A Model Predictive Interaction Control Method for a Manipulator Based on a Hysteresis Force Model

Abstract

This application relates to the field of robot technology, and particularly to a model predictive interaction control method for a robotic arm based on a hysteresis force model, including: using end-effector force modeling based on a PI model to abstract the hysteresis nonlinear phenomenon as a linear combination of multiple basic play operators, each operator with a specific weight, which are superimposed together to form a description of the overall nonlinear behavior; constructing the inverse model of the PI model in an analytical manner, where the inverse model is also a PI model and its parameters are functions of the parameters of the original PI model, and this relationship can determine the hysteresis characteristics of the inverse model, thereby effectively canceling the hysteresis effect of the original PI model; finally, using the least squares method as the method for parameter identification to accurately characterize the model parameters of the system hysteresis characteristics and obtain a more accurate output. This model predictive interaction control method significantly reduces the adverse effects of the hysteresis effect on the performance of the control system, providing greater potential and possibilities for the application of robots in the real world.

Description

Technical Field

[0001] The present invention belongs to the technical field of robotic arm control, and particularly relates to a model predictive interaction control method for a robotic arm based on a hysteresis force model. Background Art

[0002] In the fields of modern industrial production and robot applications, control precision is an important indicator of the performance of a robotic arm. In scenarios such as automated production lines, precision assembly, and human-robot interaction, the robotic arm needs to execute various tasks accurately, quickly, and stably. However, the problem of hysteresis force is a common and difficult-to-ignore challenge in the interaction between a robotic arm and the external environment. The existence of hysteresis force can cause the deviation of its motion trajectory and also affect the force control performance, thus failing to achieve the expected precise operation.

[0003] Using the classical PI hysteresis model with inverse analysis characteristics to model the contact force can accurately describe the hysteresis characteristics of soft materials and effectively compensate for the hysteresis nonlinear error of soft materials. Model predictive interaction control is a robot control strategy that can dynamically optimize the control strategy by combining system states and future prediction information. In the model predictive interaction control based on the hysteresis force model, the control system of the robotic arm can utilize the PI hysteresis model to predict the hysteresis behavior of soft materials in real time and adjust the control strategy according to the prediction results to achieve more precise force control. Summary of the Invention

[0004] The purpose of the present invention is to provide a model predictive interaction control method for a robotic arm based on a hysteresis force model to solve the technical problem of hysteresis in the contact between the robotic arm and soft materials.

[0005] To solve the above technical problems, the specific technical solution of the present invention is as follows:

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

[0007] Step 1: Among the numerous operators of the PI model, select the play operator and the stop operator;

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

[0009] Step 3: Construct the inverse model of the PI model in an analytical manner, and its parameters are functions of the parameters of the original PI model;

[0010] Step 4: Use a parameter identification method based on 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 at the same time use the output of its 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, w0 is the basic weight coefficient, w i is the weight coefficient used to determine the value of y(0), and f r is the 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, and each play operator is responsible for describing the hysteresis behavior at a specific threshold.

[0015] In some embodiments of the present application, given the input signal x(t) and a series of thresholds r i , where i = 1, 2,..., N, and the weight w i corresponding to each play operator, 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 that satisfies p(r) > 0 and when 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 different thresholds and weights, and these parameters are adjusted according to the hysteresis characteristics of the system. Among them, in the discrete-time system, the output of the PI model can be expressed as:

[0022]

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

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

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

[0026]

[0027] where the symbol represents the composition of functions. Let the output of the inverse PI model be

[0028]

[0029] where, f r (x(t - 1), u(t), z i ) is a play operator with a threshold of z i . Using the threshold r i and the weight w i of the original PI model, the threshold z i and the weight q i of the inverse PI model can be directly determined by an analytical method. Among them, the threshold z i and the weight q i are respectively

[0030]

[0031] where, z i is the threshold of the inverse PI model, q i is the weight, and i and g are index variables used to represent different terms in the summation process.

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

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

[0034] Among them, the expression form of the error function is as follows:

[0035]

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

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

[0038] Step 4.3: Based on the collected force and strain data, establish a PI hysteresis model by methods such as the least squares method;

[0039] Step 4.4: Obtain the threshold based on the number of PI model operators, and calculate the inverse PI model threshold z i and the weight q i .

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

[0041] Use the parameter identification method based on the least squares method to determine the parameters of the model, ensuring that the model can accurately reflect the relationship between force and strain;

[0042] By processing the collected data 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 ) are the medians of the deformation and contact force in the recorded data, with the units of m and N. And p recode (i) represents the position of the robotic arm in the z direction in the workspace, p(i) represents the processed position, f recode (i) is the force of the interaction between the robotic arm and the environment, and f(i) represents the processed contact force.

