ABSTRACT
Abstract
A method of obtaining the gear stiffness of a robot joint gear of a robot joint of a robot arm, where the robot joint is connectable to at least another robot joint. The robot joint comprises a joint motor having a motor axle configured to rotate an output axle via the robot joint gear. The method comprises the steps of: âapplying a motor torque to the motor axle using the joint motor; âobtaining the angular position of the motor axle; âobtaining the angular position of the output axle; âdetermining the gear stiffness based on at least the angular position of the motor axle, the angular position of the output axle and a dynamic model of the robot arm.
Description
This application is a U.S. national stage entry of PCT application no. PCT/EP2019/074075 which was filed on Sep. 10, 2019. PCT application no. PCT/EP2019/074075 claims priority to European application no. 18194683.1 which was filed on Sep. 14, 2018. This application claims priority to both PCT application no. PCT/EP2019/074075 and to European application no. 18194683.1. Both PCT application no. PCT/EP2019/074075 and European application no. 18194683.1 are incorporated into this this application by reference.
FIELD OF THE INVENTION
The present invention relates to robot joint gears for robot arms comprising a plurality of robot joints connecting a robot base and a robot tool flange.
BACKGROUND OF THE INVENTION
Robot arms comprising a plurality of robot joints and links where motors can rotate the joints in relation to each other are known in the field of robotics. Typically, the robot arm comprises a robot base which serves as a mounting base for the robot arm and a robot tool flange where to various tools can be attached. A robot controller is configured to control the robot joints to move the robot tool flange in relation to the base. For instance, in order to instruct the robot arm to carry out a number of working instructions.
Typically, the robot controller is configured to control the robot joints based on a dynamic model of the robot arm, where the dynamic model defines a relationship between the forces acting on the robot arm and the resulting accelerations of the robot arm. Often, the dynamic model comprises a kinematic model of the robot arm, knowledge about inertia of the robot arm and other parameters influencing the movements of the robot arm. The kinematic model defines a geometric relationship between the different parts of the robot arm and may comprise information of the robot arm such as, length, size of the joints and links and can for instance be described by Denavit-Hartenberg parameters or the like. The dynamic model makes it possible for the controller to determine which torques the joint motors shall provide in order to move the robot joints for instance at specified velocity, acceleration or in order to hold the robot arm in a static posture.
On many robot arms it is possible to attach various end effectors to the robot tool flange, such as grippers, vacuum grippers, magnetic grippers, screwing machines, welding equipment, dispensing systems, visual systems etc.
In some robots the robot joint comprises a joint motor having a motor axle configured to rotate an output axle via a robot joint gear. Typically, the output axle is connected to and configured to rotate parts of the robot arm in relation to each other. The robot joint gear forms a transmission system configured to transmit torque provided by the motor axle to the output axle for instance to provide a gear ratio between the motor axle and the output axle. The robot joint gear can for instance be provided as a spur gears, planetary gears, bevel gears, worm gears, strain wave gears or other kind of transmission systems. Commonly flexibility exist in the transmissions used for industrial robots due to the elasticity various type of transmissions. This flexibility may lead to an undesired dynamic time-varying displacement between the position of parts of the robot arm.
Taking into account the gear flexibility in the dynamic model makes the dynamic model more accurately resemble the dynamics of the real robot arm because the robot joint torque originating from the gear deformation can be known. A more accurate dynamic model can for instance allow the robot controller to control the robot arm with greater accuracy and precision. A more accurate dynamic model can also allow the robot controller to more accurately identify external disturbances, for instance human interference which is of great concern in terms of safety.
Research have been devoted to accurately identify the dynamic characteristics of the robot gear systems. However, one practical issue when taking into account the joint stiffness in the robot controller design is that the joint stiffness changes with wear due to material being worn off at the gear meshing [1], [2], [3].
Estimating the joint stiffness on industrial robots have been accomplished through off-line identification procedures by several researchers. Off-line identification procedures are not well suited for solving the problem of time-varying joint stiffness. Such procedures would have to be re-run from time to time to keep the joint stiffness information up to date. While the off-line identification procedure is running the robot is unable to conduct any other task with clear negative consequences to the user. Despite the shortcomings of the off-line calibration procedures for joint stiffness estimation a number of references will be given to such off-line identification procedures applied to solve the robot joint stiffness estimation problem. For the off-line identification of joint stiffness, one method is to apply external excitation on one robot joint at a time resulting in a reduced dynamic model hence easier identification as in [4], [5], [6], [7].
Another option is to evaluate joint stiffness values using an external laser-tracking sensor system to visually track the end effector displacements for a given applied wrench as in [8] and [9], where the applied wrench is equal to the applied forced and torques at the end effector. A third option is to incorporate two absolute position rotary encoders in the robot joint to enable direct measurement of the joint deflection and then manually impose a known force at the end-effector and using the kinematic model (the Jacobian) of the robot arm to calculate the joint torques as in [9]. Such procedure however requires external and known loading of the end-effector and the robot is not allowed to move during the procedure. A fourth option is to estimate the joint stiffness using a so-called locked-link joint procedure as in [10] where the end-effector is clamped to the environment and using either motor positions measurement and motor torques data or a force/torque sensor to measure the external wrench between the clamped end effector and the environment.
Very few works are available on the on-line estimation of time-varying nonlinear stiffness e.g. AwAs-II joint [11]. These works are focused towards Variable Stiffness Actuators (VSAs) as found in in the DLR Hand Arm System [12] by the DLR Institute of Robotics and Mechatronics, however most industrial robots do not comprise a VSA. In 2011, Flacco and De Luca [13] estimated the nonlinear stiffness of robot joints using only a motor position sensor by computing a dynamic residual based on the generalized momentum followed by a least squares algorithm to estimate the stiffness parameters.
