Industrial robot kinetic parameter uncertainty analysis method, device, equipment and medium

Abstract

The invention discloses an industrial robot kinetic parameter uncertainty analysis method, device and equipment and a medium, and relates to the technical field of robotics.The method comprises the steps that an expression of a kinetic parameter mean value and covariance is obtained through reasoning of a Bayesian formula and a kinetic equation, a robot joint torque actual value is obtained, and a first prediction error is set; obtaining a prediction error of the mth iteration based on the intermediate value and the actual value of the joint torque of the robot of the (m-1) th iteration; judging whether the difference value between the prediction error of the mth iteration and the prediction error of the (m-1) th iteration is smaller than a first precision threshold value or not, and if yes, obtaining a mean value and a covariance of the kinetic parameters according to the prediction error; calculating to obtain a robot joint torque target value; the industrial robot is controlled through the joint torque target value; and uncertainty analysis can be performed on the industrial robot according to the covariance of the kinetic parameters. The method can ensure the physical feasibility of the kinetic parameters.

Description

Technical Field

[0001] This application relates to the technical field of robots, and in particular, to a method, device, equipment and medium for analyzing the uncertainty of industrial robot dynamic parameters. Background Art

[0002] In the field of robot technology, industrial robots, as the core equipment of intelligent manufacturing, can effectively reduce labor costs, improve the manufacturing environment, and enhance production efficiency. They are an important symbol to measure a country's scientific and technological innovation and high-end manufacturing level. The dynamic model is an important basis for high-precision motion control to ensure the service performance of robots.

[0003] However, the existing industrial robot dynamic parameter identification methods have disadvantages such as insufficient accuracy, inability to guarantee the physical feasibility of parameters, and insufficient utilization of prior information, resulting in insufficient accuracy of the model established using these dynamic parameters, and further affecting the control accuracy of subsequent industrial robots. In addition, the existing methods are all carried out under deterministic conditions, ignoring the influence of uncertainty, and the obtained results cannot accurately describe the real behavior of the robot. Summary of the Invention

[0004] This application provides a method, device, equipment and medium for analyzing the uncertainty of industrial robot dynamic parameters. By reasonably setting prior information, the physical feasibility of dynamic parameters can be guaranteed, the mean and covariance of dynamic parameters can be obtained, the modeling accuracy of the dynamic model can be improved, and further high-precision control of industrial robots can be achieved.

[0005] To achieve the above object, this application adopts the following technical solutions: In a first aspect, this application provides a method for analyzing the uncertainty of industrial robot dynamic parameters. The expressions of the mean and covariance of the dynamic parameters are deduced in advance through Bayes' formula and dynamic equations; the method includes: Obtain the actual value of the robot joint torque; Set a first prediction error according to the actual value of the robot joint torque; Based on the intermediate value of the robot joint torque obtained in the m -(i - 1)th iteration and the actual value of the robot joint torque, obtain the prediction error of the m ith iteration, where m i is a positive integer; Judge whether the difference between the prediction error of the m ith iteration and the prediction error of the m -(i - 1)th iteration is less than a first accuracy threshold, and obtain a first judgment result; If the first judgment result indicates that the prediction error of the m ith iteration and the prediction error of the mThe difference between the prediction errors of the -1-th iteration is less than the first precision threshold. According to the expressions of the mean and covariance of the prediction error, the observation matrix, and the dynamic parameters of the m -th iteration, the mean and covariance of the dynamic parameters are obtained; According to the mean of the dynamic parameters and the observation matrix, the target value of the robot joint torque is obtained; The industrial robot is controlled by using the target value of the robot joint torque; Uncertainty analysis of the industrial robot can be performed according to the covariance of the dynamic parameters.

[0006] In some possible implementation manners, the method further includes: If the first judgment result indicates that the m prediction error obtained in the -th iteration and the m prediction error obtained in the -1-th iteration have a difference greater than the first precision threshold, continue the iteration, and obtain the intermediate value of the robot joint torque. Update the prediction error according to the intermediate value of the robot joint torque.

[0007] In some possible implementation manners, the obtaining the mean and covariance of the dynamic parameters according to the prediction error, the observation matrix, and the expressions of the mean and covariance of the dynamic parameters of the m -th iteration includes:

[0008]

[0009] Wherein, is the mean of the dynamic parameters, is the covariance of the dynamic parameters, is the observation matrix, is the transpose of, is the covariance matrix of the prediction error, is the actual value of the robot joint torque, is the prior covariance matrix of the dynamic parameters, is the prior mean of the dynamic parameters.

[0010] In some possible implementation manners, the updating the prediction error according to the intermediate value of the robot joint torque includes:

[0011] Wherein, is the prediction error, is the actual value of the i-th joint torque of the robot, is the intermediate value of the robot joint torque, is the dimension of, that is the number of rows of the matrix, is the prediction error of the i th joint of the robot, , where

[0012] In some possible implementation manners, the method further includes: According to the mean value of the dynamic parameters and the observation matrix, obtaining a target value of the robot joint torque through a dynamic model, where the dynamic model can be expressed by the following formula:

[0013] wherein, is the target value of the robot joint torque, is the observation matrix, is the mean value of the dynamic parameters.

