JP5932578B2 - Vibration suppression method, vibration suppression device, and industrial machine device having vibration suppression function - Google Patents

Description

  The present invention relates to a vibration suppression method and apparatus for suppressing vibration generated in a moving body in association with acceleration or deceleration movement, and in particular, a multi-degree of freedom generated in the moving body when the posture of the moving body itself changes during the movement. The present invention also relates to a vibration suppression method and apparatus for suppressing time-varying vibration.

  A robot arm that performs motion to perform various operations uses a speed reducer between the motor and the arm. Since the speed reducer behaves as a torsion spring, the vibration of the arm remains even after the motor stops. As a result, it is not possible to move to the next work until the vibration is settled, and work efficiency cannot be improved.

  The problem associated with such residual vibration is not limited to the robot arm, but is common to moving bodies that perform movement including acceleration or deceleration, such as machine tools, cranes, and hydraulic excavators.

  In order to suppress vibration by feedback control, a detector is required. Therefore, a method for suppressing vibration by feedforward control that does not require a detector is required.

  As a vibration suppression method in feedforward control, an input shaping method is known (for example, Patent Document 1, Patent Document 2, Non-Patent Document 1, and Non-Patent Document 2). This input shaping method is a vibration suppression method that is effective when the natural frequency does not change as in a machine tool, and various proposals have been made. In addition, a method using a notch filter and an adaptive method using a Kalman filter are known in order to remove a frequency component that causes natural vibration from a control command (Patent Document 3).

JP 2009-029617 A JP 2011-148078 A JP 2009-042179 A

Neil C. Singer and Warren P. Seering: Preshaping Command Inputs to Reduce System Vibration, Trans. ASME Journal of Dynamic Systems, Measurement, and Control, Vol.112, No.1, 76-82 (1990) Pyung Hun Chang and Hyung-Soon Park: Time-varying input shaping technique applied to vibration reduction of an industrial robot, Control Engineering Practice 13 (2005) 121-130

  The robot arm generally has multiple joints and multiple degrees of freedom in order to be able to handle various tasks. Therefore, in a robot arm, when another joint is driven while performing a motion operation in which one joint is driven, the posture of the arm itself performing the motion operation changes. Therefore, the natural frequency of the arm changes with time. In such a case, since it becomes a time-varying vibration system, simply applying the conventional input shaping method for a time-invariant vibration system cannot cope with vibration suppression.

  Several proposals have been made as methods for suppressing vibration in such a time-varying vibration system (see, for example, Patent Document 1, Patent Document 2, and Non-Patent Document 2). However, for example, Patent Document 2 relates to vibration suppression with one degree of freedom and time-varying, and there is a need for a vibration suppression method that can universally apply the input shaping method to vibration suppression with multiple degrees of freedom and time. Yes.

  Accordingly, an object of the present invention is to solve the above-mentioned problems, and to apply the input shaping method universally to multi-degree-of-freedom and time-varying vibrations that occur in a moving body with acceleration or deceleration movement. The object is to provide a vibration suppressing method.

In order to achieve the above object, the vibration suppressing method according to the present invention is a moving body that is accelerated or decelerated by an external force applied by a driving device, and is generated in the moving body with acceleration or deceleration. In the vibration suppression method for suppressing vibrations with time-varying degrees of freedom, a step of decomposing a reference input value into input values for each vibration mode, and (n−k) next-mode vibrations for the input values for each vibration mode. In order to suppress, from the impulse A ₀ ... A ₂ ^k ₋₁ in which the input position is set to the time when the displacement of the (n−k) -order mode calculated by the equation of motion modeling the robot arm becomes zero again. as (n-k) half cycle of the natural period of the following modes, as input from first impulse after half cycle, the input position of the impulse ^{_{a 2 k ··· a 2 k +}} 1 -1 , respectively Constant and, taking into account the work Coriolis force caused by the change in the posture of the moving body itself while performing acceleration or deceleration luck degree, the impulse ^{_{A 2 k ··· A 2 k +}} 1 - ₁ is set in order from the integer k = 0 to (n−1) in order, so that a total of 2 ⁿ impulses A _0. A step of shaping an input value by input shaping that superimposes ₂ ⁿ ₋₁ , and a step of generating an acceleration / deceleration pattern for each joint in consideration of a nonlinear term from the shaped input value for each of the vibration modes. It is characterized by having.

According to the present invention, when suppressing an n-degree-of-freedom (n ≧ 2) and time-varying vibration generated in a moving body with acceleration or deceleration motion using the input shaping method, (n−k) order mode In order to suppress the vibration, the (n−k) -order mode displacement calculated by the equation of motion modeling the robot arm from the impulse A ₀ ... A ₂ ^k ₋₁ in which the input position is set becomes zero again. time until a half period of the natural period of the (n-k) order mode, to enter the first impulse after half cycle, the input position of the impulse ^{_{a 2 k ··· a 2 k +}} 1 -1 , respectively The impulse A ₂ ^k ... A ₂ ^{k + 1} ₋₁ is set in consideration of the work performed by the Coriolis force generated in accordance with the posture change of the moving body itself while performing acceleration or deceleration maneuver. Set the size of each By executing sequentially from integer k = 0 to (n-1), by superimposing an impulse A ₀ ··· A ₂ ⁿ _-1 of the total 2 ⁿ the input position and size are set, respectively, effect Vibration can be suppressed.

