Mechanical arm model prediction interaction control method based on hysteresis force model

Abstract

The invention relates to the technical field of robots, in particular to a mechanical arm model prediction interaction control method based on a hysteresis force model, which comprises the following steps of: abstracting a hysteresis nonlinear phenomenon into a linear combination of a plurality of basic play operators by adopting end force modeling based on a PI (Proportional Integral) model, jointly superposing to form a description of the overall nonlinear behavior; the inverse model of the PI model is constructed in an analysis mode, the inverse model is also a PI model, the parameter of the inverse model is a function of the parameter of the original PI model, and the hysteresis characteristic of the inverse model can be determined by the relation, so that the hysteresis effect of the original PI model is effectively counteracted; and finally, a least square method is adopted as a parameter identification method, model parameters of the hysteresis characteristics of the system are accurately described, and more accurate output is obtained. According to the model prediction interaction control method, the adverse effect of the hysteresis effect on the performance of the control system is remarkably reduced, and greater potential and possibility are provided for application of the robot in the real world.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot arm control, and in particular relates to a robot arm model prediction interactive control method based on a hysteresis force model. Background Art

[0002] In modern industrial production and robotics applications, control accuracy is an important indicator of robot performance. In scenarios such as automated production lines, precision assembly, and human-machine interaction, robots need to perform various tasks accurately, quickly, and stably. However, the hysteresis problem is a common and difficult-to-ignore challenge in the interaction between robots and the external environment. The presence of hysteresis forces will cause the trajectory of their motion to deviate, and the force control performance will also be affected, making it impossible to achieve the expected precise operation.

[0003] The contact force is modeled using the classic PI hysteresis model with inverse analytical characteristics, which can accurately describe the hysteresis characteristics of soft materials and effectively compensate for the hysteresis nonlinear error of soft materials. Model predictive interactive control is a robot control strategy that can dynamically optimize the control strategy by combining system status and future prediction information. In the model predictive interactive control based on the hysteresis force model, the control system of the robot arm can use the PI hysteresis model in real time to predict the hysteresis behavior of soft materials, and adjust the control strategy according to the prediction results to achieve more accurate force control. Summary of the invention

[0004] The present invention aims to provide a robot arm model prediction interactive control method based on a hysteresis force model to solve the technical problem of hysteresis in the contact between the robot arm and soft materials.

[0005] In order to solve the above technical problems, the specific technical solutions of the present invention are as follows:

[0006] In some embodiments of the present application, a method for predictive interactive control of a robot arm model based on a hysteresis force model is provided, comprising the following steps:

[0007] Step 1: Select the play operator and the stop operator from among the many operators in the PI model;

[0008] Step 2: Linearly combine the selected operators to obtain the PI model;

[0009] Step 3: Construct the inverse model of the PI model analytically, whose parameters are functions of the original PI model parameters;

[0010] Step 4: Use the least squares method to determine the model parameters so that the model reflects the relationship between force and strain.

[0011] Step 5: Use the inverse model of the above PI model as the input of the feedforward control, and use the output of the inverse PI model as the input of the PI hysteresis model.

[0012] In some embodiments of the present application, the specific expression of the play operator in step 1 is:

[0013]

[0014] Where x(t) is the input signal, y(t) is the output signal, m0 is a parameter used to determine the value of y(0), and f r is a function definition. The initial output in the system is y(0). The subsequent output of the play operator depends on the current latest output y(t i ); Based on the play operator, the hysteresis formula of the PI model is obtained by superimposing multiple play operators with different thresholds, and each play operator is responsible for describing the hysteresis behavior under a specific threshold.

[0015] In some embodiments of the present application, given an input signal x(t) and a series of thresholds r i , where i = 1, 2, ..., N, and the weight w corresponding to each play operator i , the output y(t) of the PI model is calculated by the following formula:

[0016]

[0017] Where r0 is a positive constant, p(r) = f r (x(t), y(t-1), w i ), is an integrable density function, satisfying p(r)>0 and As r approaches infinity, p(r) approaches zero.

[0018] In some embodiments of the present application, the output expression of the stop operator in step 1 is:

[0019]

[0020] In some embodiments of the present application, the stop operator is used to study the boundedness property of the PI model, and the output of the stop operator has upper and lower bounds: -r≤Z≤r#(5).