[0014] In some possible implementation manners, the method further includes: The prediction error follows a normal distribution with a mean of zero and a covariance matrix of , where the covariance matrix of the prediction error can be calculated by the following method:

[0015] is the covariance matrix of the prediction error, is the prediction error of each joint torque of the robot at time represents the number of data points collected, is the identity matrix.

[0016] In some possible implementation manners, the method further includes: The dynamic parameters include inertia tensor parameters, first-order matrix parameters, mass parameters, total inertia matrix parameters of motors and gears, and friction parameters.

[0017] In a second aspect, the present application provides an industrial robot dynamic parameter uncertainty analysis device, which pre-infers an expression of the mean value of the dynamic parameters and an expression of the covariance through the Bayesian formula and the dynamic equation; the device includes: An acquisition module, configured to acquire the actual value of the robot joint torque; set a first prediction error according to the actual value of the robot joint torque; and acquire the prediction error of the m th iteration based on the intermediate value of the robot joint torque obtained in the m th iteration and the actual value of the robot joint torque; A judgment module, configured to judge whether the difference between the prediction error of the m -th iteration and the prediction error of the m -1-th iteration is less than a first precision threshold, so as to obtain a first judgment result, where m is a positive integer; if the first judgment result indicates that the difference between the prediction error of the m -th iteration and the prediction error of the m -1-th iteration is less than the first precision threshold, then according to the expression of the mean value and the expression of the covariance of the prediction error, the observation matrix, and the dynamic parameters of the m -th iteration, the mean value and the covariance of the dynamic parameters are obtained; A control module, configured to obtain a target value of the robot joint torque according to the mean value of the dynamic parameters and the observation matrix; and control the industrial robot by using the target value of the robot joint torque; An analysis module, configured to perform uncertainty analysis on the industrial robot according to the covariance of the dynamic parameters.

[0018] In a third aspect, the present application provides a computing device, including a memory and a processor; wherein, one or more computer programs are stored in the memory, and the one or more computer programs include instructions; when the instructions are executed by the processor, the computing device is caused to execute the method according to any one of the first aspect.

[0019] In a fourth aspect, the present application provides a computer-readable storage medium, which is used for storing a computer program, and the computer program is used for executing the method according to any one of the first aspect.

[0020] In a fifth aspect, the present application provides a computer program product, which includes one or more computer instructions, and when the computer instructions are executed by a computer, the computer executes the method according to any one of the first aspect.

[0021] It can be seen from the above technical solutions that the present application has at least the following beneficial effects: In the present application, the expressions of the mean value and the covariance of the dynamic parameters are deduced in advance through the Bayesian formula and the dynamic equation, the actual value of the robot joint torque is obtained, and the first prediction error is set according to the actual value of the robot joint torque; based on the m intermediate value of the robot joint torque obtained in the m -1-th iteration and the actual value of the robot joint torque, the prediction error of the m -th iteration is obtained; judge the prediction error of the mWhether the difference between the prediction errors of the -1th iteration is less than the first accuracy threshold, to obtain a first judgment result; if the first judgment result indicates that the difference between the prediction error of the mth iteration and the prediction error of the m -1th iteration is less than the first accuracy threshold, according to the expressions of the mean and covariance of the prediction error, the observation matrix, and the dynamic parameters of the m iteration, the mean and covariance of the dynamic parameters are obtained; according to the mean of the dynamic parameters and the observation matrix, the target value of the robot joint torque is obtained; the industrial robot is controlled by using the target value of the robot joint torque; the covariance of the dynamic parameters can be used for the uncertainty analysis of the industrial robot. In the traditional scheme, the commonly used method for identifying the dynamic parameters of an industrial robot is the least squares method, which analyzes the "input / output" behavior of the robot during the planned motion and estimates the parameters by minimizing the difference between the measured data and the output of the mathematical model. This type of method is easy to implement and has a relatively high identification accuracy, and can identify all dynamic parameters. However, this method is sensitive to measurement noise, cannot utilize prior information, and is difficult to ensure the physical consistency of the parameters, resulting in inaccurate output of the dynamic model obtained by this method, low modeling accuracy of the dynamic model, and thus inaccurate control of the industrial robot. Moreover, this method cannot consider the influence of uncertain factors and cannot accurately describe the real behavior of the robot. It can be seen that in this application, through the Bayesian formula and the dynamic equation and based on the existing prior information, the mean and covariance of the dynamic parameters are deduced. By reasonably setting the prior, the physical consistency of the parameters can be ensured. Then, by inputting the mean of the dynamic parameters into the dynamic model, the output of the dynamic model can be made more accurate, the modeling accuracy of the dynamic model can be improved, and further high-precision control of the industrial robot can be realized. In addition, the covariance of the dynamic parameters contains the uncertainty information of the dynamic parameters and can be used for the uncertainty analysis of the industrial robot.