Robustness issues were later addressed in [14] by introducing a kinematic Kalman filter to handle discretization and quantization errors and a modified recursive least squares algorithm was used to better handle poor excitation conditions. The stiffness parameters were however assumed time-invariant. Further refinements of their method were carried out in [15] modifying the stiffness estimation algorithm to deal with time-varying stiffness by using a Recursive Least Squares method based on a QR decomposition (QR-RLS) able to handle time-varying stiffness characteristics. A non-causal Savitzky-Golay (SG) filter was used to remove noise on the input/output signals. No experiments did however support their findings.
In May 2013, Menard et al. [16] developed an observer capable of on-line estimating the time-varying stiffness of a VSA. Experimental analysis on the VSA system revealed parameter uncertainties of up to 25% of the true stiffness. Friction was assumed purely viscous with a single constant coefficient. Such friction model is not capable of accurately describing real frictional characteristics of most electromechanical systems, as well-known frictional characteristics such as Coulomb friction and the Stribeck effect is then neglected completely.
In July 2013, Cirillo et al. [17] demonstrated online stiffness estimation of a VSA by measuring the elastic energy using an optoelectronic sensor built into the robot joint.
SUMMARY OF THE INVENTION
The objective of the present invention is to address the above described limitations with the prior art or other problems of the prior art. This is achieved by a method of obtaining the gear stiffness of a robot joint gear as defined by the independent claim. The dependent claims describe possible embodiments of the method according to the present invention. The advantages and benefits of the present invention are described in the detailed description of the invention. Further the objective of the present invention is addressed by a method of controlling a robot arm based on the obtained gear stiffness and a robot arm with a controller configured to control the robot arm based on the obtained gear stiffness.
A robot controller taking into account the joint flexibilities may perform well right after calibration but for a good performance over the lifetime of the robot, the joint stiffness must be estimated on-line. Further, estimating the joint stiffness on-line will allow for predictive maintenance in the case of gear unit failure. In most cases, no sensor is available for directly measuring the joint stiffness, so the stiffness information is collected by combining an accurate model of the flexibility torque with the measurements available, such as position and force/torque sensor measures, either implemented in the robot or by using external hardware.
The invention provides a simple method of obtaining the gear stiffness of a robot joint gear of a robot arm without the need to integrate expensive force/torque sensors, as the joint gear stiffness of the robot joint gear can be determined based on sensors commonly used in industrial robots, which also makes it possible to integrate such method into existing industrial robots having such sensors. Additionally, the gear stiffness can be obtained online during use of the robot and thus used as an input to the dynamic model controlling the robot whereby a more accurate controlling of the robot can be provided. Consequently, vibrations and inaccuracies of the robot's movements due to gear stiffness can be accounted for when controlling the robot. Additionally, the gear stiffness changes over time primarily due to wear of the robot joint gear and obtaining the gear stiffness online makes it possible to control the robots based on changes of gear stiffness whereby the accuracy of the robot over time is maintained/improved. Further obtaining the gear stiffness online over time makes it possible to predict failure of the robot joint gear as the gear stiffness can be used to indicate when the robot joint gear is about to fail. Consequently, the robot joint gear can be sent to service in order to exchange/repair the robot joint gear whereby unplanned downtime of the robot can be reduced.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates a robot arm configured to obtain the gear stiffness of the robot joint gears;
FIG. 2 illustrates a schematic cross-sectional view of a robot joint;
FIG. 3 illustrates a model of a robot joint gear;
FIG. 4 illustrates a simplified structural diagram of a robot arm;
FIG. 5 illustrates a flow chart of a method of obtaining the gear stiffness of a robot joint gear of a robot joint of a robot arm;
FIG. 6 illustrates a flow chart of another method of obtaining the gear stiffness of a robot joint gear of a robot joint of a robot arm;
FIG. 7 illustrates a robot arm in a pose used in an experimental analysis of the method according to the present invention;
FIG. 8 illustrates a friction torque/velocity map obtained by imposing different signals of constant velocity on the base joint of a robot arm, while measuring the joint motor current;
FIG. 9 illustrates a flexibility torque/transmission deformation map obtained by imposing a set of known torques to the tool flange of a robot arm using a force gage and measuring the deformation as the difference between absolute joint encoder readings at each side of the robot joint gear;
FIG. 10 illustrates angular position, angular velocity and angular acceleration of the base joint of the robot arm used in the experimental analysis;
FIG. 11 illustrates a schematic representation of the Generalized Maxwell-Slip friction model;
FIG. 12 illustrates a flexibility torque/transmission deformation map obtained by the method according to the present invention;
FIG. 13 illustrates gear stiffness of the robot joint gear obtained in the experimental analysis,
DETAILED DESCRIPTION OF THE INVENTION
The present invention is described in view of exemplary embodiments only intended to illustrate the principles of the present invention. The skilled person will be able to provide several embodiments within the scope of the claims. Throughout the description, the reference numbers of similar elements providing similar effects have the same last two digits. Further it is to be understood that in the case that an embodiment comprises a plurality of the same features then only some of the features may be labeled by a reference number.