It is a schematic diagram of the robot arm to which the vibration suppression method according to Embodiment 1 of the present invention is applied. It is a figure which shows the dynamic model of the robot arm of FIG. It is a figure which shows the dynamic model of the 1 degree-of-freedom system to which the input shaping method is applied. It is a figure which shows the relationship between the displacement of two impulse responses in a time-invariant system of 1 degree of freedom, and time. It is a figure which shows two impulse inputs. It is a figure which shows the frequency response of two impulse inputs. It is a figure which shows three impulse inputs. It is a figure which shows the frequency response of three impulse inputs. It is a figure which shows four impulse inputs. It is a figure which shows the frequency response of four impulse inputs. It is a figure which shows the relationship between the displacement of two impulse responses in the physical coordinate system in a 2 degrees of freedom time-varying system, and time. It is a figure which shows the relationship between the displacement of two impulse responses in a mode coordinate system, and time. It is a figure which shows the relationship between the displacement of the impulse response of a primary mode in a mode coordinate system, and time. It is a figure which shows the relationship of the displacement of the impulse response of a secondary mode in a mode coordinate system, and time. It is a figure which shows the relationship of the displacement of the impulse response of a secondary mode in a mode coordinate system, and time. It is a figure which shows the relationship between the speed of the impulse response of the primary mode in a mode coordinate system, and time. It is a figure which shows the relationship between the displacement of the impulse response of a primary mode in a mode coordinate system, and time. It is a figure which shows the relationship of the displacement of the impulse response of a secondary mode in a mode coordinate system, and time. It is a figure which shows the relationship between the displacement of the impulse response of a primary mode in a physical coordinate system, and time. It is a figure which shows the relationship between the displacement of the impulse response of a secondary mode in a physical coordinate system, and time. It is a block diagram which shows the structure of a robot controller. It is a flowchart of the procedure which applies the vibration suppression method and operates a moving body with a drive device. It is a figure which shows the acceleration pattern before shaping by this invention in the total continuation time of operation | movement of an arm. It is a figure which shows the acceleration pattern after the shaping | molding by this invention in the total duration of the operation | movement of an arm. It is a figure which shows the number and interval of an impulse input in a 1, 2, 3 and n degree-of-freedom system.

Embodiment 1 FIG.
A method for suppressing vibration of a moving body according to the first embodiment of the present invention will be described using a robot arm 10 which is an example of a moving body. A schematic diagram of this robot arm is shown in FIG.

  As shown in FIG. 1, the robot arm 10 includes a plurality of arms, a plurality of joints that connect the respective arms so as to allow rotational movement, and a hand tool attached to the arm at the tip. Specifically, the robot arm 10 includes joints 11a, 11b, and 11c, arms 12a and 12b, and a hand tool 13 attached to the tip of the arm 12b. Further, in each of the joints 11a to 11c, a driving device (for example, a motor, not shown) that rotationally drives the arms 12a and 12b, and a reduction gear that transmits the driving force from the driving device to each joint (see FIG. Not shown).

  These driving devices are controlled by the robot controller 20. The robot controller 20 controls the operation of the robot arm 10 according to a robot program stored in advance or an instruction from an operator input via the interface 30. The configuration of the robot controller 20 will be described in detail later.

In the robot arm 10 of FIG. 1, the joint 11a can turn the arm 12a around the vertical rotation axis 14a (turning angle Θ), and the joint 11b rotates the arm 12a around the horizontal rotation axis 14b. movement (rotation angle [psi ₁₎ is to be able, joints 11c can be rotated movement arm 12b around the horizontal rotation axis 14c (rotation angle [psi _2). Therefore, the movement of the robot arm 10 includes a turning motion around the vertical rotation axis 14a (hereinafter referred to as “movement in the turning direction”) and a rotation motion around the horizontal rotation shafts 14b and 14c (hereinafter “ In-plane (vertical plane) direction ").

  In the robot arm 10, when the movement in the turning direction and the movement in the in-plane direction are performed simultaneously and acceleration or deceleration movement is performed, free vibration is generated in the turning direction and the in-plane direction thereafter. In Patent Document 2, the vibration of the one-degree-of-freedom system in the turning direction is dealt with. However, in Embodiment 1, the vibration of the two-degree-of-freedom system in the in-plane direction is handled.

  In describing the vibration suppressing method of the first embodiment for suppressing such vibrations of the two-degree-of-freedom system, the equation of motion when the robot arm of FIG. 1 is modeled in the in-plane direction as shown in FIG. First, I will explain.