[0022] It should be understood that the description of technical features, technical solutions, beneficial effects or similar languages in this application does not imply that all features and advantages can be achieved in any single embodiment. On the contrary, it can be understood that the description of features or beneficial effects means that at least one embodiment includes specific technical features, technical solutions or beneficial effects. Therefore, the description of technical features, technical solutions or beneficial effects in this specification does not necessarily refer to the same embodiment. Furthermore, the technical features, technical solutions and beneficial effects described in this embodiment can be combined in any appropriate manner. Those skilled in the art will understand that an embodiment can be implemented without one or more specific technical features, technical solutions or beneficial effects of a specific embodiment. In other embodiments, additional technical features and beneficial effects can also be identified in specific embodiments that do not embody all embodiments. Description of the Drawings

[0023] Figure 1 A flowchart of a method for analyzing the uncertainty of the dynamic parameters of an industrial robot provided by an embodiment of the present application; Figure 2 A schematic diagram of a device for analyzing the uncertainty of the dynamic parameters of an industrial robot provided by an embodiment of the present application; Figure 3 A schematic diagram of a computing device provided by an embodiment of the present application. Detailed implementation manners

[0024] The terms "first", "second", "third", etc. in the specification and drawings of the present application are used to distinguish different objects, rather than to limit a specific order.

[0025] In the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations or explanations. Any embodiment or design solution described as "exemplary" or "for example" in the embodiments of the present application should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Rather, the use of words such as "exemplary" or "for example" is intended to present relevant concepts in a specific manner.

[0026] Currently, the commonly used method for identifying the dynamic parameters of industrial robots is the least squares method, which analyzes the "input / output" behavior of the robot during the planned motion and estimates the parameters by minimizing the difference between the measured data and the output of the mathematical model. This type of method is easy to implement and has a relatively high identification accuracy, and can identify all dynamic parameters.

[0027] However, this method is sensitive to measurement noise, cannot utilize prior information, is difficult to ensure the physical consistency of the parameters, and the existing dynamic parameters are inaccurate, resulting in inaccurate output of the dynamic model obtained by using this dynamic parameter method, resulting in low modeling accuracy of the dynamic model, and further resulting in inaccurate control of the industrial robot. Moreover, this method cannot consider the influence of uncertain factors and cannot accurately describe the true behavior of the robot.

[0028] In view of this, an embodiment of the present application provides a method for analyzing the uncertainty of industrial robot dynamic parameters. This method can be applied to a processing device, which can be a terminal or a server. The terminal includes but is not limited to a smart phone, a tablet computer, a laptop computer, a personal digital assistant, or a smart wearable device, etc. The server can be a cloud server, such as the central server in a central cloud computing cluster or the edge server in an edge cloud computing cluster. Of course, the server can also be a server in a local data center. A local data center refers to a data center directly controlled by a user. In this method, the expressions of the mean and covariance of the dynamic parameters are deduced in advance through the Bayesian formula and the dynamic equation, the actual value of the robot joint torque is obtained, and based on the actual value of the robot joint torque, a first prediction error is set; based on the m intermediate value of the robot joint torque obtained in the m -1th iteration and the actual value of the robot joint torque, the prediction error of the m th iteration is obtained; it is judged whether the difference between the prediction error of the m th iteration and the prediction error of the m -1th iteration is less than a first precision threshold to obtain a first judgment result; if the first judgment result indicates that the difference between the prediction error of the m th iteration and the prediction error of the m -1th iteration is less than the first precision threshold, based on the prediction error of the

[0029] th iteration, the observation matrix, and the expressions of the mean and covariance of the dynamic parameters, the mean and covariance of the dynamic parameters are obtained; based on the mean of the dynamic parameters and the observation matrix, the target value of the robot joint torque is obtained; the industrial robot is controlled by using the target value of the robot joint torque; the uncertainty analysis of the industrial robot can be performed according to the covariance of the dynamic parameters. It can be seen that the mean and covariance of the dynamic parameters obtained in the present application can ensure the physical feasibility of the dynamic parameters, improve the modeling accuracy of the dynamic model, and further realize the high-precision control of the industrial robot. To make the technical solution of the present application clearer and easier to understand, the following introduces a method for analyzing the uncertainty of industrial robot dynamic parameters provided by an embodiment of the present application with reference to the accompanying drawings. As Figure 1 shown, this figure is a flowchart of a method for analyzing the uncertainty of industrial robot dynamic parameters provided by an embodiment of the present application. The method for analyzing the uncertainty of the dynamic parameters of this industrial robot includes: S101. The processing device obtains the actual value of the robot joint torque.

