Robot trajectory generation method and system based on Kolmogorov-Arnold network

Abstract

The invention discloses a robot track generation method and a robot track generation system based on a Kolmogorov-Arnold network. The method comprises the following steps: extracting observation data and corresponding action data from a data source file for storing a robot movement track; the motion data is used as a diffusion model noise adding object, observation data is used as a condition to train a KAN strategy network, and the KAN strategy network is formed by fusing a Kolmogorov-Arnold network into a basic network architecture of a diffusion strategy in a modular form and is used for predicting noise to be added; the trained KAN strategy network is selected according to the field task scene requirement, predicted noise is generated according to actual observation data and action data of the robot, and the next action is generated by using the predicted noise through an inverse diffusion formula of the diffusion model. According to the method, an effective and smooth track can be generated, and the overall performance is remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the field of robot motion control and trajectory optimization, and specifically relates to a robot continuous trajectory generation method based on a deep learning framework, which is particularly suitable for scenarios requiring smooth motion control, such as high-precision industrial robots and service robots. Background Art

[0002] Current robot trajectory generation and planning technologies mainly cover the following two types of methods: The first category is the traditional method based on interpolation and optimization. Methods such as cubic spline interpolation and polynomial fitting all use mathematical modeling to generate continuous trajectories. Its advantage is that it can effectively guarantee the smoothness of the trajectory so that the robot can operate stably. However, this type of method has obvious limitations, that is, it is highly dependent on accurate dynamic models. Once in a complex dynamic environment, it is difficult to quickly adapt and adjust in the face of many sudden variables and uncertain factors, thus affecting the trajectory optimization effect.

[0003] The second category is the strategy model based on deep learning, including diffusion strategy models using CNN (convolutional neural network) and Transformer architecture, which generate trajectories based on data-driven. They perform well in complex pattern recognition and feature extraction, and can mine potential rules in massive data, bringing more flexibility to robot trajectory planning. However, its discrete data processing mechanism has drawbacks, which makes the generated trajectory prone to jitter and discontinuity, affecting the smoothness and accuracy of the robot's movements.

[0004] In addition, existing methods such as genetic algorithms and reinforcement learning can improve the adaptability of trajectories to a certain extent, making robots more adaptable in different environments and tasks. However, in high-dimensional space, these algorithms are very likely to fall into the dilemma of local optimality and it is difficult to find the global optimal solution. Moreover, they are not effectively combined with the ability to represent continuous functions, so they lack the fine characterization and efficient optimization of trajectories, which limits the overall development and performance improvement of robot trajectory optimization technology. Summary of the invention

[0005] Purpose of the invention: In view of the shortcomings of the prior art, the present invention provides a robot trajectory generation method and system based on the Kolmogorov-Arnold network, aiming to solve the problems of jitter and redundancy in trajectory generation based on the CNN / Transformer diffusion strategy model and the problem that traditional methods based on interpolation and optimization cannot adapt to complex dynamic environments.

[0006] Technical solution: In order to achieve the above invention objectives, the technical solution of the present invention is as follows: In a first aspect, a robot trajectory generation method based on a Kolmogorov-Arnold network comprises the following steps: Extract observation data and corresponding action data from the data source file storing the robot's motion trajectory. The observation data includes the environment and its own state information perceived by the robot, and the action data is the specific control instructions executed by the robot at each time step. The action data is used as the object of the diffusion model to add noise, and the observation data is used as a condition to train the KAN policy network. The KAN policy network is formed by integrating the Kolmogorov-Arnold network into the basic network architecture of the diffusion strategy in a modular form, including a convolutional neural network-based KAN policy network and a Transformer-based KAN policy network, which are used to predict the noise to be added; According to the requirements of the on-site task scenario, the trained KAN strategy network is selected, and the predicted noise is generated according to the actual observation data and action data of the robot. The predicted noise is used to generate the next action through the inverse diffusion formula of the diffusion model.