[0021] In some embodiments of the present application, the PI model in step 2 is constructed by the weighted sum of n play operators, each play operator has a different threshold and weight, and these parameters are adjusted according to the hysteresis characteristics of the system, wherein in a discrete time system, the output of the PI model can be expressed as:

[0022]

[0023] in, is the model output, 0=r0<r1…<r n is the probability density weight coefficient, w i is the threshold coefficient, n is the number of operators, and the weight and threshold are identified through experimentally measured hysteresis data.

[0024] In some embodiments of the present application, the inverse model of the PI model is constructed analytically in step 3, and the compensated system output is obtained by combining the feedforward hysteresis compensator with the PI model, which specifically includes:

[0025] For the reference input u(t), the output of the PI model under feedforward hysteresis compensation is

[0026]

[0027] The symbol Represents the composite function, and the output of the inverse PI model is

[0028]

[0029] Among them, f r (x(t-1),u(t),z i ) is a threshold value z i The play operator uses the threshold r of the original PI model. i and weight w i , the threshold z of the inverse PI model can be directly determined by analytical methods i and weight q i Among them, the threshold z i and weight q i They are

[0030]

[0031] Among them, z i is the threshold of the inverse PI model, q i is the weight.

[0032] In some embodiments of the present application, in step 4, the least squares-based parameter identification method is used to determine the model parameters, which is to find the parameters that best match the data by minimizing the second norm of the error, specifically:

[0033] Step 4.1: Define an error function to quantify the difference between the model output and the actual data;

[0034] The error function is expressed as follows:

[0035]

[0036] Among them, y c represents the actual measured data, while It represents the predicted output data of the model;

[0037] Step 4.2: Collect force and strain data of the interaction between the robot and the soft material in the Gazebo simulation environment;

[0038] Step 4.3: The collected force and strain data are used to establish a PI hysteresis model based on the least square method and other methods;

[0039] Step 4.4: Based on the number of PI model operators, obtain the threshold value, and use the least squares method to obtain the weight coefficient to calculate the inverse PI model threshold value z i and weight q i .

[0040] In some embodiments of the present application, the step 4.3 of establishing the PI hysteresis model includes:

[0041] The parameters of the model are determined by the parameter identification method based on the least square method to ensure that the model can accurately reflect the relationship between force and strain;

[0042] The collected data is processed as follows:

[0043] p(i)=1000*(p recode (i)-mean(p recode ))

[0044] f(i)=(f recode (i)-mean(f recode ))#(11)

[0045] Among them, mean(p recode )、mean(f recode ) is the median of deformation and contact force in the recorded data, in units of m and N. recode (i) represents the position of the robot arm in the z direction in the workspace, p(i) represents the position after artificial processing, and f recode (i) is the force of interaction between the robot and the environment, and f(i) represents the contact force after artificial processing.

[0046] In some embodiments of the present application, in step 5, the inverse model of the above-mentioned PI model is used as the input of the feedforward control, and the output of the inverse PI model is used as the input of the PI hysteresis model, specifically:

[0047] The PI hysteresis model and the inverse PI hysteresis model are used as the input of the feedforward control, the input signal is selected as u(t)=2.27sin(t), and the output of the inverse PI model is used as the input of the PI hysteresis model to obtain the result.

[0048] Compared with the prior art, the beneficial effect of the present invention is that, by adopting the end force modeling based on the PI model, the hysteresis nonlinear phenomenon is abstracted into a linear combination of multiple basic play operators, each of which has a specific weight, and is superimposed together to form a description of the overall nonlinear behavior; the inverse model of the PI model is constructed in an analytical way, and the inverse model is also a PI model, and its parameters are functions of the original PI model parameters. This relationship can determine the hysteresis characteristics of the inverse model, thereby effectively offsetting the hysteresis effect of the original PI model; finally, the least squares method is used as a parameter identification method to accurately characterize the model parameters of the system hysteresis characteristics and obtain more accurate output. This model prediction interactive control method significantly reduces the adverse effects of the hysteresis effect on the performance of the control system, and provides greater potential and possibility for the application of robots in the real world. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0050] Figure 1 A schematic diagram of a Paly operator of a PI model provided in an embodiment of the present invention;