[0030] A torque sensor is installed at the robot joint. This sensor can directly measure the torque generated during the rotation of the joint. The output signal of the torque sensor is usually proportional to the torque magnitude. Therefore, the actual value of the robot joint torque can be obtained by reading the output signal of the sensor.

[0031] S102. The processing device sets a first prediction error according to the actual value of the robot joint torque.

[0032] The prediction error follows a normal distribution with a mean of zero and a covariance matrix of where the covariance matrix of the prediction error can be calculated by the following formula (1): (1) is the covariance matrix of the prediction error, is a vector containing n elements, representing the prediction errors of the torques of each joint of the robot at time , and its specific form is , represents the prediction error of the first degree of freedom of the industrial robot; represents the prediction errors of the torques of each joint of the robot at time is the time, represents the number of data points collected within the time t , is the identity matrix.

[0033] In some embodiments, a serial industrial robot has six rotational joints and six degrees of freedom. It is considered that the error levels of each joint of the industrial robot do not change with time, that is . Taking t k as an example, The calculation formula of (2) S103. The processing device obtains the prediction error of the m -th iteration based on the intermediate value of the robot joint torque obtained from the m -1-th iteration and the actual value of the robot joint torque.

[0034] Based on the first prediction error obtained in step S102, according to the expressions of the mean and covariance of the observation matrix, dynamic parameters, the intermediate value of the robot joint torque is obtained.

[0035] Among them, the observation matrix consists of the joint angle of the robot, the joint velocity and joint acceleration It is composed of; the expressions of the mean value and covariance of the dynamic parameters are obtained by the following method. The processing device pre-infers the expressions of the mean value and covariance of the dynamic parameters through the Bayesian formula and the dynamic equation. The detailed steps are as follows: According to the classical Bayesian formula, the posterior distribution of the industrial robot's dynamic parameters can be expressed as formula (3): (3) where, is the posterior distribution probability density function of the dynamic parameters; is a constant that plays a role in normalization to ensure that the posterior distribution integral is 1; is the prior probability density function of the dynamic parameters obtained based on experience, usually a uniform distribution or a Gaussian distribution is selected; is the likelihood function, which represents the probability of obtaining the measured torque given the dynamic parameter β.

[0036] The dynamic parameters include 6 inertia tensor parameters, 3 first-order matrix parameters, 1 mass parameter, 1 total inertia matrix parameter of the motor and gear, and 2 friction parameters; among them, the inertia tensor parameters include , the first-order matrix parameters include , and the friction parameters include . I xx , I yy and I zz are the moments of inertia about the x axis, y axis, and z axis respectively, I xy , I xz and I yz represent the products of inertia, m x , m y and m z are the first-order moment parameters of the x , y and z three axes respectively, f v and f c represent the viscous friction coefficient and the Coulomb friction coefficient respectively.

[0037] Constructing the likelihood function requires considering the relationship between the prediction error and the measurement data. Since the robot is affected by multi-source uncertainties during operation, such as environmental factors like temperature, humidity, and noise, there are deviations in the joint torques. By introducing the prediction error, the torque error formula is obtained. Based on this, the likelihood function in the following form is constructed as shown in Equation (4): (4) where, is the theoretical value of the robot joint torque, calculated from the established dynamic model ; is the prediction error, representing the difference between the theoretical value of the robot joint torque and the measured torque .

[0038] Substituting into Equation (5), Equation (4) is rewritten as: (5) According to Equation (5), the measured torque follows a normal distribution with a mean of and a covariance matrix of , that is . The probability density function of the likelihood function can be expressed by Equation (6): (6) In the formula, has the specific form of Equation (7): (7) Let , Equation (7) can be simplified to Equation (8): (8) Adopting the prior information in the form of a normal distribution, the prior probability density function of the dynamic parameters obtained from experience can be expressed by Equation (9): (9) In the formula, has the specific form of Equation (10): (10) In the formula, is the prior mean of the robot dynamic parameters; is the prior covariance matrix of the robot dynamic parameters, is the identity matrix, , where is the prior standard deviation of the dynamic parameters, is the prior standard deviation of the first dynamic parameter to be identified, is the The prior standard deviation of the kinetic parameters to be identified is the number of kinetic parameters to be identified for the robot.

[0039] Similarly, let , Equation (10) can be simplified to Equation (11): (11) Therefore, through Equations (3), (8), and (11), the posterior distribution of the robot's kinetic parameter β can be expressed by Equation (12): (12) According to the properties of the normal distribution, the terms with in Equation (12) are combined, and then according to the form of the normal distribution probability density function, can be rewritten as shown in Equation (13): (13) Therefore, it can be obtained that the kinetic parameter β follows a normal distribution, , Through the above steps, the expressions for the mean and covariance of the kinetic parameters are obtained, as shown in Equations (14) and (15):

[0040]

[0041] where is the mean of the kinetic parameters, is the covariance of the kinetic parameters, is the observation matrix, is transpose of is the covariance matrix of the prediction error, is the actual value of the robot joint torque, is the prior covariance matrix of the kinetic parameters, is the prior mean of the kinetic parameters.

