A feedforward compensation control method for a flexible joint torsion angle of an industrial robot

Abstract

The application discloses a feedforward compensation control method for the torsion angle of a flexible joint of an industrial robot, which comprises the following steps: first, an asymmetric nonlinear hysteresis function is designed as a Preisach model hysteresis operator to describe the asymmetric characteristics of the flexible joint; second, output history information is added to the input end of the Preisach model, and an inertia filter link is added to the output end of the Preisach model to describe the speed-dependent characteristics of the flexible joint; third, the improved Preisach model and a full-connection neural network for realizing nonlinear mapping are connected in series to form a deep neural network hysteresis model for describing the change rule of the torque and the torsion angle with the load change. Based on the deep neural network hysteresis model, an angle prediction value is obtained, the angle setting value of the flexible joint of the robot is corrected through feedforward compensation control, the influence of the torsion angle is indirectly eliminated, and the execution precision of the flexible joint of the industrial robot is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robots, and particularly relates to a feedforward compensation control method for a torsion angle of a flexible joint of an industrial robot. BACKGROUND

[0002] Industrial robots have become an important part of the intelligent manufacturing industry and are widely used in assembly, welding, polishing and other operations. Industrial robots can learn and adapt to the environment independently, perform more complex operations, and are developing towards high precision, intelligence, flexibility and collaboration, bringing more innovation and development opportunities to industrial production, and also putting forward higher requirements for the control performance of industrial robots. Harmonic reducers have the advantages of large transmission ratio and high transmission efficiency, and are widely used in flexible joints of industrial robots. However, due to the periodic deformation of the flexible wheel of the harmonic reducer and the nonlinear friction of the meshing tooth surface during transmission, there will be hysteresis in the joint transmission process of the robot, which shows asymmetric, rate-dependent and strong nonlinear characteristics, and these characteristics seriously restrict the further improvement of the repeatability of the robot.

[0003] The modeling method of hysteresis phenomenon mainly includes two kinds of physical mechanism model and hysteresis operator model. The physical mechanism model is based on a specific physical mechanism to describe the hysteresis characteristics, and common models include Maxwell, Jiles-Atherton, Duhem, Bouc-wen and Stoner-Wohlfarth models. However, the physical mechanism of hysteresis of different objects is different, and the physical model established is only applicable to a specific type of smart material. Moreover, the calculation is complex and time-consuming, the online identification of parameters is difficult, and the model inversion is difficult, which is difficult to apply to high-precision real-time control. The hysteresis operator model is based on the input and output data of the system for modeling, and common models include Preisach, Prandtl-Ishlinskii and Krasnosel’skii-Pokrovskii models. However, these models are not based on the physical mechanism of a specific object, and the model parameters do not have a clear physical meaning. Among them, the Preisach model is widely used because of its strong modeling ability for complex hysteresis characteristics, strong hysteresis nonlinear prediction ability, and good versatility. However, the Preisach model can only describe the symmetric and rate-independent hysteresis characteristics, and for the asymmetric, rate-dependent and strong nonlinear hysteresis characteristics of the flexible joint of the industrial robot, directly using the Preisach model to describe will produce a large model error.

[0004] To this end, some documents propose a hyperbolic tangent function dynamic Preisach hysteresis operator related to the input rate to describe the rate-dependent characteristics of the magnetic hysteresis of the super-magnetostrictive driver, but the relationship between the shape function and the input rate is assumed to be a linear function, which cannot accurately describe the strong nonlinear characteristics of the hysteresis. Some documents integrate the Preisach model into the deep learning network structure, use the Fourier transform to calculate the rate of the input signal, and input the rate into the nonlinear layer to generate a rate-dependent nonlinear term and input it into the hysteresis model, thereby obtaining a rate-dependent Preisach hysteresis model and improving the generalization ability of the Preisach model. Some documents combine the Preisach model and the long short-term memory recurrent neural network to establish a rate-dependent hysteresis model. Some documents first mathematically prove that the rate-independent Preisach model is actually a diagonal recurrent neural network (DRNN) with a second-order activation function, and under certain conditions, the DRNN neuron is a multifunctional rate-dependent hysteresis system. The DRNN composed of these neurons can be used to model the rate-dependent hysteresis model. Some documents introduce historical input information into the Preisach function and use neural networks for identification to construct a new input history-dependent dynamic Preisach model. Some documents combine the Preisach model and the NARX neural network to construct a hybrid model to realize rate-dependent hysteresis modeling. However, the above documents fail to comprehensively consider the asymmetric, rate-dependent and strong nonlinear characteristics of the hysteresis, and cannot effectively describe the complex hysteresis characteristics of the asymmetric, rate-dependent and strong nonlinear characteristics of the harmonic reducer flexible joint of the industrial robot. SUMMARY