[0007] Furthermore, the KAN strategy network based on convolutional neural network includes three parts. The first part is the downsampling layer, which generates an embedding input according to the action data and passes the downsampled features to the third part using a jump connection; the second part is the embedding layer, which extracts intermediate embeddings using an embedding KAN module based on the downsampled features and the observed data as a condition, and the embedding KAN module includes a tokenization layer, a normalization layer and a linear layer; the third part is the upsampling layer, which generates the final output according to the features of the previous two parts.

[0008] Furthermore, the tokenization layer is used to convert the one-dimensional sequence into a patch embedding representation with overlapping regions. Given an input sequence , where B is the batch size and C in Indicates the number of input channels, L in is the sequence length, and a one-dimensional convolution operation is used to project it into a higher-dimensional embedding space: ; in, , W is the preset parameter of convolution, h is the convolution kernel size, C out is the embedding dimension, LN represents layer normalization, Conv represents the convolution operation, and the convolution operation includes stride s and padding , the output shape is , where L patch Determined by the following formula: ; The processing of the linear layer is described as: ; Among them, w b and w s is the weight generated by the linear layer, and the function is defined as follows: , , B i (x) represents the basis function, i is the index, c i represents the weight of each basis function; The final output f(x) of the embedded KAN module is: ; Among them, a and b are the conditional features extracted by the conditional encoder from the global feature observation data and time steps.

[0009] Furthermore, the Transformer-based KAN strategy network includes an encoder, a decoder and a GR-KAN module. The encoder generates conditional embeddings for the combination of observation data and time steps. The encoded hidden variables and action data are input into the decoder together. The features output by the decoder are nonlinearly transformed through the GR-KAN module to obtain the final result.

[0010] Furthermore, the GR-KAN module includes a linear layer and a grouped KAT. The formula of the entire module is described as: ; Among them, w 1 、w 2 and b 1 、b 2 are the weights and biases generated by two linear layers, K is a rational function, and the superscript of K represents different initialization modes of grouped KAT. Assume i is the current input channel The index of j is the output channel The index of , divides the entire input channel into g groups evenly, is the group number, then K is expressed as: ; in is the weight coefficient, and R(x) is a rational function.

[0011] Furthermore, during the training process of the KAN strategy network, the goal is to minimize the mean square error between the predicted noise and the actual noise.

[0012] Furthermore, the inverse diffusion formula of the diffusion model is expressed as: ; in, yes The action of the time step, , , is the parameter setting of noise, is the noise of the network prediction, are network parameters, is the observed data at time t, is noise that follows a specified distribution.

[0013] In a second aspect, a robot trajectory generation system based on a Kolmogorov-Arnold network comprises: The data processing module is used to extract observation data and corresponding action data from the data source file storing the robot's motion trajectory. The observation data includes the environment and its own state information perceived by the robot, and the action data is the specific control instructions executed by the robot at each time step; A model training module is used to use action data as the object of diffusion model noise addition, and to use observation data as a condition to train the KAN policy network. The KAN policy network is formed by integrating the Kolmogorov-Arnold network into the basic network architecture of the diffusion strategy in a modular form, including a convolutional neural network-based KAN policy network and a Transformer-based KAN policy network, which are used to predict the noise to be added; The trajectory generation module is used to select the trained KAN policy network according to the requirements of the on-site task scenario, generate predicted noise based on the actual observation data and action data of the robot, and use the predicted noise to generate the next action through the inverse diffusion formula of the diffusion model.

[0014] In a third aspect, an electronic device comprises: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the robot trajectory generation method based on the Kolmogorov-Arnold network as described in the first aspect are implemented.

[0015] In a fourth aspect, a computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the robot trajectory generation method based on the Kolmogorov-Arnold network as described in the first aspect.

