Non-smooth hysteresis modeling and compensation method for joint module based on neural hysteresis operator

Abstract

This invention discloses a method for modeling and compensating non-smooth hysteresis in joint modules based on a neural hysteresis operator. First, a simple neural non-smooth hysteresis operator is constructed, whose weighting coefficients can be adjusted to describe different hysteresis curve shapes. Then, based on this neural hysteresis operator, an LSTM neural network-based non-smooth hysteresis model is built to describe the relationship between the load torque borne by the joint module and the execution error torsional angle. Finally, the execution error torsional angle of the joint module is predicted based on the neural network non-smooth hysteresis model, and this torsional angle is converted to the input of the joint module to compensate for the setpoint rotation angle of the servo motor. This method uses an open-loop feedforward compensation control approach to eliminate the execution error of the joint module. This invention can effectively improve the joint execution accuracy and reliability.

Description

Technical Field

[0001] This invention relates to the field of robotics, specifically to a method for modeling and compensating non-smooth hysteresis in joint modules based on neural hysteresis operators. Background Technology

[0002] In industrial robots, collaborative robots, and humanoid robots, the joint modules composed of servo motors, reducers, and encoders exhibit a hysteresis characteristic due to the flexible wheels and frictional characteristics in the reducers. This hysteresis characteristic varies with the load borne by the joint during operation. This non-smooth, strong hysteresis characteristic inevitably affects the accuracy and reliability of joint operation. Constructing a simple, high-precision, lightweight neural network non-smooth hysteresis model that directly describes the non-smooth, strongly nonlinear characteristics of robot joint modules, fully leveraging the online learning capabilities of neural networks, and deploying it on an embedded AI platform for final application in industrial real-time control systems, represents the mainstream direction of industrial edge AI (edge ​​AI) development.

[0003] In recent years, AI-based modeling methods have many advantages, such as ease of deployment on edge AI platforms. However, existing hysteresis modeling methods based on Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTMs), Gated Recurrent Units (GRUs), Convolutional Neural Networks (CNNs), and Transformers with self-attention mechanisms all approximate non-smooth hysteresis characteristics by superimposing smooth functions, thus resulting in low accuracy. Summary of the Invention

[0004] The present invention addresses the problem of low model accuracy in existing neural network hysteresis modeling methods for robot joint modules, and provides a non-smooth hysteresis modeling and compensation method for joint modules based on neural hysteresis operators.

[0005] To solve the above problems, the present invention is achieved through the following technical solution:

[0006] A method for non-smooth hysteresis modeling and compensation of joint modules based on neural hysteresis operators includes the following steps:

[0007] Step 1: Construct a non-smooth hysteresis model for a neural network; this non-smooth hysteresis model includes an output layer, two hidden layers, and an input layer with two input nodes, which respectively input... Moment torque and Incremental torque at any moment The first hidden layer includes A neural lag operator The second hidden layer includes Long Short-Term Memory Network The output layer uses a hyperbolic function as the activation function and a weighted sum as the output node. Predicting torque angle at all times The output of the output layer is connected to the input of the first hidden layer, the output of the first hidden layer is connected to the input of the second hidden layer, and the output of the second hidden layer is connected to the input of the output layer; where... , This represents the number of hidden nodes.

[0008] Step 2: Use a torque sensor to acquire data from the joint module. Moment torque and Incremental torque at any moment The data is then fed into a non-smooth hysteresis model of a neural network to obtain the joint module. Predicting torque angle at all times ;

[0009] Step 3: Utilize the joint module Predicting torque angle at all times right Set rotation angle at all times To make compensation and utilize the obtained Constantly compensate for rotation angle Control the joint module; among which Constantly compensate for rotation angle :

[0010] ,

[0011] In the formula, This represents the reduction ratio of the joint module.

[0012] The above-mentioned The mathematical description of a neural hysteresis operator is as follows:

[0013] ,

[0014] in, For joint modules Moment torque, For joint modules Torque increment at all times For the first A neural hysteresis operator Output at all times For the first A neural hysteresis operator Output at all times For the first A neural hysteresis operator Intermediate variables at time, For the first The weighted coefficients of the neural hysteresis operator, It is a hyperbolic function. For abrupt non-smooth sign functions, , The number of neural hysteresis operators.

[0015] The above-mentioned The mathematical description of a Long Short-Term Memory (LSTM) network is as follows:

[0016] ,

[0017] In the formula, for Time input gate, for The Gate of Forgetting Time for The state of candidate cells at any given time. for Cellular state at any given moment for Cellular state at any given moment for The output gate of the moment, for The hidden state at all times for The hidden state at all times For the first LSTM Input at any time For the first LSTM Output at any moment; , , , , For input weights, , , , , This is the offset. , , , For state weights, It is an S-shaped function. It is a hyperbolic activation function. For Hadamard element-wise multiplication, , This represents the number of long short-term memory networks.