[0051] Figure 2 A schematic diagram of a stop operator of a PI model provided in an embodiment of the present invention;

[0052] Figure 3 A schematic diagram of the PI model framework provided by an embodiment of the present invention;

[0053] Figure 4 A schematic diagram of the working principle of a feedforward hysteresis compensator provided by an embodiment of the present invention;

[0054] Figure 5 A schematic diagram of a system control framework provided by an embodiment of the present invention;

[0055] Figure 6 A schematic diagram of PI model time-input and output in a PI model example provided in an embodiment of the present invention;

[0056] Figure 7 A schematic diagram of a PI model output hysteresis loop in a PI model example provided in an embodiment of the present invention;

[0057] Figure 8 A schematic diagram of PI model input-output in a PI model example provided in an embodiment of the present invention;

[0058] Fig. 9 A schematic diagram of the initial stage of PI model output in the PI model example provided in an embodiment of the present invention;

[0059] Fig.10 A schematic diagram of PI model time-input-output in an inverse PI model example provided in an embodiment of the present invention;

[0060] Fig.11 A schematic diagram of a PI model output hysteresis loop in an inverse PI model example provided in an embodiment of the present invention;

[0061] Fig.12 A schematic diagram of PI model input-output in an inverse PI model example provided in an embodiment of the present invention;

[0062] Fig.13 A schematic diagram of the initial stage of PI model output in the inverse PI model example provided in an embodiment of the present invention;

[0063] Fig.14 A schematic diagram of the compensated PI model output in the feedforward compensation result provided in an embodiment of the present invention;

[0064] Fig.15 A schematic diagram of a feedforward compensation result in a feedforward compensation result provided in an embodiment of the present invention;

[0065] Fig.16 A schematic diagram of input position-output contact force in a simulation parameter identification model provided in an embodiment of the present invention;

[0066] Fig.17 A schematic diagram of a simulation parameter identification model in a simulation parameter identification model provided in an embodiment of the present invention;

[0067] Fig.18 A schematic diagram of PI model parameters provided by an embodiment of the present invention;

[0068] Fig.19 A schematic diagram of PI model output and original data in the comparison between the PI hysteresis model and original data provided in an embodiment of the present invention;

[0069] Fig. 20 A schematic diagram of the error between the model output and the original data in the comparison between the PI hysteresis model provided by an embodiment of the present invention and the original data;

[0070] Fig.21 A schematic diagram of a simulated inverse PI hysteresis model in the PI hysteresis model and the inverse PI hysteresis model provided in an embodiment of the present invention;

[0071] Fig. 22 A schematic diagram of a simulated PI hysteresis model in a PI hysteresis model and an inverse PI hysteresis model provided in an embodiment of the present invention;

[0072] Fig.23 A schematic diagram of an inverse PI model output in an inverse PI hysteresis model-PI model output provided in an embodiment of the present invention;

[0073] Fig.24 A schematic diagram of input and output data of a feedforward compensation simulation in a feedforward compensation simulation experiment provided by an embodiment of the present invention;

[0074] Fig.25 A schematic diagram of input and output errors of feedforward compensation simulation in a feedforward compensation simulation experiment provided by an embodiment of the present invention;

[0075] Fig.26 A simulation schematic diagram of a feedforward compensation simulation comparison experiment provided by an embodiment of the present invention;

[0076] Fig. 27 A schematic diagram of feedforward compensation input-output simulation in a feedforward compensation simulation comparison experiment provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0077] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0078] In order to better understand the purpose, structure and function of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings.

[0079] See attached Figure 1-27 As shown, according to some embodiments of the present application,

[0080] The PI model abstracts the hysteresis nonlinear phenomenon into a linear combination of multiple basic play operators and stop operators, each with a specific weight, which are superimposed together to form a description of the overall nonlinear behavior. Both operators have a memory effect with a threshold r.

