Method for predicting compensation of trajectory errors of an industrial robot based on a non-autoregressive network

Abstract

The application provides a method for predicting and compensating trajectory error of an industrial robot based on a non-autoregressive network, comprising: constructing a time position embedding enhanced gated adaptive continuous time recurrent neural network model; constructing time position embedding features for the encoder and decoder inputs respectively and splicing, providing the decoder with absolute position information of the prediction subsequence in the complete work cycle and internal relative position information of the subsequence; using the time position embedding features as time sequence guidance, adopting a non-autoregressive decoding mode to output a complete prediction sequence in one time, generating a trajectory tracking error prediction value; and converting the error prediction value into a real-time correction of a theoretical trajectory by a feedforward compensation amount. Through time position embedding and non-autoregressive decoding, the application eliminates subsequence connection distortion, improves prediction efficiency and accuracy, and realizes high-precision trajectory tracking compensation.

Description

Technical Field

[0001] This invention relates to the field of industrial robot control technology, and specifically to a method for predicting and compensating for trajectory errors of industrial robots based on non-autoregressive networks. Background Technology

[0002] Industrial robots are core equipment for the development of the national manufacturing industry. As key industrial structural components become larger and more complex with curved surfaces, key national manufacturing industries have put forward urgent demands for industrial robots and their application performance. At present, there are relatively few industrial robots in my country with stable and reliable performance. In the development process, there are still problems such as difficulty in maintaining motion accuracy and system stability under heavy loads, strong impacts, and dynamic load conditions; multiple constraints leading to uneven motion trajectories; and decreased trajectory tracking capabilities. Traditional control algorithms are currently unable to meet the requirements of high-precision trajectory tracking for robots.

[0003] In the motion trajectory tracking process of industrial robots, errors can be divided into geometric errors and non-geometric errors based on their sources. Under heavy load and complex working conditions, the structural deformation, impact, and gaps generated by industrial robots are mostly non-geometric errors. These errors are characterized by nonlinearity, strong coupling, and difficulty in prediction. How to accurately and specifically compensate for them is one of the focuses of industrial robot research.

[0004] Neural networks possess advantages such as strong nonlinear mapping capabilities, automatic feature extraction, and the ability to process and fit high-dimensional data. By iteratively training and analyzing error data within the workspace of the end effector, they can effectively predict and generalize future errors and perform accuracy compensation. In robot trajectory tracking error compensation and accuracy control methods, they can be categorized into model-based methods and model-free methods.

[0005] Model-based methods require detailed modeling and analysis of the robot's dynamics and control system, combined with numerical statistical algorithms for joint space parameter identification and calibration. Commonly used methods include least squares, Levenberg-Marquardt algorithm, and genetic algorithm. For example, patent CN110977992B proposes a kinematics-free trajectory tracking method for robotic arms. This method collects the first error function of the trajectory, uses a gradient neural network to generate the state equation, then obtains the second error function based on the actual end-effector velocity, and uses a gradient neural network to generate the Jacobian matrix. Finally, the target trajectory is obtained by jointly solving these equations.

[0006] Model-free methods eliminate the need for modeling and analyzing the robot. They collect motion data and are data-driven, often combined with artificial intelligence and machine learning algorithms, such as neural networks and MPC, to achieve precise control over the robot system's trajectory tracking. For example, patent CN112518753B proposes using a neural network PID module to process the trajectory error between the desired joint data and the actual joint data. The neural network PID module controls the three parameters in the error compensation process through a linear combination, making the deviation approach zero.

[0007] However, existing technologies still have the following shortcomings: Industrial robots are complex dynamic systems. Under complex working conditions, model-based control methods, such as dynamic calibration and online measurement, are used. However, due to the severe nonlinearity of disturbance and noise parameters, the fact that joint forces, torques and joint motions are mostly periodic functions, and the serious coupling relationship between multiple sources of errors, the models are complex and difficult to model. Furthermore, inaccurate model parameter identification structures can seriously affect trajectory tracking accuracy. Limited by environmental and individual differences, the applicability and generalization are poor.