[0042] When calculating the mean and covariance matrix of the kinetic parameters, the prior information of the kinetic parameters is also considered. The prior information of the kinetic parameters is known empirical information. In this application, the known empirical information can be utilized, which can further ensure the physical consistency of the parameters and thus improve the accuracy of the output of the kinetic model.

[0043] Substitute the obtained mean of the kinetic parameters into the kinetic model to obtain the intermediate value of the robot joint torque. The kinetic model can be expressed by Equation (16): (16) Among them, is the median value of the robot joint torque, is the observation matrix, is the mean value of the dynamic parameters.

[0044] Update the prediction error according to the median value of the robot joint torque. The calculation method of the updated prediction error is shown in formula (17): (17) Among them, is the prediction error, is the actual value of the i-th joint torque of the robot, is the median value of the robot joint torque, is the dimension of, that is, the number of rows of the matrix, is for the robot i the prediction error of the -th joint, , is a positive integer.

[0045] Therefore, the prediction error of the first iteration is obtained; then, continue to iterate according to the prediction error of the first iteration to obtain the prediction error of the second iteration; and so on, and then obtain the prediction error of the m -1-th iteration and the prediction error of the m -th iteration. Among them, m is a positive integer.

[0046] S104. The processing device determines whether the difference between the prediction error of the m -th iteration and the prediction error of the m -1-th iteration is less than the first precision threshold.

[0047] The processing device determines whether the difference between the prediction error of the m -th iteration and the prediction error of the m -1-th iteration is less than the first precision threshold, and obtains the first judgment result.

[0048] If the first judgment result indicates that the difference between the prediction error of the m -th iteration and the prediction error of the m -1-th iteration is less than the first precision threshold, then execute S105; if the first judgment result indicates that the difference between the prediction error obtained in the m -th iteration and the prediction error obtained in the m -1-th iteration is greater than the first precision threshold, then execute S109.

[0049] S105. The processing device according to the mThe mean and covariance expressions of the prediction error, observation matrix, and dynamic parameters for the current iteration are used to obtain the mean and covariance of the dynamic parameters.

[0050] The processing device is based on the m mean and covariance expressions of the prediction error, observation matrix, and dynamic parameters for the current iteration to obtain the mean and covariance of the dynamic parameters. The calculation method and formula are as shown in step S103 and will not be elaborated here.

[0051] Among them, the processing device can also obtain the mean and covariance of the dynamic parameters according to the m mean and covariance expressions of the prediction error, observation matrix, and dynamic parameters for the (i - 1)-th iteration. Because the difference between the prediction error for the i-th iteration and the prediction error for the m i-th iteration and the m (i - 1)-th iteration is less than the first precision threshold, the prediction error for the m (i - 1)-th iteration and the m i-th iteration are very close in value. For the convenience of the experiment and to reduce the number of experiments, subsequent calculations can also be performed according to the prediction error for the m (i - 1)-th iteration.

[0052] S106. The processing device obtains the target value of the robot joint torque according to the mean of the dynamic parameters and the observation matrix.

[0053] According to the mean of the dynamic parameters and the observation matrix, the target value of the robot joint torque is obtained through a dynamic model, and the dynamic model can be represented by formula (18): (18) Among them, is the target value of the robot joint torque, is the observation matrix, is the mean of the dynamic parameters.

[0054] S107. The processing device controls the industrial robot using the target value of the robot joint torque.

[0055] The processing device inputs the obtained target value of the robot joint torque into the industrial robot to achieve the control of the industrial robot.

[0056] S108. The processing device can perform uncertainty analysis on the industrial robot according to the covariance of the dynamic parameters.

[0057] Based on the covariance of the kinetic parameters obtained by the processing device according to the above steps, the physical feasibility of the kinetic parameters can be ensured. For example, in the prior art, the friction coefficient obtained by the least squares method may be negative. However, based on the mean and covariance of the kinetic parameters obtained in this application, it can be ensured that the obtained friction coefficient is not negative. Because in the embodiments of this application, by adding limiting conditions, data that does not conform to common sense is screened out to ensure that the obtained kinetic parameters conform to common sense.

[0058] The processing device can also determine whether the industrial robot is operating normally through the covariance of the kinetic parameters. If a collision occurs during operation, it will cause data in the experimental data output by the industrial robot that does not conform to the output interval. In this way, technicians can eliminate abnormal data when organizing the data, thus assisting the subsequent processing process.

[0059] S109. The processing device continues to iterate and obtains the intermediate value of the robot joint torque.

[0060] If the first judgment result indicates that the difference between the prediction error obtained in the m th iteration and the prediction error obtained in the m th - 1 iteration is greater than the first accuracy threshold, then continue to iterate to m = m +1, return to S103, and obtain the intermediate value of the robot joint torque. The calculation method is as shown in S103 and will not be elaborated here.

