Feed-forward control industrial robot dynamic friction force model and measuring method

Abstract

The invention relates to the technical field of industrial robot control, in particular to a feed-forward control industrial robot dynamic friction force model and a measuring method. The method comprises a joint friction force model, and the joint friction force model is divided into a low-speed section speed-friction torque cubic polynomial fitting model and a high-speed section speed-friction torque cubic polynomial fitting model; the method comprises the following steps: robot joint speed interval division and maximum speed percentage calculation; robot joint friction torque measurement in a heat engine state; fitting a speed-friction torque curve by adopting a low-speed and high-speed segmented cubic polynomial; and determining the optimal time shift of the theoretical curve and the actual curve after the friction torque is added into the kinetic model. According to the method, all data of the whole constant-speed section are utilized, so that the friction torque result at the corresponding speed is more accurate, and finally, the model well describes the friction torque performance of the robot in the low-speed section and the high-speed section.

Description

Technical Field

[0001] The invention relates to the technical field of industrial robot control, and in particular to a feedforward controlled industrial robot dynamic friction model and a measuring method. Background Art

[0002] In industrial robot control, an accurate friction model is crucial to improving the dynamic response and positioning accuracy of the robot. However, existing friction models often have problems of insufficient accuracy or limited scope of application, especially in the low-speed and high-speed sections, where the performance of friction torque varies significantly and is difficult to accurately describe with a single model. The Coulomb viscosity model is simple but inaccurate, especially at low speeds; the nonlinear continuous model has good continuity and is not easily distorted during commutation, but six parameters need to be identified and the operation is complicated; although the complete model takes speed, temperature and load into consideration, the design experiment is cumbersome, the control of external conditions is demanding, and the temperature is difficult to synchronize during real-time control; the dynamic characteristic model differentially models the two friction surfaces, and the parameters are difficult to obtain and the versatility is poor. In summary, the existing models are either simple but inaccurate, or sophisticated but difficult to apply industrially. Chinese patent CN113051673A proposes an improved Stribeck friction model identification method to improve the accuracy and control performance of the dynamic model. However, this scheme still has problems of insufficient utilization of measurement data and torque lag, and does not effectively analyze the relationship between time shift and average residual, making it difficult to accurately compensate for the offset time, which affects the dynamic following performance of the robot. Summary of the invention

[0003] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a feedforward controlled industrial robot dynamic friction model and a measuring method.

[0004] The technical solution adopted by the present invention is as follows: A feedforward controlled industrial robot dynamic friction model, including joint friction model , joint friction model It is divided into a cubic polynomial fitting model of speed-friction torque in the low speed section, a cubic polynomial fitting model of speed-friction torque in the high speed section, and a joint friction model The calculation formula is as follows: (1) Where: , , , are the coefficients of the cubic polynomial of speed-friction torque in the low speed section respectively; , , , They are the cubic polynomial coefficients of speed-friction torque in high-speed section respectively; It is the maximum speed in the low speed section.

[0005] This technical solution describes the friction torque relationship of the joint at different speeds through segmented processing and cubic polynomial fitting, thereby improving the accuracy and efficiency of robot control; by accurately modeling and predicting the friction torque, feedforward control is more effectively achieved. Specifically, the change of joint friction torque with speed is usually nonlinear, especially showing different characteristics in the low-speed and high-speed segments; by dividing the friction model into a low-speed segment and a high-speed segment, and fitting it with a cubic polynomial, this nonlinear relationship is more accurately described; the speed-friction torque cubic polynomial fitting model of the low-speed segment and the high-speed segment respectively captures the change law of the friction torque in different speed ranges; the maximum speed of the low-speed segment is the key parameter to distinguish the low-speed segment from the high-speed segment, by defining the speed range of the low-speed segment and deciding when to switch from the low-speed segment model to the high-speed segment model; by accurately setting the maximum speed of the low-speed segment, a smooth transition of the model between different speed segments is ensured, thereby avoiding mutations and instability in the control process; the compensation torque is added to the feedforward control signal to offset the influence of the friction torque, significantly improving the robot's motion accuracy and efficiency.

[0006] In addition, the industrial robot dynamic friction force model and determination method proposed by the present invention for feedforward control also have the following additional technical features: According to one embodiment of the present invention, the low-speed segment speed-friction torque cubic polynomial fitting model and the high-speed segment speed-friction torque cubic polynomial fitting model are connected by a smooth transition function to ensure the continuity and smoothness of the friction torque in the entire speed range; The smooth transition function is based on the current speed relative to the maximum speed of the low speed segment. The ratio is dynamically adjusted to avoid sudden changes in the calculation of the friction torque when transitioning between the low-speed section and the high-speed section.

[0007] The smooth transition function of the technical solution ensures the continuity and smoothness of the friction torque in the entire speed range in the speed-friction torque cubic polynomial fitting model connecting the low-speed section and the high-speed section, thereby avoiding jitter or instability during the movement of the robot; the accuracy of the model is improved by optimizing the parameters and form of the smooth transition function.

[0008] According to one embodiment of the present invention, the joint friction model Considering the influence of temperature on joint friction, the joint friction model is According to the temperature changes in different working environments, the speed-friction torque cubic polynomial coefficients of the low-speed section and the high-speed section are dynamically adjusted to reflect the trend of the actual friction torque changing with temperature.