The invention can be embodied into a robot arm and is described in view of the robot arm illustrated in FIG. 1 . The robot arm 101 comprises a plurality of
robot joints
103 a , 103 b , 103 c , 103 d , 103 e , 103 f and
robot links
104 b , 104 c , 104 d connecting a robot base 105 and a robot tool flange 107 . A base joint 103 a is connected directly with a shoulder joint and is configured to rotate the robot arm around a base axis 111 a (illustrated by a dashed dotted line) as illustrated by <fi
This application is a U.S. national stage entry of PCT application no. PCT/EP2019/074075 which was filed on Sep. 10, 2019. PCT application no. PCT/EP2019/074075 claims priority to European application no. 18194683.1 which was filed on Sep. 14, 2018. This application claims priority to both PCT application no. PCT/EP2019/074075 and to European application no. 18194683.1. Both PCT application no. PCT/EP2019/074075 and European application no. 18194683.1 are incorporated into this this application by reference.
FIELD OF THE INVENTION
The present invention relates to robot joint gears for robot arms comprising a plurality of robot joints connecting a robot base and a robot tool flange.
BACKGROUND OF THE INVENTION
Robot arms comprising a plurality of robot joints and links where motors can rotate the joints in relation to each other are known in the field of robotics. Typically, the robot arm comprises a robot base which serves as a mounting base for the robot arm and a robot tool flange where to various tools can be attached. A robot controller is configured to control the robot joints to move the robot tool flange in relation to the base. For instance, in order to instruct the robot arm to carry out a number of working instructions.
Typically, the robot controller is configured to control the robot joints based on a dynamic model of the robot arm, where the dynamic model defines a relationship between the forces acting on the robot arm and the resulting accelerations of the robot arm. Often, the dynamic model comprises a kinematic model of the robot arm, knowledge about inertia of the robot arm and other parameters influencing the movements of the robot arm. The kinematic model defines a geometric relationship between the different parts of the robot arm and may comprise information of the robot arm such as, length, size of the joints and links and can for instance be described by Denavit-Hartenberg parameters or the like. The dynamic model makes it possible for the controller to determine which torques the joint motors shall provide in order to move the robot joints for instance at specified velocity, acceleration or in order to hold the robot arm in a static posture.
On many robot arms it is possible to attach various end effectors to the robot tool flange, such as grippers, vacuum grippers, magnetic grippers, screwing machines, welding equipment, dispensing systems, visual systems etc.
In some robots the robot joint comprises a joint motor having a motor axle configured to rotate an output axle via a robot joint gear. Typically, the output axle is connected to and configured to rotate parts of the robot arm in relation to each other. The robot joint gear forms a transmission system configured to transmit torque provided by the motor axle to the output axle for instance to provide a gear ratio between the motor axle and the output axle. The robot joint gear can for instance be provided as a spur gears, planetary gears, bevel gears, worm gears, strain wave gears or other kind of transmission systems. Commonly flexibility exist in the transmissions used for industrial robots due to the elasticity various type of transmissions. This flexibility may lead to an undesired dynamic time-varying displacement between the position of parts of the robot arm.
Taking into account the gear flexibility in the dynamic model makes the dynamic model more accurately resemble the dynamics of the real robot arm because the robot joint torque originating from the gear deformation can be known. A more accurate dynamic model can for instance allow the robot controller to control the robot arm with greater accuracy and precision. A more accurate dynamic model can also allow the robot controller to more accurately identify external disturbances, for instance human interference which is of great concern in terms of safety.
Research have been devoted to accurately identify the dynamic characteristics of the robot gear systems. However, one practical issue when taking into account the joint stiffness in the robot controller design is that the joint stiffness changes with wear due to material being worn off at the gear meshing [1], [2], [3].
Estimating the joint stiffness on industrial robots have been accomplished through off-line identification procedures by several researchers. Off-line identification procedures are not well suited for solving the problem of time-varying joint stiffness. Such procedures would have to be re-run from time to time to keep the joint stiffness information up to date. While the off-line identification procedure is running the robot is unable to conduct any other task with clear negative consequences to the user. Despite the shortcomings of the off-line calibration procedures for joint stiffness estimation a number of references will be given to such off-line identification procedures applied to solve the robot joint stiffness estimation problem. For the off-line identification of joint stiffness, one method is to apply external excitation on one robot joint at a time resulting in a reduced dynamic model hence easier identification as in [4], [5], [6], [7].
Another option is to evaluate joint stiffness values using an external laser-tracking sensor system to visually track the end effector displacements for a given applied wrench as in [8] and [9], where the applied wrench is equal to the applied forced and torques at the end effector. A third option is to incorporate two absolute position rotary encoders in the robot joint to enable direct measurement of the joint deflection and then manually impose a known force at the end-effector and using the kinematic model (the Jacobian) of the robot arm to calculate the joint torques as in [9]. Such procedure however requires external and known loading of the end-effector and the robot is not allowed to move during the procedure. A fourth option is to estimate the joint stiffness using a so-called locked-link joint procedure as in [10] where the end-effector is clamped to the environment and using either motor positions measurement and motor torques data or a force/torque sensor to measure the external wrench between the clamped end effector and the environment.
Very few works are available on the on-line estimation of time-varying nonlinear stiffness e.g. AwAs-II joint [11]. These works are focused towards Variable Stiffness Actuators (VSAs) as found in in the DLR Hand Arm System [12] by the DLR Institute of Robotics and Mechatronics, however most industrial robots do not comprise a VSA. In 2011, Flacco and De Luca [13] estimated the nonlinear stiffness of robot joints using only a motor position sensor by computing a dynamic residual based on the generalized momentum followed by a least squares algorithm to estimate the stiffness parameters.
Robustness issues were later addressed in [14] by introducing a kinematic Kalman filter to handle discretization and quantization errors and a modified recursive least squares algorithm was used to better handle poor excitation conditions. The stiffness parameters were however assumed time-invariant. Further refinements of their method were carried out in [15] modifying the stiffness estimation algorithm to deal with time-varying stiffness by using a Recursive Least Squares method based on a QR decomposition (QR-RLS) able to handle time-varying stiffness characteristics. A non-causal Savitzky-Golay (SG) filter was used to remove noise on the input/output signals. No experiments did however support their findings.