[0046] In some embodiments of the present application, in Step 5, the inverse model of the above PI model is used as the input of the feedforward control, and at the same time, the output of its inverse PI model is used as the input of the PI hysteresis model, specifically:

[0047] Taking the PI hysteresis model and the inverse PI hysteresis model as the inputs of feedforward control, with the input signal being u(t) = 2.27sin(t), and at the same time taking the output of its inverse PI model as the input of the PI hysteresis model, the obtained results.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows: By using the end-effector force modeling based on the PI model, the hysteresis nonlinear phenomenon is abstracted as a linear combination of multiple basic play operators, each operator with a specific weight, and they are superimposed together to form a description of the overall nonlinear behavior; The inverse model of the PI model is constructed in an analytical manner. The inverse model is also a PI model, and its parameters are functions of the parameters of the original PI model. This relationship can determine the hysteresis characteristics of the inverse model, thereby effectively canceling the hysteresis effect of the original PI model; Finally, the least squares method is used as the method for parameter identification to accurately characterize the model parameters of the system hysteresis characteristics and obtain more accurate outputs. This model predictive interaction control method significantly reduces the adverse effects of the hysteresis effect on the performance of the control system, providing greater potential and possibilities for the application of robots in the real world. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] By reading the following detailed description of the preferred embodiments, various other advantages and benefits will become clear to those of ordinary skill in the art. The drawings are only for the purpose of showing the preferred embodiments and are not considered to be a limitation of the present invention. Moreover, throughout the drawings, the same reference numerals are used to represent the same components. In the drawings:

[0050] Figure 1 Schematic diagram of the play operator of the PI model provided by the embodiment of the present invention;

[0051] Figure 2 Schematic diagram of the stop operator of the PI model provided by the embodiment of the present invention;

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

[0053] Figure 4 Schematic diagram of the working principle of the feedforward hysteresis compensator provided by the embodiment of the present invention;

[0054] Figure 5 Schematic diagram of the system control framework provided by the embodiment of the present invention;

[0055] Figure 6 Schematic diagram of the time-input / output of the PI model in the PI model example provided by the embodiment of the present invention;

[0056] Figure 7 Schematic diagram of the output hysteresis loop of the PI model in the PI model example provided by the embodiment of the present invention;

[0057] Figure 8 Schematic diagram of the input-output of the PI model in the PI model example provided by the embodiment of the present invention;

[0058] Figure 9 Schematic diagram of the initial stage of the output of the PI model in the PI model example provided by the embodiment of the present invention;

[0059] Figure 10 Schematic diagram of the time-input / output of the PI model in the inverse PI model example provided by the embodiment of the present invention;

[0060] Figure 11 Schematic diagram of the output hysteresis loop of the PI model in the inverse PI model example provided by the embodiment of the present invention;

[0061] Figure 12 Schematic diagram of the input-output of the PI model in the inverse PI model example provided by the embodiment of the present invention;

[0062] Figure 13 Schematic diagram of the initial stage of the output of the PI model in the inverse PI model example provided by the embodiment of the present invention;

[0063] Figure 14 Schematic diagram of the output of the compensated PI model in the feedforward compensation result provided by the embodiment of the present invention;

[0064] Figure 15 Schematic diagram of the feedforward compensation result in the feedforward compensation result provided by the embodiment of the present invention;

[0065] Figure 16 Schematic diagram of the input position-output contact force in the simulation parameter identification model provided by the embodiment of the present invention;

[0066] Figure 17 Schematic diagram of the simulation parameter identification model in the simulation parameter identification model provided by the embodiment of the present invention;

[0067] Figure 18 Schematic diagram of the PI model parameters provided by the embodiment of the present invention;

[0068] Figure 19 Schematic diagram of the output of the PI model and the original data in the comparison between the PI hysteresis model and the original data provided by the embodiment of the present invention;

[0069] Figure 20 Schematic diagram of the error between the model output and the original data in the comparison between the PI hysteresis model and the original data provided by the embodiment of the present invention;

[0070] Figure 21 Schematic diagram of the simulation inverse PI hysteresis model in the PI hysteresis model and the inverse PI hysteresis model provided by the embodiment of the present invention;

[0071] Figure 22 Schematic diagram of the simulated PI hysteresis model in the PI hysteresis model and the inverse PI hysteresis model provided by the embodiments of the present invention;

[0072] Figure 23 Schematic diagram of the output of the inverse PI model in the output of the inverse PI hysteresis model - PI model provided by the embodiments of the present invention;

[0073] Figure 24 Schematic diagram of the input and output data of the feed - forward compensation simulation in the feed - forward compensation simulation experiment provided by the embodiments of the present invention;

[0074] Figure 25 Schematic diagram of the input and output error of the feed - forward compensation simulation in the feed - forward compensation simulation experiment provided by the embodiments of the present invention;

[0075] Figure 26 Schematic diagram of the simulation in the feed - forward compensation simulation comparison experiment provided by the embodiments of the present invention;

[0076] Figure 27 Schematic diagram of the feed - forward compensation input - output simulation in the feed - forward compensation simulation comparison experiment provided by the embodiments of the present invention. Detailed implementation manners

[0077] The following combines the drawings and embodiments to further describe in detail the specific implementation manners of the present invention. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0078] In order to better understand the purpose, structure and function of the present invention, the following further describes the present invention in detail with reference to the drawings.