As parameters, the inertia moment of the arm is J ₁ (t), J ₂ (t), the rotation spring constant of the reduction gear is k ₁ , k _2, the command rotation angle of the motor is φ ₀₁ , φ ₀₂ , and the actual rotation angle of the arm is Let φ ₁ and φ ₂ . Here, (t) represents a function of time. In addition, this time neglects the viscous damping generated by the reducer. Since the change in angular momentum is equal to the moment of external force, it can be expressed as in the following equations (1) and (2).

式（１）、(２）を展開すると次の運動方程式（３）、（４）が導かれる。なお、ここで・は時間による微分を示す。

When the equations (1) and (2) are expanded, the following equations of motion (3) and (4) are derived. Here, · indicates differentiation with respect to time.

ここで、式（１）、(２）の相対角変位を式（５）（６）とおいて式（３）、（４）に代入して整理すると、次式（７）、(８）のように表すことができる。

Here, when the relative angular displacements of the equations (1) and (2) are substituted into the equations (3) and (4) with the equations (5) and (6), the following equations (7) and (8) are obtained. Can be expressed as:

  The first term on the left side of equations (7) and (8) is the Coriolis force. Moreover, since the right side is an external force, it becomes a vibration system of forced displacement by a motor. In general, the motor is operated according to a trapezoidal speed law. If the trapezoidal rule is assumed, the external force becomes a known function, and the relative angular displacement is obtained by the convolution integral of the impulse response and the external force.

  Here, it is generally used in a time-invariant system such as a machine tool in which the coefficient of motion equation does not change, and an input shaping method is a method for determining an input for canceling vibrations from the natural frequency of the system.

  For example, in the case of a one-degree-of-freedom invariant system with only external force f, displacement x, mass m, and spring k as shown in FIG. 3, the equation of motion is as follows.

FIG. 4 shows a response when an impulse having a magnitude A is input as an external force at time t ₀ and an impulse having the same magnitude A is input at time t ₁ after a half cycle of the system. Response to the sum of the two response is zero at time t ₁ and later. That is, when a pair of impulses is generated at the position of exactly half the natural period of the system, the vibration after the half period becomes zero.

  5 and 6 show the frequency response of two impulse inputs at kΔT intervals. Here, n and k are natural numbers, and ΔT is a sampling period. In the frequency domain of FIG. 6, the frequency located in the valley is a notch filter having two periods of 0.5 and 1.5 periods, so two impulse inputs of the same magnitude have a specific frequency. It can be said that vibration is not excited. 5 and 6 are based on the following equations (10) and (11).

  Next, there are two natural frequencies in a two-degree-of-freedom time-invariant system. Therefore, the notch frequency of the notch filter was examined when another impulse was input and three impulses were input.

  Equation (13) shows the Fourier series expansion of three impulses, and FIGS. 7 and 8 show calculation examples (impulsive input magnitude α = β = 1, position k = 2, l = 9. Here, n , K, l are natural numbers (l> k), ΔT is a sampling period, and it is difficult to design the notch frequency at an arbitrary position with three impulses.

  In a one-degree-of-freedom system, vibrations after a half cycle are suppressed by two impulses. Therefore, considering the suppression of the secondary natural frequency first, the interval between the two impulses is reduced to half of the secondary natural period. Set to. Next, in order to suppress the primary natural frequency, the two are set as one set, and another set is added to the system at an interval of half the primary natural period. A total of four impulses are input. FIGS. 9 and 10 show the Fourier transform of these four impulses. Here, n, k, l, and m are natural numbers (m> l, k = ml), and ΔT is a sampling period.

  In FIG. 10, the frequency located in the valley is the half cycle ω = π / (kΔT) of the first and second impulse intervals, and the half cycle ω = π / (lΔT) of the first and third impulse intervals. Thus, the notch filter corresponding to the first order and the second order can be designed. Therefore, in a two-degree-of-freedom time-varying system, vibration is suppressed by adding a total of four impulses to the system. 9 and 10 are based on the following equations (14) to (16).

  The impulse response of the time-invariant system with two degrees of freedom has been described above. Next, returning to the original model of the robot arm, the impulse response of the two-degree-of-freedom time-varying system will be described.

In a time-varying system, the moment of inertia changes with time. The right sides of Equations (7) and (8) are respectively f ₁ and f _2, and an impulse of magnitude A ₀ is input at time t ₀ on the right side f ₁ of Equation (7). When the delta function δ (t) is used, f ₁ = A ₀ δ (t−t ₀ ). This corresponds to moving only the motor 1. As a result, the following expressions (17) and (18) are derived.

  As shown in FIG. 11, in the time-varying system, the natural frequency changes with time because the moment of inertia changes with time, and the impulse that suppresses vibration because there is a coupled term in equations (17) and (18). The input position cannot be determined. Therefore, an impulse input method corresponding to a time-varying system is studied by converting to a mode coordinate system.