In May 2013, Menard et al. [16] developed an observer capable of on-line estimating the time-varying stiffness of a VSA. Experimental analysis on the VSA system revealed parameter uncertainties of up to 25% of the true stiffness. Friction was assumed purely viscous with a single constant coefficient. Such friction model is not capable of accurately describing real frictional characteristics of most electromechanical systems, as well-known frictional characteristics such as Coulomb friction and the Stribeck effect is then neglected completely.
In July 2013, Cirillo et al. [17] demonstrated online stiffness estimation of a VSA by measuring the elastic energy using an optoelectronic sensor built into the robot joint.
SUMMARY OF THE INVENTION
The objective of the present invention is to address the above described limitations with the prior art or other problems of the prior art. This is achieved by a method of obtaining the gear stiffness of a robot joint gear as defined by the independent claim. The dependent claims describe possible embodiments of the method according to the present invention. The advantages and benefits of the present invention are described in the detailed description of the invention. Further the objective of the present invention is addressed by a method of controlling a robot arm based on the obtained gear stiffness and a robot arm with a controller configured to control the robot arm based on the obtained gear stiffness.
A robot controller taking into account the joint flexibilities may perform well right after calibration but for a good performance over the lifetime of the robot, the joint stiffness must be estimated on-line. Further, estimating the joint stiffness on-line will allow for predictive maintenance in the case of gear unit failure. In most cases, no sensor is available for directly measuring the joint stiffness, so the stiffness information is collected by combining an accurate model of the flexibility torque with the measurements available, such as position and force/torque sensor measures, either implemented in the robot or by using external hardware.
The invention provides a simple method of obtaining the gear stiffness of a robot joint gear of a robot arm without the need to integrate expensive force/torque sensors, as the joint gear stiffness of the robot joint gear can be determined based on sensors commonly used in industrial robots, which also makes it possible to integrate such method into existing industrial robots having such sensors. Additionally, the gear stiffness can be obtained online during use of the robot and thus used as an input to the dynamic model controlling the robot whereby a more accurate controlling of the robot can be provided. Consequently, vibrations and inaccuracies of the robot's movements due to gear stiffness can be accounted for when controlling the robot. Additionally, the gear stiffness changes over time primarily due to wear of the robot joint gear and obtaining the gear stiffness online makes it possible to control the robots based on changes of gear stiffness whereby the accuracy of the robot over time is maintained/improved. Further obtaining the gear stiffness online over time makes it possible to predict failure of the robot joint gear as the gear stiffness can be used to indicate when the robot joint gear is about to fail. Consequently, the robot joint gear can be sent to service in order to exchange/repair the robot joint gear whereby unplanned downtime of the robot can be reduced.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates a robot arm configured to obtain the gear stiffness of the robot joint gears;
FIG. 2 illustrates a schematic cross-sectional view of a robot joint;
FIG. 3 illustrates a model of a robot joint gear;
FIG. 4 illustrates a simplified structural diagram of a robot arm;
FIG. 5 illustrates a flow chart of a method of obtaining the gear stiffness of a robot joint gear of a robot joint of a robot arm;
FIG. 6 illustrates a flow chart of another method of obtaining the gear stiffness of a robot joint gear of a robot joint of a robot arm;
FIG. 7 illustrates a robot arm in a pose used in an experimental analysis of the method according to the present invention;
FIG. 8 illustrates a friction torque/velocity map obtained by imposing different signals of constant velocity on the base joint of a robot arm, while measuring the joint motor current;
FIG. 9 illustrates a flexibility torque/transmission deformation map obtained by imposing a set of known torques to the tool flange of a robot arm using a force gage and measuring the deformation as the difference between absolute joint encoder readings at each side of the robot joint gear;
FIG. 10 illustrates angular position, angular velocity and angular acceleration of the base joint of the robot arm used in the experimental analysis;
FIG. 11 illustrates a schematic representation of the Generalized Maxwell-Slip friction model;
FIG. 12 illustrates a flexibility torque/transmission deformation map obtained by the method according to the present invention;
FIG. 13 illustrates gear stiffness of the robot joint gear obtained in the experimental analysis,
DETAILED DESCRIPTION OF THE INVENTION
The present invention is described in view of exemplary embodiments only intended to illustrate the principles of the present invention. The skilled person will be able to provide several embodiments within the scope of the claims. Throughout the description, the reference numbers of similar elements providing similar effects have the same last two digits. Further it is to be understood that in the case that an embodiment comprises a plurality of the same features then only some of the features may be labeled by a reference number.