[0005] The present application solves the problem of the influence of the asymmetric, rate-dependent and strong nonlinear complex hysteresis characteristics of the harmonic reducer flexible joint of the industrial robot on the joint execution accuracy, and provides a feedforward compensation control method for the torsion angle of the flexible joint of the industrial robot.

[0006] To solve the above problems, the present application is realized by the following technical scheme:

[0007] A feedforward compensation control method for the torsion angle of the flexible joint of an industrial robot, comprising the following steps:

[0008] Step 1, constructing a deep neural network hysteresis model and updating the parameters, i.e. weights and biases, of the deep neural network hysteresis model by gradient descent method, thereby completing the modeling of the deep neural network hysteresis model;

[0009] Step 2, inputting the actual angle value x(k-2) at time k-2 and the actual angle value x(k-1) at time k-1 output by the flexible joint of the robot, and the predicted angle value Y(k-2) at time k-2 output by the deep neural network hysteresis model into the Preisach model to obtain the predicted angle valued (k-2) and the angle prediction value Y d (k-1) are sent into the deep neural network hysteresis model to obtain the angle prediction value Y d (k) at time k.

[0010] Step 3, the angle set value Y r (k) at time k is subtracted from the angle prediction value Y d (k) at time k to obtain the feedforward compensation amount Δθ(k) at time k.

[0011] Step 4, the feedforward compensation amount Δθ(k) at time k is superimposed on the angle set value Y r (k) at time k to obtain the angle control value Y(k) at time k, and the angle control value Y(k) at time k is sent into the driving end of the robot flexible joint to realize feedforward compensation for the torsion angle of the robot flexible joint.

[0012] In the above step 1, the deep neural network hysteresis model is mathematically represented as:

[0013]

[0014] wherein x(k-2) and x(k-1) are respectively the input vectors of the deep neural network hysteresis model at time k-1 and time k, i.e. the actual angle values at time k-1 and time k; Y d (k-2), Y d (k-1) and Y d (k) are respectively the output vectors of the deep neural network hysteresis model at time k-2, time k-1 and time k, i.e. the angle prediction values at time k-2, time k-1 and time k; W y is the weight vector of the output layer, and b y is the bias vector of the output layer; H5(k) represents the fifth hidden layer output vector at time k; W h5 is the weight vector of the fifth hidden layer, and b h5 is the bias vector of the fifth hidden layer; H4(k) represents the fourth hidden layer output vector at time k; W h4 is the weight vector of the fourth hidden layer, and b h4 is the bias vector of the fourth hidden layer; H3(k-1) and H3(k) represent the third hidden layer output vectors at time k-1 and time k; W h31 , W h32 , W h33 and W h22 are the weight vectors of the third hidden layer, and b h3 is the bias vector of the third hidden layer; H1(k-1) and H1(k) are respectively the hysteresis operator output vectors at time k-1 and time k; α iis an ascending switching threshold vector, β j is a descending switching threshold vector; K(k) is a shape function layer output vector at k moment, W k is a weight vector of shape function layer, b k is a bias vector of shape function layer; H2(k) represents a second hidden layer output vector at k moment; W h21 and W h22 is a weight vector of second hidden layer, b h2 is a bias vector of second hidden layer.

[0015] Compared with the prior art, the present application aims at the complex hysteresis characteristics of asymmetry, rate correlation and strong nonlinearity shown by the flexible joint of the industrial robot in the motion process, first designs an asymmetric nonlinear hysteresis function as a Preisach model hysteresis operator to describe the asymmetric characteristics of the flexible joint; then adds output history information at the input end of the Preisach model and adds an inertia filter link at the output end of the Preisach model to describe the rate correlation characteristics of the flexible joint; finally, the improved Preisach model and a fully connected neural network for realizing nonlinear mapping are connected in series to form a deep neural network hysteresis model for describing the change law of the torque and the torsion angle with the load change. The angle prediction value is obtained based on the deep neural network hysteresis model, the angle setting value of the robot flexible joint is corrected through feedforward compensation control, the influence of the torsion angle is indirectly eliminated, and the purpose of improving the execution precision of the flexible joint of the industrial robot is achieved. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 is a schematic diagram of a feedforward compensation control method for a torsion angle of a flexible joint of an industrial robot.