Since the moment of inertia changes with time, the eigenvector changes with time. Equation (19) for the first and second natural frequencies is represented by eigenvectors R ₁ (t) and R ₂ (t), and the displacement in the mode coordinate system is [q _r (t)], (r = 1, 2). Then, Expression (20) is derived.

By substituting equation (20) for both sides of equations (17) and (18) and using orthogonality, parameters in the mode coordinate system can be obtained. Equations of motion in the mode coordinate system of equations (17) and (18) in which an impulse of magnitude A ₀ is input at time t ₀ are as shown in the following equations (21) and (22).

  However, '(dash) indicates a parameter in the mode coordinate system, and the mode mass is represented by Equation (23) and the mode rigidity is represented by Equation (24). Since the eigenvector changes with time, the mode stiffness also changes with time in the mode coordinate system.

  The impulse response in the mode coordinate system is as shown in FIG. The natural frequency changes, and the amplitude also changes due to the work of Coriolis force. The position and size of the impulse input that suppresses vibration are examined below using the superposition principle in the mode coordinate system.

Four impulse inputs corresponding to changes in amplitude and natural frequency are obtained. The four impulses are one set, and the time interval of one set is the interval at which the secondary mode is canceled, so the input position is determined first. Therefore, after determining the position of the input, the size of the input is obtained. Assume that the input size is A _i and the position is t _i (i = 1, 2,...).

13 and 14 show four impulse responses, and the time when the displacement becomes zero is a half cycle. From the response of the secondary mode in FIG. 14, the second input position is after the first half cycle, and similarly the fourth input position is after the third half cycle. The third position is obtained by canceling the first and second combined waves q ₁ (t ₀ + t ₁ ) with the third and fourth combined waves q ₁ (t ₂ + t ₃ ) from the response of the primary mode in FIG. It will be a position where you can.

Next, the size of the input is obtained. In order to suppress the secondary mode with two impulses as one set, the magnitude of the second A ₁ and the fourth A ₃ is obtained from the secondary mode, and the first one and the last one are the primary. In order to suppress the mode, the size of the third A ₂ is obtained from the primary mode. The energy relational expression (25) is obtained by multiplying both sides of the expression (22) by dq ₂ (t) / dt and integrating with time in order to consider the change in amplitude. In other words, it is only necessary to add a size that takes into account the work that the Coriolis force is exerted during the half cycle and the eigenvector that changes over time. First, we describe the magnitude _{A 1.}

The third term A ₀ dq ₂ / dt on the right side of Expression (25) does not change with time due to the energy applied to the system, but is different according to the time at which the impulse is applied, and therefore is Expression (26). The first term on the right-hand side is Coriolis force, and the second term is work due to the change of the eigenvector, which changes with time. Therefore, formulating (27) leads to formula (28).

It can be seen from equation (28) that terms corresponding to kinetic energy and potential energy change over time. In the formula (28), displacement left the second term becomes 0 at time _{t 0} and time _{t 1} from the following equation (29) (31) obtained at time becomes zero.

Impulse input is equivalent to giving initial velocity without changing system displacement. Therefore, it becomes Equation (32) at time _{t 1.} Therefore, A ₁ = α ₁ A ₀ and the ratio α _{1 of the} input that cancels the secondary mode is determined from the equations (29) to (31) from the equation (33).

From FIG. 15, it is understood that the vibration after time t ₁ is suppressed by inputting an impulse having a magnitude in consideration of work due to a change in Coriolis force and eigenvector.

Similarly, determine the magnitude value A _3. The value of the magnitude A ₂ is unknown, but the input ratio depends on the input time and does not depend on the magnitude A ₂ value. For a time to input is known, wherein in (28), time _{t 2} and time _{t 3} in the formula (29) to (31) of the relationship is established _{A 3} = ratio of alpha ₂ A ₂ become input alpha ₂ Is obtained as in the following equation (34). That is, if the size A ₂ is obtained, the size A ₃ is determined.

Next, determine the magnitude _{A 2.} When dq ₁ (t) / dt is multiplied by equation (21) and integrated over time, the following equation for the energy of the first-order mode is obtained.

A ₀ dq ₁ / dt is energy applied to the system and does not change with time. However, since it varies depending on the time at which the impulse is applied, Equation (36) is used. The first term on the right side is the Coriolis force, and the second term is the work due to the change in the eigenvector, which varies with time. Therefore, when formula (35) is rearranged in formula (37), formula (38) is derived.

It can be seen from equation (38) that terms corresponding to kinetic energy and potential energy change over time. FIG. 16 shows an impulse response with respect to the speed of the primary mode when four impulses are added. A 3 ₌ α ₂ A ₂ than the size A _2, the initial velocity may be to be equal to enter the system speed of at time t _3. Considering the change in amplitude, the following equation holds from the relationship of energy conservation at time t ₃ , whereby the magnitude A ₂ is obtained.