[0016] Beneficial effects: The present invention integrates the Kolmogorov-Arnold network (KAN) into the basic network architecture of the diffusion strategy in a modular form. For the convolutional neural network CNN, a novel modular structure Emb-KAN is proposed; for the Transformer, the GR-KAN module is introduced and expanded. This can not only generate effective and smooth trajectories, but also significantly improve the overall performance. The effectiveness of the method has been verified in simulation and real-world robot control tasks, confirming its practical application value and robustness in different environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a diagram of the KAN Policy-C framework according to the present invention; Figure 2 is a module structure diagram of Emb-KAN according to the present invention; Figure 3 is a diagram of the KAN Policy-T framework according to the present invention; Figure 4 is a block diagram of the GR-KAN module according to the present invention; Figure 5 is a schematic diagram of shared parameters according to the present invention; Figure 6 is a flow chart of a trajectory generation method according to the present invention; Figure 7 It is an example of trajectory and efficiency smoothness change according to the present invention. DETAILED DESCRIPTION

[0018] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0019] The present invention combines the traditional robot trajectory generation method based on interpolation and optimization, uses a Kolmogorov-Arnold network based on an efficient fitting function (such as a spline function) and combines it with a diffusion strategy based on CNN / Transformer to combine the advantages of both, thereby generating an efficient and smooth robot motion trajectory. In order to have a clearer understanding of the purpose, means and beneficial effects of the invention, the relevant technology is first introduced.

[0020] Kolmogorov-Arnold network The Kolmogorov-Arnold Network (KAN) is a neural network structure based on the Kolmogorov-Arnold representation theorem. The theorem was proposed by mathematicians Andrey Kolmogorov and Vladimir Arnold in the 1950s to solve the problem of representing multivariable functions. The theorem states that any multivariable continuous function can be expressed as a linear combination of a series of univariate functions, and the mathematical form is: , in, and is a single variable continuous function.

[0021] Compared with traditional neural networks, the key innovations of KAN are: ① Activation function position: The activation function is placed at the edge of the network instead of the traditional node position. ② Weight parameter replacement: Each weight parameter is replaced by a learnable univariate function, usually parameterized as a B-spline function, which can flexibly simulate complex nonlinear relationships. This design not only gives the network higher expressive power, but also provides significant explanatory advantages.

[0022] Diffusion strategy Diffusion Policy is a data-driven generative model that generates or optimizes data by gradually adding and removing noise. This strategy has achieved remarkable results in the field of robot strategy generation. Traditional strategy learning methods often have limited distribution expression capabilities and stability problems when dealing with multimodal action distribution or uncertainty. Diffusion Policy introduces a denoising diffusion probability model into robot motion generation and models the robot's visual motion strategy as a conditional denoising diffusion process. The formula for its reverse diffusion is: , in, yes The action of the time step, , , is the parameter setting of noise, is the noise of the network prediction, are network parameters, is the observation at time t, that is, the current situation observed by the robot, is the noise that obeys this distribution. The loss function corresponding to the diffusion process can be defined as: , By learning the gradient of the action score function and performing random Langevin dynamics sampling on the gradient field, this method can represent any normalizable distribution, including multimodal action distributions. At the same time, it has two basic network architectures: convolutional neural network (CNN) and Transformer.

[0023] Diffusion strategy based on KAN network The inventors have modified the diffusion strategy and integrated KAN into the basic network architecture of the diffusion strategy in a modular form. For CNN, the present invention has created a novel modular structure Emb-KAN; for Transformer, the present invention has introduced the GR-KAN module and expanded it. The present invention refers to these two structures as KAN Policy-C (KAN strategy based on CNN) and KAN Policy-T (KAN strategy based on Transformer), collectively referred to as KAN Policy. This invention is a modification of the basic network architecture of the diffusion strategy from the algorithm level. The specific method will be introduced below: 1. KAN Policy-C The inventors modified the CNN architecture in the diffusion strategy and divided the main structure into three parts. Figure 1 As shown in the figure, the first part is the downsampling layer, which is responsible for generating the embedded input and passing the downsampled features to the third part using a jump connection. The downsampling layer includes a series of convolution blocks and downsampling blocks; the second part is the embedding layer, which is the most critical modification in this method. Specifically, a new module called Embed-KAN is designed and integrated. The full name is Embedding KAN, which can be called Embedding KAN. This newly developed Embed-KAN module, as the intermediate embedding layer in the architecture, is a key mechanism for high-dimensional feature extraction. With the power of Embed-KAN, the entire model is able to capture more detailed and discriminative representations, thereby generating more efficient actions. The third part is the upsampling layer, which includes a series of convolution blocks and upsampling blocks. It integrates the feature information of the first two parts and then generates the output through the final convolution block. The global feature is a global condition generated by observations and time steps, which will be processed by the conditional encoder.