[0079] Refer to the attached Figure 1-27 As shown, in 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 operator with a specific weight, and they 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 that makes up 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, m0 is a parameter, w0 is the basic weight coefficient, w i is the weight coefficient used to determine the value of y(0). f rThis is the 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 at a specific threshold. Specifically, given the 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 when r approaches infinity, p(r) approaches zero. In practical applications, a finite number of play operators are usually sufficient to simulate the hysteresis phenomenon. The PI model can be constructed by the weighted sum of n play operators. Each play operator has different thresholds and weights, 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] where, is the model output, 0 = r0 < r1... < r n is the probability density threshold coefficient, w i is the weight coefficient, and n is the number of operators. The weights and thresholds can be identified from the hysteresis data measured experimentally.

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

[0090]

[0091] The definitions of each parameter are 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 property of the PI model.

[0094] The inverse model of the PI model can be constructed analytically, and its parameters can be obtained through mathematical calculations without complex iteration or approximation. In addition, the inverse model is also a PI model, and its parameters are functions of the parameters of the original PI model. This relationship can determine the hysteresis characteristics of the inverse model, thereby effectively canceling 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-cancels the hysteresis effect in the system by adding a compensation signal at the input end of the system. It uses the output of the inverse model as the compensation signal, which is combined with the input of the original PI model to eliminate or reduce the influence of the hysteresis effect on the system output. By combining the feedforward hysteresis compensator with the PI model, the compensated system output can be obtained, which will be closer to the reference input. The hysteresis effect is effectively canceled, and at the same time, 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] where the symbol denotes the composition of functions. Let the output of the inverse PI model be

[0098]

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

[0100]

[0101] In practical applications, due to the complex non-linear characteristics of the measured hysteresis loop, 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, using the inverse model of P When performing inverse compensation, the hysteresis effect can only be approximated rather than completely canceled. Although this approximate compensation can reduce the impact of hysteresis on system performance, there are still errors, 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, completely eliminating the error may be very difficult, and various factors need to be weighed according to the application scenario and requirements, and the best modeling and compensation methods should be selected to achieve the best system performance.

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

[0103] The threshold z i of the inverse PI model is calculated by formula #(8) as z i ={0, 0.324, 0.918, 1.728, 2.7, 3.78, 4.914}, and the weights q i can be calculated by formula #(9) as q i ={1.3889, -0.6313, -0.2020, -0.0926, -0.00463, -0.0198, -0.0019}. Setting the input signal of the inverse PI model as u(t)=10sin(2πt), the output signal X * can be obtained as shown in Figure 10 . The play operator output hysteresis loop of the inverse PI model is as Figure 11 shown. Figure 12shows the relationship between the reference input and output, depicting the hysteresis curve of the inverse hysteresis model, whose image is symmetric with Figure 14 respect to y = x. It can be clearly seen from Figure 15 that there is a linear relationship between the output signal y(t) and the reference input u(t). This indicates that when the inverse PI model compensates for the hysteresis effect, it can maintain the linear mapping relationship between the input and output, enabling the output signal to more accurately track the reference input. When the reference input u(t) changes, the output y(t) will change in proportion accordingly, without generating additional non-linear deviations. This linear characteristic makes the system behavior more predictable and controllable, contributing to simplifying the system analysis and design process.

[0104] Parameter identification is crucial in constructing the 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 also directly relate to the response quality and control effectiveness of the system to the input signal. In simulation analysis, 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 through experiments, and the threshold coefficient and weight coefficient of the PI model are extracted from it.

[0105] This method mainly uses the least squares method as the parameter identification method. This method finds the parameters that best match the data through the minimum of the two-norm of the error. Therefore, realizing the parameter identification of the PI hysteresis model plays a crucial 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 form of the error function is as follows:

[0107]

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

[0109] To verify the effectiveness of the feedforward hysteresis compensation in the robotic arm grinding process and evaluate its actual application effect, it is first necessary to collect the force and strain data of the interaction between the robotic 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 exerted by the robotic arm on the soft material and the strain of the soft material.

