Improved method for intrinsic friction and torque ripple compensation using an integrated robot joint torque sensor

Abstract

The invention concerns a method for measuring torque using a torque sensor integrated in a robot arm joint (17) including the following method steps: - in a calibration step measuring torque using the integrated torque sensor and determining position and velocity and acceleration of a rotating element of the joint during no-load rotation of the joint to obtain training data; - in a training step performing linear regression analysis to obtain a correction function indicative of intrinsic dynamics of the robot arm joint; wherein the correction function is a linear combination of at least four basis functions: i. at least one frictional torque basis function that comprises a first velocity dependent sigmoid function and / or a velocity dependent linear function; and ii. at least one torque ripple basis function that comprises a first position dependent periodic function; and iii. at least one inertia basis function that comprises a first acceleration dependent linear function; and iv. at least one torque offset basis function being a constant; - in an operational measurement step measuring torque using the integrated torque sensor under load condition and obtaining a corrected torque value based on the measured torque value and the correction function.

Description

[0001] Improved method for intrinsic friction and torque ripple compensation using an integrated robot joint torque sensor The invention generally concerns the field of measuring torque using a torque sensor integrated in a robot arm joint. Additionally, the invention concerns a method for inspecting a bearing using a robot arm with integrated joint torque sensors. The invention also concerns a system for measuring torque, a robot arm comprising such system and a system for inspecting a bearing comprising such robot arm. Most of the industrial robots present in use are designed to be operated as collaborative robots (cobots) to work either in close proximity with humans or even engage in physical interaction with them. These cobots are typically equipped with inbuilt joint torque sensors in contrast to using a single force / torque sensor at the end-effector as the former offer advantages, particularly in addressing safety concerns in the event of a collision, ensuring safe levels of interaction forces. However, one major drawback with this arrangement is that the joint torque sensor measurements are inclusive of the intrinsic dynamics of the robot, that is, the torques arising from the power transmission system, additionally to the rigid body dynamics of the robot itself. While the primary contributing factors to this phenomenon are the inertia and the friction caused by the moveable parts, the ripple torque arising from the gear motion is also a prevalent source of noise in the torque measurement. Consequently, the possibility of using cobots as sensors during motion tasks, e.g., during inspections involving, for example, constant rotary motions for inspection of bearings is challenged. Currently, inspection of bearings is typically performed by humans where the bearing is rotated manually and based on the frictional torque sensed by the human the quality of the bearing is determined. Automating this inspection process with an off-the-shelf robot arm with integrated joint torque sensors poses the risk of wrongly disqualifying the product as the sensed torque also reads the intrinsic dynamics of the robot in addition to the actual frictional torques offered by the bearing. Thus, there is a need for more accurate torque measurement methods that make use of robot arm with integrated joint torque sensors. A prior art system and method to compensate for errors caused by torque disturbance in a robot arm joint is known from WO 2021 / 006038 A1. This torque compensation system comprises a data acquisition section configured to acquire a torque detected by a torque sensor attached to a robot arm and a joint angle of the robot arm when the torque sensor detects the torque. A periodic compensation function of a torque disturbance is determined and used for obtaining a compensated torque value. Against this background the problem to be solved is to provide an improved method for intrinsic friction and torque ripple compensation using a torque sensor integrated in a robot arm joint which allows to enable reliable bearing inspection using the robot arm. For solving the problem, the invention proposes a method for measuring torque using a torque sensor integrated in a robot arm joint including the following method steps: ^ in a calibration step measuring torque using the integrated torque sensor and determining position and velocity and acceleration of a rotating element of the joint during no-load rotation of the joint to obtain training data; ^ in a training step performing linear regression analysis to obtain a correction function indicative of intrinsic dynamics of the robot arm joint, wherein the correction function is a linear combination of at least four basis functions: i. at least one frictional torque basis function that comprises a first velocity dependent sigmoid function and / or a velocity dependent linear function; and ii. at least one torque ripple basis function that comprises a first position dependent