[0024] Reference Figure 2 , the specific implementation of Emb-KAN is as follows: Tokenization is designed to convert a one-dimensional sequence into a patch embedding representation with overlapping regions, which is particularly useful for extracting local features from sequential data while maintaining continuity between patches. The key operations are described as follows: Given an input sequence ,in is the batch size, Indicates the number of input channels, is the sequence length, and a one-dimensional convolution operation is used to project it into a higher-dimensional embedding space: , in, , W is the preset parameter of convolution, h is the convolution kernel size, is the embedding dimension, LN is the layer normalization. Conv represents the convolution operation, which includes the stride and fill , to ensure that the patches overlap. The output shape is ,in Determined by the following formula: , The features are then processed along the embedding dimension by layer normalization. After completing the patch embedding representation of the features, the main feature processing of this module is performed by the KAN linear layer, whose output Mathematically it can be described as: , in, and are the weights generated by the Linear layer. is the silu activation function, which is defined as follows: . , represents the basis function (spline function), is the index, represents the weights, i.e. coefficients, of each basis function. This approach constructs an interpolation framework in the input feature space that can simultaneously extract linear and nonlinear features. In addition, the conditional encoder is responsible for extracting conditional features a and b from the global features. Specifically, the conditional encoder FiLM (activation function + linear layer + reconstruction) generates an embedded representation that changes shape (e.g., by adjusting the dimension) into a and b.

[0025] The final output f(x) of Emb-KAN has the following structure: , At this point, all processing of the Emb-KAN module is completed.

[0026] 2. KAN Policy-T In this structure, spline functions are not used as the basis functions, but rational functions are used, and the method of sharing parameters is used in groups. Figure 3, KAN Policy-T uses a custom GR-KAN module to replace the linear layer at the end of the Transformer architecture. This is an operation similar to an activation function, which introduces nonlinear characteristics at the end of the model, enabling the neural network to learn complex nonlinear relationships. KAN Policy-T combines observations and time step Generate conditional embeddings, input as hidden variables after encoder encoding, and action noise All of them are input into the decoder, and the output features are passed through GR-KAN to obtain the final result.

[0027] Reference Figure 4 GR-KAN introduces Group KAT to achieve complex nonlinear transformations, thereby enhancing the representation ability of the network. The formula of the entire module can be described as: , in, , and , are the weights and biases generated by the two linear layers, is a rational function, The superscripts of represent different initialization modes of grouped KAT. Grouped KAT shares parameters for input groups, which is the main part of KAN with rational basis functions and is responsible for forming features with KAN style.

[0028] Assume i is the current input channel The index of j is the output channel , divide the entire input channel into g groups evenly, is the group number, so It can be expressed as: , is the weight coefficient. This means that the input features of the same group will share parameters. Figure 5 As shown in the figure, compared with the general KAN on the left, the GR-KAN on the right shares the weights generated by the network in groups.

[0029] R(x) is a rational function and can be expressed as: , Where m and n are the orders of the polynomials. , is a coefficient and also a weight. In practice, GR-KAN can be applied to various policy learning models. When integrated into different models, it can also achieve the effect of trajectory optimization.

[0030] Robot trajectory generation method based on KAN Policy The following is a specific method for implementing robot trajectory planning and generation based on the proposed KAN Policy. Figure 6 , the method comprises the following steps: Step 1: Data processing, extracting observations and corresponding actions from the data source file.

[0031] Data is collected from the log files generated during the simulation environment (such as MuJoCo) or the real robot operation, including observation data and action data. Observation data includes robot status (position, speed), environmental information (target point, obstacles), sensor data (images, depth maps, etc.). Action data is the corresponding real action sequence, such as joint angles and end coordinates recorded when the robot performs a task.

[0032] The data is processed as follows: Normalization: Standardize the observation and action data separately to eliminate dimensional differences.

[0033] Sequence segmentation: Use the sliding window method to divide the data into continuous segments of fixed length (such as 30 steps as a sequence).

[0034] The processed sequence is encapsulated as PyTorch's TensorDataset and loaded in batches through DataLoader to support parallel training.