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

[0111] The deformation of soft materials is usually at the centimeter or millimeter level. 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] where mean(p recode ) and mean(f recode ) are the medians of the deformation and contact force in the recorded data, with the units of m and N. And p recode (i) represents the position of the robotic arm in the z - direction in the workspace, p(i) represents the position after artificial processing, f recode (i) is the force of the robotic arm interacting with the environment, and f(i) represents the contact force after artificial processing. According to this processing method, the data read in the Gazebo simulation environment is processed as shown in Figure 16 . In addition, the raw data mentioned later are all the data processed by Equation #(11).

[0115] Using the collected force and strain data, a PI hysteresis model is established based on methods such as the least - squares method. Set the number of play operators of the PI model to 7, that is, n = 7. First, the threshold r i is determined based on the transformation division of the graph. Set the threshold r at the turning points of the image. Based on such a selection, the obtained rule is as shown in the PI model threshold of Figure 18 . The weight coefficient w i , i = 1, …, 7, is obtained by the least - squares method, and the weight coefficient is determined as the optimized value just calculated. Figure 18 Lists the weight parameters of the identified PI hysteresis model and the calculated inverse PI model threshold z i and weight q i .

[0116] According to the data in Figure 18 , the PI hysteresis model, inverse PI hysteresis model, etc. of pressure and deformation can be plotted. Figure 17 Shows the scatter plot with deformation as the input and contact force as the output, as well as the PI hysteresis model obtained by parameter identification. The comparison between the contact force and the output of the PI model obtained by parameter identification is as shown in Figure 19 . From Figure 20As can be seen from the blue line, 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 indicates that the model has a high degree of fit. The PI hysteresis model fits well with the actual data, with low RMSE, MSE, and SSE values, and the R - Square coefficient close to 1, showing a better fitting effect than the linear elastic model.

[0117] Taking the inverse model of the above - mentioned PI model as the input of the feed - forward control, and selecting the input signal as u(t)=2.27sin(t), its inverse PI hysteresis model is as Figure 21 . At the same time, taking the output of its inverse PI model as the input of the PI hysteresis model, the obtained result is as Figure 22 shown.

[0118] The relationship between the output y(t) of the PI hysteresis and the input u(t) of the inverse hysteresis model is as Figure 23 . The image shows that, under ideal conditions, after compensation by the inverse PI model, the input and output present a linear relationship, y(t)=u(t), effectively canceling the hysteresis behavior in the interaction between the robotic arm and the soft material. In Gazebo, adding the inverse PI model to the control program, the obtained data is as shown in the following figure.

[0119] Figure 24 In the figure, the red curve is the desired force, This force is used as the input of the inverse PI hysteresis model. The output obtained after the system runs is the blue line in this figure. Among the two curves, the difference between the system - running output and the desired force is as shown by the blue line in Figure 26 . It can be seen that most of the force tracking errors are within 0.2 N, and compared with the errors of the linear elastic model, the overall error of the output force after compensation is smaller.

[0120] In Figure 25-26 , after the system is compensated, it successfully cancels the hysteresis behavior between the contact of the robotic arm and the soft material, indicating that the system has achieved good results in dealing with the difference between the desired force and the actual output. The output after compensation presents linear characteristics, and its linear fit is y = x - 0.04247, with an SSE of 22.79, an R - square of 0.9957, an Adjusted R - square of 0.9957, and an RMSE of 0.1073. These indicators show that the fitting data has small errors and a good fitting effect, further verifying the effect after system compensation. In some embodiments of the present application,

[0121] In the description of the present application, it should be understood that the orientation or positional relationship indicated by the terms "center", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present application and simplifying the description, rather than indicating or implying 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 construed as a limitation on the present application.

[0122] The terms "first" and "second" are used only for descriptive purposes and should not be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present application, unless otherwise specified, the meaning of "a plurality" is two or more.

[0123] In the description of the present application, it should be noted that unless otherwise clearly specified and limited, the terms "installed", "connected", and "coupled" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to specific circumstances.

[0124] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments, and the same or similar parts among the various embodiments can be referred to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0125] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can 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 will be accorded 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; The specific expression of the play operator in step 1 is: Among them, x(t) is the input signal, y(t) is the output signal, m0 is a parameter, w0 is the basic weight coefficient, and w i is the weight coefficient used to determine the value of y(0), 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; Where, 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 When r approaches infinity, p(r) approaches zero; The output expression of the stop operator in step 1 is: 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); 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 threshold coefficient, w i is the weight coefficient, n is the number of operators, and the weight and threshold are identified by experimentally measured hysteresis data; 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, i and g are index variables used to represent different items in the summation process.

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: 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 .

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: 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 )) 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.

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: In step 5, the inverse model of the above 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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