WO2014021433A1 - ロボット装置およびその制御方法 - Google Patents
ロボット装置およびその制御方法 Download PDFInfo
- Publication number
- WO2014021433A1 WO2014021433A1 PCT/JP2013/070918 JP2013070918W WO2014021433A1 WO 2014021433 A1 WO2014021433 A1 WO 2014021433A1 JP 2013070918 W JP2013070918 W JP 2013070918W WO 2014021433 A1 WO2014021433 A1 WO 2014021433A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- joint
- torque
- force torque
- frictional force
- estimation unit
- Prior art date
Links
Images
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position control
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1641—Programme controls characterised by the control loop compensation for backlash, friction, compliance, elasticity in the joints
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/39—Robotics, robotics to robotics hand
- G05B2219/39181—Compensation of coulomb friction in joint
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/39—Robotics, robotics to robotics hand
- G05B2219/39187—Coriolis and centripetal compensation
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/39—Robotics, robotics to robotics hand
- G05B2219/39194—Compensation gravity
Definitions
- the present invention relates to a robot apparatus that drives a joint by a drive motor and a control method thereof.
- Non-Patent Document 1 In a conventional robot apparatus that controls driving in consideration of friction, control is performed by arbitrarily providing a hysteresis called a dead zone in a region where the speed is near 0 (Patent Document 1).
- Patent Document 1 On the other hand, when controlling the drive of a controlled object in consideration of friction, since the controlled object is affected by Coulomb friction and viscous friction, both are identified and compensated (Patent Literature). 2).
- the area is affected by the Coulomb friction and the area affected by the viscous friction, and the friction force in each area is estimated based on the model formula of the discontinuous friction model.
- the present invention solves the above-mentioned problem that occurs in a conventional robot apparatus that controls the driving of a joint in consideration of the frictional force torque acting on the joint. It is an object of the present invention to provide a robot apparatus that is smoothly driven and controlled even when shifting to an affected area or when shifting from an area affected by viscous friction to an area affected by Coulomb friction. .
- a robot apparatus includes a joint driven by a drive motor, a rotation angle detection unit that detects a rotation angle of the drive motor, and a detection value of the rotation angle detection unit.
- a control device that performs correction based on an estimated value of a joint torque estimator that estimates a joint torque acting on the joint when controlling driving, and the joint torque estimator includes an inertia torque estimator and a Coriolis force torque estimator.
- the friction force torque estimation unit includes a Coulomb friction force torque estimation unit, a viscous friction force torque estimation unit, and a Coulomb friction force torque.
- a transition interval calculation unit that smoothes the transition from the estimation unit to the viscous friction force torque estimation unit and the transition from the viscous friction force torque estimation unit to the Coulomb friction force torque estimation unit. And butterflies.
- control method of the robot apparatus of the present invention is a control method of the robot apparatus that performs correction from the estimated value of the joint torque acting on the joint when driving the joint from the detected value of the rotation angle of the drive motor.
- the transition from coulomb friction force torque to viscous friction force torque is made.
- the frictional force torque during the transition from the frictional force torque and the viscous frictional force torque to the coulomb frictional force torque is calculated and estimated by the transition interval calculation unit.
- FIG. 1 is a perspective view showing a robot apparatus according to an embodiment of the present invention.
- FIG. 2 is a schematic diagram illustrating a structure of a joint of the robot apparatus.
- FIG. 3 is a control block diagram of the controller of the robot apparatus.
- FIG. 4 is a control block diagram of a joint torque estimation unit of the control device.
- FIG. 5 is a graph showing the friction torque estimated by the friction torque estimation unit of the joint torque estimation unit.
- 6 is a flowchart of the robot apparatus shown in FIG.
- FIG. 7 is a flowchart of the joint torque estimation unit.
- FIG. 8 is a flowchart of the friction torque estimating unit.
- FIG. 1 to FIG. 8 are diagrams showing an embodiment of the present invention.
- the robot apparatus 1 includes a robot body 2 and a control device 3 connected to the robot body 2 and controlling the driving of the robot body 2.
- the robot body 2 is provided with a base 10 and sequentially from the base 10 and includes six joints 20 to 25 (first joint 20, second joint 21, third joint 22, fourth joint 23, fifth joint 24, and Six arm bodies 30 to 35 (the first arm body 30, the second arm body 31, the third arm body 32, the fourth arm body 33, the fifth arm body) connected to each other via the sixth joint 25). 34, and a sixth arm body 35).
- the arm shaft 40 that is provided integrally with the first arm body 30 and constitutes the first joint 20 is connected at one end to the output side of the speed reducer 41 attached to the base 10. Yes.
- a drive motor 42 is connected to the input side of the speed reducer 41, and the drive motor 42 is provided with an encoder 43 that is a rotation angle detection means for detecting the rotation angle.
- the drive motor 42 rotates forward or backward, the rotation is decelerated by the speed reducer 41 and transmitted to the arm shaft 40, and the first arm body 30 rotates in the forward or reverse direction.
- the second joint 21 to the sixth joint 25 also have the arm shaft 40 as in the first joint 20, and are provided with a speed reducer 41, a drive motor 42, and an encoder 43, and operate in the same manner. Is omitted.
- control device 3 will be described with reference to FIGS.
- the control device 3 includes a position command unit 50, a ⁇ ⁇ ⁇ ′ ⁇ ⁇ ”calculation unit 51, a servo control calculation unit 52, a joint torque estimation unit 53, an external force calculation unit 54, A compliance model calculation unit 55 and a control target unit 56 are provided.
- the control device 3 Based on the detection value of the encoder 43 provided in each drive motor 42 of each joint 20 to 25 of the robot body 2, the control device 3 causes the position command unit 50 to issue a command regarding the target position / posture at a predetermined control cycle.
- the control target unit 56 that has issued the command and operates the respective drive motors 42 drives the joints 20-25.
