Classifications

• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
  • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
  • B25J13/00—Controls for manipulators
  • B25J13/08—Controls for manipulators by means of sensing devices, e.g. viewing or touching devices

Definitions

• This disclosure relates to a vibration suppression device, a robot system, and a vibration suppression method for suppressing vibrations in a robot.
• Patent Document 1 discloses a vibration suppression device that reduces vibration by applying a biquad notch filter to modify motion commands, thereby preventing the transmission of vibrations at a preset frequency.
• the vibration suppression device described in Patent Document 1 can suppress robot vibration by setting the robot's excitation frequency to the notch frequency of the biquad notch filter.
• the pump frequency which is the frequency of the parametric resonance
• the notch frequency cannot be determined unless the robot is operated to generate vibrations. Occurrence of vibrations in the robot, that is, causing the robot to perform unstable operations, can lead to malfunctions due to robot vibrations.
• the conventional technology disclosed in Patent Document 1 poses the problem of having to make the robot perform unstable operations in preparation for suppressing the robot's vibrations.
• the present disclosure has been made in light of the above, and aims to provide a vibration suppression device that can prevent a robot from performing unstable movements when preparing to suppress vibrations in the robot.
• the vibration suppression device disclosed herein is a vibration suppression device that suppresses vibrations in a robot having a sensor that detects the state of the robot, a robot controller that outputs operation commands based on the state detection values output by the sensor and a set operation procedure, and an actuator that operates the robot's mechanism in accordance with the operation commands.
• the vibration suppression device disclosed herein outputs to the robot controller an identification command that is a command regarding the operation of the mechanism when identifying the system characteristics that are the characteristics of the mechanism, and generates a stability command that avoids unstable operation periods, which are the operation periods of the mechanism when operation of the mechanism becomes unstable, based on the system characteristics identified based on the state detection values output by the sensor when the mechanism operates in accordance with the identification command, and outputs the stability command to the robot controller to suppress vibrations of the mechanism.
• the vibration suppression device disclosed herein has the advantage of being able to avoid causing the robot to perform unstable movements when preparing to suppress vibrations in the robot.
• FIG. 1 is a diagram showing a configuration example of a robot system according to a first embodiment
• 1 is a flowchart showing an example of an operation procedure of a vibration suppression device according to a first embodiment.
• FIG. 10 is a diagram showing an example of parameters used in a simulation using the vibration suppression device according to the first embodiment.
• FIG. 1 is a first diagram showing an example of a result of a simulation using the vibration suppression device according to the first embodiment;
• FIG. 2 is a second diagram showing an example of a result of a simulation using the vibration suppression device according to the first embodiment;
• FIG. 1 is a diagram showing an example of the configuration of a hardware circuit according to a first embodiment;
• FIG. 1 is a diagram showing an example of the configuration of a control circuit according to a first embodiment;
• Embodiment 1. 1 is a diagram showing an example configuration of a robot system 1 according to a first embodiment.
• the robot system 1 includes a vibration suppression device 2 and a robot 3.
• the vibration suppression device 2 suppresses vibrations of the robot 3.
• the robot 3 is, for example, an industrial robot. Note that the vibration suppression device 2 has various built-in functions and various means, but in the first embodiment, only the functions and means related to the characteristic processing of the vibration suppression device 2 according to the present disclosure will be described.
• the robot 3 comprises a robot controller 21, an actuator 22, a mechanism 23, and a sensor 24.
• the robot controller 21 controls the operation of the robot 3 by outputting operation commands to the actuator 22.
• the actuator 22 operates the mechanism 23 in accordance with the operation commands input to the actuator 22.
• the actuator 22 comprises a servo motor, which serves as a drive source, and a reducer.
• the mechanism 23 comprises an arm with multiple joints, and an end effector attached to the tip of the arm. The servo motor, reducer, arm, and end effector are not shown in the figure.
• the sensor 24 detects the state of the robot 3. Specifically, the sensor 24 detects physical quantities related to the posture of the robot 3 or the environment in which the robot 3 is installed. Examples of the sensor 24 that detects physical quantities related to the posture of the robot 3 are a displacement sensor, a velocity sensor, an acceleration sensor, or an angular velocity sensor. Examples of physical quantities related to the posture of the robot 3 are position, velocity, or acceleration. An example of the sensor 24 that detects physical quantities related to the environment in which the robot 3 is installed is a temperature sensor. An example of a physical quantity related to the environment in which the robot 3 is installed is temperature. The sensor 24 outputs a state detection value, which is a detected value of the physical quantity, to the robot controller 21. The robot controller 21 outputs an operation command based on the state detection value output by the sensor 24 and a set operation procedure. The set operation procedure is an operation procedure that has been programmed in advance. Note that the physical quantities detected by the sensor 24 are not limited to the above physical quantities.