[0017] Figure 2 is a structure diagram of a traditional Preisach model.

[0018] Figure 3 is a description of a hysteresis operator of a traditional Preisach model.

[0019] Figure 4 is an input-output hysteresis curve of a robot flexible joint.

[0020] Figure 5 is a description of an asymmetric nonlinear hysteresis operator.

[0021] Figure 6 is a rate correlation characteristic diagram of an inertia filter link.

[0022] Figure 7 is a structure diagram of a deep neural network hysteresis model. DETAILED DESCRIPTION

[0023] 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.

[0024] A feedforward compensation control method for the torsional angle of a flexible joint in an industrial robot, such as Figure 1 As shown, the steps are as follows:

[0025] Step 1: Construct a deep neural network hysteresis model, and update the parameters, namely weights and biases, of the deep neural network hysteresis model using the gradient descent method, thereby completing the modeling of the deep neural network hysteresis model.

[0026] To address the complex hysteresis characteristics exhibited by flexible joints in industrial robots, this invention improves the Preisach model from both internal and external perspectives, using internal operators to describe the asymmetric, rate-dependent, and strongly nonlinear complex hysteresis characteristics of flexible joints.

[0027] Traditional Preisach model structure, such as Figure 2 As shown, it describes hysteresis nonlinearity through superimposed weighted hysteresis operators. The offline model of the traditional Preisach model is as follows:

[0028]

[0029] Where y(k) is the model output and x(k-1) is the model input. i,j=0,1,2,...,N, where N is the discretization coefficient. μ(α) i ,β j ) is the weighting function. It is a hysteresis operator. α i β is the threshold for increasing switching. j The threshold for decreasing the switching threshold.

[0030] Hysteresis operator in the traditional Preisach model It can be represented as:

[0031]

[0032] like Figure 3 As shown, α i and β j These are the rising and falling switching thresholds for transitioning from one state to another. The rising switching threshold α i and the decreasing switching threshold β j Calculated using the following formula:

[0033]

[0034] Where, x max and x minare the maximum and minimum values of the model input, respectively.

[0035] Since the traditional Preisach model is symmetrical and rate-independent, the output of the hysteresis operator of the model is completely determined by the extreme value sequence of the input, and the input and output rates do not affect the hysteresis loop of the model operator, so the traditional Preisach model cannot accurately describe the complex hysteresis characteristics with non-symmetry, rate dependence and strong nonlinearity.

[0036] Considering that the complex hysteresis characteristics of the flexible joint of the industrial robot are different from the general hysteresis nonlinearity (as shown in Figure 4 ), as the input rate increases, the hysteresis curve becomes wider and rotates clockwise, which is difficult to describe directly by using the traditional Preisach model. Therefore, the traditional Preisach model is improved to obtain a deep neural network hysteresis model.

[0037] 1) An asymmetric nonlinear hysteresis function more suitable for the contour of the hysteresis curve of the flexible joint is designed to replace the hysteresis operator inside the Preisach model, and the asymmetric hysteresis characteristics of the flexible joint are described.

[0038] According to the forward and reverse changes of the hysteresis curve of the flexible joint as shown in Figure 4 , an asymmetric nonlinear hysteresis function is designed as the hysteresis operator of the improved Preisach model, as shown in Figure 5 , the designed hysteresis operator is expressed as:

[0039]

[0040] , wherein f(x) = 3-4 / 1+e 2x ; g(x) = 1-4 / 1+e 2x . max[·] represents the maximum function, and min[·] represents the minimum function. H1(k-1) is the output of the hysteresis operator, x(k-1) is the input of the hysteresis operator, and is the rising switching threshold. is the falling switching threshold. K(k) is a shape function, which is a function of the output true value history information, and is fitted by a neural network to generate different values in the forward and reverse processes, thereby realizing the asymmetry of the asymmetric nonlinear hysteresis function. i j

[0041] The hysteresis operator of formula (4) is equivalent to:

[0042]

[0043] 2) The input and output history information is introduced at the input end of the Preisach model, and the inertia filter link is introduced at the output end of the Preisach model, so as to describe the rate-dependent hysteresis characteristics of the flexible joint. ​​

[0044] The input-output characteristics of inertial filtering are as follows: Figure 6 As shown, it exhibits a hysteresis-like characteristic. With increasing input signal rate, the hysteresis-like characteristic curve widens and rotates clockwise, similar to the hysteresis response of a flexible joint to changes in input signal rate. Therefore, this invention introduces an inertial filter at the output of the Preisach model. Simultaneously, drawing on the method of including output history information in the input of the inertial filter, input-output history information is introduced at the input of the Preisach model to enhance the model's rate-dependent characteristics.