- the ⁇ ⁇ ⁇ ′ ⁇ ⁇ ”calculation unit 51 adds a command related to the target position / posture calculated by the position command unit 50 and a correction amount obtained by the compliance model calculation unit 55 described later, and is based on inverse kinematics. Calculation is performed to calculate a joint angle command ⁇ , a joint angular velocity command ⁇ ′, and a joint angular acceleration command ⁇ ′′.
- the servo control calculation unit 52 generates a torque command issued to the control target unit 56 based on the joint angle command ⁇ , the joint angular velocity command ⁇ ′, and the joint angular acceleration command ⁇ ′′ calculated by the ⁇ ⁇ ⁇ ′ ⁇ ⁇ ′′ calculation unit 51. Is calculated.
- the joint torque estimation unit 53 estimates the joint torque acting on each joint 20 to 25 based on the dynamic model, and details thereof will be described later.
- the external force calculation unit 54 calculates the estimated external force based on the error torque obtained by subtracting the estimated torque value of the joint torque estimated by the joint torque estimation unit 53 from the torque command calculated by the servo control calculation unit 52. calculate.
- the compliance model calculation unit 55 calculates a correction amount related to the target position / attitude based on the estimated external force calculated by the external force calculation unit 54.
- the joint torque estimating unit 53 estimates the joint torque based on the model formula of the dynamic model.
- Estimated joint torque T ( ⁇ ) acting on n joints is expressed by the following equation.
- T ( ⁇ ) M ( ⁇ ) ⁇ ′′ + B ( ⁇ ) [ ⁇ a′ ⁇ b ′] + C ( ⁇ ) [ ⁇ ′ 2 ] + G ( ⁇ ) + F ( ⁇ ′)
- T ( ⁇ ) M ( ⁇ ) ⁇ ′′ + B ( ⁇ ) [ ⁇ a′ ⁇ b ′] + C ( ⁇ ) [ ⁇ ′ 2 ] + G ( ⁇ ) + F ( ⁇ ′)
- ⁇ ′ 2 Joint angular velocity product matrix of the same joint (matrix of n rows and 1 column)
- ⁇ a′ ⁇ b ′ Joint angular velocity product matrix of different joints ( ⁇ n ⁇ (n ⁇ 1) / 2 ⁇ ⁇ 1 matrix)
- the joint torque estimation unit 53 is based on the above-described equation of the estimated joint torque T ( ⁇ ), and the inertia torque estimation unit 60, the Coriolis force torque estimation unit 61, the centrifugal force torque estimation unit 62, and the gravity torque.
- An estimation unit 63 and a frictional force torque estimation unit 64 are provided.
- the inertia torque estimation unit 60 applies a joint angle command ⁇ and a joint angular acceleration command ⁇ ′′ issued at a predetermined control period based on the term M ( ⁇ ) ⁇ ′′ in the above-described estimated joint torque T ( ⁇ ). Thus, the inertia torque generated by the inertia is calculated.
- the Coriolis force torque estimation unit 61 generates a joint angle command ⁇ and a joint angular velocity command issued at a predetermined control cycle based on the term B ( ⁇ ) [ ⁇ a′ ⁇ b ′] in the above-described estimated joint torque T ( ⁇ ). Coriolis force torque generated by Coriolis force is calculated with respect to ⁇ ′.
- the centrifugal torque estimation unit 62 generates a joint angle command ⁇ and a joint angular velocity command ⁇ issued in a predetermined control cycle based on the term C ( ⁇ ) [ ⁇ ′ 2 ] in the above-described estimated joint torque T ( ⁇ ). For ', calculate the centrifugal torque generated by the centrifugal force.
- the gravitational torque estimating unit 63 calculates the gravitational torque generated by gravity with respect to the joint angle command ⁇ issued at a predetermined control cycle based on the term G ( ⁇ ) in the above-described estimated joint torque T ( ⁇ ). To do.
- the frictional force torque estimation unit 64 applies a joint angle command ⁇ and a joint angular velocity command ⁇ ′ issued at a predetermined control cycle based on the term F ( ⁇ ′) in the above-described estimated joint torque T ( ⁇ ).
- the frictional force torque generated by the frictional force is calculated.
- the joint torque estimation unit 53 includes the inertia torque calculated by the inertia torque estimation unit 60, the Coriolis force torque calculated by the Coriolis force torque estimation unit 61, the centrifugal force torque calculated by the centrifugal force torque estimation unit 62, The joint torque is estimated by adding the gravity torque calculated by the gravity torque estimation unit 63 and the friction force torque calculated by the friction force torque estimation unit 64 to obtain an estimated value of the joint torque.
- the friction force torque estimation unit 64 includes a Coulomb friction force torque estimation unit 70 based on a model equation of the Coulomb friction model, and viscous friction. And a viscous frictional force torque estimating unit 71 based on the model equation of the model.
- the frictional force torque estimation unit 64 further includes a transition from the Coulomb frictional force torque estimation unit 70 to the viscous frictional force torque estimation unit 71, and a viscous frictional force torque estimation unit 71. Is provided with a transition interval calculation unit 72 that smoothes the transition from the coulomb friction force torque estimation unit 70 to the coulomb friction force torque estimation unit 70.
- the frictional force torque estimation unit 64 selects one of the coulomb frictional force torque estimation unit 70, the viscous frictional force torque estimation unit 71, and the transition section calculation unit 72 according to the joint angular velocity. Also have.
- fv ( ⁇ ′) represents a predetermined function according to the model formula of the viscous friction model using the joint angular velocity command ⁇ ′ as a variable.
- k represents a frictional force torque coefficient which will be described later
- ⁇ s represents a joint angle command at the previous command in a predetermined control cycle.
- the frictional force torque coefficient k is applied to each joint 20-25 when the joints 20-25 are driven in advance, and the friction affecting each joint 20-25 shifts from coulomb friction to viscous friction as the joint angle increases. It is determined by measuring the acting joint torque and analyzing the measurement result. A plurality of current values of the drive motor 42 and detection values of the encoder 43 of each joint 20 to 25 are measured at a predetermined sampling period, and the current value of the drive motor 42 is converted into a joint torque and the detection value of the encoder 43 is converted into a joint angle. To do.