periodic function; and iii. at least one inertia basis function that comprises a first acceleration dependent linear function; and iv. at least one torque offset basis function being a constant; ^ in an operational measurement step measuring torque using the integrated torque sensor under load condition and obtaining a corrected torque value based on the measured torque value and the correction function. The inventive method for measuring torque includes a calibration step in which, during no- load rotation of the joint, torque and position are measured using sensors integrated into the joint. In the training step, which can be executed either in parallel to or following the calibration step, linear regression analysis is performed on the training data. In other words, the training data acquired in the calibration step is analysed in order to obtain the correction function which is indicative of intrinsic dynamics of the robot arm joint. Because the correction function is a linear combination of several basis functions, linear regression analysis can be used to learn parameters of the correction function even though the intrinsic dynamics are nonlinear. The correction function can, in the operational measurement step following the training step, be employed to correct measured torque values and thereby obtain corrected torque values. The above-mentioned basis functions relate to the main contributions of the intrinsic dynamics of the robot arm joint. The at least one frictional torque basis function relates to the friction due to robotic joint bearings. In particular, viscous friction can be modelled as a linear function while Coulomb friction can be modelled with a sigmoid function. The at least one torque ripple basis function relates to the position-dependent torque ripple due to the robotic joint transmission. The at least one inertia basis function relates to the inertia of the transmission and the at least one torque offset basis function relates to the offset of the torque sensor. The inventors have found out that the proposed method enables high accuracy torque measurement using the torque sensor integrated into the robot arm joint. Therefore, the method is well suited for bearing quality inspection, wherein a good bearing is identified from a faulty one based on the frictional force offered during its rotation. According to a preferred embodiment of the invention, the frictional torque basis function comprises a first velocity dependent sigmoid function and a velocity dependent linear function. This embodiment comes with the benefit that both viscous friction and Coulomb friction can be represented in the frictional torque basis function. According to a preferred embodiment of the invention, the at least one frictional torque basis function further comprises a second velocity dependent sigmoid function. By using a second velocity dependent sigmoid function in addition to the first velocity dependent sigmoid function, the Coulomb friction can be modelled for both negative and positive velocities as well as zero velocity. According to a preferred embodiment of the invention, the at least one torque ripple basis function comprises a second position dependent periodic function. Even more preferably the torque ripple basis function comprises more than two position dependent periodic functions. The torque ripples of the robot arm joint, in particular of the gear mechanism of the robot arm joint, can be expressed in terms of the Fourier series. Therefore, multiple periodic functions, in particular multiple sine and cosine functions can be employed as basis functions to model the contribution of torque ripple. According to a preferred embodiment of the invention, in the calibration step, determining position and velocity and acceleration of the rotating element is carried out using a position sensor integrated in the joint. The position sensor can directly measure the absolute or relative position of the rotating element of the robot arm joint. The velocity can be obtained from the position measurement as time derivative of the position measurement, that is to say, measured indirectly. The acceleration can be obtained from the position measurement as (second) time derivative of the position measurement, that is to say, measured indirectly. The position sensor is preferably attached to rotor of an electric motor of the robot arm joint. According to a preferred embodiment of the invention the robot arm joint is part of a robot arm which is operated in a gravity compensated mode in the calibration step. In gravity compensated mode gravitational torques generated by the masses of parts of the robot can be compensated. Preferably, the robot arm joint is an end-effector joint. The robot arm joint may, e.g., be configured to rotatably connect a gripper to an arm of the robot. According to a preferred embodiment of the invention, the robot arm joint is part of a robot arm that includes further robot arm joints, wherein the further robot arm joints, in the calibration step, are operated in an impedance control mode. Preferably the further robot arm joints are operated in the impedance control mode with high stiffness. If, as mentioned above, the robot arm joint that includes the integrated torque sensor for measuring torque is an end-effector joint, the further robot arm joints preferably are all