[0009] This technical solution introduces a joint friction force model with a temperature coefficient, which reflects the trend of actual friction torque changing with temperature by dynamically adjusting the speed-friction torque cubic polynomial coefficients in the low-speed and high-speed sections, thereby improving the accuracy and stability of industrial robot control, especially in environments with large temperature changes. By considering the impact of temperature on joint friction, the model can more accurately predict and compensate for friction torque, thereby ensuring the smoothness of robot movement.

[0010] According to one embodiment of the present invention, the joint friction model The integrated load effect compensation mechanism dynamically adjusts the calculation parameters of the friction torque according to the load size borne by each joint of the industrial robot to compensate for the changes in friction torque caused by load changes.

[0011] The joint friction force model of this technical solution integrates a load effect compensation mechanism to compensate for the changes in friction torque caused by load changes by real-time monitoring or estimating the load borne by each joint of the industrial robot and dynamically adjusting the calculation parameters of the friction torque, thereby improving the accuracy and stability of industrial robot control, especially in application scenarios with large load changes.

[0012] To achieve the above object, the present invention also provides a method for measuring a dynamic friction force model of an industrial robot under feedforward control.

[0013] A method for determining a dynamic friction force model of an industrial robot under feedforward control comprises the following steps: S1, robot joint speed interval division and maximum speed percentage calculation; S2, measurement of friction torque of robot joints in hot state; S3, using low-speed and high-speed piecewise cubic polynomials to fit the speed-friction torque curve; S4. Determine the optimal time shift between the theoretical curve and the actual curve after the friction torque is added to the dynamic model.

[0014] This technical solution realizes the accurate measurement of the dynamic friction model of the feedforward controlled industrial robot. Specifically, firstly, through step S1, the robot joint speed interval is divided, and the maximum speed percentage of each speed interval is calculated to ensure that the change of friction torque can be accurately captured at different speeds; through step S2, the friction torque of the robot joint is measured in the hot engine state, and the hot engine state can more truly reflect the performance of the robot in actual work, thereby ensuring that the measured friction torque data has practical significance; through step S3, the speed-friction torque curve is fitted by low-speed and high-speed piecewise cubic polynomials to more accurately describe the nonlinear relationship between the friction torque and the speed change; through step S4, the optimal time shift of the theoretical curve and the actual curve after the friction torque is added to the dynamic model is determined to ensure that the theoretical model can more accurately reflect the actual robot's motion state, and the prediction performance of the model is optimized by adjusting the time shift.

[0015] According to one embodiment of the present invention, the robot joint speed interval division and maximum speed percentage calculation in step S1 include the following steps: The low speed interval is taken as the joint speed is less than 0.1rad / s, that is, the joint speed is in the range of [0,0.1]rad / s. According to the maximum speed of the joint servo motor And corresponding joint reducer The maximum speed of the robot joint is calculated by the reduction ratio The calculation formula is as follows: (2) Where: is the maximum speed of the joint servo motor, in r / min; is the reduction ratio of the joint reducer.

[0016] This technical solution achieves scientific division of robot joint speed ranges and accurate calculation of maximum speed through in-depth understanding and analysis of the robot joint motion characteristics and accurate grasp of the performance parameters of key components.

[0017] According to one embodiment of the present invention, the measurement of the friction torque of the robot joint in the hot state of step S2 includes the following steps: For the positive measurement starting position, is the end position of the positive measurement, For sports The robot position after the angle, is the angle of the starting position from the zero position of the 2 axes. , when collecting its speed-friction torque data, the following steps are included: S21, lock all joints except the movement, control joints by Percentage of maximum speed from Forward movement to , , collect the torque curve and speed curve data from the beginning to the end, remove the torque data of the acceleration and deceleration section, and record the torque data of the uniform speed section For the following sequence: (3) If the joint The axis is in the same direction as gravity. When the joint moves at a constant speed, the joint torque only includes the friction torque, which is in the middle position. Positive joint torque for: (4) Where: For joints Forward movement to The joint torque at is the friction torque at the corresponding speed; If the joint The axis cannot be adjusted to the direction of gravity, because the joint moves at a constant speed, and the joint torque includes friction and gravity, which is in the middle position. Positive joint torque for: (5) Where: For joints Forward motion time The joint torque, Forward movement of the joint to The gravitational moment at angle , is the friction torque at the corresponding speed; S22, lock other joints and control joints by Percentage of maximum speed from Reverse movement to , collect the torque curve and speed curve data from the beginning to the end, remove the torque data of the acceleration and deceleration section, and record the torque data of the uniform speed section For the following sequence: (6) If the joint The axis is in the same direction as gravity. When the joint moves at a constant speed, the joint torque only includes the friction torque, which is in the middle position. Reverse joint torque for: (7) Where: For joints Reverse movement to The joint torque at is the friction torque at the corresponding speed; If the joint The axis cannot be adjusted to the direction of gravity, because the joint moves at a constant speed, and the joint torque includes friction and gravity. Reverse joint torque for: (8) Where: For joints Reverse movement to The joint torque at Reverse the joint movement to The gravitational moment at angle , is the friction torque at the corresponding speed; S23, calculate the friction torque value of each joint, for the joints whose axis is in the same direction as the gravity or adjusted to the same direction , according to formula (3), its friction torque The calculation formula is: (9) For joints whose axis cannot be adjusted to the direction of gravity , because the industrial robot uses a high-precision reducer and is evenly lubricated in the hot state, the friction torque of the robot is considered to be approximately equal at the same joint speed, that is, according to formula (5) and formula (8): (10) Also because: (11) Combining formula (10) and formula (11), we get: (12) Formula (12) calculates an intermediate point The friction torque value of , according to the series in formula (3) and formula (6), for any intermediate point, There is one in the forward motion array that matches The corresponding torque data can be used to deduce the friction torque value under the entire uniform motion. for: (13) In this way, the friction torque of each joint axis of the robot at low speed and high speed can be measured and calculated.