- the inertia torque, the Coriolis torque, the centrifugal torque, and the gravity torque acting on each joint 20 to 25 at the time of measurement are calculated and subtracted from the converted joint torque.
- the frictional force torque acting on each joint 20 to 25 at the time of measurement is extracted.
- Fm ( ⁇ ) between the joint angle and the friction force torque based on the measurement is obtained.
- the relationship Fm ( ⁇ ) between the joint angle based on the measurement and the friction force torque is such that, in the region where the joint angle is small, the friction force torque is substantially constant with respect to the change in the joint angle due to the effect of Coulomb friction. Beyond this minute region, the friction torque increases smoothly as the joint angle increases. In the region where the frictional force torque increases smoothly, the frictional torque gradient km with respect to the joint angle is extracted, and the inclination km is defined as the frictional force torque coefficient k.
- the current value of the drive motor 42 is converted into the joint torque, and the detection value of the encoder 43 is converted into the joint angle.
- the joint torque and the joint angle are measured using another measuring device. Good.
- the frictional force torque coefficient k for each robot device 1, but any one of the plurality of robot devices 1 of the same specification manufactured in the same process is selected.
- the frictional force torque coefficient k of one robot apparatus 1 may be obtained and the frictional force torque coefficient k may be applied to the remaining robot apparatuses 1.
- the changeover switch 73 is one of the coulomb friction force torque estimation unit 70, the viscous friction force torque estimation unit 71, and the transition section calculation unit 72 in accordance with the joint angular velocity command ⁇ ′ of each joint 20-25. Select.
- the joint angular velocity command ⁇ ′ is a positive value
- the joint angular velocity command ⁇ ′ is a negative value.
- the changeover switch 73 selects and connects the Coulomb friction force torque estimation unit 70 to estimate the friction force torque.
- the unit 64 estimates the frictional force torque acting on each joint 20 to 25 by being calculated by the Coulomb frictional force torque estimating unit 70.
- ⁇ 1 ′ represents a Coulomb friction switching joint speed command ⁇ 1 ′, which will be described later.
- the changeover switch 73 selects and connects the transition section calculation unit 72 to estimate the frictional force torque.
- the unit 64 estimates the frictional force torque acting on each of the joints 20 to 25 by being calculated by the transition section calculating unit 72.
- ⁇ 2 ′ represents a viscous friction switching joint speed command ⁇ 2 ′, which will be described later.
- the changeover switch 73 selects and connects the viscous frictional force torque estimating unit 71, and the frictional force torque estimating unit 64 selects the viscous frictional force torque.
- the frictional force torque acting on each joint 20 to 25 is estimated. Note that the direct switching from the coulomb friction force torque estimating unit 70 to the viscous friction force torque estimating unit 71 and the direct switching from the viscous friction force torque estimating unit 71 to the coulomb friction force torque estimating unit 70 are not performed.
- the Coulomb friction switching joint speed command ⁇ 1 ′ is calculated based on the Coulomb friction force torque Fc ( ⁇ ) calculated by the Coulomb friction force torque estimation unit 70 according to the Coulomb friction model, and the relationship Fm ( ⁇ ) and the joint angular velocity when Fm ( ⁇ ) exceeds Fc ( ⁇ ) is applied.
- the viscous friction switching joint speed command ⁇ 2 ′ includes the viscous frictional force torque Fv ( ⁇ ) calculated by the viscous frictional force torque estimating unit 71 according to the viscous friction model, and the relationship Fm ( ⁇ ) and the joint angular velocity when Fm ( ⁇ ) reaches the minimum value of Fv ( ⁇ ) is applied.
- the changeover switch 73 switches between the Coulomb friction force torque estimation unit 70 and the transition section calculation unit 72, and the switch between the viscous friction force torque estimation unit 71 and the transition section calculation unit 72 is a joint angular velocity command. This is performed by comparing ⁇ ′ with the Coulomb friction switching joint speed command ⁇ 1 ′ and the viscous friction switching joint speed command ⁇ 2 ′, but the conditions for switching may be changed or added as appropriate.
- the switching from the transition section calculating unit 72 to the viscous friction force torque estimating unit 71 is such that the joint angular velocity command ⁇ ′ is equal to or greater than the viscous friction switching joint velocity command ⁇ 2 ′ ( ⁇ 2 ′ ⁇
- the joint angular velocity command ⁇ ′ becomes faster than the viscous friction switching joint velocity command ⁇ 2 ′ ( ⁇ 2 ′ ⁇
- FIG. 5 shows a graph of the friction force torque estimated by the friction force torque estimation unit 64 of the present embodiment for each joint 20-25.
- the horizontal axis indicates the joint angular velocity
- the vertical axis indicates the friction force torque
- the white circle ( ⁇ ) indicates the friction force torque estimated by the friction force torque estimation unit 64.
- the joint angular velocity command ⁇ ′ is in the range of 0 ⁇
- the frictional torque estimation unit 64 performs the Coulomb frictional force torque estimation unit in a predetermined control cycle.
- the frictional torque is estimated by calculation at 70.
- the joint angular velocity command ⁇ ′ is in the range of ⁇ 1 ′ ⁇
- the frictional torque estimation unit 64 performs the transition section calculation unit 72 in a predetermined control cycle. And the frictional torque is estimated.
- the joint angular velocity command ⁇ ′ is in the range of ⁇ 2 ′ ⁇
- the frictional torque estimation unit 64 is the viscous frictional force torque estimation unit 71 in a predetermined control cycle.
- the frictional torque is calculated and estimated.
- the friction torque of the sections B and B ′ estimated by the transition section calculation unit 72 is estimated based on the friction force torque of the sections A and A ′ estimated based on the model expression of the Coulomb friction model and the model expression of the viscous friction model.
- the frictional force torques in the sections C and C ′ are smoothly connected.
