarchical model. The core region employs the existing high-precision solution logic, using a fast nullification neural network to fully calculate the time-varying potential of all nodes within this region, ensuring the accuracy of real-time decision-making. The structural advantages of the Laplace matrix and the fast transformation algorithm are still utilized during the solution process to guarantee efficiency. A simplified solution model is used for the edge region. The Laplace matrix in this region is sparsified, retaining only the key conductance correlations with nodes adjacent to the core region and nodes surrounding the endpoint, ignoring subtle conductance differences between distant nodes. This reduces the computational load by lowering the matrix dimension. Simultaneously, the potential calculation frequency in the edge region is reduced to one-third that of the core region, with the edge region potential updated synchronously only after three core region potential updates, further freeing up computational resources.

[0186] Energy consumption perception factors are integrated into the path decision-making process to optimize the composite scoring function. First, the robot's energy consumption characteristics are preset, including energy consumption coefficients for straight-line movement, turning, and energy compensation coefficients under different potential gradients—straight-line movement energy consumption is lower than turning energy consumption, and the energy consumption of movement with a small potential gradient is lower than that of movement with a sudden change in large potential gradient. Based on these parameters, an energy cost function is constructed to calculate the energy consumption value corresponding to each target candidate node: if the target candidate node is directly adjacent to the current position, the basic straight-line energy consumption is used; if turning occurs, the turning energy consumption at the corresponding angle is added; if the potential gradient change between the node and the previous node exceeds a threshold, additional energy compensation is added. Then, the energy cost function is integrated into the original composite scoring function, and the expression of the new scoring function is adjusted as follows: ,in This is the energy consumption value. This is an energy consumption weighting coefficient, which can be flexibly set according to the operational requirements of "energy saving priority" or "efficiency priority".

[0187] A dynamic adaptation mechanism for the solution range is designed synchronously. During robot movement, the core region translates in real time with the current position, ensuring that it always covers the local mesh required for the next decision. When an environmental change (such as the addition of an obstacle) is detected in the edge region, the changed region is temporarily upgraded to a "temporary core region," and high-precision solving is initiated while the potential of that region is updated synchronously to avoid sudden impacts of far-end environmental changes on subsequent paths. After the robot completes a section of the path, the computational power consumption and decision accuracy of the core region potential solution are statistically analyzed, and the preset range of the core region is automatically calibrated—if the computational power is redundant, the range is appropriately expanded; if the computational power is insufficient, the range is reduced, achieving a dynamic balance between solution efficiency and accuracy.

[0188] This improved implementation addresses both computational redundancy and high path energy consumption in large-scale scenarios through hierarchical solution and energy optimization. Its core advantage lies in not disrupting the original framework of potential calculation and path decision-making. Optimization is achieved solely through spatial hierarchical solution, differentiated solution, and score function extension, maintaining compatibility with existing methods while specifically enhancing applicability in large-scale, long-endurance operation scenarios. Locally focused solution significantly reduces ineffective computational consumption, while energy-aware optimization makes the path more aligned with the robot's energy characteristics, making it particularly suitable for battery-powered mobile robots. This ensures safe and efficient path operation while extending operational endurance.

[0189] The above description is merely a preferred embodiment and the technical principles employed in this application. This application is not limited to the specific embodiments described herein, and various obvious changes, readjustments, and substitutions that can be made by those skilled in the art will not depart from the scope of protection of this application. Therefore, although this application has been described in detail through the above embodiments, this application is not limited to the above embodiments, and may include more other equivalent embodiments without departing from the concept of this application, the scope of which is determined by the scope of the claims.

Claims

1. A path planning method based on the fusion of a zeroization neural network and a resistance network, characterized in that, The method comprises the following steps: S1, discretizing a robot working area into a grid map, and establishing a mapping relationship between the grid map and a time-varying conic surface resistance network, wherein an obstacle grid in the grid map corresponds to a disconnected resistance in the time-varying conic surface resistance network, a starting point of the grid map corresponds to a current injection point of the time-varying conic surface resistance network, and an end point of the grid map corresponds to a current outflow point of the time-varying conic surface resistance network; S2, constructing a fast nulling neural network based on a mathematical model of the time-varying conic surface resistance network, and solving time-varying potentials of nodes in the time-varying conic surface resistance network through the fast nulling neural network; S3, controlling the robot to start from the starting point, screening candidate nodes meeting a condition at each current grid position, determining a grid for next movement based on a time-varying potential of the candidate node and a deviation of a forward direction from a direction of the end point, and repeating the S3 until the robot reaches the end point.

2. The method of claim 1, wherein, The S1 of establishing the mapping relationship between the grid map and the time-varying conic surface resistance network specifically comprises the following steps: S1.1, constructing a mathematical model of the time-varying conic surface resistance network based on a Laplacian matrix method, wherein the mathematical model is a mobility linear system equation of the time-varying conic surface resistance network; S1.2, corresponding each grid in the grid map to a node of the time-varying conic surface resistance network, and the resistance parameter of the time-varying conic surface resistance network having a time-varying characteristic; S1.3, setting the node of the time-varying conic surface resistance network corresponding to the obstacle grid as a disconnected resistance, setting the node corresponding to the starting point as a node injecting current, and setting the node corresponding to the end point as a node flowing out current.