[0018] The mathematical description of the above output layer is as follows:

[0019] ,

[0020] In the formula, for Predict the torque angle at all times. For the first LSTM Output at any moment It is a hyperbolic function. , This represents the number of hidden nodes.

[0021] The above-mentioned joint module Incremental torque at any moment for:

[0022] ,

[0023] In the formula, for Moment torque, for Momental torque.

[0024] Compared with the prior art, the present invention has the following characteristics:

[0025] 1. Construct a neural hysteresis operator with a simple structure that can describe different hysteresis curve shapes by adjusting the weighting coefficients. Since the weighting coefficients of the neural hysteresis operator can be updated based on the steepest descent method, the problem of non-smoothness and non-differentiability is cleverly avoided.

[0026] 2. Construct a neural network non-smooth hysteresis model to describe the relationship between the load torque borne by the joint module and the torsional angle of the execution error. The first layer of the model extracts hysteresis features by a neural hysteresis operator, and the middle layer uses a long short-term memory network (LSTM) as nodes to achieve a strong nonlinear mapping.

[0027] 3. Based on the non-smooth hysteresis model of the neural network, the torsional angle of the joint module execution error is predicted and converted to the input end of the joint module to compensate the rotation angle of the servo motor setpoint. The joint module execution error is eliminated by using an open-loop feedforward compensation control method.

[0028] 4. Open-loop compensation does not affect the stability of the joint. It can be used not only in robot joint design, but also in robot products through secondary development using software programming, thereby improving the robot's execution accuracy and operational reliability. Attached Figure Description

[0029] Figure 1This is a structural diagram of the neural hysteresis operator.

[0030] Figure 2 This is a comparison chart showing the hysteresis curve as a function of the weighting coefficients of the neural hysteresis operator. The first column shows the curve as a function of the weighting coefficients. Comparison of hysteresis curve changes; the second column shows the changes with weighting coefficients. Comparison of hysteresis curve changes, the third column shows the changes with weighting coefficients. Comparison of changes in hysteresis curves.

[0031] Figure 3 This is a structural diagram of a non-smooth hysteresis model of a neural network.

[0032] Figure 4 This is a schematic diagram of the feedforward compensation control principle for the joint module. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific examples and the accompanying drawings.

[0034] The joint module, consisting of a servo motor and a reducer, outputs an angle that is not the rotation angle set by the servo motor when the torque load changes. of ,Right now ,in This refers to the reduction ratio. The torsion angle of the joint module. For ideal output angle Compared with the actual output angle The difference is used to represent the error in the actual execution angle of the joint module. In order to achieve compensation control of the torsional angle of the joint module and eliminate the execution error caused by the joint structure, the prerequisite is to establish a high-precision hysteresis model describing the hysteresis characteristics of the joint module, with the load torque borne by the joint as the input of the hysteresis model and the torsional angle as the output of the hysteresis model.

[0035] The neural network non-smooth hysteresis model of the present invention is based on hysteresis feature extraction and dynamic nonlinear mapping.

[0036] For hysteresis feature extraction, this invention uses a neural hysteresis operator as a generalized activation node to extract non-smooth features of the hysteresis characteristics of joint modules. The designed neural hysteresis operator consists of two parts: one is a description of the dynamic characteristics, and the other is a hyperbolic function with a sign function containing abrupt changes in the independent variable, used to describe the non-smooth characteristics.

[0037] See Figure 1 The mathematical description of the neural hysteresis operator is as follows:

[0038] ,

[0039] in, It is the first A neural hysteresis operator Output at all times It is the first A neural hysteresis operator The moment before the moment Output at all times It is the first A neural hysteresis operator The hyperbolic function output at time t, containing the sign function It is the first A neural hysteresis operator The input of the hyperbolic function at time t, and They are The joint is constantly subjected to torque and torque increments. It is the first The weighted coefficients of the neural hysteresis operator, , The number of neural hysteresis operators. It is a hyperbolic function. It is a sign function that is abruptly nonsmooth.

[0040] Analysis of the hysteresis characteristics of neural hysteresis operators:

[0041] Adjust the weighting coefficients in the neural hysteresis operator respectively , and The changes in the hysteresis curves are as follows: Figure 2 As shown. From Figure 2 As can be seen, the shape of the hysteresis loop can be adjusted by adjusting the parameters of the neural hysteresis operator with a simple structure. Therefore, the neural hysteresis operator can directly describe non-smooth characteristics and can be used to construct non-smooth hysteresis models of neural networks.