other robot arm joints of the robot arm. Preferably, those other root arm joints are operated in the impedance control mode with high stiffness. According to a preferred embodiment of the invention, the joint comprises an electric motor and / or a gear mechanism. The electric motor may be brushless DC electric motor, in particular a permanent magnet synchronous motor. Alternatively, the electric motor may be a brushed motor. The gear mechanism may be a strain wave gearing. Such strain wave gearings have high gear-reduction ratios which enable higher torque transmission in robot joints within a compact geometry. They consist of three main components namely, wave- generator, flex spline and an outer circular spline. The elliptical wave generator causes a periodic deformation of the flexspline when the strain wave gearing is operational. Preferably, the integrated torque sensor is part of the gear mechanism. If the gear mechanism is implemented as a strain wave gearing, the torque sensor is preferably integrated in a flexspline of the strain wave gearing. For solving the above-mentioned problem, the invention further provides a method for inspecting a bearing using a robot arm having a robot arm joint with an integrated torque sensor, wherein a torque measurement is carried out using a method for measuring torque as disclosed above, wherein – in the operational measurement step – the bearing is rotated using the robot arm, in particular using the robot arm joint with the integrated torque sensor, wherein the corrected torque measurement value obtained in the operational measurement step is compared to a predetermined torque threshold in order to determine if the bearing is functional or faulty. For solving the above-mentioned problem, the invention further provides a system for measuring torque comprising a robot arm joint with an integrated torque sensor, an integrated position sensor and an analysis unit that is configured to carry out the following method steps: ^ in a calibration step, obtaining training data by determining torque using torque measurement data provided by the integrated torque sensor and by determining position and velocity and acceleration of a rotating element of the joint during no-load rotation of the joint using position measurement data provided by the integrated position sensor; ^ in a training step, performing linear regression analysis to obtain a correction function indicative of intrinsic dynamics of the robot arm joint; wherein the correction function is a linear combination of at least four basis functions: i. at least one frictional torque basis function that comprises a first velocity dependent sigmoid function; and ii. at least one torque ripple basis function that comprises a first position dependent periodic function; and iii. at least one inertia basis function that comprises a first acceleration dependent linear function; and iv. at least one torque offset basis function being a constant; ^ in an operational measurement step, obtaining a corrected torque value based on measuring torque using the integrated torque sensor under load condition and based on the correction function. For solving the above-mentioned problem, the invention further provides a robot arm comprising a system for measuring torque as disclosed above. For solving the above-mentioned problem, the invention further provides system for inspecting a bearing comprising a robot arm as disclosed above and a bearing holder configured to hold the bearing during the operational measurement step. With the inventive method for inspecting a bearing and inventive system for measuring torque and inventive robot arm and inventive system for inspecting a bearing the same technical effects and advantages can be reached that have been discussed in conjunction with the inventive method for measuring torque. The preferred embodiments and preferred features presented with regard to the inventive method for measuring torque can, as such or in combination with each other, also be used in conjunction with the inventive method for inspecting a bearing and the inventive system for measuring torque and inventive robot arm and inventive system for inspecting a bearing. These and other characteristics, features and advantages of the present invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawing, which illustrates, by way of example, the principles of the invention. The description is given for the sake of example only, without limiting the scope of the invention. The reference figures quoted below refer to the attached drawing. Fig.1 shows a system for inspecting a bearing according to an embodiment of the present invention; Fig.2 shows a schematic representation of a typical robot arm joint being part of the system of Fig.1; Fig.3a shows velocity dependent sigmoid functions for modelling Coulomb friction; Fig.3b shows a velocity dependent linear function for modelling viscous friction; Fig.4 shows position dependent periodic functions for modelling torque ripple; Fig.5 shows an acceleration dependent linear function for modelling torque produced by inertia; and Fig.6 shows torque measured by the robot arm joint integrated torque sensor without and with compensation and torque measured by an external reference sensor. The present invention will be described with respect to particular embodiments and with reference