[0008] Model-free control methods employing data-driven approaches and machine learning, such as ANN, LSTM, and TCN, suffer from drawbacks due to the inherent characteristics of machine learning and neural networks. These include large datasets, long training times, and high computational requirements. In complex operating conditions, achieving ideal fitting results necessitates multiple training iterations, leading to high control costs and insufficient robustness to variable-period signals. The applicant previously proposed a gated adaptive continuous-time recurrent neural network (GACTRNN) to process periodic signals using adaptive time-scale parameters; however, in practical multi-dimensional feature prediction, it still suffers from issues such as subsequence concatenation distortion and low prediction efficiency. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for predicting and compensating the trajectory error of industrial robots based on non-autoregressive networks. By introducing a time-position embedding mechanism and a non-autoregressive decoding strategy, this invention solves the problems of subsequence connection distortion, low prediction efficiency, and poor adaptability under variable period conditions in existing trajectory error prediction methods, thereby achieving high-precision tracking and real-time compensation of the end-effector trajectory of industrial robots.

[0010] To achieve the above objectives, the present invention adopts the following technical solution: A method for predicting and compensating for trajectory errors of industrial robots based on non-autoregressive networks includes the following steps: S1. Construct a time-position embedding-enhanced gated adaptive continuous-time recurrent neural network model, namely the TPE-GACTRNN model. This model includes an encoder and a decoder. The encoder is used to encode the input sequence into a semantic vector, and the decoder is used to generate prediction sequences in parallel based on the semantic vector. S2. Construct temporal position embedding features for the inputs of the encoder and decoder respectively, and concatenate the temporal position embedding features with the original input features to construct the enhanced encoder input and enhanced decoder input; wherein, the temporal position embedding features are used to provide the decoder with the absolute position information of each predicted subsequence in the complete job cycle and the relative position information within the subsequence, thereby enhancing the model's ability to perceive the global temporal background; S3. Using time position embedding features as temporal guidance, a non-autoregressive decoding method is adopted, in which the decoder outputs the complete prediction sequence in parallel at one time to generate the trajectory tracking error prediction value of the end effector of the industrial robot; the non-autoregressive decoding method is as follows: the output of the decoder at each time step depends only on the semantic vector and the input of the enhanced decoder, and does not depend on the decoding output of the previous time step, thereby generating the entire prediction sequence in parallel and eliminating the cumulative error and connection distortion caused by autoregressive decoding; S4. The predicted value of trajectory tracking error is used as the feedforward compensation amount to correct the theoretical motion trajectory of the industrial robot in real time, so as to improve the trajectory tracking accuracy. In specific implementation, the predicted value of trajectory tracking error is negative to obtain the Cartesian space compensation direction, which is mapped to the joint space through the inverse kinematics Jacobian matrix to generate the feedforward compensation amount, and then superimposed with the theoretical trajectory command of the corresponding time step to generate the corrected control command. Furthermore, the TPE-GACTRNN model is pre-trained using simulation data and real motion data. During training, at least one of the position, velocity, or current signal in the joint space is used as the input feature, and the Cartesian trajectory error of the end effector is used as the prediction label. Simulation data is used for pre-training, and real motion data is used for fine-tuning.

[0011] Furthermore, the neural units in the gated adaptive continuous-time recurrent neural network model employ adaptively adjustable time scale parameters, and their internal states and time scale parameter update methods are dynamically controlled by external inputs, thereby achieving adaptive processing of signals with different frequency periods.

[0012] Furthermore, the time position embedding feature includes the following four features: static velocity features for characterizing trajectory periodic information under different speed tasks; absolute timestamps for characterizing the absolute position information of the current prediction task throughout the entire job cycle; relative subsequence positions for characterizing the relative position information of the current time step within the current prediction subsequence; and sinusoidal position encoding for providing dynamic periodic information for prediction tasks at different speeds.

[0013] Furthermore, the decoder continuously generates trajectory tracking error prediction values ​​in a sliding window manner. Adjacent prediction windows provide global start and end position information through absolute timestamps and provide intra-window position indexes through relative subsequence positions, ensuring that the prediction values ​​of adjacent windows are continuous without jumps at the junction.