[0081] The play operator is the basic module of the PI model. The basic expression of the play operator is

[0082]

[0083] Where x(t) is the input signal, y(t) is the output signal, and m0 is a parameter used to determine the value of y(0). r is a function definition. The initial output in the system is y(0), and the subsequent output of the play operator depends on the current latest output y(t i). Based on the play operator, the hysteresis formula of the PI model is obtained by superimposing multiple play operators with different thresholds. Each play operator is responsible for describing the hysteresis behavior under a specific threshold. Specifically, given an input signal x(t) and a series of thresholds r i (where (i=1,2,…,N)), and the weight w corresponding to each play operator i , the output y(t) of the PI model can be calculated by the following formula:

[0084]

[0085] Where r0 is a positive constant, p(r) = f r (x(t), y(t-1), w i ), is an integrable density function, satisfying p(r)>0 and As r approaches infinity, p(r) approaches zero. In practical applications, a finite number of play operators is usually sufficient to simulate hysteresis. The PI model can be constructed by the weighted sum of n play operators. Each play operator has a different threshold and weight, and these parameters are adjusted according to the hysteresis characteristics of the system.

[0086] In a discrete-time system, the output of the PI model can be expressed as:

[0087]

[0088] in, is the model output, 0=r0<r1...<r n is the probability density weight coefficient, w i is the threshold coefficient, and n is the number of operators. The weight and threshold can be identified through experimentally measured hysteresis data.

[0089] The output of the stop operator can be expressed as:

[0090]

[0091] The definition of each parameter is the same as above. The output of the stop operator has upper and lower bounds:

[0092] -r≤Z≤r#(5)

[0093] Therefore, the stop operator can be used to study the boundedness properties of the PI model.

[0094] The inverse model of the PI model can be constructed analytically, and its parameters can be obtained by mathematical calculation without complex iteration or approximation. In addition, the inverse model is also a PI model, and its parameters are functions of the original PI model parameters. This relationship can determine the hysteresis characteristics of the inverse model, which effectively offsets the hysteresis effect of the original PI model. In practical applications, the inverse function can be used as a feedforward compensator. A feedforward compensator is a control strategy that pre-offsets the hysteresis effect in a system by adding a compensation signal to the input of the system. It uses the output of the inverse model as a compensation signal, combined with the input of the original PI model, to eliminate or reduce the impact of hysteresis on the system output. By combining the feedforward hysteresis compensator with the PI model, a compensated system output can be obtained, which will be closer to the reference input. The hysteresis effect is effectively offset, and the response speed and accuracy of the system can be improved, thereby improving the overall performance.

[0095] For the reference input u(t), the output of the PI model under feedforward hysteresis compensation is

[0096]

[0097] The symbol represents the composite of functions. Assume that the output of the inverse PI model is

[0098]

[0099] Among them, f r (x(t-1),u(t),z i ) is a threshold value z i The play operator uses the threshold r of the original PI model. i and weight w i , the threshold z of the inverse PI model can be directly determined by analytical methods i and weight q i Among them, the threshold z i and weight q i They are

[0100]

[0101] In practical applications, since the measured hysteresis loop has complex nonlinear characteristics, an approximate model is usually used for modeling. Although this approximate model can describe the hysteresis behavior, it cannot fully and accurately reflect its true characteristics. Therefore, the inverse model of P is used When performing inverse compensation, the hysteresis effect can only be approximately offset rather than completely. Although this approximate compensation can reduce the impact of hysteresis on system performance, there is still an error, resulting in a deviation between the system output y and the reference input u. To reduce the error, the accuracy of the approximate model can be improved, the inverse compensation algorithm can be optimized, or a feedback mechanism can be introduced. However, it may be very difficult to completely eliminate the error. It is necessary to weigh various factors according to the application scenario and requirements and select the best modeling and compensation method to achieve the best system performance.

[0102] This method gives an example to verify the characteristics of the PI model with seven play operators and its inverse model, where the threshold of each play operator is defined as r i ={0, 0.45, 0.9, 1.35, 1.8, 2.25, 2.7}, weight w i Select w i ={0.72, 0.6, 0.48, 0.36, 0.24, 0.12, 0.012}, with i=1,...,7 in thresholds and weights. Figure 6 The input signal x(t) and the output signal y(t) in the PI model are shown in FIG. , where the input signal x(t) = 3sin(2πt). For a given threshold r i , the corresponding play operator outputs a hysteresis loop as Figure 7 As shown in the figure, the hysteresis characteristics of each play operator can be seen. The hysteresis curve between input x(t) and output y(t) and the initial operation curve are shown in Figure 8 As shown in the figure, this figure describes the hysteresis phenomenon between input and output in the system. Fig. 9 When the output value is greater than the maximum threshold r max If the value is doubled, the effect of the initial conditions will disappear.