to the appended drawings but the invention is not limited thereto but only by the claims. Fig.1 depicts an embodiment of a system 100 for inspecting a bearing 30, in particular a wheel bearing, comprising a robot arm 10 and a bearing holder 20 configured to hold the bearing 30 during an operational measurement step. The bearing holder 20 may be fixed to the ground so as to hold a first part of the bearing fixed when a second part of the bearing is rotated by the robot arm 10. The system 100 can be used to carry out a method for inspecting the bearing 30 using the robot arm 10. The robot arm 10 includes a robot arm joint 17 with an integrated torque sensor, wherein a torque measurement is carried out, wherein – in an operational measurement step – the bearing 30 is rotated using the robot arm 10, in particular using the robot arm joint 17 with the integrated torque sensor. The method includes obtaining a corrected torque measurement value in the operational measurement step and comparing this value to a predetermined torque threshold in order to determine if the bearing 30 is functional or faulty. In addition to the robot arm joint 17 mentioned above, the robot arm 10 of the embodiment includes further robot arm joints 11, 12, 13, 14, 15, 16 which may also include integrated torque sensors. For the method for inspecting the bearing 30, however, it is not essential that those further robot arm joints 11, 12, 13, 14, 15, 16 include torque sensors. The robot arm joint 17 mentioned above is connected to a gripper 18, here in the form of a parallel jaw gripper. Thus, the robot arm joint 17 is an end-effector joint. The gripper 18 includes jaws that conform to the shape of a bearing flange. The further robot arm joints 11, 12, 13, 14, 15, 16 can be used to align the robot arms 10 gripper axis with the rotational axis of the bearing to be tested. The bearing 30 is fastened to the bearing holder 20 and then engaged and rotated by the gripper 18. The gripper 18 will transmit the axial torque generated by the bearing reliably so that the resulting torque can be measured using the torque sensor integrated in the robot arm joint 17. In order to reliably distinguish faulty from good bearings 30, a high accuracy measurement method according to the present invention is employed. The method for measuring torque using a torque sensor integrated in a robot arm joint 17 includes the following method steps carried out by an analysis unit 40 of the system 100: ^ in a calibration step, measuring torque using the integrated torque sensor and determining position and velocity and acceleration of a rotating element of the joint 17 during no-load rotation of the joint to obtain training data; ^ in a training step, performing linear regression analysis to obtain a correction function indicative of intrinsic dynamics of the robot arm joint 17, wherein the correction function is a linear combination of at least four basis functions: i. at least one frictional torque basis function that comprises a first velocity dependent sigmoid function and / or a velocity dependent linear function; and ii. at least one torque ripple basis function that comprises a first position dependent periodic function; and iii. at least one inertia basis function that comprises a first acceleration dependent linear function; and iv. at least one torque offset basis function being a constant; ^ in an operational measurement step, measuring torque using the integrated torque sensor under load condition and obtaining a corrected torque value based on the measured torque value and the correction function. Fig.2 depicts a schematic representation of a typical robot arm joint 17 to be used in the system of Fig.1. The robot arm joint 17 includes a position sensor 1 in the form of a rotary encoder. The position sensor 1 is configured to sense the position of a rotor of an electric motor 2 of the robot arm joint 17. The joint 17 further includes gear mechanism 3 coupled to the electric motor, in particular to the rotor of the electric motor 2. Even though the gear mechanism 3 in Fig.2 is depicted to comprise toothed gear wheels, the gear mechanism 3 preferably is configured as a strain wave gearing. The gear mechanism 3 preferably includes the torque sensor, e.g., in the form of a flexspline of the strain wave gearing. The output shaft 5 of the robot arm joint 17 is rotatable in a bearing 4. The robot arm joint 17 has intrinsic dynamics which are caused by the aforementioned elements 2, 3, 4 of the robot arm joint 17. For the system in, the dynamics can be expressed as follows: Where, ^^is the electric motor output torque, ^ is the lumped inertia and ^̈^is the angular acceleration. Here, ^^is the resistance torque due to the friction of the moveable parts. This friction torque can be expressed as ^^= ^ ^̇^+ ^^where, ^̇^is the angular velocity, B is the lumped viscous friction coefficient and ^^is the Coulomb friction. The joint torque sensor, which is embedded in the robot arm joint can, e.g., be integrated in to the gear mechanism 3 or can be arranged in series with the transmission system, typically after the gear mechanism 3 and before the output bearing. The joint torque sensor measures the torque ripples generated by the gear mechanism 3 in addition to the frictional and inertial torques. Therefore, to accurately measure the external contact forces