[0014] As can be seen from the above technical solutions, compared with the prior art, the beneficial effects of the present invention are: 1. This invention provides an explicit global spatiotemporal background reference for recurrent networks through a time-position embedding mechanism. Combined with the adaptive time scale adjustment capability of GACTRNN, it significantly improves the prediction accuracy of trajectory tracking errors under variable period and variable speed conditions. 2. By introducing absolute timestamps and relative subsequence position encoding, this invention enables the decoder to accurately identify the global position of the current prediction window in the complete job cycle and its relative position within the window. Combined with a non-autoregressive decoding strategy, it completely solves the problem of sawtooth oscillations and accumulated errors that are easily generated at the subsequence junctions in traditional autoregressive models, ensuring the smoothness and global consistency of the compensation signal. 3. This invention adopts a non-autoregressive decoding method, in which the decoder outputs the complete prediction sequence in parallel at one time, without the need for iterative calculations step by step, which significantly shortens the prediction time, reduces the computing power requirements of the controller, and meets the application requirements of real-time compensation for industrial robots. 4. This invention converts the prediction error into a feedforward compensation amount and adds it to the theoretical trajectory command, thereby achieving active suppression of trajectory tracking error; 5. This invention directly uses a data-driven neural network model to learn and predict end-effector errors, without the need for precise modeling and parameter identification of the robot's complex dynamic system. This effectively avoids the accuracy degradation caused by model mismatch and has good applicability and generalization ability. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the encoder-decoder structure of the GACTRNN model of this invention; Figure 2 This is a schematic diagram of the structure and parameter transmission of the neural unit in the GACTRNN model of this invention; Figure 3 This is a schematic diagram illustrating the composition and structure of the Time Position Embedding (TPE) feature in this invention; Figure 4 This is a schematic diagram illustrating the process of concatenating the time position embedding feature with the encoder and decoder inputs in this invention; where a represents the construction method for enhancing the encoder input, and b represents the construction method for enhancing the decoder input. Figure 5This is a schematic diagram of the TPE-GACTRNN model, which employs a time-position embedding and non-autoregressive decoding architecture, as described in this invention. Figure 6 This is a schematic diagram of the TPE-GACTRNN model in this invention continuously generating trajectory tracking error prediction sequences using a sliding window method. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. The illustrative embodiments and descriptions of this invention are for illustrative purposes only and are not intended to limit the invention.

[0017] Example 1: Construction of TPE-GACTRNN Model like Figure 1 As shown, the Temporal Position Embedding Enhanced Gated Adaptive Continuous-Time Recurrent Neural Network (TPE-GACTRNN) model constructed in this invention includes an encoder and a decoder. The input sequence... Inputted sequentially into the encoder, it is encoded into a semantic vector. This semantic vector This is then used as input to the decoder at each decoding time step to output the predicted sequence. ,in and These represent the lengths of the input and output sequences, respectively. Due to semantic vectors... It contains hidden information from the input sequence, and the output sequence can be seen as a reasonable processing and prediction of the input sequence.

[0018] The neural unit structure used in this model is as follows: Figure 2 As shown. When processing discrete-time tasks, a neural unit can be regarded as a discrete model, and its neuron parameters are calculated and updated as follows: ; ; ; in: Input for time series; For time steps The predicted output; , They are time steps and The internal state at that time; , These are the external and internal weight matrices of the neuron, respectively; For bias; The base value for the time scale; In this embodiment, the hyperbolic tangent function is used as the activation function. To achieve a faster convergence speed. For time steps The timescale parameter represents the rate at which the internal state of a neuron is updated. Trainable parameters. , and middle, and These are the weight matrices for the input and the neuron activity at the previous time step, respectively. This is the bias of the time scale parameter. Due to the parameter... External input Directly related, GACTRNN can dynamically adjust the update / forgetting rate of internal neurons based on the current external input, thereby achieving adaptive processing of periodic signals.