[0018] This technical solution can accurately measure the friction torque of the robot joint in the hot engine state by accurately controlling the joint movement, collecting and analyzing data, and eliminating interference factors. Specifically, first of all, considering that the robot joint is affected by other factors such as gravity and inertia in addition to the friction torque during the movement, these interference factors need to be eliminated in order to accurately measure the friction torque. In steps S21 and S22, by locking other joints except the moving joints, it is ensured that only the target joint is moving, thereby simplifying the problem; in order to obtain the friction torque of the joint at different speeds, the joint is controlled to move forward and reverse at a certain percentage of the maximum speed, and its torque curve and speed curve data are collected. Since the data of the acceleration and deceleration section is affected by factors such as inertia, this part of the data is eliminated, and only the data of the uniform speed section is retained for analysis; in the uniform motion state, if the joint axis is in the same direction as the gravity, then the joint torque only includes the friction torque. At this time, the friction torque is calculated directly by measuring the joint torque; however, in practical applications, the axis of many joints cannot be adjusted to the same direction as gravity. In this case, the joint torque includes the gravity term in addition to the friction torque; to accurately calculate the friction torque, it is necessary to first determine the size of the gravity term; to eliminate the influence of the gravity term, the forward and reverse motion measurement method is used. By comparing the joint torques at the middle position of the forward and reverse motions, the size of the gravity term is calculated; using this gravity term and the measured joint torque, the friction torque is calculated; to obtain the friction torque value under the entire uniform motion, the series processing method is used; based on the measured torque series, the friction torque value under the entire uniform motion is derived, which not only reflects the friction torque characteristics of the joint at different speeds, but also provides important data support for the subsequent establishment of the dynamic model.

[0019] According to one embodiment of the present invention, the step S3 of fitting the speed-friction torque curve using low-speed and high-speed piecewise cubic polynomials includes the following steps: For a given speed-friction torque point , put it into formula (1) and perform cubic polynomial fitting, then we get the following matrix: Description format: (14) Where: is the polynomial coefficient vector to be determined, is the predicted torque value, the right side of the equation The matrix is ​​the coefficient matrix ; Polynomial fitting is used to find the coefficient vector , so that the predicted moment value The actual torque value Closest, in order to minimize the deviation between the predicted value and the true value, the least squares method is used to find the minimum coefficient vector so that: (15) The solution is obtained by the following matrix operation: (16) The cubic polynomial speed-friction torque coefficient of each joint of the robot in the low speed section and the high speed section is obtained by formula (16).

[0020] This technical solution achieves accurate description and solution of the speed-friction torque curve by adopting cubic polynomial fitting and least square method.

[0021] According to one embodiment of the present invention, the step S4 of determining the optimal time shift between the theoretical curve and the actual curve after the friction torque is added to the dynamic model includes the following steps: Assume that the control cycle of the servo is , the data queue of theoretical data is , the length is , the data queue of the measured torque is , the length is , let the offset time be ,but: (17) According to formula (17), the following optimization function is constructed: (18) Where: is the total time of trajectory motion, Offset in multiples of the control period; The average residual of the actual torque curve at each time node offset is calculated in sequence, and then the minimum value of the average residual is determined to obtain the optimal solution of formula (18).

[0022] This technical solution realizes accurate determination of the optimal time shift of the theoretical curve and the actual curve after the friction torque is added to the dynamic model by constructing an optimization function and solving the optimal solution.

[0023] Compared with the prior art, the present invention has the following beneficial effects: (1) By utilizing all the data of the entire uniform speed segment, the friction torque results at the corresponding speed are more accurate. Finally, the model better describes the friction torque performance of the robot in the low and high speed segments.

[0024] (2) In order to solve the problem of actual torque value lag when torque feedforward control is performed after the friction torque term is added to the robot dynamics model, the relationship between the time shift and the average residual of the curve is analyzed to find the curve with the optimal time shift. By compensating the controller for the offset time, the torque feedforward control of the robot is realized, which greatly improves the dynamic following performance of the robot and lays the foundation for the robot to be used in high-speed and high-precision applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a flow diagram of the method of the present invention.

[0026] Figure 2 It is a schematic diagram of joint torque measurement of the present invention.

[0027] Figure 3 It is a cubic polynomial curve in the low speed section.

[0028] Figure 4 It is a cubic polymorphic curve diagram of the high-speed section.

[0029] Figure 5 It is a graph of the theory and actual motion of a single axis.

[0030] Figure 6 It is a 2-axis single-axis motion theory and actual curve diagram.

[0031] Figure 7 It is a 1-axis single-axis time-shift-average residual curve.

[0032] Figure 8 It is a 2-axis single-axis time-shift-average residual curve.

[0033] Fig. 9 It is the optimal time-shift torque curve of axis 1.