- the frictional force torque estimation unit 64 includes the transition section calculation unit 72
- the coulomb frictional force torque estimation unit 70 changes to the viscous frictional force torque estimation unit 71 via the transition section calculation unit 72. Then, the transition is smoothly made from the viscous frictional force torque estimation unit 71 to the coulomb frictional force torque estimation unit 70 via the transition interval calculation unit 72.
- the robot apparatus 1 is servo-on in step S100, and the control apparatus 3 is activated.
- step S101 the control device 3 reads the parameter of the equation of the estimated joint torque T ( ⁇ ) based on the dynamic model stored in the memory.
- the parameters to be read are applied to the inertia torque estimating unit 60, the Coriolis force torque estimating unit 61, the centrifugal torque estimating unit 62, and the gravity torque estimating unit 63 of the joint torque estimating unit 53, and based on the dimensions and mass of the robot body 2 in advance.
- step S102 the control device 3 reads the target position and posture to be reached at the tip of the robot body 2 stored in the memory.
- step S103 the control device 3 uses the position command section 50 to set the target position / value at a predetermined control cycle based on the detection value of the encoder 43 provided in each drive motor 42 of each joint 20-25. Posture is calculated and a command related to the target position / posture is issued.
- step S104 the control device 3 performs a calculation based on the inverse kinematics in the ⁇ ⁇ ⁇ ' ⁇ ⁇ "calculation unit 51 based on the command related to the target position / orientation, thereby obtaining the joint angle command ⁇ and the joint angular velocity command.
- ⁇ ′ and the joint angular acceleration command ⁇ ′′ are calculated.
- step S105 the control device 3 calculates a torque command value by the servo control calculation unit 52 based on the joint angle command ⁇ , the joint angular velocity command ⁇ ′, and the joint angular acceleration command ⁇ ′′.
- step S106 based on the torque command, the control device 3 causes the control target unit 56 to operate the respective drive motors 42 to rotate the joints 20 to 25 of the robot body 2.
- step S107 if the position / posture of each joint 20-25 of the robot body 2 has reached the target value to be reached, the control device 3 proceeds to step S108 and servo-off. If the target value has not been reached, the process returns to step S103.
- step S109 the control device 3 uses the joint torque estimation unit 53 to calculate each joint based on the joint angle command ⁇ , the joint angular velocity command ⁇ ′, and the joint angular acceleration command ⁇ ′′ calculated in step S104.
- the joint torque acting on each of 20 to 25 is estimated, and in step S110, the error command is calculated by subtracting the torque command calculated in step S105 from the estimated torque value of the estimated joint torque.
- step S111 the control device 3 calculates an estimated external force in the external force calculation unit 54 based on the error torque, and in step S112, the compliance model calculation unit 55 calculates the target position based on the estimated external force. ⁇ Calculate the amount of posture correction.
- the correction amount of the target position / posture is added to the target position / posture calculated in step S103, and the calculated target position / posture becomes the target position / posture considering the compliance control.
- the joint torque estimation unit 53 starts estimating the joint torque in step S200.
- step S201 the joint torque estimation unit 53 calculates the inertia torque by the inertia torque estimation unit 60.
- step S202 the joint torque estimation unit 53 calculates the Coriolis force torque by the Coriolis force torque estimation unit 61.
- step S203 the joint torque estimating unit 53 calculates the centrifugal force torque by the centrifugal torque estimating unit 62.
- step S204 the joint torque estimation unit 53 calculates the gravity torque by the gravity torque estimation unit 63.
- step S205 the joint torque estimating unit 53 calculates the friction force torque by the friction force torque estimating unit 64.
- step S206 the joint torque estimation unit 53 adds the inertia torque, the Coriolis force torque, the centrifugal force torque, the gravity torque, and the friction force torque calculated in steps S201 to S205 to estimate the joint torque.
- step S207 the joint torque estimation unit 53 ends the estimation of the joint torque.
- the frictional force torque estimation unit 64 starts estimating the frictional force torque in step S300.
- step S301 the frictional torque estimation unit 64 determines whether or not the coulomb frictional force torque estimation section is in the coulomb frictional force torque estimation section, that is, the joint angular velocity command ⁇ ′ is in the range of 0 ⁇
- step S ⁇ b> 305 the frictional force torque estimation unit 64 estimates the frictional force torque by calculating the Coulomb frictional force torque Fc ( ⁇ ) in the coulomb frictional force torque estimation unit 70.
- step S302 the frictional torque estimation unit 64 determines whether or not the changeover switch 73 is in the transition section, that is, whether the joint angular velocity command ⁇ ′ is in the range of ⁇ 1 ′ ⁇
- step S ⁇ b> 306 the frictional force torque estimation unit 64 estimates the frictional force torque by calculating the transitional interval frictional force torque Ft ( ⁇ ) in the transitional interval calculating unit 72.
- step S303 the frictional torque estimation unit 64 determines whether the frictional torque torque estimation section 64 is in the viscous frictional force torque estimation section, that is, whether the joint angular velocity command ⁇ ′ is in the range of ⁇ 2 ′ ⁇
- step S307 the frictional force torque estimation unit 64 calculates the viscous frictional force torque Fv ( ⁇ ) by the viscous frictional force torque estimation unit 71, thereby estimating the frictional force torque.
- step S304 the frictional force torque estimation unit 64 ends the estimation of the frictional force torque.
- the present invention can be implemented with appropriate modifications depending on the specific configuration of the robot apparatus. Depending on the work to be performed, the number of joints and arm bodies of the robot body and the number of control points of the control device that controls them are determined.