The invention can be embodied into a robot arm and is described in view of the robot arm illustrated in FIG. 1 . The robot arm 101 comprises a plurality of
robot joints
103 a , 103 b , 103 c , 103 d , 103 e , 103 f and
robot links
104 b , 104 c , 104 d connecting a robot base 105 and a robot tool flange 107 . A base joint 103 a is connected directly with a shoulder joint and is configured to rotate the robot arm around a base axis 111 a (illustrated by a dashed dotted line) as illustrated by rotation arrow 113 a . The shoulder joint 103 b is connected to an elbow joint 103 c via a robot link 104 b and is configured to rotate the robot arm around a shoulder axis 111 b (illustrated as a cross indicating the axis) as illustrated by rotation arrow 113 b . The elbow joint 103 c connected to a first wrist joint 103 d via a robot link 104 c and is configured to rotate the robot arm around an elbow axis 111 c (illustrated as a cross indicating the axis) as illustrated by rotation arrow 113 c . The first wrist joint 103 d connected to a second wrist joint 103 e via a robot link 104 d and is configured to rotate the robot arm around a first wrist axis 111 d (illustrated as a cross indicating the axis) as illustrated by rotation arrow 113 d . The second wrist joint 103 e is connected to a robot tool joint 103 f and is configured to rotate the robot arm around a second wrist axis 111 e (illustrated by a dashed dotted line) as illustrate by rotation arrow 113 e . The robot tool joint 103 f comprising the robot tool flange 107 , which is rotatable around a tool axis 111 f (illustrated by a dashed dotted line) as illustrated by rotation arrow 113 f . The illustrated robot arm is thus a six-axis robot arm with six degrees of freedom, however it is noticed that the present invention can be provided in robot arms comprising less or more robot joints, and the robot joints can be connected directly to the neighbor robot joint or via a robot link. It is to be understood that the robot joints can be identical and/or different and that the robot joint gear may be omitted in some of the robot joints. The direction of gravity 123 is also indicated in the figure.
The robot arm comprises at least one robot controller 115 configured to control the robot joints by controlling the motor torque provided to the joint motors based on a dynamic model of the robot. The robot controller 115 can be provided as a computer comprising an interface device 117 enabling a user to control and program the robot arm. The controller can be provided as an external device as illustrated in FIG. 1 or as a device integrated into the robot arm. The interface device can for instance be provided as a teach pendent as known from the field of industrial robots which can communicate with the controller via wired or wireless communication protocols. The interface device can for instance comprise a display 119 and a number of input devices 121 such as buttons, sliders, touchpads, joysticks, track balls, gesture recognition devices, keyboards etc. The display may be provided as a touch screen acting both as display and input device.
FIG. 2 illustrates a schematic cross-sectional view of a robot joint 203 . The schematic robot joint 203 can reflect any of the robot joints 103 a - 103 f of the robot 101 of FIG. 1 . The robot joint comprises a joint motor 209 having a motor axle 225 . The motor axle 225 is configured to rotate an output axle 227 via a robot joint gear 229 . The output axle 227 rotates around an axis of rotation 211 (illustrated by a dot-dash line) and can be connected to a neighbor part (not shown) of the robot. Consequently, the neighbor part of the robot can rotate in relation to the robot joint 203 around the axis of rotation 211 as illustrated by rotation arrow 213 . In the illustrated embodiment the robot joint comprises an output flange 231 connected to the output axle and the output flange can be connected to a neighbor robot joint or an arm section of the robot arm. However, the output axle can be directly connected to the neighbor part of the robot or by any other way enabling rotation of the neighbor part of the robot by the output axle.
The joint motor is configured to rotate the motor axle by applying a motor torque to the motor axle as known in the art of motor control, for instance based on a motor control signal 233 indicating the torque, Ï control, motor , applied by said motor axle.
The robot joint gear 229 forms a transmission system configured to transmit the torque provided by the motor axle to the output axle for instance to provide a gear ratio between the motor axle and the output axle. The robot joint gear can for instance be provided as spur gears, planetary gears, bevel gears, worm gears, strain wave gears or other kind of transmission systems. The robot joint comprises at least one joint sensor providing a sensor signal indicative of at least the angular position, q, of the output axle and an angular position, Î, of the motor axle. For instance, the angular position of the output axle can be indicated by an output encoder 235 , which provide an output encoder signal 236 indicating the angular position of the output axle in relation to the robot joint. Similarly, the angular position of the motor axle can be provided by an input encoder 237 providing an input encoder signal 238 indicating the angular position of the motor axle in relation to the robot joint. The output encoder 235 and the input encoder 237 can be any encoder capable of indicating the angular position, velocity and/or acceleration of respectively the output axle and the motor axle. The output/input encoders can for instance be configured to obtain the position of the respective axle based on the position of an encoder wheel 239 arrange on the respective axle. The encoder wheels can for instance be optical or magnetic encoder wheels as known in the art of rotary encoders. The output encoder indicating the angular position of the output axle and the input encoder indicating the angular position of the motor axle makes it possible to determine a relationship between the input side (motor axle) and the output side (output axle) of the robot joint gear.
The robot joints may optionally comprise one or more motor torque sensors 241 providing a motor torque signal 242 indicating the torque provided by the motor axle. For instance, the motor torque sensor can be provided as current sensors obtaining the current through the coils of the joint motor whereby the motor torque can be determined as known in the art of motor control. For instance, in connection with a multiphase motor, a plurality of current sensors can be provided in order to obtain the current through each of the phases of the multiphase motor and the motor torque can then be obtained based on the quadrature current obtained from the phase currents through a Park Transformation. Alternatively, the motor torque can be obtained using other kind of sensors for instance force-torque sensors, strain gauges etc.
FIG. 3 illustrates a model of a robot joint 303 connecting robot link 304 iâ 1 and robot link 304 i , where the joint motor 309 i is arranged on robot link 304 iâ 1 and rotates robot link 304 i in relation to robot link 304 iâ 1. The motor axle 325 i of the joint motor is connected to an output axle 327 i via robot joint gear 329 i (illustrated in schematic form) and the robot link 304 i rotates together with the output axle 327 i . The robot joint gear provides a gear ratio between the motor axle and the output axle and in an ideal gear the rotation of the motor axle is immediately transformed into rotation of the output axle according to the gear ratio of the robot joint gear. However as described in the background of the invention flexibility exist in the types of robot joint gears used in the field of robot arms. The flexibility of a robot joint gear can be indicated by the gear stiffness of the robot joint gear which defines a relationship between torque through the robot joint gear and the deformation between the input side (motor axle) and the output side (output axle) of the robot joint gear. The flexibility of a robot joint gear can be represented as a spring 326 and a damper 328 coupled in parallel between the input side (motor axle) and the output side (output axle) of the robot joint gear. The spring constant K i of the spring indicates the gear stiffness of the robot joint gear and the damping constant of the damper D i indicates the damping of the robot joint gear. As described in the background of the invention the gear stiffness and damping of the robot joint gear can vary; consequently, K i and D i need not to be constants.