[0019] Example 2: Construction of Temporal Location Embedded Features Based on the original GACTRNN network, this invention designs a Temporal Position Embedding (TPE) encoding, the composition of which is as follows: Figure 3 As shown, it includes the following four features: (1) Static Speed ​​Feature (SSF): Under a specific speed task condition, the robot's movement speed is considered a fixed constant value. The trajectory period changes at different speeds, so the static characteristics under different speed tasks are also different. These characteristics provide the model with reference information under different speed conditions, which is used to characterize the speed condition of the current prediction task, enabling the model to distinguish the trajectory period characteristics under different speed conditions.

[0020] (2) Absolute Timestamp (AT): Because the robot automatically records the time information of each waypoint in the ROS planner, the timestamps of the entire sequence are known. This feature provides the model with the absolute position information of each prediction task within the complete job cycle, which is of great help in connecting the initial positions in the case of two consecutive predictions and effectively eliminates the generation of jagged predictions.

[0021] (3) Relative Subsequence Position (RSP): ,in belong , This indicates the length of the predicted subsequence, i.e., the number of time steps contained within each prediction window. This feature provides the relative positional relationships within the subsequences within each prediction window, offering crucial positional information for converting the model to non-autoregressive decoding.

[0022] (4) Sinusoidal Positional Encoding (SPE): ,in The position within the entire sequence. This refers to the velocity-related frequency. This feature is consistent with the position encoding in the Transformer, where the static velocity feature determines the generation of the sine function, providing dynamic periodic information for prediction tasks at different velocities.

[0023] Example 3: Enhanced encoder input and enhanced decoder input construction The model uses temporal location embedding features to enhance the inputs of the encoder and decoder, respectively. The specific construction method is as follows: Figure 4 As shown.

[0024] like Figure 4 As shown in part a, when constructing the input to the augmented encoder, the original features at each time step are... Embedded features with time location splicing to enhance encoder input .

[0025] like Figure 4 As shown in part b, when constructing the input to the enhanced decoder, the original decoder input at each time step is set to a zero-spaced vector with the same dimension as the trajectory error label, and then embedded with the time position feature. spliced ​​as Apart from the temporal features and the context provided by the encoder, the decoder provides no other information and relies entirely on the temporal features to generate predictions. Because the inputs to both the encoder and decoder are configured in this way, the decoder's prediction output at each step does not affect subsequent decoding; therefore, the generation of this model no longer depends on the sequence information in the autoregressive model.

[0026] Example 4: Non-autoregressive decoding and sliding window prediction The non-autoregressive decoding architecture used in this model is as follows: Figure 5 As shown, since the decoder input provides temporal location embedding features, the contextual information of the error prediction sequence output by decoding is entirely provided by the temporal features, and the temporal features contain the positional information of the current prediction subsequence in the complete job flow. Therefore, a non-autoregressive mode can be used for decoding output to directly generate the prediction sequence of the entire length.

[0027] The motion state (position, angle) of the robotic arm belongs to physical perception data, while the temporal position embedding belongs to temporal metadata. By splicing the two together, a fusion vector that combines spatial state and temporal index is formed, enabling the decoder to directly identify the absolute position of the current feature in the entire operation cycle.

[0028] like Figure 6 As shown, after constructing and training the TPE-GACTRNN network, the model continuously generates trajectory tracking error predictions using a sliding window approach. Each prediction is based on the semantic vector and temporal location embedding features of the current window, outputting the error sequence within the entire window in parallel. Adjacent prediction windows are connected by providing global start and end position information via absolute timestamps and intra-window position indices via relative subsequence positions. This ensures that the predictions at the junctions of adjacent windows are continuous and without jumps, eliminating the sawtooth oscillations and accumulated errors that are common in traditional autoregressive models at subsequence junctions.