Landscapes
- Engineering & Computer Science (AREA)
- Robotics (AREA)
- Mechanical Engineering (AREA)
- Manipulator (AREA)
- Retarders (AREA)
Abstract
Description
一方、摩擦を考慮して制御対象の駆動を制御する場合に、制御対象がクーロン摩擦の影響と粘性摩擦の影響を受けることから、両者を同定して補償することも行われている(特許文献2)。
なお、移動物体の速度に応じて、クーロン摩擦の影響を受ける領域と粘性摩擦の影響を受ける領域とに区分し、それぞれの領域における摩擦力を不連続摩擦モデルのモデル式に基づいて推定することも行われている(非特許文献1)。
なお、第2関節21~第6関節25についても、それぞれ第1関節20と同様にアーム軸40を有し、減速機41、駆動モータ42、エンコーダ43が設けられ、同様に動作するので、説明を省略する。
制御装置3は、ロボット本体2の各関節20~25のそれぞれの駆動モータ42に設けられたエンコーダ43の検出値に基づき、所定の制御周期にて位置指令部50が目標位置・姿勢に関する指令を発し、指令を受けた制御対象部56がそれぞれの駆動モータ42を作動させ、各関節20~25を駆動する。
n個の関節に作用する推定関節トルクT(Θ)は、以下の式で表される。
T(Θ)=M(Θ)Θ”+B(Θ)[Θa’Θb’]+C(Θ)[Θ’2]+G(Θ)+F(Θ’)
上式の各項は以下の通りである。
T(Θ):推定関節トルク行列(n行1列の行列)
Θ、Θ’、Θ”:それぞれ関節角度行列、関節角速度行列、関節角加速度行列(n行1列の行列)
Θ’2:同じ関節の関節角速度積行列(n行1列の行列)
Θa’Θb’:異なる関節の関節角速度積行列({n・(n-1)/2}行1列の行列)
M(Θ):慣性(質量)行列(n行n列の行列)
B(Θ):コリオリ力行列(n行{n・(n-1)/2}列の行列)
C(Θ):遠心力行列(n行n列の行列)
G(Θ):重力行列(n行1列の行列)
F(Θ’):摩擦力行列(n行1列の行列)
なお、本実施形態では、ロボット本体2が6個の関節20~25を有するので、n=6となる。
そして、クーロン摩擦モデルのモデル式と粘性摩擦モデルのモデル式が不連続である場合に、その接続が不連続となる関節角速度の前後で、推定される摩擦力トルクが急激に変化して各関節20~25の駆動が乱れることを避けるために、摩擦力トルク推定部64は、さらに、クーロン摩擦力トルク推定部70から粘性摩擦力トルク推定部71への移行と、粘性摩擦力トルク推定部71からクーロン摩擦力トルク推定部70への移行を滑らかにする移行区間演算部72を備えている。
摩擦力トルク推定部64は、クーロン摩擦力トルク推定部70と粘性摩擦力トルク推定部71と移行区間演算部72との中から、関節角速度に応じて、いずれか1つを選択する切替えスイッチ73も有している。
各関節20~25の回転方向が正回転の場合、関節角速度指令θ’は正の値となり、逆回転の場合、関節角速度指令θ’は負の値となる。
関節角速度指令θ’が、0≦|θ’|≦θ1’(0<θ1’)の範囲にあるとき、切替えスイッチ73はクーロン摩擦力トルク推定部70を選択して接続し、摩擦力トルク推定部64は、クーロン摩擦力トルク推定部70にて演算することにより、各関節20~25に作用する摩擦力トルクを推定する。なお、θ1’は、クーロン摩擦切替え関節速度指令θ1’を表し、これについては後述する。
関節角速度指令θ’が、θ1’<|θ’|<θ2’(θ1’<θ2’)の範囲にあるとき、切替えスイッチ73は移行区間演算部72を選択して接続し、摩擦力トルク推定部64は、移行区間演算部72にて演算することにより、各関節20~25に作用する摩擦力トルクを推定する。なお、θ2’は、粘性摩擦切替え関節速度指令θ2’を表し、これについては後述する。
関節角速度指令θ’が、θ2’≦|θ’|の範囲にあるとき、切替えスイッチ73は粘性摩擦力トルク推定部71を選択して接続し、摩擦力トルク推定部64は、粘性摩擦力トルク推定部71にて演算することにより、各関節20~25に作用する摩擦力トルクを推定する。
なお、クーロン摩擦力トルク推定部70から粘性摩擦力トルク推定部71への直接の切替えと、粘性摩擦力トルク推定部71からクーロン摩擦力トルク推定部70への直接の切替えは行われない。
粘性摩擦切替え関節速度指令θ2’は、粘性摩擦力トルク推定部71が粘性摩擦モデルに準じて算出した粘性摩擦力トルクFv(θ)と、測定に基づく関節角度と摩擦力トルクとの関係Fm(θ)とを比較し、Fm(θ)がFv(θ)の最小値に到達するときの関節角速度が適用される。
例えば、本実施の形態において、移行区間演算部72から粘性摩擦力トルク推定部71への切替えは、関節角速度指令θ’が粘性摩擦切替え関節速度指令θ2’以上になった(θ2’≦|θ’|)時点で切替わるとしているが、関節角速度指令θ’が粘性摩擦切替え関節速度指令θ2’よりも速くなり(θ2’<|θ’|)、かつ、移行区間摩擦力トルクFt(θ)が粘性摩擦力トルクFv(θ)の最小値よりも大きくなった(|Fv(θ)の最小値|<|Ft(θ)|)時点で切替わるとしてもよい。
横軸は関節角速度を、縦軸は摩擦力トルクを示し、白丸(○)印は摩擦力トルク推定部64により推定された摩擦力トルクを示す。
区間Bと区間B’は、関節角速度指令θ’がθ1’<|θ’|<θ2’の範囲であって、所定の制御周期にて、摩擦力トルク推定部64が、移行区間演算部72で演算して、摩擦力トルクを推定したものである。
区間Cと区間C’は、関節角速度指令θ’がθ2’≦|θ’|の範囲であって、所定の制御周期にて、摩擦力トルク推定部64が、粘性摩擦力トルク推定部71で演算して、摩擦力トルクを推定したものである。
移行区間演算部72で推定された区間B、B’の摩擦トルクは、クーロン摩擦モデルのモデル式に基づき推定された区間A、A’の摩擦力トルクと、粘性摩擦モデルのモデル式に基づき推定された区間C、C’の摩擦力トルクを滑らかに接続している。
本実施形態によれば、摩擦力トルク推定部64が移行区間演算部72を備えているので、クーロン摩擦力トルク推定部70から移行区間演算部72を介して粘性摩擦力トルク推定部71へ、および、粘性摩擦力トルク推定部71から移行区間演算部72を介してクーロン摩擦力トルク推定部70へ、滑らかに移行する。
ロボット装置1は、図6に示すフローチャートの如く制御される。
ステップS111において、制御装置3は、誤差トルクを基に、その外力演算部54にて、推定外力を算出し、ステップS112において、推定外力を基に、そのコンプライアンスモデル演算部55にて、目標位置・姿勢の修正量を演算する。
この目標位置・姿勢の修正量は、ステップS103において演算される目標位置・姿勢に加算され、算出された目標位置・姿勢はコンプライアンス制御を考慮した目標位置・姿勢となる。
そして、ステップS207において、関節トルク推定部53は、関節トルクの推定を終了する。
ステップS305において、摩擦力トルク推定部64は、クーロン摩擦力トルク推定部70にてクーロン摩擦力トルクFc(θ)を演算することにより、摩擦力トルクを推定する。
ステップS306において、摩擦力トルク推定部64は、移行区間演算部72にて移行区間摩擦力トルクFt(θ)を演算することにより、摩擦力トルクを推定する。
ステップS307において、摩擦力トルク推定部64は、粘性摩擦力トルク推定部71にて粘性摩擦力トルクFv(θ)を演算することにより、摩擦力トルクを推定する。
Claims (4)
- ロボット装置において、
駆動モータにより駆動される関節と、
前記駆動モータの回転角を検出する回転角検出手段と、
前記回転角検出手段の検出値より前記関節の駆動を制御する際に、前記関節に作用する関節トルクを推定する関節トルク推定部の推定値より補正を行う制御装置とを備え、
前記関節トルク推定部は、慣性トルク推定部と、コリオリ力トルク推定部と、遠心力トルク推定部と、重力トルク推定部と、摩擦力トルク推定部とを有し、