3. The method of claim 2, wherein, The S2 specifically comprises the following steps: S2.1, constructing a basic nulling neural network based on the mobility linear system equation of the time-varying conic surface resistance network, and solving the time-varying potential through the basic nulling neural network by constructing an error function and driving the error function to converge to zero; S2.2, analyzing structural characteristics of a Laplacian matrix of the time-varying conic surface resistance network, wherein the Laplacian matrix is formed by a combination of a circulant tri-diagonal matrix and a tri-diagonal quasi-Toeplitz matrix; S2.3, optimizing the basic nulling neural network based on the structural characteristics to obtain the fast nulling neural network; S2.4, solving the time-varying potentials of the nodes in the time-varying conic surface resistance network through the fast nulling neural network.

4. The method of claim 3, wherein, The S2.3 specifically comprises the following steps: S2.3.1, decomposing the Laplacian matrix to obtain a combined form composed of the circulant tri-diagonal matrix and the tri-diagonal quasi-Toeplitz matrix; S2.3.2, introducing fast Fourier transform and fourth-type discrete sine transform, and designing corresponding fast calculation algorithms for the circulant tri-diagonal matrix and the tri-diagonal quasi-Toeplitz matrix, respectively; S2.3.3, integrating the fast calculation algorithm into a solving process of the basic nullifying neural network, optimizing an operation flow of the basic nullifying neural network, and obtaining the fast nullifying neural network.

5. The method of claim 3, wherein, The S2.1 specifically comprises the following steps: S2.1.

1. Constructing an error function based on the admittance linear system equation of the time-varying conic surface resistance network , the error function is the difference between the actual output and the target output in the admittance linear system equation, expressed as , wherein is the Laplace matrix of the time-varying conic surface resistance network, is the node potential vector of the time-varying conic surface resistance network, is the current vector; S2.1.2, designing a time derivative of the error function, and driving the error function to converge to zero through the time derivative; S2.1.3, determining a dynamic equation of the basic nullifying neural network based on the error function and the time derivative, and completing construction of the basic nullifying neural network.

6. The method of claim 1, wherein, The S3 specifically comprises the following steps: S3.1, obtaining a current grid position of the robot in the grid map, the current grid position being initially the starting point; S3.2, determining a main direction pointing to the terminal point based on the current grid position, screening adjacent grids in the main direction and a preset angle range on both sides as initial candidate nodes, excluding obstacle grids and visited grids in the initial candidate nodes, and obtaining target candidate nodes; S3.3, calculating a normalized electric potential and a direction deviation of each target candidate node, constructing a composite scoring function based on the normalized electric potential and the direction deviation, and obtaining a scoring value of each target candidate node through the composite scoring function; S3.4, selecting the target candidate node with the minimum scoring value as a target grid position of the next step of movement of the robot, and marking the grid position as the visited grid; S3.5, judging whether the target grid position of the next step of movement is the terminal point, if not, updating the target grid position of the next step of movement as a new current grid position, and returning to S3.2; if yes, completing path planning.

7. The method of claim 6, wherein, The S3.3 specifically comprises the following steps: S3.3.1, obtaining the time-varying electric potential of all nodes in the time-varying conic surface resistance network, determining the maximum value and the minimum value of the time-varying electric potential, calculating the normalized electric potential of each target candidate node based on the maximum value and the minimum value, the expression of the normalized electric potential is wherein is the time-varying electric potential of the target candidate node, is the maximum value of the time-varying electric potential of all nodes, is the minimum value of the time-varying electric potential of all nodes; S3.3.2, calculate the advancing direction vector of the target candidate node relative to the current grid position, and the target direction vector of the current grid position pointing to the terminal point, calculate the direction deviation by the dot product of the advancing direction vector and the target direction vector, the expression of the direction deviation is where the main direction is the normalized result of the target direction vector, and the candidate direction is the normalized result of the advancing direction vector; S3.3.3, constructing a composite scoring function based on the normalized potentials and the directional bias, the composite scoring function having an expression of wherein is a weight coefficient of the directional bias, and the scoring value of each of the target candidate nodes is calculated by the composite scoring function.

8. The method of claim 6, wherein, The S3.2 further comprises the following steps: S3.2.1, judging whether the target candidate nodes are screened, if yes, executing S3.3; if not, executing S3.2.2; S3.2.2, returning the current grid position of the robot to a previous grid position, and marking the current grid position as the obstacle grid; S3.2.3, taking the returned previous grid position as a new current grid position, re-executing S3.2, and continuing to execute S3.3 after screening new target candidate nodes.

9. The method of claim 6, wherein, The S3 further comprises the following steps during execution: S3.3a, detecting environmental changes of the grid map in real time through a sensing device of the robot, the environmental changes including obstacle position changes and working area range changes; S3.3b, when detecting the environmental changes, synchronously updating the resistance parameters of the time-varying conic surface resistance network, and adjusting the admittance linear system equation of the time-varying conic surface resistance network based on the updated resistance parameters; S3.3c, re-solving the adjusted admittance linear system equation through the fast nullifying neural network, and obtaining the updated time-varying electric potentials of the nodes. S3.3d, based on the updated time-varying electric potential, continue to perform S3.2 to S3.

5.

10. The method of claim 5, wherein, In the process of constructing the basic nullifying neural network, the S2.1 further includes the following steps: S2.1.4, selecting a monotonically increasing odd function as an activation function of the basic nullifying neural network, the activation function including a linear activation function, a bipolar S-shaped activation function, a power S-shaped activation function, a smooth power S-shaped activation function, and a hyperbolic sine activation function; S2.1.5, determining an adaptive target activation function from the activation functions according to an environmental complexity of the grid map and a task demand of the robot; S2.1.6, integrating the target activation function into a dynamic equation of the basic nullifying neural network, and completing the complete construction of the basic nullifying neural network.

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