[0045] By incorporating input-output history information into the input of the Preisach model, the input of the Preisach model is represented as follows:

[0046]

[0047] Introducing an inertial filter at the output of the Preisach model, the output of the Preisach model is then expressed as:

[0048]

[0049] 3) By concatenating the Preisach model with a fully connected neural network that implements nonlinear mapping, a deep neural network hysteresis model is obtained.

[0050] like Figure 7 As shown, the deep neural network hysteresis model consists of 5 hidden layers and 1 shape function layer. Each of the 5 hidden layers has 4 hidden nodes, i.e., n1 = n2 = n3 = n4 = n5 = 4. The first hidden layer is the historical information input layer, the second hidden layer is the hysteresis operator layer, the third hidden layer is the inertial filter layer, and the fourth, fifth, and sixth layers are all fully connected layers. The two inputs of the first hidden layer form the two feedback inputs of the deep neural network hysteresis model, respectively inputting Y... d (k-2) and Y d (k-1). The output of the first hidden layer is connected to the input of the shape function layer. The output of the shape function layer is connected to one input of the second hidden layer. The other input of the second hidden layer forms one input of the deep neural network hysteresis model, inputting x(k-1). The output of the second hidden layer is connected to one input of the third hidden layer; the other input of the third hidden layer forms another input of the deep neural network hysteresis model, inputting x(k-2); and yet another input of the third hidden layer forms the feedback input of the deep neural network hysteresis model, inputting Y. d(k-1). The output of the third hidden layer is connected to the input of the fourth hidden layer. The output of the fourth hidden layer is connected to the input of the fifth hidden layer. The output of the fifth hidden layer forms the output of the deep neural network hysteresis model. The mathematical representation of the deep neural network hysteresis model is:

[0051]

[0052] wherein:

[0053] x(k-2) and x(k-1) are the deep neural network hysteresis model input vectors at time k-1 and k, respectively, with dimension 1x1, i.e., scalar, and are the actual values of the angle at time k-1 and k.

[0054] Y d (k-2), Y d (k-1), and Y d (k) are the deep neural network hysteresis model outputs at time k-2, k-1, and k, respectively, with dimension 1x1, i.e., scalar, and are the predicted values of the angle at time k-2, k-1, and k, respectively.

[0055] W y is the weight vector of the output layer with dimension 1x4. b y is the bias vector of the output layer with dimension 1x1, i.e., scalar. H5(k) represents the fifth hidden layer output vector at time k with dimension 4x1.

[0056] W h5 is the weight vector of the fifth hidden layer with dimension 4x4. b h5 is the bias vector of the fifth hidden layer with dimension 4x1. H4(k) represents the fourth hidden layer output vector at time k with dimension 4x1.

[0057] W h4 is the weight vector of the fourth hidden layer with dimension 4x4. b h4 is the bias vector of the fourth hidden layer with dimension 4x1. H3(k-1) and H3(k) represent the third hidden layer output vectors at time k-1 and k, respectively, with dimension 4x1.

[0058] W h31 , W h32 , W h33 , and W h22 are the weight vectors of the third hidden layer, W h31 , W h32 have dimension 4x4, W h33 , and W h22 have dimension 4x1. b h3is the bias vector of the second hidden layer, whose dimension is 4x1. H1(k-1) and H1(k) are the hysteresis operator output vectors at k-1 and k time, whose dimension is 4x1.

[0059] is the rising switching threshold vector, whose dimension is 4x1. i is the rising switching threshold vector, whose dimension is 4x1. j is the falling switching threshold vector, whose dimension is 4x1. k is the weight vector of the shape function layer, whose dimension is 4x4. k is the bias vector of the shape function layer, whose dimension is 4x1. K(k) is the shape function output vector at k time, whose dimension is 4x1.