前記摩擦力トルク推定部は、クーロン摩擦力トルク推定部と、粘性摩擦力トルク推定部と、前記クーロン摩擦力トルク推定部から前記粘性摩擦力トルク推定部への移行と前記粘性摩擦力トルク推定部から前記クーロン摩擦力トルク推定部への移行を滑らかにする移行区間演算部とを有することを特徴とするロボット装置。 - 前記移行区間演算部は、予め測定された前記関節の関節トルクより抽出された摩擦力トルク係数を用いて、前記関節の摩擦力トルクを演算することを特徴とする請求項1に記載のロボット装置。
- 駆動モータの回転角の検出値より関節を駆動する際に、前記関節に作用する関節トルクの推定値より補正を行うロボット装置の制御方法において、
前記関節に作用する慣性トルクとコリオリ力トルクと遠心力トルクと重力トルクと摩擦力トルクとを推定して前記関節の関節トルクの推定値を得る工程を備え、
前記関節の関節トルクの推定値を得る工程は、クーロン摩擦力トルクから粘性摩擦力トルクへ移行する間の摩擦力トルクと、粘性摩擦力トルクからクーロン摩擦力トルクへ移行する間の摩擦力トルクとを、移行区間演算部で演算して推定する工程を含むことを特徴とするロボット装置の制御方法。 - 前記移行区間演算部は、予め測定された前記関節の関節トルクより抽出された摩擦力トルク係数を用いて、前記関節の摩擦力トルクを演算することを特徴とする請求項3に記載のロボット装置の制御方法。
Priority Applications (4)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US14/418,416 US9434073B2 (en) | 2012-08-02 | 2013-08-01 | Robot apparatus and control method therefor |
JP2014528226A JP5727103B2 (ja) | 2012-08-02 | 2013-08-01 | ロボット装置およびその制御方法 |
CN201380041006.7A CN104507645B (zh) | 2012-08-02 | 2013-08-01 | 机器人装置及其控制方法 |
GB1501379.0A GB2518576B (en) | 2012-08-02 | 2013-08-01 | Robotic apparatus and control method therefor |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP2012-172007 | 2012-08-02 | ||
JP2012172007 | 2012-08-02 |
Publications (1)
Publication Number | Publication Date |
---|---|
WO2014021433A1 true WO2014021433A1 (ja) | 2014-02-06 |
Family
ID=50028100
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
PCT/JP2013/070918 WO2014021433A1 (ja) | 2012-08-02 | 2013-08-01 | ロボット装置およびその制御方法 |
Country Status (5)
Country | Link |
---|---|
US (1) | US9434073B2 (ja) |
JP (1) | JP5727103B2 (ja) |
CN (1) | CN104507645B (ja) |
GB (1) | GB2518576B (ja) |
WO (1) | WO2014021433A1 (ja) |
Cited By (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN109129525A (zh) * | 2017-06-15 | 2019-01-04 | 电装波动株式会社 | 机器人的负载重心位置推定装置及负载重心位置推定方法 |
JP6906711B1 (ja) * | 2020-03-26 | 2021-07-21 | 三菱電機株式会社 | 摩擦補償装置、衝突検知装置、トルクフィードフォワード演算装置およびロボット制御装置並びに摩擦補償方法 |
US11161242B2 (en) | 2016-12-16 | 2021-11-02 | Panasonic Intellectual Property Management Co., Ltd. | Method for controlling robot |
CN114425770A (zh) * | 2020-10-29 | 2022-05-03 | 北京配天技术有限公司 | 一种工业机器人示教控制方法、电子设备和存储介质 |
JP2022553260A (ja) * | 2019-10-17 | 2022-12-22 | フランカ エーミカ ゲーエムベーハー | ロボットマニピュレータのトルク制限ブレーキ |
Families Citing this family (15)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
WO2016196512A1 (en) * | 2015-05-29 | 2016-12-08 | Abb Technology Ag | Method and system for robotic adaptive production |
DE112016004725B4 (de) * | 2015-10-14 | 2021-09-16 | Kawasaki Jukogyo Kabushiki Kaisha | Verfahren zum Teach-ln eines Roboters und Roboterarmsteuervorrichtung |
KR102584754B1 (ko) * | 2015-11-11 | 2023-10-05 | 마코 서지컬 코포레이션 | 로봇식 시스템 및 그를 역구동하는 방법 |
DE102016000187B3 (de) * | 2016-01-11 | 2017-01-26 | Kuka Roboter Gmbh | Bestimmung einer Orientierung eines Roboters relativ zu einer Gravitationsrichtung |
EP3653347A4 (en) * | 2017-07-11 | 2020-08-12 | Panasonic Intellectual Property Management Co., Ltd. | ROBOT CONTROL DEVICE |
JP6844462B2 (ja) * | 2017-07-21 | 2021-03-17 | 株式会社デンソーウェーブ | 角度検出器の偏心誤差補正方法、ロボットシステム |
JP6661676B2 (ja) * | 2018-01-18 | 2020-03-11 | ファナック株式会社 | ロボット制御装置 |
JP7124440B2 (ja) * | 2018-05-23 | 2022-08-24 | セイコーエプソン株式会社 | ロボット制御装置およびロボットシステム |
JP6989542B2 (ja) * | 2019-01-31 | 2022-01-05 | ファナック株式会社 | ロボット制御装置 |
CN113128018B (zh) * | 2019-12-31 | 2023-04-07 | 深圳市优必选科技股份有限公司 | 摩擦力计算方法、装置、机器人及可读存储介质 |
JP7283421B2 (ja) * | 2020-03-05 | 2023-05-30 | トヨタ自動車株式会社 | トルク推定システム、トルク推定方法、及びプログラム |
US11691285B2 (en) * | 2020-05-07 | 2023-07-04 | Mujin, Inc. | Method and computing system for estimating parameter for robot operation |
CN114102603B (zh) * | 2021-12-13 | 2023-12-26 | 佗道医疗科技有限公司 | 一种基于笛卡尔空间的零力拖动方法 |