[0061] Based on the above content, the expressions of the mean and covariance of the kinetic parameters are deduced in advance through the Bayesian formula and the kinetic equation. The actual value of the robot joint torque is obtained, and the first prediction error is set according to the actual value of the robot joint torque; based on the intermediate value of the robot joint torque obtained in the m th - 1 iteration and the actual value of the robot joint torque, the prediction error of the m th iteration is obtained; it is judged whether the difference between the prediction error of the m th iteration and the prediction error of the m th - 1 iteration is less than the first accuracy threshold to obtain the first judgment result; if the first judgment result indicates that the difference between the prediction error of the m th iteration and the prediction error of the m th - 1 iteration is less than the first accuracy threshold, according to the mThe expressions for the mean and covariance of the prediction error, observation matrix, and dynamic parameters in the current iteration are used to obtain the mean and covariance of the dynamic parameters. Based on the mean of the dynamic parameters and the observation matrix, the target value of the robot joint torque is obtained. The industrial robot is controlled using the target value of the robot joint torque. Uncertainty analysis of the industrial robot can be performed based on the covariance of the dynamic parameters. It can be seen that obtaining the mean and covariance of the dynamic parameters in this application can ensure the physical feasibility of the dynamic parameters, improve the modeling accuracy of the dynamic model, and further achieve high-precision control of the industrial robot.

[0062] In the embodiment of this application, taking the Staubli TX-40 industrial robot as an example, specific implementation cases are introduced, and the detailed steps are as follows: Step 1: Use the Newton-Euler method to perform dynamic modeling of the TX-40 industrial robot, and obtain a dynamic model in linear form as shown in Equation (16). Step 2: Based on Bayesian inference, construct a classical Bayesian formula for identifying the dynamic parameters of the industrial robot. Step 3: Introduce the joint torque prediction error, and establish a likelihood function based on the linear form of the robot dynamic model. Step 4: Given a prior in the form of a Gaussian distribution, derive the analytical expressions for the dynamic parameters of the industrial robot as shown in Equations (14) and (15). Step 5: Control the industrial robot to run a predetermined trajectory, collect the joint angle and torque data for filtering, and calculate the observation matrix W. Step 6: Given the initial values of the joint torque prediction errors, calculate the mean and covariance matrix of the dynamic parameters of the industrial robot through Equations (14) and (15). Step 7: Use the mean calculated in Step 6 as the identification value of the dynamic parameters of the industrial robot, and obtain the model output torque through Equation (16). Step 8: Update the torque prediction error through Equation (17). The model needs to be iterated at least 2 times. The accuracy judgment is not performed in the first iteration. Go to Step 6 to re-identify the parameters using the updated prediction error. Starting from the second iteration, judge whether to converge based on the difference between the results of two adjacent parameter identifications. If the difference between the results of two adjacent parameter identifications is less than the set accuracy threshold, stop the iteration. If not satisfied, go to Step 6 to continue the iteration.

[0063] Step 9: After the iteration ends, obtain the mean and covariance of the dynamic parameters of the industrial robot. Substitute the mean into Equation (16) to obtain a high-precision dynamic model, and the covariance matrix can be used for subsequent uncertainty propagation research.

[0064] Step 10: Verify the accuracy of the obtained dynamic model by comparing the calculated model output (the target value of each joint torque of the robot) with the experimental data.

[0065] As described above in combination with Figure 1 A method for analyzing the uncertainty of industrial robot dynamic parameters provided by an embodiment of the present application has been introduced in detail. Next, the devices and equipment provided by the embodiments of the present application will be introduced with reference to the accompanying drawings.

[0066] An embodiment of the present application also provides an apparatus for analyzing the uncertainty of industrial robot dynamic parameters, as Figure 2 shown. This figure is a schematic diagram of an apparatus for analyzing the uncertainty of industrial robot dynamic parameters provided by an embodiment of the present application. The mean expression and covariance expression of the dynamic parameters are deduced in advance through the Bayesian formula and the dynamic equation; the apparatus includes: an acquisition module 201, a judgment module 202, a control module 203, and an analysis module 204; The acquisition module 201 is configured to acquire the actual value of the robot joint torque; set a first prediction error according to the actual value of the robot joint torque; and obtain the prediction error of the m -th iteration based on the intermediate value of the robot joint torque and the actual value of the robot joint torque obtained in the m -1-th iteration, where m is a positive integer; The judgment module 202 is configured to judge whether the difference between the prediction error of the m -th iteration and the prediction error of the m -1-th iteration is less than a first accuracy threshold to obtain a first judgment result; if the first judgment result indicates that the difference between the prediction error of the m -th iteration and the prediction error of the m -1-th iteration is less than the first accuracy threshold, obtain the mean and covariance of the dynamic parameters according to the prediction error of the m -th iteration, the observation matrix, and the mean expression and covariance expression of the dynamic parameters; The control module 203 is configured to obtain the target value of the robot joint torque according to the mean of the dynamic parameters and the observation matrix; and control the industrial robot by using the target value of the robot joint torque; The analysis module 204 is configured to perform uncertainty analysis on the industrial robot according to the covariance of the dynamic parameters.