[0042] Differentiability analysis of neural nonsmooth hysteresis operators:

[0043] Output of the neural hysteresis operator With the desired output difference We learn and update the weighted coefficients of the neural hysteresis operator based on the gradient descent method, and explain the differentiability of the neural hysteresis operator from the parameter learning process.

[0044] Let the loss function be defined. Obtain weighted increment They are represented as follows:

[0045] , , ,

[0046] ,

[0047] In the formula, yes time The increment, yes The derivative, It is the learning rate.

[0048] As can be seen from the above analysis, although the constructed neural hysteresis operator contains abrupt and non-smooth sign functions, the weighting coefficients of the neural hysteresis operator can be based on partial derivatives. In the update learning, the special structure of this neural hysteresis operator ingeniously avoids the problem of non-differentiability of sign functions, thereby solving the problem of non-smoothness and non-differentiability (non-differentiability) in the modeling of non-smooth characteristics of neural networks when learning weighted parameters based on gradient method.

[0049] For dynamic nonlinear mappings, this invention uses a Long Short-Term Memory (LSTM) network as the generalized hidden nodes. The mathematical description of LSTM is as follows:

[0050] ,

[0051] In the formula, for Time input gate, for The Gate of Forgetting Time for The state of candidate cells at any given time. for Cellular state at any given moment for Cellular state at any given moment for The output gate of the moment, for The hidden state at all times for The hidden state at all times For the first LSTM Input at any time For the first LSTM Output at any moment; , , , , For input weights, , , , , This is the offset. , , , For state weights, , The number of LSTMs, It is an S-shaped function. It is a hyperbolic activation function. This is Hadamard's element-wise multiplication.

[0052] Based on this, the present invention establishes a non-smooth hysteresis model for neural networks, such as... Figure 3 As shown, it includes an input layer, two hidden layers, and an output layer. The output layer includes two input nodes, which respectively input... Moment torque and Incremental torque at any moment The first hidden layer includes A neural lag operator The second hidden layer includes Long Short-Term Memory Network The output layer uses a hyperbolic function as the activation function and a weighted sum as the output node. Predicting torque angle at all times ;in , The number of hidden nodes is used. The non-smooth hysteresis of the neural network is calculated by using the difference between the actual torsion angle output by the joint module and the predicted torsion angle output by the model. The model is trained using the velocity descent method, and finally the model weighting coefficients are obtained.

[0053] The compensation for the execution error of the joint module, i.e., the torsional angle, is achieved through feedforward control before the joint's set angle is executed. First, information on the torque load and torque change of the joint is obtained through sensors (or calculated using current). This information serves as the input vector for a neural network hysteresis model describing the joint's characteristics. Based on the corresponding load information, the hysteresis model predicts the torsional angle one step in advance. Then, according to the reducer ratio in the joint, the error at the joint output is converted to the joint input (servo motor drive) to obtain the correction amount. This correction amount is then used to compensate for the set rotation angle of the servo motor. Using an open-loop feedforward approach to compensate for the joint module's execution error does not affect the stability of joint operation. Another characteristic of this open-loop feedforward compensation control is that it can not only be used for robot joint design but also, through secondary development using software, for use in robot products.

[0054] Accordingly, the non-smooth hysteresis modeling and compensation method for joint modules based on neural hysteresis operators proposed in this invention, such as... Figure 4 As shown, it includes the following steps:

[0055] Step 1: Construct a non-smooth hysteresis model for the neural network. This model includes an output layer, two hidden layers, and an output layer. The output of the output layer is connected to the input of the first hidden layer, the output of the first hidden layer is connected to the input of the second hidden layer, and the output of the second hidden layer is connected to the input of the output layer. The input layer includes two input nodes, which respectively input... Moment torque and Incremental torque at any moment The first hidden layer includes A neural lag operator The second hidden layer includes Long Short-Term Memory Network The output layer uses a hyperbolic function as the activation function and a weighted sum as the output node. Predicting torque angle at all times ;in , This represents the number of hidden nodes.

[0056] No. The mathematical description of a neural hysteresis operator is as follows:

[0057] ,

[0058] in, For joint modules Moment torque, For joint modules Torque increment at all times For the first A neural hysteresis operator Output at all times For the first A neural hysteresis operator Output at all times For the first A neural hysteresis operator Intermediate variables at time, For the first The weighted coefficients of the neural hysteresis operator, It is a hyperbolic function. For abrupt non-smooth sign functions, , The number of neural hysteresis operators.