Impulse is to give the initial velocity to the system. From the superposition principle, the energy value of each term is expressed by the following equations (40) to (46). _{However, dq 1t0 (t 0) /} dt of the _{dq 1t0} / dt is the impulse response when given an impulse at time _{t 0, (t 0)} is the velocity at time _{t 0.}

  From the above, the magnitudes of all four impulse inputs that suppress vibration are theoretically obtained. FIGS. 17 and 18 show impal responses when four lines are input in the mode coordinate system. 17 and 18, the impulse response when input at each time is indicated by a broken line, a one-dot chain line, and a two-dot chain line.

In the response waveform of the primary mode in FIG. 17, the response q ₁ (t ₀ + t ₁ ) obtained by adding the responses at time t ₀ and time t ₁ is added with the thin solid line, and the responses at time t ₂ and time t ₃ are added. The response q ₁ (t ₂ + t ₃ ) is indicated by a solid line, and the response q ₁ (t ₀ + t ₁ + t ₂ + t ₃ ) obtained by adding all the responses from time t ₀ to time t ₃ is indicated by a thick solid line. The primary mode is suppressed in the first set and the last set.

Further, in the response waveform of the secondary mode in FIG. 18, the secondary mode is suppressed in the first and second lines of one set. Therefore, the vibration at time t ₃ or later be seen to have been suppressed.

  19 and 20 show impulse responses when four impulses are input to the physical coordinate system without changing the position / size of the four impulse inputs input to the mode coordinate system. 19 and 20, the impulse response when input at each time is shown by a broken line, a one-dot chain line, and a two-dot chain line.

In Figure 19 and 20, the response time _{t 0} and time _t thin solid line response obtained by adding the response of _1, the time _{t 2} and time _t solid line response sum of responses of _3, time _{t 3} from time _{t 0} The response obtained by adding all of these is indicated by a thick solid line. As can be seen from the response obtained by adding all the responses from time t ₀ to time t ₃ , the vibration after time t ₃ is suppressed. It can be said that it is possible.

Further, the vibration time t ₃ or later is suppressed, this is because when the short natural period as compared to essentially vibration of the vibrating primary mode of second mode in varying system, the first-order mode half It shows that it is possible to suppress the vibration in the secondary mode only by adding a slight time to the period.

  Based on the above, we proposed a time-varying vibration suppression method in which the natural frequency changes because the robot arm is modeled in a two-degree-of-freedom system and the posture of the robot arm changes. In a one-degree-of-freedom system, vibration is suppressed by inputting two impulses. In a two-degree-of-freedom system, two impulses are considered as one set, and in this one set, impulses are generated at intervals where the secondary mode is not excited. Arranged. The first set does not excite the secondary mode but excites the primary mode. Therefore, the second set is arranged so as to cancel the primary mode excited by the first set. Eventually, four impulses were arranged, and the amplitude of each impulse was determined by considering the balance of energy in consideration of Coriolis force and mode change. This makes it possible to suppress the free vibration of the time-varying system with two degrees of freedom theoretically.

  Next, the configuration of the robot controller 20 for controlling the drive device using the above-described vibration suppression method will be described with reference to FIG.

  The robot controller 20 includes a calculation unit (CPU) 201 that executes a robot program and calculates a robot command value, a storage device (ROM, RAM, hard disk, and the like) 202 that stores a robot program and calculation results, an interface 30, and the like. The hardware configuration may include an input / output device 203 that communicates with an external device and a servo control unit 204 that drives and controls the drive device based on the command value calculated by the calculation unit 201.

  The calculation unit 201 includes an acceleration / deceleration pattern calculation unit 201a in order to realize the vibration suppression method described above. The acceleration / deceleration pattern calculation unit 201a calculates (shapes) an acceleration / deceleration pattern of the driving device for causing the robot arm 10 to perform an operation with suppressed vibration.

  Next, a procedure for causing the robot controller 10 to perform a vibration-suppressed operation by the robot controller 20 will be described in detail with reference to the flowchart of FIG.

  In step S1, the physical parameters of the moving body operated using the drive device are identified. That is, first, the natural frequency is measured by the number of degrees of freedom by changing the posture of the moving body. Next, the torsion spring constant of each joint is calculated by the least square method so that the natural frequency obtained by the real eigenvalue analysis from the moving body equation without considering damping becomes a good approximation to the actually measured natural frequency. Identify.

  In step S2, an acceleration / deceleration pattern for driving the moving body is set. That is, first, the parameter obtained from the design value and the parameter identified in step S1 are input. Next, a reference input value (reference acceleration / deceleration pattern) is determined and input for each joint.

  In step S3, based on the acceleration / deceleration pattern of the moving body set in step S2, shaping of the acceleration pattern of the moving body by the driving device that suppresses residual vibration is performed. In this acceleration pattern shaping, first, the reference input value input in step S2 is decomposed into inputs for each vibration mode. Next, the input value shaping is performed by the above-described vibration suppression method, that is, input shaping that also considers correction for the change of the natural period for each vibration mode. Finally, an acceleration / deceleration pattern for each joint is generated from the shaped input value for each mode in consideration of a nonlinear term. In addition, it is desirable that the shaping of the acceleration pattern is performed in a deceleration section where free vibration is likely to be a problem.