[0035] Step 2: Take the action as the object of the diffusion model to add noise, and use the observation as a condition to train the network. The network is mainly used to predict the added noise.

[0036] As described above, in the task of robot trajectory generation based on diffusion strategy, KAN Policy-C (based on CNN) and KAN Policy-T (based on Transformer) are two different network architecture designs, and their selection needs to be weighed in combination with task characteristics and data features. Table 1 shows the specific analysis of the two networks.

[0037] Table 1 Network architecture differences and applicable scenarios characteristic KAN Policy-C (CNN) KAN Policy-T (Transformer) Core Modules Embedding layer of Embed-KAN + convolution down / up sampling GR-KAN module + self-attention mechanism Feature extraction capabilities Good at capturing local spatial features (such as joint status, obstacle distribution) Good at modeling global temporal dependencies (such as the coherence of long sequences of actions) Computational efficiency The number of parameters is large and the calculation efficiency is low Small number of parameters and high computational efficiency Data requirements There are no special requirements for the dataset, but there may be requirements for the machine that performs the task (such as degrees of freedom) Currently, all experiments have no special requirements for the dataset Based on the above analysis, in actual applications, the corresponding network architecture can be selected according to the task scenario. For example, for tasks where action generation depends on local observation features and has weak temporal dependence, such as robotic arms grasping static targets and short-distance gait control of quadruped robots, KAN Policy-C is selected; for tasks where action generation requires modeling of long-range temporal dependencies and observation data contains complex temporal relationships, such as humanoid robots continuously crossing obstacles and drones dynamically replanning paths, KAN Policy-T is selected.

[0038] The network training process is as follows: Input: Action data , Observation data , time step ;

[0039] Goal: Minimize prediction noise Mean square error (MSE) with the true noise; Optimizer: Use AdamW, set the learning rate to 1e-4, and add gradient clipping to prevent training instability.

[0040] For KAN Policy-C, action data The embedded input is generated through the downsampling layer, and the downsampled features are passed to the upsampling layer through the skip connection; the embedded input is then passed through the Emb-KAN module to extract a high-dimensional intermediate embedding to observe the data and time step k As a constraint or precondition to guide the network learning process, the time step k Converted into vectors through sine / cosine processing and spliced ​​into the observed data sequence After that, multiple Emb-KAN modules can be applied and the extracted intermediate embeddings can be integrated through skip connections. Finally, the upsampling layer integrates the feature information of the first two parts to generate the final prediction noise.

[0041] For KAN Policy-T, the observation data and time step k Combining conditional embeddings, encoded by the encoder and combined with action noise All of them are input into the decoder, and the output features are transformed nonlinearly by the GR-KAN module to obtain the prediction result.

[0042] Step 3: Generate the current action using the predicted noise through the inverse diffusion formula of the diffusion model. The inverse diffusion formula has been described above and will not be repeated here.

[0043] In order to verify the performance of the proposed method, the inventors conducted some experiments, and the experimental results are as follows: Experiment 1: Verify the performance of KAN strategy in generating trajectories. Figure 7As shown in the figure, in terms of intuitive trajectory, the KAN strategy (KP-C) has a smoother action trajectory than the CNN-based diffusion model (DP-C) (the figure contains three important nodes of the task); in terms of completion efficiency, the time to complete a single task is shortened by 10.7%; the curvature is reduced by nearly six times. The experimental results strongly prove the effectiveness of modularizing and integrating the Kolmogorov-Arnold network (KAN) into the diffusion strategy. This method makes full use of the powerful nonlinear expression ability of KAN to generate a more efficient and smooth trajectory.

[0044] Experiment 2: Verify the robustness of the KAN strategy to the data. The Multi-Human dataset is collected by operators with different skill levels and may show significant differences in the motion planning process. For example, there may be large differences in trajectory lengths, and noise or errors may also occur in the robot's motion, such as grasping failures. Three tasks, Lift, Can, and Square, were designed. Lift: use a robotic arm to clamp and lift a small cube; Can: use a robotic arm to transport a cylinder to a designated area; Square: use a robotic arm to clamp a ring and put it on a column of the correct shape. The KAN strategy of the present invention also achieved significant improvements on the Multi-Human dataset, as shown in Table 2. Where Succ is the success rate, Time is the task completion time, and Cur is the curvature. It shows that the KAN strategy is highly robust to changes in the dataset and can improve performance even on relatively poor datasets.