[0067] In some possible implementation manners, the judgment module 202 is further configured to, if the first judgment result indicates that the prediction error obtained in the m -th iteration and the prediction error obtained in the mIf the difference between the prediction errors obtained in the -1 -th iteration is greater than the first accuracy threshold, continue the iteration, obtain the intermediate value of the robot joint torque, and update the prediction error according to the intermediate value of the robot joint torque.

[0068] In some possible implementation manners, the determining module 202 is further configured to obtain the mean value and covariance of the dynamic parameters according to the expression of the mean value and covariance of the prediction error, the observation matrix, and the dynamic parameters in the m th iteration, including:

[0069]

[0070] Wherein, is the mean value of the dynamic parameters, is the covariance of the dynamic parameters, is the observation matrix, is transpose of, is the covariance matrix of the prediction error, is the actual value of the robot joint torque, is the prior covariance matrix of the dynamic parameters, is the prior mean value of the dynamic parameters.

[0071] In some possible implementation manners, the device further includes: An updating module, configured to update the prediction error according to the intermediate value of the robot joint torque, including:

[0072] Wherein, is the prediction error, is the actual value of the i -th joint torque of the robot, is the intermediate value of the robot joint torque, is dimension of, that is, number of rows of the matrix, is the i th joint prediction error of the robot, , is a positive integer.

[0073] In some possible implementation manners, the control module 203 is further configured to obtain the target value of the robot joint torque through a dynamic model according to the mean value of the dynamic parameters and the observation matrix, and the dynamic model can be expressed by the following formula:

[0074] Wherein, is the target value of the robot joint torque, is the observation matrix, is the mean value of the dynamic parameters.

[0075] In some possible implementation manners, the prediction error follows a normal distribution with a mean of zero and a covariance matrix of , where the covariance matrix of the prediction error can be calculated by the following method:

[0076] is the covariance matrix of the prediction error, is the prediction error of each joint torque of the robot at time represents the number of data points collected, is the identity matrix.

[0077] In some possible implementation manners, the dynamic parameters include inertia tensor parameters, first-order matrix parameters, mass parameters, total inertia matrix parameters of the motor and the gear, and friction parameters.

[0078] The embodiment of the present application further provides a computing device. As Figure 3 shown, this figure is a schematic diagram of a computing device provided by the embodiment of the present application. The computing device 400 includes a bus 401, a processor 402, a communication interface 403, and a memory 404. The processor 402, the memory 404, and the communication interface 403 communicate with each other through the bus 401.

[0079] The bus 401 may be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc. For the sake of simplicity of representation, Figure 3 only a thick line is used in

[0080] to represent it, but it does not mean that there is only one bus or one type of bus.

[0081] The communication interface 403 is used for external communication. For example, when the computing device is the first switch, the communication interface 403 can be used for communication between the first switch and the first user terminal, or for communication between the first switch and the second switch.

[0082] The memory 404 may include volatile memory, such as random access memory (RAM). The memory 404 may also include non-volatile memory, such as read-only memory (ROM), flash memory, hard disk drive (HDD), or solid state drive (SSD).

[0083] The executable code is stored in the memory 404, and the processor 402 executes the executable code to perform the foregoing method for analyzing the uncertainty of the dynamic parameters of an industrial robot.

[0084] The embodiment of the present application also provides a computer-readable storage medium. The computer-readable storage medium may be any available medium that can be stored by a computing device or a data storage device such as a data center including one or more available media. The available medium may be a magnetic medium (such as a floppy disk, a hard disk, a magnetic tape), an optical medium (such as a DVD), or a semiconductor medium (such as a solid-state drive), etc. The computer-readable storage medium includes instructions that direct the computing device to execute the method for analyzing the uncertainty of the dynamic parameters of the industrial robot described above.

[0085] The embodiment of the present application also provides a computer program product, which includes one or more computer instructions. When the computer instructions are loaded and executed on the computing device, the processes or functions according to the embodiments of the present application are generated in whole or in part.

[0086] The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions may be transmitted from one website, computer, or data center to another website, computer, or data center by wire (such as coaxial cable, optical fiber) or wirelessly (such as infrared, wireless, microwave, etc.).

[0087] When the computer program product is executed by a computer, the computer executes any one of the foregoing methods for analyzing the uncertainty of the dynamic parameters of an industrial robot. The computer program product can be a software installation package. In the case where any one of the foregoing methods for analyzing the uncertainty of the dynamic parameters of an industrial robot is needed, the computer program product can be downloaded and executed on the computer.

[0088] The descriptions of the processes or structures corresponding to the foregoing respective drawings each have their own focuses. For parts not detailed in a certain process or structure, reference can be made to the relevant descriptions of other processes or structures.