  In step S4, a command value for each joint obtained by integrating the acceleration pattern shaped in step S3 twice is commanded to the moving body, and the driving device is driven to perform acceleration, constant speed, and deceleration operations of the moving body. To do. Accordingly, it is possible to perform an operation in which the residual vibration is suppressed in the moving body.

  According to the above flowchart, it is possible to calculate the acceleration / deceleration pattern of the driving device for causing the robot arm 10 to perform a motion with suppressed vibration. FIG. 23 shows an example of reference input values (reference acceleration / deceleration pattern before shaping) that are input for each joint. FIG. 24 shows an acceleration / deceleration pattern (post-reference reference acceleration / deceleration pattern) as a result of shaping the reference input value of FIG. 23 by the above-described method. As can be seen by comparing the acceleration / deceleration patterns before and after shaping, the total time from the start of acceleration to the end of deceleration does not become very long even after shaping.

  Note that calculation processing such as parameter identification and acceleration / deceleration pattern shaping in steps S1 to S4 can be performed by the robot controller 20, for example. In addition, instead of such a case, using a computer device in which a program for performing the above-described calculation processing is installed, the parameters of steps S1 to S3 are identified and calculated, and information on the shaped acceleration pattern is obtained. The robot controller 20 may control the driving operation of the driving device by inputting to the robot controller 20.

  In addition, when the moving body has a plurality of driving patterns, an acceleration pattern by the driving device that suppresses the residual vibration is calculated for each driving pattern and input to the control device. The driving operation of the driving device can also be controlled by an acceleration pattern corresponding to the selected driving pattern. In selecting the operation pattern, means for selecting an appropriate operation pattern (for example, means using a sensor or the like) can be used.

  Note that the magnitude of acceleration that can be selected is limited by the capability of the drive device (motor capability, etc.), and therefore the limit for similar deformation of the acceleration pattern must be within the range of the capability of the drive device. For this reason, when the capacity of the driving device is exceeded, the number of the pair of sections is increased, that is, the duration of the operation is increased, and the speed pattern and the acceleration pattern are calculated again.

  In addition, in a time-varying system, even when the moving body is moving at a constant speed, an excitation force is generated. Therefore, acceleration is set to zero in the first half of a pair of adjacent sections, and vibration in the first half is canceled in the second half. The acceleration / deceleration value may be determined as described above.

Embodiment 2. FIG.
In the first embodiment, the method for suppressing vibration of a two-degree-of-freedom time-varying system has been described. Next, as a second embodiment, the case of a three-degree-of-freedom time-varying system will be described with reference to FIG. FIG. 25 is a diagram showing the number of impulse inputs and their intervals in the 1, 2, 3 and n-degree-of-freedom systems.

In the case of a three-degree-of-freedom system, the number of input impulses necessary to suppress vibration can be considered in the same manner as in the case of a two-degree-of-freedom system. That is, in the two-degree-of-freedom system, the vibration after the half cycle is suppressed by four impulses. Therefore, in the case of the three-degree-of-freedom system, considering the suppression of the third-order mode vibration first, two impulses A The interval between _{0 and} A ₁ (ie, between t ₀ and t ₁ ) is set to a half cycle of the third-order mode. Next, in order to suppress the vibration of the secondary mode, the two are set as one set, and another set A _{2 and} A _{3 is} added to the system at intervals of a half cycle of the secondary mode. Further, in order to suppress the vibration of the primary mode, these four are made into one set, and another set A _4, A _5, A _6, A _{7 is} added to the system at intervals of a half cycle of the primary mode.

Therefore, the number of impulses to be input is A ₀ to A ₇ and 2 ⁿ = 2 ² = 8 in total, and the input positions of all these impulses are determined first.

  Here, similarly to the energy conservation equations (28) and (38) in the two-degree-of-freedom system, the energy conservation equation of the third-order mode is obtained from the first-order mode in the three-degree-of-freedom system. ) In addition, detailed calculation is saved here.

From these energy conservation equations (47) to (49), the input ratio α where A ₁ = α ₁ A ₀ , A ₃ = α ₂ A _2, A ₅ = α ₃ A _4, A ₇ = α ₄ A _{6 1} , α _2, α _{3, and} α ₄ are obtained from the following equations (50) to (53), respectively.

Next, when convergence calculation is performed from the energy conservation formula (48) of the second-order mode, the following formulas (54) and (55) are established for the magnitudes of A ₂ and A ₆ , respectively.

Subsequently, when the convergence calculation than the energy conservation equation for the first order mode (47), the following equation holds for the size of A _4.

  From the above, the magnitudes of all eight impulse inputs that suppress vibration are theoretically obtained. Therefore, it is possible to suppress the free vibration of the time varying system with three degrees of freedom.