[0045] Table 2 Performance of KAN strategy on multi-person dataset

[0046] Experiment 3: Verify the applicability of the GR-KAN module to multiple policy learning models. Significant performance gains were observed by integrating the GR-KAN module at the end of multiple policy learning architectures. All methods benefited from integrating GR-KAN, and significant performance gains were observed on multiple metrics, as shown in Table 3. More importantly, models that initially performed poorly also showed considerable improvements after integrating GR-KAN. This shows that GR-KAN is not only an effective enhancement module for the diffusion policy model, but also has the potential to improve the performance of other models, thus establishing its wide application in the policy learning paradigm.

[0047] Table 3 Performance of GR-KAN module integrated into various strategy learning models

[0048] Experiment 4: Verify the performance of the KAN strategy in different action spaces. The experiment shows that in a larger action space, the KAN strategy still performs well, as shown in Table 4. Where Succ is the success rate, Time is the task completion time, and Coverage is the target coverage area. When the maximum number of steps in the action space increases from 300 to 1000 (extending the maximum completion deadline of the task), the method of the present invention can completely complete the task and complete it in a relatively short time. This shows that the KAN strategy (KP-C and KP-T) can still maintain high efficiency and stability in a larger action space, and has better task final completion.

[0049] Table 4 Performance of KAN strategy in different action spaces

[0050] The embodiment of the present invention also provides a robot trajectory generation system based on a Kolmogorov-Arnold network, comprising: The data processing module is used to extract observation data and corresponding action data from the data source file storing the robot's motion trajectory. The observation data includes the environment and its own state information perceived by the robot, and the action data is the specific control instructions executed by the robot at each time step; A model training module is used to use action data as the object of diffusion model noise addition, and to use observation data as a condition to train the KAN policy network. The KAN policy network is formed by integrating the Kolmogorov-Arnold network into the basic network architecture of the diffusion strategy in a modular form, including a convolutional neural network-based KAN policy network and a Transformer-based KAN policy network, which are used to predict the noise to be added; The trajectory generation module is used to select the trained KAN policy network according to the requirements of the on-site task scenario, generate predicted noise based on the actual observation data and action data of the robot, and use the predicted noise to generate the next action through the inverse diffusion formula of the diffusion model.

[0051] It should be understood that the robot trajectory generation system based on the Kolmogorov-Arnold network in the embodiment of the present invention can implement all the technical solutions in the above method embodiment, and the functions of its various functional modules can be specifically implemented according to the methods in the above method embodiments. The specific implementation process can refer to the relevant description in the above embodiment, which will not be repeated here.

[0052] The present invention also provides an electronic device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the robot trajectory generation method based on the Kolmogorov-Arnold network as described above are implemented.

[0053] The present invention also provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of the robot trajectory generation method based on the Kolmogorov-Arnold network as described above are implemented.

[0054] It should be understood by those skilled in the art that the embodiments of the present invention may be provided as methods, devices (systems), electronic devices or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0055] The present invention is described with reference to a flowchart of a method according to an embodiment of the present invention. It should be understood that each process in the flowchart and a combination of processes in the flowchart can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the process in the flowchart. Figure 1 A device that specifies functions in a process or multiple processes.

[0056] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A function specified in a process or multiple processes.

[0057] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 The steps of a specified function in a process or multiple processes.

Claims

1. A robot trajectory generation method based on Kolmogorov-Arnold network, characterized in that: The following steps are involved: Extract observation data and corresponding action data from the data source file storing the robot's motion trajectory. The observation data includes the environment and its own state information perceived by the robot, and the action data is the specific control instructions executed by the robot at each time step. The action data is used as the object of the diffusion model to add noise, and the observation data is used as a condition to train the KAN policy network. The KAN policy network is formed by integrating the Kolmogorov-Arnold network into the basic network architecture of the diffusion strategy in a modular form, including a convolutional neural network-based KAN policy network and a Transformer-based KAN policy network, which are used to predict the noise to be added; According to the requirements of the on-site task scenario, the trained KAN strategy network is selected, and the predicted noise is generated according to the actual observation data and action data of the robot. The predicted noise is used to generate the next action through the inverse diffusion formula of the diffusion model.