[0103] Threshold z of the inverse PI model i Calculate z by formula #(8) i ={0, 0.324, 0.918, 1.728, 2.7, 3.78, 4.914}, weight q i q can be calculated by formula #(9) i ={1.3889, -0.6313, -0.2020, -0.0926, -0.00463, -0.0198, -0.0019}. Setting the input signal of the inverse PI model to u(t) = 10sin(2πt), the output signal X * As in Fig.10 The play operator output hysteresis loop of the inverse PI model is as follows: Fig.11 shown. Fig.12The relationship between the reference input and output is shown, and the hysteresis curve of the inverse hysteresis model is depicted. Fig.14 Symmetric about y=x. Fig.15 It can be clearly seen that there is a linear relationship between the output signal y(t) and the reference input u(y). This shows that the inverse PI model can maintain the linear mapping relationship between input and output when compensating for the hysteresis effect, so that the output signal can track the reference input more accurately. When the reference input u(y) changes, the output y(t) will change in the corresponding proportion without generating additional nonlinear deviations. This linear characteristic makes the system behavior more predictable and controllable, which helps to simplify the system analysis and design process.

[0104] Parameter identification is crucial when building a PI hysteresis model. Its core purpose is to accurately determine the model parameters that can characterize the hysteresis characteristics of the system. These parameters not only shape the behavior and performance of the model, but are also directly related to the quality of the system's response to the input signal and the control effectiveness. In simulation analysis, in order to simplify the problem, it is often assumed that the PI model parameters are known. However, in real application scenarios, the correlation data between displacement and pressure is recorded experimentally, and the threshold coefficient and weight coefficient of the PI model are extracted from them.

[0105] This method mainly uses the least square method as the parameter identification method. This method finds the parameters that best match the data by minimizing the second norm of the error. Therefore, the parameter identification of the PI hysteresis model plays a key role in the compensation of the control system.

[0106] First, an error function is defined to quantify the difference between the model output and the actual data. This difference is usually expressed in the form of the sum of squared errors. Specifically, the error function is as follows:

[0107]

[0108] Among them, y c represents the actual measured data, while It represents the predicted output data of the model.

[0109] In order to verify the effectiveness of feedforward hysteresis compensation in the robot arm grinding process and evaluate its practical application effect, it is first necessary to collect the force and strain data of the interaction between the robot arm and the soft material in the Gazebo simulation environment. This will provide a basis for establishing a PI hysteresis model to describe the relationship between the force applied by the robot arm on the soft material and the strain of the soft material.

[0110] The least squares-based parameter identification method is used to determine the parameters of the model to ensure that the model can accurately reflect the relationship between force and strain. By establishing an accurate PI hysteresis model, the interaction process between the robot arm and the soft material can be better understood.

[0111] The deformation of soft materials is usually at the centimeter or millimeter level. In order to analyze the collected data more intuitively, the data is processed as follows:

[0112] p(i)=1000*(p recode (i)-mean(p recode ))

[0113] f(i)=(f recode (i)-mean(f recode ))#(11)

[0114] Among them, mean(p recode )、mean(f recode ) is the median of deformation and contact force in the recorded data, in units of m and N. recode (i) represents the position of the robot arm in the z direction in the workspace, p(i) represents the position after artificial processing, and f recode (i) is the force of interaction between the robot and the environment, and f(i) is the contact force after artificial processing. According to this processing method, the data read in the gazebo simulation environment is processed as follows Fig.16 In addition, the raw data mentioned below are all processed by formula #(11).