• the vibration suppression device 2 and the robot 3 are connected so that they can communicate with each other.
• the vibration suppression device 2 includes an identification command generator 11, a system characteristic identifier 12, a fluctuation characteristic calculator 13, an unstable operating period estimator 14, and a stability command generator 15.
• the identification command generator 11 generates an identification command.
• the identification command is a command regarding the operation of the mechanism 23 when identifying the system characteristics, which are the characteristics of the mechanism 23.
• the identification command generator 11 outputs the identification command to both the system characteristic identifier 12 and the robot controller 21.
• the robot controller 21 outputs the identification command input to the robot controller 21 to the actuator 22.
• the actuator 22 operates the mechanism 23 in accordance with the identification command.
• the sensor 24 outputs the state detection value detected when the mechanism 23 is operated in accordance with the identification command to the system characteristic identifier 12.
• the system characteristic identifier 12 identifies the system characteristics based on the identification command input to the system characteristic identifier 12 and the state detection value output by the sensor 24 when the mechanism 23 operates in accordance with the identification command.
• the system characteristic identifier 12 outputs information about the system characteristics to the fluctuation characteristic calculator 13.
• the fluctuation characteristic calculator 13 divides the system characteristics identified by the system characteristic identifier 12 into fluctuation characteristics that change over time and non-fluctuating characteristics that do not change over time.
• the fluctuation characteristic calculator 13 calculates normalized fluctuation characteristics, which are normalized fluctuation characteristics, and normalized non-fluctuating characteristics, which are normalized non-fluctuating characteristics.
• the fluctuation characteristic calculator 13 outputs information on the normalized fluctuation characteristics and information on the normalized non-fluctuating characteristics to the unstable operating period estimator 14.
• the unstable operation period estimator 14 estimates the unstable operation period, which is the operation period of the mechanism 23 when the operation of the mechanism 23 becomes unstable due to parametric resonance of the mechanism 23, based on the normalized fluctuation characteristic and the normalized non-fluctuation characteristic.
• the unstable operation period estimator 14 outputs information on the unstable operation period to the stability command generator 15. Note that in the first embodiment, the operation period is defined as the time from the start to the completion of each repeated operation when the robot 3 performs a repetitive operation.
• the stability command generator 15 generates a stability command that avoids the unstable operating period estimated by the unstable operating period estimator 14.
• the stability command generator 15 outputs the stability command to the robot controller 21.
• the robot controller 21 outputs the stability command input to the robot controller 21 to the actuator 22.
• the actuator 22 operates the mechanism 23 in accordance with the stability command.
• the stability command can also be considered an operating command for causing the mechanism 23 to perform stable operation.
• the vibration suppression device 2 outputs to the robot controller 21 an identification command, which is a command regarding the operation of the mechanism 23 when identifying the system characteristics, which are the characteristics of the mechanism 23.
• the vibration suppression device 2 generates a stability command that avoids the unstable operation cycle, which is the operation cycle of the mechanism 23 when its operation becomes unstable, based on the system characteristics identified based on the state detection values output by the sensor 24 when the mechanism 23 operates in accordance with the identification command.
• the vibration suppression device 2 suppresses the vibration of the mechanism 23 by outputting the stability command to the robot controller 21.
• Equation (1) is the equation of motion normalized by the moment of inertia about one axis of the mechanism 23.
• x represents the joint angle, which is the angle of the joint of the mechanism 23.
• the unit of x is rad.
• ⁇ (t) represents the coefficient of the first-order differential term.
• the unit of ⁇ (t) is rad/s.
• ⁇ 2 (t) represents the coefficient of the zeroth-order differential term.
• the unit of ⁇ 2 (t) is rad 2 /s 2 .
• the identification command generator 11 generates an identification command that reduces the operating speed of the mechanism 23 below the speed at which parametric resonance occurs. This allows the vibration suppression device 2 to operate the mechanism 23 when identifying the system characteristics in a way that does not cause parametric resonance.