CN114102636B (zh) * | 2021-12-31 | 2024-03-19 | 华中科技大学 | 遥操作机器人的焊缝打磨控制***及其设计方法和应用 |
CN116460859B (zh) * | 2023-06-19 | 2023-10-03 | 广东隆崎机器人有限公司 | Scara机器人运动补偿方法、装置、设备及存储介质 |
Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2006146572A (ja) * | 2004-11-19 | 2006-06-08 | Yaskawa Electric Corp | サーボ制御装置および方法 |
JP2010076012A (ja) * | 2008-09-24 | 2010-04-08 | Toshiba Corp | マニピュレータシステムおよびその制御方法 |
Family Cites Families (20)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4641251A (en) * | 1982-02-16 | 1987-02-03 | Inoue-Japax Research Incorporated | Robot |
CA1233222A (en) * | 1984-03-09 | 1988-02-23 | Nobuhiko Onda | Movable apparatus driving system |
US5101472A (en) * | 1990-10-04 | 1992-03-31 | Repperger Daniel W | Military robotic controller with majorizing function and nonlinear torque capability |
JPH0728527A (ja) | 1993-07-12 | 1995-01-31 | Fanuc Ltd | クーロン摩擦の補正処理方法 |
JP3463355B2 (ja) | 1994-06-03 | 2003-11-05 | 株式会社安川電機 | 制御対象の特性を表す関数の定数の同定・補償方法 |
SE9700767D0 (sv) * | 1997-03-04 | 1997-03-04 | Asea Brown Boveri | Förfarande för bestämning av lastparametrar hos en industrirobot |
JP3981773B2 (ja) | 1997-05-28 | 2007-09-26 | 株式会社安川電機 | ロボット制御装置 |
US6385508B1 (en) * | 2000-10-31 | 2002-05-07 | Fanuc Robotics North America, Inc. | Lead-through teach handle assembly and method of teaching a robot assembly |
SE0301531L (sv) * | 2003-05-22 | 2004-11-23 | Abb Ab | A Control method for a robot |
EP1915963A1 (en) * | 2006-10-25 | 2008-04-30 | The European Atomic Energy Community (EURATOM), represented by the European Commission | Force estimation for a minimally invasive robotic surgery system |
EP1932629B1 (en) * | 2006-12-11 | 2019-04-24 | ABB Research Ltd. | A method and a control system for monitoring the condition of an industrial robot |
US7986118B2 (en) * | 2007-04-23 | 2011-07-26 | Honda Motor Co., Ltd. | Open-loop torque control on joint position-controlled robots |
JP2009066685A (ja) * | 2007-09-11 | 2009-04-02 | Sony Corp | ロボット装置及びロボット装置の制御方法 |
US7912612B2 (en) * | 2007-11-30 | 2011-03-22 | Caterpillar Inc. | Payload system that compensates for rotational forces |
JP5242342B2 (ja) * | 2008-10-31 | 2013-07-24 | 株式会社東芝 | ロボット制御装置 |
WO2011036750A1 (ja) * | 2009-09-24 | 2011-03-31 | 株式会社 東芝 | ロボット制御装置 |
JP5198514B2 (ja) * | 2010-07-22 | 2013-05-15 | 株式会社東芝 | ロボット制御装置 |
KR20120060578A (ko) * | 2010-12-02 | 2012-06-12 | 삼성전자주식회사 | 보행 로봇 및 그 자세 제어 방법 |
KR101778027B1 (ko) * | 2010-12-21 | 2017-09-13 | 삼성전자주식회사 | 보행 로봇 및 그 자세 제어 방법 |
KR101953113B1 (ko) * | 2011-05-30 | 2019-03-05 | 삼성전자주식회사 | 로봇 및 그 제어방법 |
-
2013
- 2013-08-01 GB GB1501379.0A patent/GB2518576B/en active Active
- 2013-08-01 US US14/418,416 patent/US9434073B2/en active Active
- 2013-08-01 CN CN201380041006.7A patent/CN104507645B/zh active Active
- 2013-08-01 WO PCT/JP2013/070918 patent/WO2014021433A1/ja active Application Filing
- 2013-08-01 JP JP2014528226A patent/JP5727103B2/ja active Active
Patent Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2006146572A (ja) * | 2004-11-19 | 2006-06-08 | Yaskawa Electric Corp | サーボ制御装置および方法 |
JP2010076012A (ja) * | 2008-09-24 | 2010-04-08 | Toshiba Corp | マニピュレータシステムおよびその制御方法 |
Cited By (9)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US11161242B2 (en) | 2016-12-16 | 2021-11-02 | Panasonic Intellectual Property Management Co., Ltd. | Method for controlling robot |
CN109129525A (zh) * | 2017-06-15 | 2019-01-04 | 电装波动株式会社 | 机器人的负载重心位置推定装置及负载重心位置推定方法 |
JP2022553260A (ja) * | 2019-10-17 | 2022-12-22 | フランカ エーミカ ゲーエムベーハー | ロボットマニピュレータのトルク制限ブレーキ |
JP6906711B1 (ja) * | 2020-03-26 | 2021-07-21 | 三菱電機株式会社 | 摩擦補償装置、衝突検知装置、トルクフィードフォワード演算装置およびロボット制御装置並びに摩擦補償方法 |