[0115] Using the collected force and strain data, the PI hysteresis model is established based on the least squares method and other methods. The number of play operators of the PI model is set to 7, that is, n = 7. First, the threshold r i It is determined based on the transformation division of the graph. The threshold r is set at the turning point of the image. Based on this choice, the rule is selected as follows Fig.18 The PI model threshold is shown in Figure 1, and the weight coefficient w is obtained by the least squares method. i , i=1,…,7, determine the weight coefficient to be the optimized value just calculated. Fig.18 The weight parameters of the identified PI hysteresis model and the calculated inverse PI model threshold z are listed. i and weight q i .

[0116] according to Fig.18 The data in can be used to draw PI hysteresis models and inverse PI hysteresis models related to pressure and deformation. Fig.17 The scatter plot with deformation as input and contact force as output is shown, as well as the PI hysteresis model obtained through parameter identification. The contact force is compared with the output of the PI model obtained through parameter identification. Fig.19 As shown. Fig. 20From the blue line, we can see that its root mean square error (RMSE) is 0.0956, the sum of squares for error (SSE) is 5.7160, the mean square error (MSE) is 0.0091, and the coefficient of determination (R2-R-Square) is 0.9966. This shows that the model has a high degree of fit, and the PI hysteresis model fits the actual data very well, with low RMSE, MSE and SSE values, and the R-Square coefficient is close to 1, which is better than the linear elastic model.

[0117] The inverse model of the above PI model is used as the input of the feedforward control, and the input signal is selected as u(t) = 2.27sin(t). The inverse PI hysteresis model is as follows: Fig.21 At the same time, the output of the inverse PI model is used as the input of the PI hysteresis model, and the results are as follows: Fig. 22 shown.

[0118] The relationship between the PI hysteresis output y(t) and the inverse hysteresis model input u(t) is as follows: Fig.23 The image shows that, ideally, after compensation by the inverse PI model, the input and output present a linear relationship, y(t) = u(t), which effectively offsets the hysteresis behavior in the interaction between the robot and the soft material. In gazebo, the inverse PI model is added to the control program, and the data obtained is as shown in the figure below.

[0119] Fig.24 The red curve is the desired force,

[0120] This force is used as the input of the inverse PI hysteresis model. The output obtained by the system operation is the blue line in the figure. In the two curves, the system operation output minus the expected force is as follows Fig.26 As shown by the blue line in the figure, it can be seen that most of the force tracking errors are within 0.2N, and compared with the error of the linear elastic model, the overall error of the output force after compensation is smaller.

[0121] exist Figure 25-26 In the figure, the system successfully offsets the hysteresis behavior between the robot and the soft material after compensation, which shows that the system has achieved good results in dealing with the difference between the expected force and the actual output. The output after compensation shows a linear characteristic, and its straight line fit is y=x-0.04247, its SSE is 22.79, R-square is 0.9957, AdjustedR-square is 0.9957, and RMSE is 0.1073. These indicators show that the fitting data error is small and the fitting effect is good, which further verifies the effect of the system after compensation. In some embodiments of the present application,

[0122] In the description of the present application, it should be understood that the terms "center", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present application.

[0123] The terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of this application, unless otherwise specified, "plurality" means two or more.

[0124] In the description of this application, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in this application can be understood according to specific circumstances.

[0125] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0126] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A robot arm model predictive interactive control method based on hysteresis force model, characterized in that: The following steps are involved: Step 1: Select the play operator and the stop operator from among the many operators in the PI model; Step 2: Linearly combine the selected operators to obtain the PI model; Step 3: Construct the inverse model of the PI model analytically, whose parameters are functions of the original PI model parameters; Step 4: Use the least squares method to determine the model parameters so that the model reflects the relationship between force and strain. Step 5: Use the inverse model of the above PI model as the input of the feedforward control, and use the output of the inverse PI model as the input of the PI hysteresis model.

2. The method for predictive interactive control of a robot arm model based on a hysteresis force model according to claim 1, characterized in that: The specific expression of the play operator in step 1 is: Where x(t) is the input signal, y(t) is the output signal, m0 is a parameter used to determine the value of y(0), and f r is a function definition. The initial output in the system is y(0). The subsequent output of the play operator depends on the current latest output y(t i ); Based on the play operator, the hysteresis formula of the PI model is obtained by superimposing multiple play operators with different thresholds, and each play operator is responsible for describing the hysteresis behavior under a specific threshold.