• the system characteristic identifier 12 identifies, as system characteristics, the coefficients of the first-order differential terms and the coefficients of the zeroth-order differential terms in a normalized equation of motion, which is an equation of motion for each of the multiple axes of the mechanism 23 and is normalized with respect to inertia. That is, the system characteristic identifier 12 identifies ⁇ (t) and ⁇ 2 (t) shown in equation (1) as system characteristics. The system characteristic identifier 12 identifies ⁇ (t) and ⁇ 2 (t) based on detected state values. Note that the method for identifying ⁇ (t) and ⁇ 2 (t) based on detected state values in the system characteristic identifier 12 is arbitrary.
• ⁇ 2 (t) is expressed by the following equation (5).
• ⁇ (t) can be expressed as in the following equation (6):
• ⁇ 2 (t) can be expressed as in the following equation (7):
• ⁇ 0 represents the damped natural frequency
• b represents the normalized non-varying characteristic
• g(t) represents the first normalized varying characteristic
• h(t) represents the second normalized varying characteristic
• Equation (5) ⁇ 2 (t) shown in equation (5) can be expressed as the following equation (8).
• f(t) represents the third normalized fluctuation characteristic.
• ⁇ n 2 is expressed by the following equation (9) by comparing equations (5) and (8).
• ⁇ n represents the natural frequency in the normalized equation of motion after coordinate transformation.
• the fluctuation characteristic calculator 13 calculates the normalized fluctuation characteristics, i.e., the first normalized fluctuation characteristic, the second normalized fluctuation characteristic, and the third normalized fluctuation characteristic, as well as the normalized non-fluctuation characteristic. That is, the fluctuation characteristic calculator 13 calculates g(t), h(t), f(t), and b.
• Equation (11) can be rewritten as the following equation (12).
• the parametric resonance occurring in mechanism 23 is caused by the reducer.
• the number of points where the teeth of the reducer contact each other changes periodically.
• the first normalized fluctuation characteristic g(t) and the second normalized fluctuation characteristic h(t) can be approximated as square waves with the same period and phase. Therefore, from equation (10), the third normalized fluctuation characteristic f(t) has the same period as the excitation period and is a periodic function composed of a square wave and an impulse, which is the first-order differential term in equation (10).
• the third normalized fluctuation characteristic f(t) can be expressed as in the following equation (14): f k (t) shown in equation (14) is expressed by the following equation (15).
• f k (t) represents the k-th frequency component of f(t).
• f k -(t) represents terms of f(t) other than the k-th frequency component.
• f k represents the k-th spectral amplitude of the fluctuating part in the coefficient of the zeroth-order differential term of the normalized equation of motion after coordinate transformation.
• ⁇ p represents the pump frequency, which is the frequency of parametric resonance.
• the pump frequency is set to ⁇ e , which is the excitation frequency of the mechanism 23.
• the pump frequency can also be said to be the frequency of parametric excitation.
• Equations (19) and (20) can be rewritten as the following equation (21):
• equation (21) can be rewritten as the following equation (23).
• Equation (22) can be rewritten as the equation of state, which is the following equation (24).
• Re(X) represents the real part of X when X is a complex number.
• D satisfies the following equation (27). Note that " D " represents a symbol with a period above " D ".
• g min represents the minimum value of g(t), which is the first normalized fluctuation characteristic.
• the sufficiently stable condition shown in equation (28) can be derived.
• the sufficiently stable condition is considered to be a sufficient condition for stabilizing the operation of mechanism 23.
• equation (28) represents the attenuation rate.
• a stable pump frequency is a pump frequency that satisfies the sufficiently stable condition.
• An unstable pump frequency is a pump frequency that does not satisfy the sufficiently stable condition.
• the unstable operating period estimator 14 determines whether the pump frequency, which is the frequency of the parametric resonance, satisfies the conditional expression (28), and calculates the unstable operating period by finding the pump frequency that does not satisfy the conditional expression.
• the unstable operating period estimator 14 outputs information about the unstable operating period to the stability command generator 15.
• the stability command generator 15 generates a stability command representing an operation adjusted to avoid the unstable operation period estimated by the unstable operation period estimator 14.
• the stability command generator 15 outputs the generated stability command to the robot controller 21.
• the robot controller 21 outputs a stability command to the actuator 22.
• the actuator 22 operates the mechanism 23 in accordance with the stability command. This allows the mechanism 23 to perform the operation desired by the user of the robot 3 without generating parametric resonance.
• Figure 2 is a flowchart showing an example of the operating procedure of the vibration suppression device 2 according to embodiment 1.