The non-infinite gear stiffness of the robot joint results in a deflection between the input side and the output side of the robot joint gear when a torque is applied to the robot joint gear. The deflection of the robot joint gear can be indicated by a deflection variable indicating the differences between the angular position Î of the motor axle and the angular position q of the of the output axle, thus the deflection variable is defined as:
Φ joint,i =Î i âq i ââeq. 1
The joint transmission torque Ï joint,i defines the torque that is transferred from the motor axle to the output axle via the robot joint gear and can be modeled as a function of the deflection variable Φ joint and its time-derivative:
Ï joint,i (Φ joint,i ,{dot over (Φ)} joint,i )=Ï E,i (Φ joint,i )+Ï D,i ({dot over (Φ)} joint,i )ââeq. 2
where Ï E,i (Φ joint,i ) is a flexibility torque depending on the gear stiffness K i and the deflection of the robot joint gear and Ï D,i ({dot over (Φ)} joint,i ) is damping torque depending on the damping coefficient D i and the first time derivative of the deflection of the robot joint gear and the time derivative of the deflection of the robot joint gear.
The Ï D,i ({dot over (Φ)} joint,i ) damping torque of the robot joint gear can for instance be obtained by following the steps:
Fix the output axle of the robot joint gear; Apply a torque to the motor axle of the robot joint gear to yield a gear deflection; Keep the motor axle of the robot joint gear still and remove the applied torque from the motor axle of the robot joint gear; Observe the position of the motor axle of the robot joint gear over time as the motor axle of the robot joint gear undergoes a damped harmonic motion with an amplitude that decreases over time; The damping torque is a measure of the energy dissipation during the motion. Assuming an underdamped harmonic motion, the damping coefficient D i can be obtained as:
D
i
=
-
2
â¢
B
â¢
â¢
log
e
â¡
(
A
2
A
1
)
t
2
-
t
1
eq
.
â¢
3
where B is the mass moment of inertia of the motor axle, A 1 and A 2 are, respectively, amplitudes of the first and second vibration, and t 1 and t 2 are, respectively, times for the first and second motion.
If the motion is not underdamped, a larger mass moment of inertia is added to the input axle.
The gear stiffness K i of the robot joint gear can be characterized by how much the flexible torque Ï E causing the gear deflection changes as a function of the gear deflection. The gear stiffness can thus be expressed as:
K
i
â¡
(
Φ
j
â¢
o
â¢
i
â¢
n
â¢
t
,
i
)
=
δ
â¢
Ï
E
â¡
(
Φ
joint
,
i
)
δ
â¢
Φ
joint
,
i
â
Î
â¢
Ï
E
â¡
(
Φ
joint
,
i
)
Î
â¢
Φ
joint
,
i
eq
.
â¢
4
Assuming that that no flexibility torque exists for the undeformed transmission and that the transmission has the same behavior in compression and extension, thus:
Ï E,i (0)=0 âΦ joint,i ââeq. 5
Ï E,i (âΦ joint,i )=âÏ E (Φ joint,i ) âΦ joint,i ââeq. 6
FIG. 4 illustrates a simplified structural diagram of a robot arm comprising a plurality of n number of robot joints
403 i , 403 i +1 . . . 403 n . The robot arm can for instance be embodied like the robot arm illustrated in FIG. 1 with a plurality of interconnected robot joints, where the robot joints can be embodied like the robot joint illustrated in FIG. 2 . It is to be understood that some of the robot joints and robot links between the robot joints have been omitted for sake of simplicity. The controller is connected to an interface device comprising a display 119 and a number of input devices 121 , as described in connection with FIG. 1 . The controller 415 comprises a processor 443 , a memory 445 and at least one input and/or output port enabling communication with at least one peripheral device.
The controller is configured to control the joint motors of the robot joints by providing motor control signals to the joint motors. The motor control signals 433 i , 433 i +1 . . . 433 n are indicative of the motor torque Ï control,motor,i , Ï control,motor,i+1 , and Ï control,motor,n that each joint motor shall provide by the motor axles. The motor control signals can indicate the desired motor torque, the desired torque provided by the output axle, the currents provided by the motor coils or any other signal from which the motor torque can be obtained. The motor torque signals can be sent to a motor control driver (not shown) configured to drive the motor joint with the motor current resulting in the desired motor torque. The robot controller is configured to determine the motor torque based on a dynamic model of the robot arm as known in the prior art. The dynamic model makes it possible for the controller to calculate which torque the joint motors shall provide to each of the joint motors to make the robot arm perform a desired movement and/or be arranged in a static posture. The dynamic model of the robot arm can be stored in the memory 445 .
As described in connection with FIG. 2 the robot joints comprise an output encoder providing output encoder signals 436 i , 436 i +1 . . . 436 n indicating the angular position q, i , q, i+1 . . . q, n of the output axle in relation to the respective robot joint; an input encoder providing an input encoder signal
438 i , 438 i +1 . . . 438 n indicating the angular position of the motor axle Î, i , Î, i+1 . . . Î, n in relation to the respective robot joint and a motor torque sensor providing a motor torque signal
442 i , 442 i +1 . . . 442 n indicating the torque Ï actually,motor,i , Ï actually,motor,i+1 , Ï actually,motor,n , provided by the motor axle of the respective robot joint. The controller is configured to receive the output encoder signal 436 i , 436 i+ 1 . . . 436 n , the input encoder signal 438 i , 438 i+ 1 . . . 438 n and the motor torque signals 442 i , 442 i+ 1 . . . 442 n.