[0089] As described above, the foregoing is only the specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions within the technical scope disclosed in the present application should be covered within the protection scope of the present application.

Claims

1. A method for analyzing uncertainty in dynamic parameters of an industrial robot, characterized in that: The expression of the mean value and the expression of the covariance of the kinetic parameters are obtained in advance by Bayesian formula and kinetic equation reasoning; the method comprises: Get the actual value of the robot joint torque; According to the actual value of the robot joint torque, a first prediction error is set; Based on m -1 iterations to obtain the intermediate value of the robot joint torque and the actual value of the robot joint torque, and obtain the m The prediction error of the iterations is, m is a positive integer; Judgement m The prediction error of the first iteration is m -Whether the difference between the prediction errors of 1 iterations is less than the first accuracy threshold, obtaining a first judgment result; If the first judgment result indicates m The prediction error of the first iteration is m The difference between the prediction errors of the first and second iterations is less than the first accuracy threshold. m The prediction error of the iteration, the observation matrix and the expression of the mean and covariance of the kinetic parameters are obtained to obtain the mean and covariance of the kinetic parameters; Obtaining a target value of the robot joint torque according to the mean value of the dynamic parameters and the observation matrix; Controlling the industrial robot using the robot joint torque target value; Uncertainty analysis of industrial robots can be performed based on the covariance of dynamic parameters.

2. The method according to claim 1, characterized in that: The method further comprises: If the first judgment result indicates m The prediction error obtained by the first iteration is m If the difference between the prediction errors obtained after -1 iterations is greater than the first accuracy threshold, the iteration is continued to obtain the intermediate value of the robot joint torque, and the prediction error is updated according to the intermediate value of the robot joint torque.

3. The method according to claim 1, characterized in that: According to the said m The prediction error of the iteration, the observation matrix and the expression of the mean and covariance of the kinetic parameters are obtained to obtain the mean and covariance of the kinetic parameters, including: in, is the mean value of the kinetic parameters, is the covariance of the kinetic parameters, is the observation matrix, for The transpose of is the covariance matrix of the forecast error, is the actual value of the robot joint torque, is the prior covariance matrix of the kinetic parameters, is the prior mean of the kinetic parameters.

4. The method according to claim 2, characterized in that: The updating of the prediction error according to the intermediate value of the robot joint torque comprises: in, is the prediction error, is the actual value of the torque of the robot’s ith joint, is the intermediate value of the robot joint torque, for The dimension of The number of rows in the matrix, For the robot i The prediction error of each joint is , Is a positive integer.

5. The method according to claim 1, characterized in that The method further comprises: According to the mean value of the dynamic parameters and the observation matrix, the target value of the robot joint torque is obtained through the dynamic model, and the dynamic model can be expressed by the following formula: in, is the target value of the robot joint torque, is the observation matrix, is the mean value of the kinetic parameters.

6. The method according to claim 3, characterized in that The method further comprises: The prediction error has a mean of zero and a covariance matrix of The covariance matrix of the forecast error is It can be calculated as follows: is the covariance matrix of the forecast error, for The prediction error of the torque of each joint of the robot at time Indicates the number of data points collected. is the identity matrix.

7. The method according to claim 1, characterized in that The method further comprises: The dynamic parameters include inertia tensor parameters, first-order matrix parameters, mass parameters, total inertia matrix parameters of the motor and gear, and friction parameters.

8. An industrial robot dynamic parameter uncertainty analysis device, characterized in that: The expression of the mean value and the expression of the covariance of the kinetic parameters are obtained in advance by Bayesian formula and kinetic equation reasoning; the device comprises: The acquisition module is used to acquire the actual value of the robot joint torque; set the first prediction error according to the actual value of the robot joint torque; m -1 iterations to obtain the intermediate value of the robot joint torque and the actual value of the robot joint torque, and obtain the m The prediction error of the iteration; The judgment module is used to judge the m The prediction error of the first iteration is m -1 iterations of the prediction error is less than the first accuracy threshold, and a first judgment result is obtained, wherein: m is a positive integer; if the first judgment result represents the m The prediction error of the first iteration is m The difference between the prediction errors of the first and second iterations is less than the first accuracy threshold. m The prediction error of the iteration, the observation matrix and the expression of the mean and covariance of the kinetic parameters are obtained to obtain the mean and covariance of the kinetic parameters; A control module, used to obtain a target value of the robot joint torque according to the mean value of the dynamic parameters and the observation matrix; and to control the industrial robot using the target value of the robot joint torque; The analysis module is used to perform uncertainty analysis on industrial robots based on the covariance of dynamic parameters.

9. A computing device, characterized in that including memory and processor; One or more computer programs are stored in the memory, and the one or more computer programs include instructions; when the instructions are executed by the processor, the computing device executes the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium is used to store a computer program, and the computer program is used to execute the method according to any one of claims 1 to 7.

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