• step S1 the identification command generator 11 generates an identification command and outputs the identification command.
• the identification command generator 11 generates an identification command that causes the mechanism 23 to operate at a speed that is slower than the operating speed in accordance with the operating command when the robot 3 is actually used. In this way, the identification command generator 11 generates an identification command that causes the mechanism 23 to operate in a way that does not cause parametric resonance.
• step S2 the system characteristic identifier 12 identifies the system characteristic based on the identification command generated in step S1 and the state detection value output by the sensor 24 when the mechanism 23 operates in accordance with the identification command.
• the system characteristic identifier 12 identifies ⁇ (t) and ⁇ 2 (t) shown in equation (1).
• step S3 the fluctuation characteristic calculator 13 calculates normalized fluctuation characteristics and normalized non-variable characteristics based on the system characteristics identified in step S2.
• the fluctuation characteristic calculator 13 divides the system characteristics identified in step S2 into fluctuation characteristics and non-variable characteristics, and obtains the normalized fluctuation characteristics and normalized non-variable characteristics.
• the fluctuation characteristic calculator 13 calculates the normalized fluctuation characteristics g(t), h(t), and f(t), and the normalized non-variable characteristic b.
• Steps S4 and S5 are steps for estimating an unstable operating period based on the normalized varying characteristic and normalized non-varying characteristic obtained in step S3.
• the unstable operating period estimator 14 determines whether the pump frequency is stable or unstable based on a sufficiently stable condition.
• step S5 the unstable operation cycle estimator 14 calculates the unstable operation cycle by estimating that T e when equation (28) is not satisfied is an unstable operation cycle.
• step S6 the stability command generator 15 generates a stability command and outputs the stability command.
• the stability command generator 15 generates a stability command that represents an operation adjusted to avoid the unstable operation period calculated in step S5.
• the stability command generator 15 outputs the generated stability command to the robot controller 21. With this, the vibration suppression device 2 completes the operation according to the procedure shown in FIG. 2.
• Figure 3 is a diagram showing examples of parameters used in a simulation using the vibration suppression device 2 according to embodiment 1.
• Figure 3 shows symbols representing the parameters, their meanings, and example parameter values.
• the parameter "g” represents the first normalized variation characteristic g(t).
• g(t) is represented by a square wave with a frequency of 100 ⁇ p . That is, the frequency of g(t) is 100 times the pump frequency ⁇ p .
• the parameter "h” represents the second normalized variation characteristic h(t).
• h(t) is represented by a square wave with a frequency of 500 ⁇ p . That is, the frequency of h(t) is 500 times the pump frequency ⁇ p .
• FIG. 4 is a first diagram showing an example of the results of a simulation using the vibration suppression device 2 according to embodiment 1.
• FIG. 4 shows a graph representing the relationship between the kth spectral amplitude of f(t), which is the third normalized fluctuation characteristic, and the excitation frequency.
• the vertical axis of the graph shown in FIG. 4 represents the kth spectral amplitude of f(t).
• the horizontal axis of the graph shown in FIG. 4 represents the excitation frequency.
• FIG. 5 is a second diagram showing an example of the results of a simulation using the vibration suppression device 2 according to embodiment 1.
• FIG. 5 shows a graph representing the relationship between the damping rate and the excitation period.
• the vertical axis of the graph shown in FIG. 5 represents the damping rate.
• the damping rate is expressed by the left side of equation (28).
• the horizontal axis of the graph shown in FIG. 5 represents the excitation period.
• the stability command generator 15 generates a stability command in which the excitation frequency is adjusted so as to avoid excitation periods when the operation of the mechanism 23 becomes unstable.
• g(t) and h(t) are each represented by a square wave.
• g(t) and h(t) may also be represented by something other than a square wave.
• the waveforms representing g(t) and h(t) may be any stepped waveform that corresponds to the movement pattern desired for the robot 3.
• the above processing by the vibration suppression device 2 can also be applied when g(t) and h(t) are each represented by something other than a square wave.
• the parametric resonance occurring in mechanism 23 is assumed to be caused by the reducer.
• the parametric resonance may also be caused by a system characteristic that changes over time other than the reducer.
• the above processing by vibration suppression device 2 can be applied even if g(t) and h(t) are each expressed by a wave other than a square wave.
• the vibration suppression device 2 applies the above method to all axes.
• the stability command generator 15 generates a stability command for each of the multiple axes based on the union of the unstable operating periods estimated for each of the multiple axes of the mechanism 23.