Embodiment 3 FIG.
Next, the case of an n-degree-of-freedom time-varying system (n is a natural number) as Embodiment 3 will be described below with reference to FIG.

The case of the n-degree-of-freedom system can be considered in the same manner as the case of the 2- or 3-degree-of-freedom system. That is,
In the case of an n-degree-of-freedom system, considering the suppression of the vibration of the n-th mode _first , the interval between the two impulses A _{0 and} A ₁ (ie, between t ₀ and t ₁ ) is set to a half cycle of the n-th mode To do. Next, (n-1) for suppressing the vibration of the following modes, the two as one set (n-1) intervals of the half cycle of the next mode (i.e., from t ₀ t between ₂₎ anymore system at Add 1 set _A 2, _{A 3.} Further, (n-2) for suppressing the vibration of the following modes, these four were one set (n-2) other to the system at intervals of half cycle of the following modes (i.e., between t ₄ from t ₀₎ set _{A 4, A 5, A 6} , A 7 is added. Similarly, in order to suppress vibration of the (n−k) th order mode, a predetermined impulse input A ₀ ... A ₂ ^k ₋₁ is set as one set, and (n−k) the half-cycle interval of the next mode is set in the system. Adding another set of impulse inputs A ₂ ^k ... A ₂ ^{k + 1} ₋₁ is executed sequentially from integer k = 3 to (n−1).

Therefore, in the case of an n-degree-of-freedom system, the total ^number of impulses to be input is ^2n, and the input positions of all these impulses are determined first.

  Here, the energy conservation formula from the first-order mode to the n-th order mode in the n-degree-of-freedom system is the following formula (57). In addition, detailed calculation is saved here.

Next, from the energy conservation equation of the nth-order mode in the equation (57), the odd-numbered input ratio α where A _i = αA _i−1 is obtained as the following equation.

When the convergence calculation is performed from the energy conservation equation of the (n−1) th mode in the equation (57), the even-numbered impulse magnitude A _i is expressed by the following equation.

As described above, the magnitudes of all 2 ⁿ impulse inputs for suppressing vibration are theoretically obtained. Therefore, it is possible to suppress the free vibration of the time varying system with n degrees of freedom.

  In the description of the above-described embodiment, when performing acceleration or deceleration motion, vibration with n degrees of freedom and time-varying generated in a moving body accompanied by a change in posture of the moving body itself (for example, change in moment of inertia) is obtained. The method of suppressing using the input shaping method was demonstrated. In a robot arm which is a typical example of such a moving body, a multi-joint structure having a high degree of freedom is employed in order to increase the degree of freedom of movement. Therefore, in reality, when the robot arm is driven, a plurality of degrees of freedom and time-varying vibrations are generated. On the other hand, in such a moving body, the most serious problem is low-frequency vibration. Therefore, when time-varying vibrations with respect to a plurality of degrees of freedom occur in this way, the low-frequency vibrations that pose a problem among the generated low-frequency vibrations to high-frequency vibrations (for example, in the case of a three-degree-of-freedom system) The vibration suppression method of the present embodiment may be applied only to the vibrations of the primary mode and the secondary mode.

  In addition, the vibration suppression method of the present embodiment can be applied to vibrations generated when the moving body performs acceleration motion or deceleration motion. However, when the posture of the moving body changes during constant speed motion. When the Coriolis force performs work, the present invention can also be applied to vibration generated by performing such a constant speed motion.

  In the present embodiment, the case where the rotational motion is mainly performed has been described by taking the case where the motion in the in-plane direction is performed as an example, but the present invention can also be applied to motions other than the rotational motion.

According to the present invention, when suppressing an n-degree-of-freedom (n ≧ 2) and time-varying vibration generated in a moving body with acceleration or deceleration motion using the input shaping method, (n−k) order mode to suppress the vibration of, (n-k) from the impulse a ₀ ··· a ₂ ^k _-1 which is set an input position to enter after elapse half cycle of the natural period of the following modes, impulse a ₂ ^k · .. A ₂ ^{k + 1} ₋₁ input positions are set, and the impulses A ₂ ^k ... A ₂ ^{k +} are set in consideration of the work performed by the Coriolis force caused by the posture change of the moving body itself. By sequentially setting the magnitudes of ¹ ₋₁ from integer k = 0 to (n−1), a total of 2 ⁿ impulses A _0. · by superposing _{a 2} ⁿ _-1, effectively vibrate It can be suppressed.

  Therefore, it is possible to effectively suppress vibration generated in an industrial machine device that performs an operation with a posture change during its operation, such as a robot arm, a machine tool, a crane, and a hydraulic excavator, by feedforward control. it can.

  Moreover, the drive source of the said moving body is not limited to an electric rotary machine or an electric linear motion machine. That is, the present invention can be applied without any trouble even when the power generator is a non-electric power generator such as a hydraulic pump.