[0034] Fig.10 It is the optimal time-shift torque curve of 2 axes. DETAILED DESCRIPTION

[0035] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0036] Example 1 like Figure 1 As shown, this embodiment provides a feedforward controlled industrial robot dynamic friction model, including a joint friction model , joint friction model It is divided into a cubic polynomial fitting model of speed-friction torque in the low speed section, a cubic polynomial fitting model of speed-friction torque in the high speed section, and a joint friction model The calculation formula is as follows: (1) Where: , , , are the coefficients of the cubic polynomial of speed-friction torque in the low speed section respectively; , , , They are the cubic polynomial coefficients of speed-friction torque in high-speed section respectively; It is the maximum speed in the low speed section.

[0037] This technical solution describes the friction torque relationship of the joint at different speeds through segmented processing and cubic polynomial fitting, thereby improving the accuracy and efficiency of robot control; by accurately modeling and predicting the friction torque, feedforward control is more effectively achieved. Specifically, the change of joint friction torque with speed is usually nonlinear, especially showing different characteristics in the low-speed and high-speed segments; by dividing the friction model into a low-speed segment and a high-speed segment, and fitting it with a cubic polynomial, this nonlinear relationship is more accurately described; the speed-friction torque cubic polynomial fitting model of the low-speed segment and the high-speed segment respectively captures the change law of the friction torque in different speed ranges; the maximum speed of the low-speed segment is the key parameter to distinguish the low-speed segment from the high-speed segment, by defining the speed range of the low-speed segment and deciding when to switch from the low-speed segment model to the high-speed segment model; by accurately setting the maximum speed of the low-speed segment, a smooth transition of the model between different speed segments is ensured, thereby avoiding mutations and instability in the control process; the compensation torque is added to the feedforward control signal to offset the influence of the friction torque, significantly improving the robot's motion accuracy and efficiency.

[0038] In addition, the industrial robot dynamic friction force model and determination method proposed by the present invention for feedforward control also have the following additional technical features: According to one embodiment of the present invention, the low-speed segment speed-friction torque cubic polynomial fitting model and the high-speed segment speed-friction torque cubic polynomial fitting model are connected by a smooth transition function to ensure the continuity and smoothness of the friction torque in the entire speed range; The smooth transition function is based on the current speed relative to the maximum speed of the low speed segment. The ratio is dynamically adjusted to avoid sudden changes in the calculation of the friction torque when transitioning between the low-speed section and the high-speed section.

[0039] The smooth transition function of the technical solution ensures the continuity and smoothness of the friction torque in the entire speed range in the speed-friction torque cubic polynomial fitting model connecting the low-speed section and the high-speed section, thereby avoiding jitter or instability during the movement of the robot; the accuracy of the model is improved by optimizing the parameters and form of the smooth transition function.

[0040] According to one embodiment of the present invention, the joint friction model Considering the influence of temperature on joint friction, the joint friction model is According to the temperature changes in different working environments, the speed-friction torque cubic polynomial coefficients of the low-speed section and the high-speed section are dynamically adjusted to reflect the trend of the actual friction torque changing with temperature.

[0041] This technical solution introduces a joint friction force model with a temperature coefficient, which reflects the trend of actual friction torque changing with temperature by dynamically adjusting the speed-friction torque cubic polynomial coefficients in the low-speed and high-speed sections, thereby improving the accuracy and stability of industrial robot control, especially in environments with large temperature changes. By considering the impact of temperature on joint friction, the model can more accurately predict and compensate for friction torque, thereby ensuring the smoothness of robot movement.

[0042] According to one embodiment of the present invention, the joint friction model The integrated load effect compensation mechanism dynamically adjusts the calculation parameters of the friction torque according to the load size borne by each joint of the industrial robot to compensate for the changes in friction torque caused by load changes.

[0043] The joint friction force model of this technical solution integrates a load effect compensation mechanism to compensate for the changes in friction torque caused by load changes by real-time monitoring or estimating the load borne by each joint of the industrial robot and dynamically adjusting the calculation parameters of the friction torque, thereby improving the accuracy and stability of industrial robot control, especially in application scenarios with large load changes.

[0044] Example 2 like Figure 1 As shown, this embodiment provides a method for determining a dynamic friction force model of an industrial robot under feedforward control, comprising the following steps: S1, robot joint speed interval division and maximum speed percentage calculation; S2, measurement of friction torque of robot joints in hot state; S3, using low-speed and high-speed piecewise cubic polynomials to fit the speed-friction torque curve; S4. Determine the optimal time shift between the theoretical curve and the actual curve after the friction torque is added to the dynamic model.

[0045] This technical solution realizes the accurate measurement of the dynamic friction model of the feedforward controlled industrial robot. Specifically, firstly, through step S1, the robot joint speed interval is divided, and the maximum speed percentage of each speed interval is calculated to ensure that the change of friction torque can be accurately captured at different speeds; through step S2, the friction torque of the robot joint is measured in the hot engine state, and the hot engine state can more truly reflect the performance of the robot in actual work, thereby ensuring that the measured friction torque data has practical significance; through step S3, the speed-friction torque curve is fitted by low-speed and high-speed piecewise cubic polynomials to more accurately describe the nonlinear relationship between the friction torque and the speed change; through step S4, the optimal time shift of the theoretical curve and the actual curve after the friction torque is added to the dynamic model is determined to ensure that the theoretical model can more accurately reflect the actual robot's motion state, and the prediction performance of the model is optimized by adjusting the time shift.