• the vibration suppression device 2 can suppress vibrations when multiple axes are moved.
• the vibration suppression device 2 operates the mechanism 23 by outputting an identification command to identify system characteristics, and generates a stability command that avoids unstable operating periods based on the identified system characteristics.
• the mechanism 23 When operating the mechanism 23 based on the identification command, there is no need to generate parametric resonance.
• the vibration suppression device 2 can generate a stability command to suppress vibrations in the robot 3 without causing vibrations in the robot 3. Therefore, the vibration suppression device 2 can avoid having the robot 3 perform unstable operations when preparing to suppress vibrations in the robot 3.
• the vibration suppression device 2 can avoid problems that arise from having the robot 3 perform unstable operations.
• the vibration suppression device 2 can output a stability command through processing that takes less time than when performing a convolution operation on multiple signals. When parameters change rapidly, the vibration suppression device 2 can generate a stability command that matches the change in parameters.
• the vibration suppression device 2 can suppress parametric resonance caused by rapidly changing parameters. The vibration suppression device 2 can suppress parametric resonance even when there is a change in inertia, friction, or stiffness over time in each axis of the robot 3.
• the robot 3 is described as an industrial robot, but is not limited to this.
• the robot 3 may also be a service robot, rescue robot, medical robot, care robot, entertainment robot, forestry robot, agricultural robot, etc.
• the vibration suppression device 2 can be applied to suppressing vibrations in any device that includes a controller that outputs operation commands based on state detection values and a set operation procedure, and an actuator that operates a mechanism according to the operation procedure.
• the robot 3 according to embodiment 1 is considered to include such devices in general.
• the vibration suppression device 2 is realized using a processing circuit.
• the processing circuit may be a dedicated circuit, or a circuit in which a processor executes software.
• FIG. 6 is a diagram showing an example configuration of the hardware circuit 30 according to the first embodiment.
• the hardware circuit 30 includes an input unit 31, a processing circuit 32, and an output unit 33.
• the input unit 31 is an interface circuit that receives data input from outside the hardware circuit 30 and provides it to the processing circuit 32.
• the output unit 33 is an interface circuit that sends data from the processing circuit 32 to outside the hardware circuit 30.
• the processing units of the vibration suppression device 2 namely the identification command generator 11, system characteristic identifier 12, fluctuation characteristic calculator 13, unstable operating period estimator 14, and stability command generator 15, are realized by a dedicated circuit, the processing circuit 32.
• the processing circuit 32 is a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or a combination of these.
• the processing units of the vibration suppression device 2 may be realized by the processing circuit 32 on a function-by-function basis, or all functions may be realized together by the processing circuit 32.
• FIG. 7 is a diagram showing an example configuration of a control circuit 34 according to embodiment 1.
• the control circuit 34 includes an input unit 31, an output unit 33, a processor 35, and a memory 36.
• the input unit 31 of the control circuit 34 is an interface circuit that receives data input from outside the control circuit 34 and provides it to the processor 35.
• the output unit 33 of the control circuit 34 is an interface circuit that sends data from the processor 35 or memory 36 to outside the control circuit 34.
• the processing unit of the vibration suppression device 2 is realized by software, firmware, or a combination of software and firmware.
• the software or firmware is written as a program and stored in memory 36.
• the processing circuit realizes the functions of the processing unit of the vibration suppression device 2 by having the processor 35 read and execute the program stored in memory 36.
• the processing circuit has memory 36 for storing the program that will result in the processing of the vibration suppression device 2 being executed. It can also be said that these programs cause a computer to execute the procedures and methods of the vibration suppression device 2.
• Processor 35 is a CPU (Central Processing Unit).
• Processor 35 may be a central processing unit, processing unit, arithmetic unit, microprocessor, microcomputer, processor, or DSP (Digital Signal Processor).
• Memory 36 may be, for example, a non-volatile or volatile semiconductor memory such as RAM (Random Access Memory), ROM (Read Only Memory), flash memory, EPROM (Erasable Programmable Read Only Memory), EEPROM (Electrically Erasable Programmable Read Only Memory), a magnetic disk, a flexible disk, an optical disk, a compact disk, a minidisk, or a DVD (Digital Versatile Disc).
• the processing unit of vibration suppression device 2 may be realized by combining control circuit 34 and processing circuit 32 shown in FIG. 6.