[0029] Example 5: Model Training and Deployment The temporal position embedding enhanced gating adaptive continuous-time recurrent neural network model of this invention is pre-trained using simulation data and real motion data. During training, at least one of the position, velocity, or current signals in joint space is used as input features, and the Cartesian space trajectory error of the end effector is used as the prediction label. Specifically, pre-training is first performed using simulation data to allow the model to initially learn the basic laws of trajectory error; then, fine-tuning is performed using real motion data to adapt the model to the nonlinear and strongly coupled error characteristics under actual working conditions.

[0030] After training, the model is exported in ONNX format and integrated into the robot control system during deployment. During actual operation, the trajectory in joint space is used as input, and the model outputs real-time predicted end-effector trajectory errors, while feedforward compensation is used to correct the theoretical trajectory in real time.

[0031] Example 6: Feedforward Compensation Conversion and Trajectory Correction In step S4, the specific implementation method for converting the trajectory tracking error prediction value into the feedforward compensation amount is as follows: First, the predicted value of the trajectory tracking error (the deviation of the actual trajectory at the end from the expected trajectory) is negative to obtain the compensation direction vector in Cartesian space. Secondly, the compensation direction vector (including position and attitude increments) in Cartesian space is mapped to the joint space through the inverse kinematics Jacobi matrix of the robot, generating the feedforward compensation amount in the joint space. Finally, the feedforward compensation amount in the joint space is superimposed with the theoretical trajectory command of the corresponding time step to generate the corrected control command, thereby realizing the real-time correction of the theoretical motion trajectory of the industrial robot.

[0032] In practical control systems, the network predicts a sequence of future windows (e.g., predicting the future). arrive The control system needs to accurately superimpose these compensation values ​​onto the theoretical trajectory points corresponding to the timestamps. Therefore, the conversion process is performed using a sliding window superposition strategy: each time, only the error value of the first time step or the first few time steps in the current window prediction sequence is converted into a feedforward compensation value and superimposed onto the theoretical trajectory command of the corresponding time step. After the sliding window is updated in the next control cycle, a new error prediction sequence is regenerated and the above process is repeated.

[0033] Example 7: Experimental Verification Results The TPE-GACTRNN method of this invention was used to conduct experiments on trajectory tracking error prediction and compensation for industrial robots. The experimental results show that: (1) The generalization performance under variable speed conditions is improved by 25%-49% compared with the original S2S-GACTRNN; (2) By using absolute timestamps and relative subsequence position encoding, the problem of sawtooth oscillations between subsequence predictions is completely solved, and the consistency of the global trajectory is improved; (3) The non-autoregressive decoding method is adopted, which significantly improves the prediction efficiency and meets the real-time compensation requirements of industrial robots; (4) The measured mean absolute error (MAE) decreased from 3.55 mm to 0.94 mm, and the trajectory accuracy improved by 73.6%, with a significant compensation effect.

[0034] The above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for predicting and compensating for trajectory errors of industrial robots based on non-autoregressive networks, characterized in that, Includes the following steps: S1. Construct a time-position embedding-enhanced gated adaptive continuous-time recurrent neural network model, namely the TPE-GACTRNN model. The TPE-GACTRNN model includes an encoder and a decoder. The encoder is used to encode the input sequence into a semantic vector, and the decoder is used to generate a prediction sequence in parallel based on the semantic vector. S2. Construct temporal position embedding features for the inputs of the encoder and the decoder respectively, and concatenate the temporal position embedding features with the original input features to construct the enhanced encoder input and the enhanced decoder input; The temporal location embedding feature is used to provide the decoder with the absolute position information of each predicted subsequence in the complete job cycle and the relative position information within the subsequence; S3. Using the time position embedding features as temporal guidance, and employing a non-autoregressive decoding method, the decoder outputs the complete prediction sequence in parallel at one time to generate the trajectory tracking error prediction value of the industrial robot end effector. The non-autoregressive decoding method is as follows: the output of the decoder at each time step depends only on the semantic vector and the input of the enhanced decoder, and does not depend on the decoding output of the previous time step, thereby generating the entire prediction sequence in parallel; S4. The predicted trajectory tracking error value is used as a feedforward compensation value to correct the theoretical motion trajectory of the industrial robot in real time, so as to improve the trajectory tracking accuracy.