[0046] According to one embodiment of the present invention, at present, in the national standards in the field of robots, there is no general provision for the low-speed and high-speed boundary values ​​of robot joint speeds. The low speed and high speed of the robot are usually defined according to the specific robot type, application scenario and safety standards. In actual use, generally, for industrial robots, the low speed of joint movement is within 0.1-0.5rad / s, and the high speed usually exceeds 1rad / s. The present invention takes the low-speed interval as the joint speed is less than 0.1rad / s, that is, the joint speed is low in the range of [0,0.1]rad / s. Since the nonlinear effect of friction is more significant in the low-speed section, the speed value in the low-speed section should be more dense, that is, in the low-speed section, the joint speed should increase slowly. After determining the low-speed interval of the robot, the maximum speed value in the high-speed interval of the robot joint should be determined. The present invention takes the low-speed interval as the joint speed is less than 0.1rad / s, that is, the joint speed is low in the range of [0,0.1]rad / s. Since the nonlinear effect of friction is more significant in the low-speed section, the speed values ​​in the low-speed section should be more dense, that is, in the low-speed section, the joint speed should increase slowly. After determining the low-speed range of the robot, the maximum speed value in the high-speed range of the robot joint should be determined. The theoretical maximum speed of the robot joint is calculated in the non-weak magnetic state based on the maximum speed calibrated on the joint servo motor and the reduction ratio of the corresponding joint reducer. The calculation formula for the maximum speed of the robot joint is as follows: (2) Where: is the maximum speed of the joint servo motor, in r / min; is the reduction ratio of the joint reducer.

[0047] When using a teach pendant to control the movement of the robot joints in automatic mode, it is necessary to set the maximum speed percentage of the robot's operation. Since the maximum speed percentage of the teach pendant mostly increases at a rate of 1%, it cannot be adjusted to a decimal place, so when this mode is used for control, the speed value in the low-speed range is small. For example, when the robot is 0.1rad / s, the corresponding maximum speed percentage is 3%. Then, when using the teach pendant to collect speed-friction torque data in the low-speed section, there will be only two, and the speed-friction torque characteristics of the low-speed section cannot be described. In order to solve this problem, the present invention uses serial communication to send the corresponding message code, and by changing the corresponding maximum speed percentage at the current speed in the open source controller, the maximum speed percentage changes according to the set equal interval value. For example, the 50kg load robot 1 axis used in this test uses the TDA180-19115GA1-11B00 model motor of Qingneng Dechuang, and its motor parameters are shown in Table 1: Table 1 TDA180-19115GA1-11B00 model motor parameter table

[0048] The interval division principle adopted by the present invention is to divide the low-speed section into dense and uniform intervals, and divide the high-speed section into sparse and uniform intervals. Specifically, the low-speed interval [0,0.1] rad / s is divided into Speed ​​collection at each point, in high-speed section rad / s The speed of each point is collected. and The larger the value of is, the more point data is obtained, but considering the time cost, and The value of should not be too large.

[0049] This technical solution achieves scientific division of robot joint speed ranges and accurate calculation of maximum speed through in-depth understanding and analysis of the robot joint motion characteristics and accurate grasp of the performance parameters of key components.

[0050] According to one embodiment of the present invention, the measurement of the friction torque of the robot joint in the hot state of step S2 includes the following steps: The premise of fitting the model parameters is to first obtain the friction torque data of each joint of the robot at low and high speeds. However, since temperature affects the viscosity of the lubricating oil between the joints, it further affects the friction torque of the robot's joints. Unlike other solutions that take temperature into account in the model, the present invention measures the friction torque of the robot's joints in a hot engine state based on the actual operating conditions of the robot. The present invention directly reads the torque data of the robot during operation from the servo drive, but in addition to friction, the joints of the robot are also affected by factors such as gravity, inertia and Coriolis force during movement. Therefore, when measuring friction, it is necessary to balance or reduce the effects of these factors.