the intrinsic dynamics of the robot arm joint 17 has to be compensated. A linear regression-based learning of the joint intrinsic dynamics is performed with a set of basis functions which reflect the underlying sources of disturbance. By expressing the intrinsic dynamics (which is a nonlinear function) as a linear combination of a set of appropriately chosen basis functions (i.e. linear in the parameter space), a linear- regression can be performed to learn the parameters. For this purpose, the basis functions are selected as described in the following. With reference to Fig.3a and 3b, while the viscous friction can be modelled as a linear function (see Fig. 3b), the Coulomb friction is modelled with a non-linear discontinuous function to capture the asymmetry in its nature which is expressed as follows: To maintain the continuity in the zero-velocity vicinity, sigmoid functions can be used to approximate the coulomb friction. Thus, the frictional torques can be represented as where, ^^^, ^^^are the parameters which best fit the sigmoid functions ^^^^^ ^̇^, ^^^^−^ ^̇^ to the coulomb friction data. Here, ^ is a tuning parameter which helps control the shape of the curve in the zero-velocity region. Hence, the basis functions are chosen as which are graphically represented in Fig.3a and 3b. With reference to Fig.4, gear mechanisms particularly strain wave gearings generate ripple torques when its flexspline undergoes periodic deformation resulting in a disturbance torque in the torque sensor measurement. Being periodic in nature with respect to the angle of rotation, the ripple torque can be expressed in terms of Fourier series as ^^=[(cos(^), sin(^)) … , (cos(^^), sin(^^))] [(^^^, ^^^), … , (^^^, ^^^)]^ Therefore, we consider n harmonics of sine and cosine signals as the basis functions ^^= [(cos(^^), sin(^^)), … , (cos(^^^), sin(^^^))], as shown graphically in Fig.4. With reference to Fig.5, the inertial torque experienced by the sensor can be expressed as where, ^ represent the lumped inertia of the system. Here, the basis function is chosen = ^̈^and the parameter as ^^= ^. Apart from the robot intrinsic dynamics, the sensor reading can also be corrupted by the improper calibration of the sensor. To account for this factor, a basis function to account for the offset in the sensed torque is introduced as follows: ^^= ^^where, the basis function is ^^= 1. In the training step section, the intrinsic dynamics is estimated via linear regression with the help of a set of non-linear radial basis functions as discussed above. Each of these basis functions represent one of the contributing factor of the intrinsic dynamics. Consider the basis functions discussed above, ^ = [^^, ^^^, ^^^, ^^, ^^, ^^] such that ^ ∶ ^ → ℝ maps kinematics states x ≡ (^, ^̇, ^̈ ) into scalar torques. Given a set of measurements {^^, , a vector of ^ parameters ^ = [^^, … , ^^]^is to be determ which best fits the target data (in this case torques) ^ =[^^, … , ^^]^≡ where ^ is a vector of residuals and ^ is the design matrix, defined as Assuming a full ranked design matrix, i.e. , rank(^) = ^ < ^, the solution ^∗to the over- determined linear problem is ^∗=(^^^)^^^^^ Once the parameters have been determined then for a new robot state, the intrinsic dynamics can be predicted as: For benchmarking the inventive approach with the system 100 depicted in Fig.1, an external torque sensor in the form of a loadcell has been mounted on the load side (i.e. the bearing side). The robot arm 10 was operated in gravity compensation mode and a human operator physically guided the robot arm 10 to a suitable position to for grasping the bearing 30. Once the position was decided, the gripper 18 was controlled to grasp the adapter (to which the loadcell was connected) on the bearing 30. Since the robot arm, 10 is compliant (in gravity compensation mode) the robot arm tries and self-align with the axis of rotation of the bearing 30. Subsequently all the robot arm joints 11, 12, 13, 14, 15, 16 except the 7th robot arm joint 17 (i.e. the end effector joint) were switched into impedance control mode with a high stiffness to maintain the respective positions. This was done to avoid lifting of the robot arm 10 during the bearing 30 rotation due to possible misalignments of the axes of the robot arm joint 17 and the bearing 30. A torque which followed a trapezoidal profile was applied to the robot arm joint 17 to complete two revolutions in both clockwise and anticlockwise direction one alternatively. The kinematic parameters along with the joint torque sensor readings were logged along with the data from the external loadcell. Data collected from the robot arm joint encoder was used to compute the intrinsic dynamics which upon subtracting from the sensed torque isolated bearing torque. The obtained bearing torque was then compared against the torque read by the external load cell (that was not corrupted by the intrinsic dynamics of the robot arm 10) which is considered as the ground truth, see Fig.6. The relative error between the joint torque sensor data and the load cell before and after the intrinsic dynamics compensation is found to be 43.6 % and 8.44% respectively. Therefore, without intrinsic dynamic compensation there is a higher possibility that a good bearing is wrongly categorized as a faulty one due to the higher levels of sensed torques.