  It is to be noted that, by appropriately combining any of the above-described various embodiments, the effects possessed by them can be produced.

10 robot arm (moving body), 11 a to 11 c joints, 12a-12b arm, 13 hand tools, 14 a to 14 c rotating shaft, 20 model, 21 arm, 22 conveyed, 24 drive, _{A 0} first impulse input, a ₁ second impulse input, _{a 2} third impulse input, _{a 3} fourth impulse input, the impulse response of _{q 1} 1 order mode, impulse response _{q 2} 2-order mode

Claims (3)

In a moving body in which an external force is applied by a driving device and acceleration or deceleration motion is performed, in a vibration suppressing method for suppressing vibration with n degrees of freedom and time-varying generated in the moving body along with the acceleration or deceleration motion,
Decomposing the reference input value into input values for each vibration mode;
The input value for each vibration mode was calculated from an impulse A ₀ ... A ₂ ^k ₋₁ in which the input position was set according to an equation of motion modeling the robot arm in order to suppress (n−k) order mode vibration . The impulse A ₂ ^k ... Is input so that the time until the time when the displacement of the next mode becomes zero again is a half cycle of the natural cycle of the (n−k) next mode, and is input after a half cycle has elapsed from the first impulse . In consideration of the work of Coriolis force generated by the posture change of the moving body itself while performing the acceleration or deceleration maneuver while setting the input position of A ₂ ^{k + 1} ₋₁ , the impulse A ₂ ^k ... A ₂ ^{k + 1} ₋₁ is set in order from the integer k = 0 to (n−1) in order to set the size of A ₂ ^k ... A ₂ ^{k + 1} _−1. ⁿ book of Inpa A step for shaping the input value by the input shaping superposing scan A ₀ ... A ₂ ⁿ _-1,
A step of generating an acceleration / deceleration pattern for each joint in consideration of a nonlinear term from the shaped input value for each vibration mode;
A vibration suppression method comprising: In a vibration body in which an external force is applied by a driving device and acceleration or deceleration motion is performed, the vibration suppression device suppresses n-degree-of-freedom and time-varying vibration generated in the motion body along with the acceleration or deceleration motion.
Disassemble the reference input value into input values for each vibration mode,
The input value for each vibration mode was calculated from an impulse A ₀ ... A ₂ ^k ₋₁ in which the input position was set according to an equation of motion modeling the robot arm in order to suppress (n−k) order mode vibration . The impulse A ₂ ^k ... Is input so that the time until the time when the displacement of the next mode becomes zero again is a half cycle of the natural cycle of the (n−k) next mode, and is input after a half cycle has elapsed from the first impulse . In consideration of the work of Coriolis force generated by the posture change of the moving body itself while performing the acceleration or deceleration maneuver while setting the input position of A ₂ ^{k + 1} ₋₁ , the impulse A ₂ ^k ... A ₂ ^{k + 1} ₋₁ is set in order from the integer k = 0 to (n−1) in order to set the size of A ₂ ^k ... A ₂ ^{k + 1} _−1. ⁿ book of Inpa Shaping the input value by the input shaping superposing scan _A 0 ... _{A 2} ⁿ _-1,
A vibration suppression apparatus that suppresses vibration of a moving body by generating an acceleration / deceleration pattern for each joint in consideration of a nonlinear term from the shaped input value for each vibration mode. A plurality of driving devices and a control device for controlling the driving devices are provided, and vibrations with n degrees of freedom and time-varying that occur when performing acceleration or deceleration motion by the driving device while changing the posture of the device itself are suppressed. In industrial machinery with vibration suppression function,
The controller is
Disassemble the reference input value into input values for each vibration mode,
The input value for each vibration mode was calculated from an impulse A ₀ ... A ₂ ^k ₋₁ in which the input position was set according to an equation of motion modeling the robot arm in order to suppress (n−k) order mode vibration . The impulse A ₂ ^k ... Is input so that the time until the time when the displacement of the next mode becomes zero again is a half cycle of the natural cycle of the (n−k) next mode, and is input after a half cycle has elapsed from the first impulse . The impulse A ₂ is set in consideration of the work performed by the Coriolis force caused by the change in the attitude of the apparatus itself while setting the input position of A ₂ ^{k + 1} ₋₁ and accelerating or decelerating. ^k ... A ₂ ^{k + 1} ₋₁ is set in order from the integer k = 0 to (n−1) in order, so that a total of 2 ⁿ input positions and sizes are set. Impulse A ₀ ... Shape the input value by input shaping that superimposes A ₂ ⁿ _-1 ,
An acceleration / deceleration pattern calculation unit that generates an acceleration / deceleration pattern for each joint in consideration of a nonlinear term from the shaped input value for each vibration mode,
An industrial machine apparatus characterized by controlling the drive device based on the acceleration / deceleration pattern generated by the acceleration / deceleration pattern calculation unit, thereby suppressing vibrations with n degrees of freedom and time.

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