The controller is further configured to obtain the gear stiffness of at least one of the robot joint gears of the robot joints of the robot arm by:
applying a motor torque to the motor axle of the at least one robot joint using the joint motor; obtaining the angular position of the motor axle of the robot joint; obtaining the angular position of the output axle of the robot joint;
and determining the gear stiffness based on the motor torque applied to the motor axle, the angular position of the motor axle, the angular position of the output axle and the dynamic model of the robot arm.
The controller can for instance be configured to carry out the method of obtaining the gear stiffness of a robot joint gear obtained by the method illustrated in FIGS. 5 - 6 and described in following paragraphs [0034]-[0066].
FIG. 5 illustrates a flow chart of a method of obtaining the gear stiffness of a robot joint gear of a robot joint of a robot arm, where the robot joint is connectable to at least another robot joint and where the robot joint comprises a joint motor having a motor axle configured to rotate an output axle via the robot joint gear. The method can for instance be used to obtain the gear stiffness of the joint gears of the robot arm illustrated in FIGS. 1 - 4 and the method is described in view of the robot arm illustrated in FIGS. 1 - 4 . It is noted that the method in the following is described in view of a method where the gear stiffness of all the robot joint gears of the robot arm are obtained, however it is to be understood that the method can be used to obtain the gear stiffness of a single robot joint gear or some of the robot joint gears.
The method comprises a step of initializing 550 , a step 552 of applying a motor torque to the motor axles of the joint motors; a step 554 of obtaining the angular position of the motor axles of the joint motors; a step 556 of obtaining the angular position of the output axle of the robot joint gears and a step 560 of determining the gear stiffness of the robot joint gears based on the motor torques applied to the motor axles, the obtained angular positions of the motor axles, the obtained angular positions of the output axles and the dynamic model of the robot arm.
Step of initializing 550 comprises a step of obtaining the dynamic model D robot of the robot arm and can be based on prior knowledge of the robot arm and robot joints, KoR [Knowledge of Robot], such as the dimensions and weight of robot joints and robot links; joint motor properties; information relating to an eventual payload attached to the robot arm, orientation of the robot arm in relation to gravity and frictional properties of the robot arm and robot joints.
The dynamic model of the robot arm can be defined and pre-stored in the memory of the controller and the user can in some embodiment be allowed to modify the dynamic model op the robot arm, for instance by providing payload information of a payload attached to the robot arm or defining the orientation of the robot arm in relation to gravity.
The dynamic model of the robot arm can be obtained by considering the robot arm as an open kinematic chain having a plurality of (n+1) rigid robot links and a plurality of n revolute robot joints, comprising a joint motor configured to rotate at least one robot link. In this example the dynamic model is provided by making the following assumptions:
A1: The rotors of the joint motors are uniform bodies having their center of mass at the axis of rotation (motor axle);
A2: The joint motors are located on the robot links preceding the driven robot links; and
A3: The angular velocity of the rotors of the joint motors are due to their own spinning.
Assumption A1 is a basic requirement for long life of a joint motor such as electric motors and also implies that the dynamics of the robot joint will be independent of the angular position of the motor axle. The kinematic arrangement of joint motors and robot links described in assumption A2 is illustrated in FIG. 3 . It is to be understood that the assumption A2 may not be physically true when comparing with an actual robot where joint motor driving the robot links can be arrange at other positions of the robot arm, however there exist always a theoretical equivalent to this assumption. Assumption A3 is reasonable in connection with robot joint gears having large reduction ratios [18] typical in the order of 50-200, or more specific in the order of 100-150. The assumptions are equivalent to neglecting energy contributions due to the inertial couplings between the joint motor and the robot links and also implies that Coriolis and centripetal terms become independent of the rotor's angular velocity.
The configuration of robot arm can be characterized by the generalized coordinates (q Î)â
2N where q is a vector comprising the angular position of the output axles of the robot joint gears and Î is a vector comprising the angular position of the motor axles as seen in âspaceâ of the output side of the robot joint gear. Consequently:
Î =
Î</mi
CLAIMS
Claims ( 18 )
The invention claimed is:
1. A method of obtaining a stiffness of a gear of a joint on a robotic arm, where the joint is connectable to at least one other joint on the robotic arm, where the joint comprises a motor having a motor axle, where the motor axle is configured to rotate an output axle through the gear, and where the method comprises:
applying torque to the motor axle using the motor;
obtaining an angular position of the motor axle;
obtaining an angular position of the output axle,
obtaining a deflection of the gear based on the angular position of the motor axle and the angular position of the output axle;
obtaining a flexibility torque of the gear at the deflection of the gear based on at least the angular position of the motor axle, the angular position of the output axle, and a dynamic model of the robotic arm, where the dynamic model defines a relationship between forces acting on the robotic arm and resulting accelerations of the robotic arm;
performing operations repetitively, the operations comprising:
applying a new torque to the motor axle using the motor;
obtaining a new angular position of the motor axle;
obtaining a new angular position of the output axle;
obtaining a new deflection of the gear based on the new angular position of the motor axle and the new angular position of the output axle; and
obtaining a new flexibility torque of the gear at the new deflection of the gear based on at least the new angular position of the motor axle, the new angular position of the output axle, and the dynamic model;
storing each deflection of the gear and each flexibility torque of the gear at a corresponding deflection of the gear;
fitting, to a mathematical function, the flexibility torques and deflections of the gear that were stored, where the mathematical function comprises a polynomial function that is based on a recursive least squares estimation; and
determining the stiffness of the gear based on the mathematical function.