[0059] No. The mathematical description of a Long Short-Term Memory (LSTM) network is as follows:

[0060] ,

[0061] In the formula, for Time input gate, for The Gate of Forgetting Time for The state of candidate cells at any given time. for Cellular state at any given moment for Cellular state at any given moment for The output gate of the moment, for The hidden state at all times for The hidden state at all times For the first LSTM Input at any time For the first LSTM Output at any moment; , , , , For input weights, , , , , This is the offset. , , , For state weights, It is an S-shaped function. It is a hyperbolic activation function. For Hadamard element-wise multiplication, , This represents the number of long short-term memory networks.

[0062] The mathematical description of the output layer is as follows:

[0063] ,

[0064] In the formula, for Predict the torque angle at all times. For the first LSTM Output at any moment It is a hyperbolic function. , This represents the number of hidden nodes.

[0065] Step 2: Use a torque sensor to acquire data from the joint module. Moment torque and Incremental torque at any moment ,in The data is then fed into a non-smooth hysteresis model of a neural network to obtain the joint module. Predicting torque angle at all times .

[0066] Step 3: Utilize the joint module Predicting torque angle at all times right Set rotation angle at all times To make compensation and utilize the obtained Constantly compensate for rotation angle Control the joint module; among which Constantly compensate for rotation angle :

[0067] ,

[0068] In the formula, This represents the reduction ratio of the joint module.

[0069] This invention constructs a neural network non-smooth hysteresis model with neural hysteresis operators as activation functions, and implements feedforward compensation control for execution errors caused by joint hysteresis based on this neural network non-smooth hysteresis model, thereby improving the accuracy and reliability of joint execution.

[0070] It should be noted that although the embodiments described above are illustrative, they are not intended to limit the invention. Therefore, the invention is not limited to the specific embodiments described above. Any other embodiments obtained by those skilled in the art under the guidance of this invention without departing from its principles are considered to be within the protection scope of this invention.

Claims

1. A method for modeling and compensating the non-smooth hysteresis of joint module based on neural hysteresis operator, characterized in that, The steps include the following: Step 1: Construct a non-smooth hysteresis model for a neural network; this non-smooth hysteresis model includes an output layer, two hidden layers, and an input layer with two input nodes, which respectively input... Moment torque and Incremental torque at any moment The first hidden layer includes A neural lag operator The second hidden layer includes Long Short-Term Memory Network The output layer uses a hyperbolic function as the activation function, with weighted summation as the output node. Predicting torque angle at all times The output of the output layer is connected to the input of the first hidden layer, the output of the first hidden layer is connected to the input of the second hidden layer, and the output of the second hidden layer is connected to the input of the output layer; where... , This represents the number of hidden nodes. Step 2: Use a torque sensor to acquire data from the joint module. Moment torque and Incremental torque at any moment The data is then fed into a non-smooth hysteresis model of a neural network to obtain the joint module. Predicting torque angle at all times ; Step 3: Utilize the joint module Predicting torque angle at all times right Set rotation angle at all times To make compensation and utilize the obtained Constantly compensate for rotation angle Control the joint module; among which Constantly compensate for rotation angle : ， In the formula, This represents the reduction ratio of the joint module.

2. The method for non-smooth hysteresis modeling and compensation of joint modules based on neural hysteresis operators according to claim 1, characterized in that, No. The mathematical description of a neural hysteresis operator is as follows: ， in, For joint modules Moment torque, For joint modules Incremental torque at all times For the first A neural hysteresis operator Output at all times For the first A neural hysteresis operator Output at all times For the first A neural hysteresis operator Intermediate variables at time, For the first The weighted coefficients of the neural hysteresis operator, It is a hyperbolic function. For abrupt non-smooth sign function, , The number of neural hysteresis operators.

3. The method for non-smooth hysteresis modeling and compensation of joint modules based on neural hysteresis operators according to claim 1, characterized in that, No. The mathematical description of a Long Short-Term Memory (LSTM) network is as follows: ， In the formula, for Time input gate, for The Gate of Forgetting Time for The state of candidate cells at any given time. for Cellular state at any given moment for Cellular state at any given moment for The output gate of the moment, for The hidden state at all times for The hidden state at all times For the first LSTM Input at any time For the first LSTM Output at any moment; , , , , For input weights, , , , , This is the offset. , , , For state weights, It is an S-shaped function. It is a hyperbolic activation function. For Hadamard element-wise multiplication, , This represents the number of long short-term memory networks.

4. The method for non-smooth hysteresis modeling and compensation of joint modules based on neural hysteresis operators according to claim 1, characterized in that, The mathematical description of the output layer is as follows: ， In the formula, for Predict the torque angle at all times. For the first LSTM Output at any moment It is a hyperbolic function. , This represents the number of hidden nodes.

5. The method for non-smooth hysteresis modeling and compensation of joint modules based on neural hysteresis operators according to claim 1, characterized in that, In step 2, the joint module Incremental torque at any moment for: ， In the formula, for Moment torque, for Momental torque.

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