3. The method for predictive interactive control of a robot arm model based on a hysteresis force model according to claim 2, characterized in that: Given an input signal x(t) and a series of thresholds r i , where i = 1, 2, ..., N, and the weight w corresponding to each play operator i , the output y(t) of the PI model is calculated by the following formula: Where r0 is a positive constant, p(r) = f r (x(t), y(t-1), w i ), is an integrable density function, satisfying p(r)>0 and As r approaches infinity, p(r) approaches zero.

4. The method for predictive interactive control of a robot arm model based on a hysteresis force model according to claim 1, characterized in that: The output expression of the stop operator in step 1 is:

5. The method for predictive interactive control of a robot arm model based on a hysteresis force model according to claim 4, characterized in that: The stop operator is used to study the boundedness of the PI model. The output of the stop operator has upper and lower bounds: -r≤Z≤r#(5).

6. The method for predictive interactive control of a robot arm model based on a hysteresis force model according to claim 1, characterized in that: The PI model in step 2 is constructed by the weighted sum of n play operators, each play operator has a different threshold and weight, and these parameters are adjusted according to the hysteresis characteristics of the system. In the discrete time system, the output of the PI model can be expressed as: in, is the model output, 0=r0<r1...<r n is the probability density weight coefficient, w i is the threshold coefficient, n is the number of operators, and the weight and threshold are identified through experimentally measured hysteresis data.

7. The method for predictive interactive control of a robot arm model based on a hysteresis force model according to claim 1, characterized in that: The inverse model of the PI model is constructed analytically in step 3, and the compensated system output is obtained by combining the feedforward hysteresis compensator with the PI model, which specifically includes: For the reference input u(t), the output of the PI model under feedforward hysteresis compensation is The symbol Represents the composite function, and the output of the inverse PI model is Among them, f r (x(t-1),u(t),z i ) is a threshold value z i The play operator uses the threshold r of the original PI model. i and weight w i , the threshold z of the inverse PI model can be directly determined by analytical methods i and weight q i Among them, the threshold z i and weight q i They are Among them, z i is the threshold of the inverse PI model, q i is the weight.

8. The method for predictive interactive control of a robot arm model based on a hysteresis force model according to claim 1, characterized in that: In step 4, the parameter identification method based on the least square method is used to determine the model parameters, which is to find the parameters that best match the data by minimizing the second norm of the error, specifically: Step 4.1: Define an error function to quantify the difference between the model output and the actual data; The error function is expressed as follows: Among them, y c represents the actual measured data, while It represents the predicted output data of the model; Step 4.2: Collect force and strain data of the interaction between the robot and the soft material in the Gazebo simulation environment; Step 4.3: The collected force and strain data are used to establish a PI hysteresis model based on the least square method and other methods; Step 4.4: Based on the number of PI model operators, obtain the threshold value, and use the least squares method to obtain the weight coefficient to calculate the inverse PI model threshold value z i and weight q i .

9. The method for predictive interactive control of a robot arm model based on a hysteresis force model according to claim 8, characterized in that: The step 4.3 of establishing the PI hysteresis model includes: The parameters of the model are determined by the parameter identification method based on the least square method to ensure that the model can accurately reflect the relationship between force and strain; The collected data is processed as follows: p(i)=1000*((p recode (i)-mean(p recode )) f(i)=(f recode (i)-mean(f recode ))#(11) Among them, mean(p recode )、mean(f recode ) is the median of deformation and contact force in the recorded data, in units of m and N. recode (i) represents the position of the robot arm in the z direction in the workspace, p(i) represents the position after artificial processing, and f recode (i) is the force of interaction between the robot and the environment, and f(i) represents the contact force after artificial processing.

10. The method for predictive interactive control of a robot arm model based on a hysteresis force model according to claim 1, characterized in that: In step 5, the inverse model of the above-mentioned PI model is used as the input of the feedforward control, and the output of the inverse PI model is used as the input of the PI hysteresis model, specifically: The PI hysteresis model and the inverse PI hysteresis model are used as the input of the feedforward control, the input signal is selected as u(t)=2.27sin(t), and the output of the inverse PI model is used as the input of the PI hysteresis model to obtain the result.

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