[0060] is the weight vector of the shape function layer, whose dimension is 4x4. h21 is the weight vector of the shape function layer, whose dimension is 4x4. h22 is the weight vector of the second hidden layer, whose dimension is 4x1. h2 is the bias vector of the second hidden layer, whose dimension is 4x1. H2(k) represents the second hidden layer output vector at k time, whose dimension is 4x1.

[0061] Step 2, the k-2 time angle actual value x(k-2) and the k-1 time angle actual value x(k-1) output by the robot flexible joint, and the k-2 time angle prediction value Y d (k-2) and the k-1 time angle prediction value Y d (k-1) output by the modeled deep neural network hysteresis model are sent together into the modeled deep neural network hysteresis model to obtain the k time angle prediction value Y d (k).

[0062] Step 3, the k time angle set value Y r (k) is subtracted from the k time angle prediction value Y d (k) to obtain the k time feedforward compensation amount Δθ(k), Δθ(k) = Y r (k) - Y d (k).

[0063] Step 4, the k time feedforward compensation amount Δθ(k) is superimposed on the k time angle set value Y r (k) to obtain the k time angle control value Y(k), Y(k) = Y r (k) + Δθ(k), and the k time angle control value Y(k) is sent into the driving end of the robot flexible joint to realize the feedforward compensation of the robot flexible joint torsion angle.

[0064] It should be noted that the above embodiments of the present application are illustrative, and not restrictive, of the present application, and therefore the present application is not limited to the above specific embodiments. Other embodiments of the present application, which are obtained by those skilled in the art under the teachings of the present application, without departing from the principles of the present application, are considered to be within the scope of the present application.

Claims

1. A feedforward compensation control method for the torsional angle of a flexible joint in an industrial robot, characterized in that, The steps include the following: Step 1: Construct a deep neural network hysteresis model and update the parameters, namely weights and biases, of the deep neural network hysteresis model using the gradient descent method, thereby completing the modeling of the deep neural network hysteresis model. The mathematical representation of the deep neural network hysteresis model is as follows: In the formula, x(k-2) and x(k-1) are the input vectors of the deep neural network hysteresis model at time k-1 and time k, respectively, i.e., the actual angle values ​​at time k-1 and time k; Y d (k-2), Y d (k-1) and Y d (k) represent the output vectors of the deep neural network hysteresis model at times k-2, k-1, and k, respectively, i.e., the angle prediction values ​​at times k-2, k-1, and k; W y b is the weight vector of the output layer. y H5(k) represents the bias vector of the output layer; H5(k) represents the output vector of the fifth hidden layer at time k; W h5 Let b be the weight vector of the fifth hidden layer. h5 H4(k) represents the bias vector of the fifth hidden layer; H4(k) represents the output vector of the fourth hidden layer at time k; W h4 Let b be the weight vector of the fourth hidden layer. h4 H3(k-1) and H3(k) represent the bias vector of the fourth hidden layer; H3(k-1) and H3(k) represent the output vectors of the third hidden layer at time k-1 and time k, respectively; W h31 W h32 W h33 and W h34 Let b be the weight vector of the third hidden layer. h3 H1(k-1) and H1(k) are the bias vectors of the third hidden layer, respectively; H1(k-1) and H1(k) are the output vectors of the hysteresis operator at time k-1 and time k, respectively; α i For the rising switching threshold vector, β j The descent switching threshold vector; K(k) is the shape function layer output vector at time k, W k b is the weight vector of the shape function layer. k H2(k) represents the bias vector of the shape function layer; H2(k) represents the output vector of the second hidden layer at time k; W h21 and W h22 Let b be the weight vector of the second hidden layer. h2 This is the bias vector for the second hidden layer; Step 2: Combine the actual angle values ​​x(k-2) and x(k-1) at time k-2 output by the robot's flexible joint with the predicted angle value Y at time k-2 output by the deep neural network hysteresis model. d The predicted angle values ​​Y at times (k-2) and (k-1) d (k-1) is fed into the deep neural network hysteresis model to obtain the angle prediction value Y at time k. d (k); Step 3: Set the angle setting value Y at time k. r (k) minus the angle prediction value Y at time k d (k), to obtain the feedforward compensation amount Δθ(k) at time k; Step 4: Set the angle Y at time k. r The feedforward compensation amount Δθ(k) at time k is superimposed on (k) to obtain the angle control value Y(k) at time k. The angle control value Y(k) at time k is then sent to the drive end of the robot's flexible joint to achieve feedforward compensation of the torsional angle of the robot's flexible joint.

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