[0051] When the joints move at a uniform speed, the inertial force and the Coriolis force are small and can be ignored. Therefore, the present invention collects torque data when the joints move at a uniform speed. For joint axes whose rotation axis is in the same direction as the gravity, the joints are not affected by gravity. Therefore, to control the robot joints to rotate in a larger range, it is sufficient to directly collect the torque data of the uniform speed segment; for joint axes whose rotation axis is different from the gravity direction but can be adjusted to the gravity direction, the present invention first adjusts the initial position of the joint axis to the gravity direction, and then collects the torque data of the uniform speed segment; for joint axes whose rotation axis is different from the gravity direction and cannot be adjusted to be consistent with the gravity direction, in order to eliminate the influence of gravity, the present invention proposes a joint torque gravity balance measurement method. Taking the 2 axes of the robot as an example, its schematic diagram is shown as follows Figure 2 As shown in the figure, For the positive measurement starting position, is the end position of the positive measurement, For sports The robot position after the angle, is the angle of the starting position from the zero position of the 2 axes. , when collecting its speed-friction torque data, the following steps are included: S21, lock all joints except the movement, control joints by Percentage of maximum speed from Forward movement to , , collect the torque curve and speed curve data from the beginning to the end, remove the torque data of the acceleration and deceleration section, and record the torque data of the uniform speed section For the following sequence: (3) If the joint The axis is in the same direction as gravity. When the joint moves at a constant speed, the joint torque only includes the friction torque, which is in the middle position. Positive joint torque for: (4) Where: For joints Forward movement to The joint torque at is the friction torque at the corresponding speed; If the joint The axis cannot be adjusted to the direction of gravity, because the joint moves at a constant speed, and the joint torque includes friction and gravity, which is in the middle position. Positive joint torque for: (5) Where: For joints Forward motion time The joint torque, Forward movement of the joint to The gravitational moment at angle , is the friction torque at the corresponding speed; S22, lock other joints and control joints by Percentage of maximum speed from Reverse movement to , collect the torque curve and speed curve data from the beginning to the end, remove the torque data of the acceleration and deceleration section, and record the torque data of the uniform speed section For the following sequence: (6) If the joint The axis is in the same direction as gravity. When the joint moves at a constant speed, the joint torque only includes the friction torque, which is in the middle position. Reverse joint torque for: (7) Where: For joints Reverse movement to The joint torque at is the friction torque at the corresponding speed; If the joint The axis cannot be adjusted to the direction of gravity, because the joint moves at a constant speed, and the joint torque includes friction and gravity. Reverse joint torque for: (8) Where: For joints Reverse movement to The joint torque at Reverse the joint movement to The gravitational moment at angle , is the friction torque at the corresponding speed; S23, calculate the friction torque value of each joint, for the joints whose axis is in the same direction as the gravity or adjusted to the same direction , according to formula (3), its friction torque The calculation formula is: (9) For joints whose axis cannot be adjusted to the direction of gravity , because the industrial robot uses a high-precision reducer and is evenly lubricated in the hot state, the friction torque of the robot is considered to be approximately equal at the same joint speed, that is, according to formula (5) and formula (8): (10) Also because: (11) Combining formula (10) and formula (11), we get: (12) Formula (12) calculates an intermediate point The friction torque value of , according to the series in formula (3) and formula (6), for any intermediate point, There is one in the forward motion array that matches The corresponding torque data can be used to deduce the friction torque value under the entire uniform motion. for: (13) In this way, the friction torque of each joint axis of the robot at low speed and high speed can be measured and calculated.

[0052] This technical solution can accurately measure the friction torque of the robot joint in the hot engine state by accurately controlling the joint movement, collecting and analyzing data, and eliminating interference factors. Specifically, first of all, considering that the robot joint is affected by other factors such as gravity and inertia in addition to the friction torque during the movement, these interference factors need to be eliminated in order to accurately measure the friction torque. In steps S21 and S22, by locking other joints except the moving joints, it is ensured that only the target joint is moving, thereby simplifying the problem; in order to obtain the friction torque of the joint at different speeds, the joint is controlled to move forward and reverse at a certain percentage of the maximum speed, and its torque curve and speed curve data are collected. Since the data of the acceleration and deceleration section is affected by factors such as inertia, this part of the data is eliminated, and only the data of the uniform speed section is retained for analysis; in the uniform motion state, if the joint axis is in the same direction as the gravity, then the joint torque only includes the friction torque. At this time, the friction torque is calculated directly by measuring the joint torque; however, in practical applications, the axis of many joints cannot be adjusted to the same direction as gravity. In this case, the joint torque includes the gravity term in addition to the friction torque; to accurately calculate the friction torque, it is necessary to first determine the size of the gravity term; to eliminate the influence of the gravity term, the forward and reverse motion measurement method is used. By comparing the joint torques at the middle position of the forward and reverse motions, the size of the gravity term is calculated; using this gravity term and the measured joint torque, the friction torque is calculated; to obtain the friction torque value under the entire uniform motion, the series processing method is used; based on the measured torque series, the friction torque value under the entire uniform motion is derived, which not only reflects the friction torque characteristics of the joint at different speeds, but also provides important data support for the subsequent establishment of the dynamic model.

[0053] According to one embodiment of the present invention, the step S3 of fitting the speed-friction torque curve using low-speed and high-speed piecewise cubic polynomials includes the following steps: The torque data collected by the present invention is the thousandth of the rated torque of the motor. Before fitting the curve, the collected torque data needs to be converted into the international unit system (Nm). For a given speed-friction torque point , put it into formula (1) and perform cubic polynomial fitting, then we get the following matrix: Description format: (14) Where: is the polynomial coefficient vector to be determined, is the predicted torque value, the right side of the equation The matrix is ​​the coefficient matrix ; Polynomial fitting is used to find the coefficient vector , so that the predicted moment value The actual torque value Closest, in order to minimize the deviation between the predicted value and the true value, the least squares method is used to find the minimum coefficient vector so that: (15) The solution is obtained by the following matrix operation: (16) The cubic polynomial speed-friction torque coefficient of each joint of the robot in the low speed section and the high speed section is obtained by formula (16). Taking the 1st axis of the 50kg robot as an example, the friction torque curves of the low speed and high speed sections are fitted as follows: Figure 3 and Figure 4 As shown in the figure, the curve of the low-speed section is close to the true value at most speeds, and the curve of the high-speed section is very close to the true value. Because the robot is in high-speed motion in most cases, this friction model is used in the actual working production environment of the robot.

[0054] This technical solution achieves accurate description and solution of the speed-friction torque curve by adopting cubic polynomial fitting and least square method.