2. The method for predicting and compensating for trajectory errors of industrial robots based on non-autoregressive networks according to claim 1, characterized in that, The TPE-GACTRNN model is pre-trained using simulation data and real motion data. During training, at least one of the position, velocity, or current signal in the joint space is used as the input feature, and the Cartesian trajectory error of the end effector is used as the prediction label. Simulation data is used for pre-training, and real motion data is used for fine-tuning.

3. The method for predicting and compensating for trajectory errors of industrial robots based on non-autoregressive networks according to claim 1, characterized in that, The update method for the internal state and time scale parameters of the neurons in the gated adaptive continuous-time recurrent neural network model is as follows: ； ； ； in: Input for time series; For time steps The predicted output; , They are time steps and The internal state at that time; For time steps Time scale parameters; , , , This is the weight matrix; , For bias; The base value for the time scale; This is the activation function.

4. The method for predicting and compensating for trajectory errors of industrial robots based on non-autoregressive networks according to claim 1, characterized in that, In step S2, the enhanced encoder input is constructed by taking the original features of each time step. Embedded features with time location splicing to enhance encoder input .

5. The method for predicting and compensating for trajectory errors of industrial robots based on non-autoregressive networks according to claim 1, characterized in that, In step S2, the enhanced decoder input is constructed as follows: the original decoder input at each time step is set to a zero-spaced vector with the same dimension as the trajectory error label, and then embedded with the time position feature. spliced ​​as .

6. The method for predicting and compensating for trajectory errors of industrial robots based on non-autoregressive networks according to claim 1, characterized in that, In step S3, the decoder continuously generates trajectory tracking error prediction values ​​in a sliding window manner. Each prediction is based on the semantic vector and time position embedding features of the current window, and the error sequence within the entire window is output in parallel.

7. The method for predicting and compensating for trajectory errors of industrial robots based on non-autoregressive networks according to claim 6, characterized in that, The time location embedding feature includes the following four features: For Static velocity features characterize trajectory period information under different speed tasks, and the static velocity features are used to distinguish trajectory period information under different speed conditions. An absolute timestamp is used to characterize the absolute location information of the current prediction task throughout the entire job cycle, and the absolute timestamp is used to provide the global location of the current prediction window in the complete job cycle. The relative subsequence position is used to characterize the relative position of the current time step within the current prediction subsequence, and the relative subsequence position is used to maintain the continuity of prediction within the subsequence; In addition, a sinusoidal position code for providing dynamic periodic information for prediction tasks at different speeds, the sinusoidal position code being adapted to periodic signals of different frequencies.

8. The method for predicting and compensating for trajectory errors of industrial robots based on non-autoregressive networks according to claim 7, characterized in that, When the decoder continuously generates trajectory tracking error prediction values ​​in a sliding window manner, adjacent prediction windows have overlapping or non-overlapping temporal connections. The absolute timestamp in the time position embedding feature is used to provide global start and end position information for each prediction window in the complete job cycle, and the relative subsequence position is used to provide the relative position index within the subsequence for each time step within the same window. Based on the global start position and the relative position index within the subsequence, the decoder generates the complete error prediction sequence within the current window in parallel without relying on the decoding output of the previous moment, and ensures that the prediction values ​​of adjacent windows are continuous without jumps at the connection points.

9. The method according to claim 1, characterized in that, Step S4 is implemented in the following way: The predicted trajectory tracking error value is negative to obtain the compensation direction vector in Cartesian space. By using the Jacobian matrix of the robot's inverse kinematics, the compensation direction vector in the Cartesian space is mapped to the joint space to generate the feedforward compensation amount in the joint space. The feedforward compensation amount of the joint space is superimposed with the theoretical trajectory command of the corresponding time step to generate a corrected control command, so as to correct the theoretical motion trajectory of the industrial robot in real time.

10. The method for predicting and compensating for trajectory errors of industrial robots based on non-autoregressive networks according to claim 1, characterized in that, The TPE-GACTRNN model is exported in ONNX format during deployment and integrated into the robot control system.

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