2. The method according to claim 1, characterized in that The KAN strategy network based on convolutional neural network includes three parts. The first part is the downsampling layer, which generates embedded input according to the action data and passes the downsampled features to the third part using skip connections. The second part is the embedding layer, which extracts intermediate embeddings using the embedding KAN module based on the downsampled features and the observed data as conditions. The embedding KAN module includes a tokenization layer, a normalization layer, and a linear layer. The third part is the upsampling layer, which generates the final output based on the features of the previous two parts.

3. The method according to claim 2, characterized in that The tokenization layer is used to convert a one-dimensional sequence into a patch embedding representation with overlapping regions. Given an input sequence , where B is the batch size and C in Indicates the number of input channels, L in is the sequence length, and a one-dimensional convolution operation is used to project it into a higher-dimensional embedding space: ； in, , W is the preset parameter of convolution, h is the convolution kernel size, C out is the embedding dimension, LN represents layer normalization, Conv represents the convolution operation, and the convolution operation includes stride s and padding , the output shape is , where L patch Determined by the following formula: ； The processing of the linear layer is described as: ； Among them, w b and w s is the weight generated by the linear layer, and the function is defined as follows: , , B i (x) represents the basis function, i is the index, c i represents the weight of each basis function; The final output f(x) of the embedded KAN module is: ； Among them, a and b are the conditional features extracted by the conditional encoder from the global feature observation data and time steps.

4. The method according to claim 1, characterized in that: The Transformer-based KAN policy network includes an encoder, a decoder, and a GR-KAN module. The encoder generates conditional embeddings for the combination of observation data and time steps. The encoded hidden variables and action data are input into the decoder together. The features output by the decoder are nonlinearly transformed through the GR-KAN module to obtain the final result.

5. The method according to claim 4, characterized in that The GR-KAN module includes a linear layer and a grouped KAT. The formula of the entire module is described as: ； Among them, w1, w2 and b1, b2 are weights and biases generated by two linear layers, K is a rational function, and the superscript of K represents different initialization modes of grouped KAT. Assume i is the current input channel The index of j is the output channel The index of , divides the entire input channel into g groups evenly, is the group number, then K is expressed as: ； in is the weight coefficient, and R(x) is a rational function.

6. The method according to claim 1, characterized in that During the training process of the KAN strategy network, the goal is to minimize the mean square error between the predicted noise and the actual noise.

7. The method according to claim 1, characterized in that The inverse diffusion formula of the diffusion model is expressed as: ； in, yes The action of the time step, , , is the parameter setting of noise, is the noise of the network prediction, are network parameters, is the observed data at time t, is noise that follows a specified distribution.

8. A robot trajectory generation system based on Kolmogorov-Arnold network, characterized in that: include: The data processing module is used to extract observation data and corresponding action data from the data source file storing the robot's motion trajectory. The observation data includes the environment and its own state information perceived by the robot, and the action data is the specific control instructions executed by the robot at each time step; A model training module is used to use action data as the object of diffusion model noise addition, and to use observation data as a condition to train the KAN policy network. The KAN policy network is formed by integrating the Kolmogorov-Arnold network into the basic network architecture of the diffusion strategy in a modular form, including a convolutional neural network-based KAN policy network and a Transformer-based KAN policy network, which are used to predict the noise to be added; The trajectory generation module is used to select the trained KAN policy network according to the requirements of the on-site task scenario, generate predicted noise based on the actual observation data and action data of the robot, and use the predicted noise to generate the next action through the inverse diffusion formula of the diffusion model.

9. An electronic device, characterized in that: include: one or more processors; Memory; And one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the robot trajectory generation method based on the Kolmogorov-Arnold network as described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the robot trajectory generation method based on the Kolmogorov-Arnold network as described in any one of claims 1 to 7 are implemented.

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