[0055] According to one embodiment of the present invention, the step S4 of determining the optimal time shift between the theoretical curve and the actual curve after the friction torque is added to the dynamic model includes the following steps: The ultimate purpose of adding friction torque term to the dynamic model is to perform torque feedforward control. However, during control, due to factors such as the communication delay of the servo communication cycle and the bandwidth limitation of the control loop, the command torque value actually executed by the servo lags behind the theoretical torque value calculated by the dynamic model, which is inconsistent with the concept of feedforward control. Figure 5 After the robot uses the above method to compensate for the friction torque, the single-axis motion of the robot with the axis in the same direction as the gravity is given ( Figure 5 ) and 2-axis single-axis motion where the axis cannot be adjusted to the direction of gravity ( Figure 6 )'s actual torque curve and theoretical torque curve. Figure 5 and Figure 6 In the figure, the horizontal axis is time, the vertical axis is the rated torque of the motor in thousandths, wherein axis 1 moves from -90 degrees to 90 degrees, axis 2 moves from -60 degrees to 60 degrees, the blue line is the theoretical torque value after compensating for the friction torque under the thermal engine, and the green line is the measured torque value. As can be seen from the figure, the theoretical value curve after compensating for the friction torque is consistent with the actual value in both value and trend, but there is a time lag phenomenon. In order to solve this problem, the present invention proposes to use the minimum average residual as the optimization index, analyze the time shift-average residual curve of the theoretical torque and the actual torque, and find the optimal time shift.

[0056] Assume that the control cycle of the servo is , the data queue of theoretical data is , the length is , the data queue of the measured torque is , the length is , let the offset time be ,but: (17) According to formula (17), the following optimization function is constructed: (18) Where: is the total time of trajectory motion, Offset in multiples of the control period; The average residual of the actual torque curve at each time node offset is calculated in sequence, and then the minimum value of the average residual is determined to obtain the optimal solution of formula (18). Taking the above data as an example, the time shift-average residual curve obtained is as follows: Figure 7 and Figure 8 As shown. Figure 7 and Figure 8 As shown in the figure, the actual torque curve of axis 1 has the best average residual value after the time shift of 78.125ms, and the actual torque curve of axis 2 has the best average residual value after the time shift of 81.25ms. Fig. 9 and Fig.10 As shown. Fig. 9 and Fig.10 It is known that the high-speed and low-speed two-stage speed-friction torque cubic polynomial model established by the present invention has good effects on the axis that can be adjusted in the single-axis direction to be the same as or different from the gravity direction. Finally, the present invention performs well in the dynamic torque feedforward control of a 50kg robot after adding friction torque, reducing the dynamic response of the original servo loop from 80ms to 50ms, greatly improving the dynamic tracking ability of the robot at high speed.

[0057] This technical solution solves the optimal solution by constructing an optimization function, and accurately determines the optimal time shift between the theoretical curve and the actual curve after the friction torque is added to the dynamic model. The friction torque model and measurement method used for feedforward control of robots cover the fields of robot joint friction compensation and torque feedforward control. The modeling of similar robot joint friction models and torque feedforward control using similar optimal time shifts are all within the scope of protection of this patent. During implementation, the low-speed section of the robot is densely divided at equal intervals, and the high-speed section is evenly divided at equal intervals to construct a two-segment cubic polynomial robot friction model; when measuring the joint friction torque, the gravity balance torque measurement method is used to calculate the friction torque using the full data of the uniform speed section due to the different directions of the axis and gravity of each axis; after integrating the friction model into the dynamic model, the optimal time shift is calculated based on the theoretical torque curve and the measured torque curve, and torque feedforward control is implemented to enhance the dynamic response of the system.

[0058] Although the present invention is described in detail by referring to the accompanying drawings and in combination with the preferred embodiments, the present invention is not limited thereto. Without departing from the spirit and essence of the present invention, a person of ordinary skill in the art may make various equivalent modifications or substitutions to the embodiments of the present invention, and these modifications or substitutions shall be within the scope of the present invention. Any person of ordinary skill in the art may easily think of changes or substitutions within the technical scope disclosed by the present invention, and these shall be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A feedforward controlled industrial robot dynamic friction model, characterized in that: Including joint friction model , joint friction model It is divided into a cubic polynomial fitting model of speed-friction torque in the low speed section, a cubic polynomial fitting model of speed-friction torque in the high speed section, and a joint friction model The calculation formula is as follows: (1) Where: , , , are the coefficients of the cubic polynomial of speed-friction torque in the low speed section respectively; , , , They are the cubic polynomial coefficients of speed-friction torque in high-speed section respectively; It is the maximum speed in the low speed section.

2. The feedforward controlled industrial robot dynamic friction model according to claim 1, characterized in that: The low-speed section speed-friction torque cubic polynomial fitting model and the high-speed section speed-friction torque cubic polynomial fitting model are connected by a smooth transition function to ensure the continuity and smoothness of the friction torque in the entire speed range; The smooth transition function is based on the current speed relative to the maximum speed of the low speed segment. The ratio is dynamically adjusted to avoid sudden changes in the calculation of the friction torque when transitioning between the low-speed section and the high-speed section.

3. The feedforward controlled industrial robot dynamic friction model according to claim 1, characterized in that: The joint friction model Considering the influence of temperature on joint friction, the joint friction model is According to the temperature changes in different working environments, the speed-friction torque cubic polynomial coefficients of the low-speed section and the high-speed section are dynamically adjusted to reflect the trend of the actual friction torque changing with temperature.

4. The feedforward controlled industrial robot dynamic friction model according to claim 1, characterized in that: The joint friction model The integrated load effect compensation mechanism dynamically adjusts the calculation parameters of the friction torque according to the load size borne by each joint of the industrial robot to compensate for the changes in friction torque caused by load changes.