2. The method of claim 1 , wherein applying the torque to the motor axle results in movement of at least a part of the robotic arm.
3. The method of claim 1 , further comprising:
comparing the stiffness of the gear with to prior knowledge of the stiffness of gear; and
providing a status of the gear based on a result of the comparing.
4. The method of claim 1 , wherein the dynamic model comprises information modeling a parallel spring and damper coupling between the motor axle and the output axle.
5. The method of claim 1 , where the robotic arm comprises joints including the joint comprising the gear, where a combination of the joints are for connecting a base and a tool flange, and wherein the method further comprises:
controlling the joint based on the dynamic model and the stiffness of the gear.
6. The method of claim 5 , further comprising:
modifying the dynamic model based on the stiffness of the gear.
7. A method of obtaining a stiffness of a gear of a joint on a robotic arm, where the joint is connectable to at least one other joint on the robotic arm, where the joint comprises a motor having a motor axle, where the motor axle is configured to rotate an output axle through the gear, and where the method comprises:
applying torque to the motor axle using the motor;
obtaining an angular position of the motor axle;
obtaining an angular position of the output axle;
obtaining a deflection of the gear based on the angular position of the motor axle and the angular position of the output axle;
obtaining a flexibility torque of the gear at the deflection of the gear based on at least the angular position of the motor axle, the angular position of the output axle, and a dynamic model, where the dynamic model defines a relationship between forces acting on the robotic arm and resulting accelerations of the robotic arm;
performing operations repetitively, the operations comprising:
applying a new torque to the motor axle using the motor;
obtaining a new angular position of the motor axle;
obtaining a new angular position of the output axle;
obtaining a new deflection of the gear based on the new angular position of the motor axle and the new angular position of the output axle; and
obtaining a new flexibility torque of the gear at the new deflection of the gear based on at least the new angular position of the motor axle, the new angular position of the output axle, and the dynamic model;
storing each deflection of the gear and each flexibility torque of the gear at a corresponding deflection of the gear;
fitting, to a mathematical function, the flexibility torques and the deflections of the gear that were stored; and
determining the stiffness of the gear is based on a slope of flexibility torque relative to the deflection of the gear, the slope being based on the mathematical function.
8. The method of claim 7 , wherein applying the torque to the motor axle results in movement of at least a part of the robotic arm.
9. The method of claim 7 , further comprising:
comparing the stiffness of the gear with to prior knowledge of the stiffness of gear; and
providing a status of the gear based on a result of the comparing.
10. The method of claim 7 , wherein the dynamic model comprises information modeling a parallel spring and damper coupling between the motor axle and the output axle.
11. The method of claim 7 , where the robotic arm comprises joints including the joint comprising the gear, where a combination of the joints are for connecting a base and a tool flange, and wherein the method further comprises:
controlling the joint based on the dynamic model and the stiffness of the gear.
12. The method of claim 11 , further comprising:
modifying the dynamic model based on the stiffness of the gear.
13. A method of obtaining a stiffness of a gear of a joint on a robotic arm, where the joint is connectable to at least one other joint on the robotic arm, where the joint comprises a motor having a motor axle, where the motor axle is configured to rotate an output axle through the gear, and where the method comprises:
applying torque to the motor axle using the motor, where applying the torque to the motor axle results in rotation of the motor axle and the output axle;
obtaining an angular position of the motor axle;
obtaining an angular position of the output axle;
obtaining a deflection of the gear based on the angular position of the motor axle and the angular position of the output axle;
obtaining a flexibility torque of the gear at the deflection of the gear based on at least the angular position of the motor axle, the angular position of the output axle, and a dynamic model, where the dynamic model defines a relationship between forces acting on the robotic arm and resulting accelerations of the robotic arm;
fitting, to a mathematical function, the flexibility torque and the deflection of the gear that were obtained, where the mathematical function comprises a polynomial function that is based on a recursive least squares estimation; and
determining the stiffness of the gear is based on a slope that is based on the mathematical function.
14. The method of claim 13 , wherein applying the torque to the motor axle results in movement of at least a part of the robotic arm.
15. The method of claim 13 , further comprising:
repeating operations comprising:
applying a new torque to the motor axle using the motor;
obtaining a new angular position of the motor axle;
obtaining a new angular position of the output axle;
obtaining a new deflection of the gear based on the angular position of the motor axle and the angular position of the output axle; and
obtaining a new flexibility torque of the gear at the new deflection of the gear based on at least the new angular position of the motor axle, the new angular position of the output axle, and the dynamic model; and
for each repetition of the operations, storing the deflection of the gear and the flexibility torque of the gear at the deflection of the gear;
wherein each deflection of the gear and each flexibility torque of the gear is fit to the mathematical function.
16. The method of claim 15 , further comprising:
comparing the stiffness of the gear to prior knowledge of the stiffness of gear; and
providing a status of the gear based on a result of the comparing.
17. The method of claim 13 , where the robotic arm comprises joints including the joint comprising the gear, where a combination of the joints are for connecting a base and a tool flange, and wherein the method further comprises:
controlling the joint based on the dynamic model and the stiffness of the gear.
18. The method of claim 17 , further comprising:
modifying the dynamic model based on the stiffness of the gear.
US17/275,726
2018-09-14
2019-09-10
Obtaining the gear stiffness of a robot joint gear of a robot arm
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