[0002] Reference signs 1 encoder 2 electric motor 3 gear mechanism 4 bearing 5 output (to load) 10 robot 11 robot arm joint 12 robot arm joint 13 robot arm joint 14 robot arm joint 15 robot arm joint 16 robot arm joint 17 robot arm joint 18 gripper 20 holder 30 bearing 40 analysis unit 100 system for inspecting a bearing A reference torque B measured torque without correction C corrected torque

Claims

Patent Claims 1. A method for measuring torque using a torque sensor integrated in a robot arm joint (17) including the following method steps: ^ in a calibration step measuring torque using the integrated torque sensor and determining position and velocity and acceleration of a rotating element of the joint during no-load rotation of the joint to obtain training data; ^ in a training step performing linear regression analysis to obtain a correction function indicative of intrinsic dynamics of the robot arm joint; wherein the correction function is a linear combination of at least four basis functions: i. at least one frictional torque basis function that comprises a first velocity dependent sigmoid function and / or a velocity dependent linear function; and ii. at least one torque ripple basis function that comprises a first position dependent periodic function; and iii. at least one inertia basis function that comprises a first acceleration dependent linear function ; and iv. at least one torque offset basis function being a constant; ^ in an operational measurement step measuring torque using the integrated torque sensor under load condition and obtaining a corrected torque value based on the measured torque value and the correction function.

2. The method according to claim 1, characterized in that the at least one frictional torque basis function comprises a first velocity dependent sigmoid function and a velocity dependent linear function.

3. The method according any of the preceding claims, characterized in that the at least one frictional torque basis function further comprises a second velocity dependent sigmoid function.

4. The method according to any of the preceding claims, characterized in that the at least one torque ripple basis function comprises a second position dependent periodic function.

5. The method according to any of the preceding claims, characterized in that, in the calibration step, determining position and velocity and acceleration of the rotating element is carried out using a position sensor integrated in the joint.

6. The method according to any of the preceding claims, characterized in that the robot arm joint is part of a robot arm which is operated in a gravity compensated mode in the calibration step.

7. The method according to any of the preceding claims, characterized in that the robot arm joint (17) is an end-effector joint.

8. The method according to any of the preceding claims, characterized in that the robot arm joint is part of a robot arm that includes further robot arm joints (11, 12, 13, 14, 15, 16), wherein the further robot arm joints (11, 12, 13, 14, 15, 16), in the calibration step, are operated in an impedance control mode.

9. The method according to claim 8, wherein the further robot arm joints (11, 12, 13, 14, 15, 16) are all other robot arm joints (11, 12, 13, 14, 15, 16) of the robot arm (10).

10. The method according to any of the preceding claims, characterized in that the joint comprises an electric motor and / or a gear mechanism.

11. A method for inspecting a bearing using a robot arm (10) having a robot arm joint (17) with an integrated torque sensor, wherein a torque measurement is carried out using a method according to any of the preceding claims, wherein – in the operational measurement step – the bearing is rotated using the robot arm, in particular using the robot arm joint (17) with the integrated torque sensor, wherein the corrected torque measurement value obtained in the operational measurement step is compared to a predetermined torque threshold in order to determine if the bearing is functional or faulty.

12. A system for measuring torque comprising a robot arm joint (17) with an integrated torque sensor, an integrated position sensor and an analysis unit that is configured to carry out the following method steps: ^ in a calibration step, obtaining training data by determining torque using torque measurement data provided by the integrated torque sensor and bydetermining position and velocity and acceleration of a rotating element of the joint during no-load rotation of the joint using position measurement data provided by the integrated position sensor; ^ in a training step, performing linear regression analysis to obtain a correction function indicative of intrinsic dynamics of the robot arm joint; wherein the correction function is a linear combination of at least four basis functions: i. at least one frictional torque basis function that comprises a first velocity dependent sigmoid function; and ii. at least one torque ripple basis function that comprises a first position dependent periodic function; and iii. at least one inertia basis function that comprises a first acceleration dependent linear function; and iv. at least one torque offset basis function being a constant; ^ in an operational measurement step, obtaining a corrected torque value based on measuring torque using the integrated torque sensor under load condition and based on the correction function.

13. A robot arm (10) comprising a system according to claim 12.

14. A system (100) for inspecting a bearing (30) comprising a robot arm according to claim 13 and a bearing holder (20) configured to hold the bearing (30) during the operational measurement step.

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