5. A method for measuring a dynamic friction force model of an industrial robot with feedforward control, using the dynamic friction force model of an industrial robot with feedforward control as claimed in any one of claims 1 to 4, characterized in that: The steps include: S1, robot joint speed interval division and maximum speed percentage calculation; S2, measurement of friction torque of robot joints in hot state; S3, using low-speed and high-speed piecewise cubic polynomials to fit the speed-friction torque curve; S4. Determine the optimal time shift between the theoretical curve and the actual curve after the friction torque is added to the dynamic model.

6. The method for determining the dynamic friction force model of an industrial robot with feedforward control according to claim 5, characterized in that: The robot joint speed interval division and maximum speed percentage calculation of step S1 include the following steps: The low speed interval is taken as the joint speed is less than 0.1rad / s, that is, the joint speed is in the range of [0,0.1]rad / s. According to the maximum speed of the joint servo motor And corresponding joint reducer The maximum speed of the robot joint is calculated by the reduction ratio The calculation formula is as follows: (2) Where: is the maximum speed of the joint servo motor, in r / min; is the reduction ratio of the joint reducer.

7. The method for determining the dynamic friction force model of an industrial robot with feedforward control according to claim 6, characterized in that: The measurement of the friction torque of the robot joint in the hot state of step S2 includes the following steps: For the positive measurement starting position, is the end position of the positive measurement, For sports The robot position after the angle, is the angle of the starting position from the zero position of the 2 axes. , when collecting its speed-friction torque data, the following steps are included: S21, lock all joints except the movement, control joints by Percentage of maximum speed from Forward movement to , , collect the torque curve and speed curve data from the beginning to the end, remove the torque data of the acceleration and deceleration section, and record the torque data of the uniform speed section For the following sequence: (3) If the joint The axis is in the same direction as gravity. When the joint moves at a constant speed, the joint torque only includes the friction torque, which is in the middle position. Positive joint torque for: (4) Where: For joints Forward movement to The joint torque at is the friction torque at the corresponding speed; If the joint The axis cannot be adjusted to the direction of gravity, because the joint moves at a constant speed, and the joint torque includes friction and gravity, which is in the middle position. Positive joint torque for: (5) Where: For joints Forward motion time The joint torque, Forward movement of the joint to The gravitational moment at angle , is the friction torque at the corresponding speed; S22, lock other joints and control joints by Percentage of maximum speed from Reverse movement to , collect the torque curve and speed curve data from the beginning to the end, remove the torque data of the acceleration and deceleration section, and record the torque data of the uniform speed section For the following sequence: (6) If the joint The axis is in the same direction as gravity. When the joint moves at a constant speed, the joint torque only includes the friction torque, which is in the middle position. Reverse joint torque for: (7) Where: For joints Reverse movement to The joint torque at is the friction torque at the corresponding speed; If the joint The axis cannot be adjusted to the direction of gravity, because the joint moves at a constant speed, and the joint torque includes friction and gravity. Reverse joint torque for: (8) Where: For joints Reverse movement to The joint torque at Reverse the joint movement to The gravitational moment at angle , is the friction torque at the corresponding speed; S23, calculate the friction torque value of each joint, for the joints whose axis is in the same direction as the gravity or adjusted to the same direction , according to formula (3), its friction torque The calculation formula is: (9) For joints whose axis cannot be adjusted to the direction of gravity , because the industrial robot uses a high-precision reducer and is evenly lubricated in the hot state, the friction torque of the robot is considered to be approximately equal at the same joint speed, that is, according to formula (5) and formula (8): (10) Also because: (11) Combining formula (10) and formula (11), we get: (12) Formula (12) calculates an intermediate point The friction torque value of , according to the series in formula (3) and formula (6), for any intermediate point, There is one in the forward motion array that matches The corresponding torque data can be used to deduce the friction torque value under the entire uniform motion. for: (13) In this way, the friction torque of each joint axis of the robot at low speed and high speed can be measured and calculated.

8. The method for determining the dynamic friction force model of an industrial robot with feedforward control according to claim 7, characterized in that: The step S3 of fitting the speed-friction torque curve using low-speed and high-speed piecewise cubic polynomials includes the following steps: For a given speed-friction torque point , put it into formula (1) and perform cubic polynomial fitting, then we get the following matrix: Description format: (14) Where: is the polynomial coefficient vector to be determined, is the predicted torque value, the right side of the equation The matrix is ​​the coefficient matrix ; Polynomial fitting is used to find the coefficient vector , so that the predicted moment value The actual torque value Closest, in order to minimize the deviation between the predicted value and the true value, the least squares method is used to find the minimum coefficient vector so that: (15) The solution is obtained by the following matrix operation: (16) The cubic polynomial speed-friction torque coefficient of each joint of the robot in the low speed section and the high speed section is obtained by formula (16).

9. The method for determining the dynamic friction force model of an industrial robot with feedforward control according to claim 8, characterized in that: The step S4 of determining the optimal time shift between the theoretical curve and the actual curve after the friction torque is added to the dynamic model includes the following steps: Assume that the control cycle of the servo is , the data queue of theoretical data is , the length is , the data queue of the measured torque is , the length is , let the offset time be ,but: (17) According to formula (17), the following optimization function is constructed: (18) Where: is the total time of trajectory motion, Offset in multiples of the control period; The average residual of the actual torque curve at each time node offset is calculated in sequence, and then the minimum value of the average residual is determined to obtain the optimal solution of formula (18).

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