• the program stored in memory 36 may be provided in a state stored on a recording medium such as a CD (Compact Disc)-ROM or DVD-ROM, or may be provided via a communication line.
• a recording medium such as a CD (Compact Disc)-ROM or DVD-ROM
• the robot controller 21 is realized by using a processing circuit.
• the robot controller 21 has the configuration of the hardware circuit 30 shown in FIG. 6, or a configuration similar to the control circuit 34 shown in FIG. 7.
• the functions of the robot controller 21 may be realized by combining a configuration similar to the processing circuit 32 shown in FIG. 6 with a configuration similar to the control circuit 34 shown in FIG. 7.
• the vibration suppression device 2 may be connected to the robot 3 via a network.
• the network may be, for example, a WAN (Wide Area Network) such as the Internet, but may also be a LAN (Local Area Network).
• the vibration suppression device 2 may also be configured as a server built in a cloud environment.
• the vibration suppression device 2 outputs an identification command to the robot controller 21, and generates a stability command that avoids unstable operation periods, which are operation periods of the mechanism 23 when the operation of the mechanism 23 becomes unstable, based on the system characteristics identified based on the state detection values output by the sensor 24 when the mechanism 23 operates in accordance with the identification command, and suppresses vibration of the mechanism 23 by outputting the stability command to the robot controller 21.
• the vibration suppression device 2 can generate a stability command for suppressing vibration of the robot 3 without causing vibration in the robot 3 during preparatory operations. This makes it possible for the vibration suppression device 2 to avoid having the robot 3 perform unstable operations during preparations for suppressing vibration of the robot 3.
• the vibration suppression device 2 also includes an identification command generator 11 that generates an identification command; a system characteristic identifier 12 that identifies system characteristics based on the identification command and the state detection value output by the sensor 24 when the mechanism 23 operates in accordance with the identification command; a fluctuation characteristic calculator 13 that divides the identified system characteristics into fluctuating characteristics and non-fluctuating characteristics and outputs information on the normalized fluctuation characteristics and information on the normalized non-fluctuating characteristics; an unstable operation period estimator 14 that estimates an unstable operation period based on the normalized fluctuation characteristics and the normalized non-fluctuating characteristics; and a stability command generator 15 that generates a stability command that avoids the estimated unstable operation period.
• the vibration suppression device 2 can also suppress parametric resonance caused by rapidly changing parameters.
• the identification command generator 11 generates an identification command that reduces the operating speed of the mechanism 23 below the speed at which parametric resonance may occur. This allows the vibration suppression device 2 to avoid the occurrence of parametric resonance in preparation for suppressing vibrations of the robot 3.
• the system characteristic identifier 12 identifies, as system characteristics, the coefficient of the first-order differential term and the coefficient of the zeroth-order differential term in a normalized equation of motion, which is an equation of motion for each of the multiple axes of the mechanism 23 and which is normalized with respect to inertia. Furthermore, the coefficient of the first-order differential term, ⁇ (t), is expressed by the above equation (6). The coefficient of the zeroth-order differential term, ⁇ 2 (t), is expressed by the above equation (7). This allows the vibration suppression device 2 to suppress parametric resonance even when there is a time change in inertia, friction, or stiffness in each axis of the robot 3.
• the unstable operating period estimator 14 also determines whether the pump frequency, which is the frequency of the parametric resonance, satisfies a conditional expression, and calculates the unstable operating period by determining the pump frequency that does not satisfy the conditional expression.
• the conditional expression is expressed by the above equation (28). This allows the vibration suppression device 2 to estimate the unstable operating period based on the normalized fluctuation characteristic and the normalized non-fluctuation characteristic.
• the pump frequency is set to the excitation frequency of the mechanism 23. This allows the vibration suppression device 2 to generate a stability command that avoids unstable operating periods.
• the stability command generator 15 generates a stability command for each of the multiple axes of the mechanism 23 based on the union of the unstable operating periods estimated for each of the multiple axes. This allows the vibration suppression device 2 to suppress vibrations when the multiple axes of the mechanism 23 are moved.
• Robot system 2. Vibration suppression device, 3. Robot, 11. Identification command generator, 12. System characteristic identifier, 13. Fluctuation characteristic calculator, 14. Unstable operation period estimator, 15. Stability command generator, 21. Robot controller, 22. Actuator, 23. Mechanism, 24. Sensor, 30. Hardware circuit, 31. Input unit, 32. Processing circuit, 33. Output unit, 34. Control circuit, 35. Processor, 36. Memory.

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