WO2021192181A1 (ja) * | 2020-03-26 | 2021-09-30 | 三菱電機株式会社 | 摩擦補償装置、衝突検知装置、トルクフィードフォワード演算装置およびロボット制御装置並びに摩擦補償方法 |
CN115336167A (zh) * | 2020-03-26 | 2022-11-11 | 三菱电机株式会社 | 摩擦补偿装置、碰撞检测装置、扭矩前馈运算装置及机器人控制装置以及摩擦补偿方法 |
US11691282B2 (en) | 2020-03-26 | 2023-07-04 | Mitsubishi Electric Corporation | Friction compensation device, and robot control device |
CN115336167B (zh) * | 2020-03-26 | 2023-09-22 | 三菱电机株式会社 | 摩擦补偿装置、碰撞检测装置、扭矩前馈运算装置及机器人控制装置以及摩擦补偿方法 |
CN114425770A (zh) * | 2020-10-29 | 2022-05-03 | 北京配天技术有限公司 | 一种工业机器人示教控制方法、电子设备和存储介质 |
Also Published As
Publication number | Publication date |
---|---|
CN104507645A (zh) | 2015-04-08 |
US9434073B2 (en) | 2016-09-06 |
US20150258685A1 (en) | 2015-09-17 |
JPWO2014021433A1 (ja) | 2016-07-21 |
GB201501379D0 (en) | 2015-03-11 |
GB2518576A (en) | 2015-03-25 |
CN104507645B (zh) | 2016-04-27 |
JP5727103B2 (ja) | 2015-06-03 |
GB2518576B (en) | 2015-09-02 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
JP5727103B2 (ja) | ロボット装置およびその制御方法 | |
JP5902425B2 (ja) | ロボット制御装置、外乱判定方法およびアクチュエータ制御方法 | |
CN111788040B (zh) | 机器人的动力学参数辨识方法、机器人和存储装置 | |
EP3078459B1 (en) | Robot controlling method, robot apparatus, program and recording medium | |
US10690558B2 (en) | Robot collision detection method | |
JP2012024877A (ja) | ロボット制御装置 | |
US9533414B2 (en) | Torque detecting method and arm device | |
WO2011161765A1 (ja) | ロボット制御装置 | |
JP4858229B2 (ja) | ロボットに取り付けられた負荷の質量と重心位置の算出方法 | |
WO2003068464A1 (fr) | Procede de commande d'entrainement et controleur d'entrainement | |
Madsen et al. | Adaptive feedforward control of a collaborative industrial robot manipulator using a novel extension of the Generalized Maxwell-Slip friction model | |
JP2015089584A (ja) | ロボットの制御方法及びロボットシステム | |
JP2019181610A (ja) | モータエンコーダ及びセンサを用いて学習制御を行うロボットシステム | |
JP2018158418A (ja) | ロボットの負荷重心位置推定装置及びロボットの負荷重心位置推定方法 | |
CN114102606A (zh) | 机器人运动信息规划方法及相关装置 | |
US20170261529A1 (en) | Method for identifying friction parameter for linear module | |
JP5708091B2 (ja) | ロボットの制御方法およびロボットの制御装置 | |
JP4305340B2 (ja) | ロボットに取り付けられた負荷の質量と重心位置の算出方法 | |
Du et al. | Current-Based direct teaching for industrial manipulator | |
JP4449693B2 (ja) | ロボット制御装置およびその制御方法 | |
WO2020149020A1 (ja) | ロボット制御装置、ロボット制御方法、及びロボット制御プログラム | |
WO2019216416A1 (ja) | 撓み量推定装置、ロボット制御装置、及び撓み量推定方法 | |
JP5473889B2 (ja) | 力制御装置 | |
JP5343725B2 (ja) | ロボット制御装置 | |
JP7182952B2 (ja) | 制御方法、制御プログラム、記録媒体、制御装置、ロボットシステム、および物品の製造方法 |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
WWE | Wipo information: entry into national phase |
Ref document number: 201380041006.7 Country of ref document: CN |
|
121 | Ep: the epo has been informed by wipo that ep was designated in this application |
Ref document number: 13826398 Country of ref document: EP Kind code of ref document: A1 |
|
ENP | Entry into the national phase |
Ref document number: 2014528226 Country of ref document: JP Kind code of ref document: A |
|
ENP | Entry into the national phase |
Ref document number: 1501379 Country of ref document: GB Kind code of ref document: A Free format text: PCT FILING DATE = 20130801 |
|
WWE | Wipo information: entry into national phase |
Ref document number: 1501379.0 Country of ref document: GB |
|
WWE | Wipo information: entry into national phase |
Ref document number: 14418416 Country of ref document: US |
|
NENP | Non-entry into the national phase |
Ref country code: DE |
|
122 | Ep: pct application non-entry in european phase |
Ref document number: 13826398 Country of ref document: EP Kind code of ref document: A1 |