CN108908338B - Robot tail end jitter suppression method and system based on ZVD shaper - Google Patents

Robot tail end jitter suppression method and system based on ZVD shaper Download PDF

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CN108908338B
CN108908338B CN201810856742.2A CN201810856742A CN108908338B CN 108908338 B CN108908338 B CN 108908338B CN 201810856742 A CN201810856742 A CN 201810856742A CN 108908338 B CN108908338 B CN 108908338B
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vibration
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CN108908338A (en
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李耀斌
曾雨权
廖济文
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Shenzhen Shanlong Intelligent Control Co ltd
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    • 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
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J19/00—Accessories fitted to manipulators, e.g. for monitoring, for viewing; Safety devices combined with or specially adapted for use in connection with manipulators

Abstract

The invention relates to a robot tail end jitter suppression method and a system thereof based on a ZVD shaper; the robot tail end jitter suppression method based on the ZVD shaper comprises the following steps of; s1, obtaining a position instruction; s2, judging whether the terminal shaking function is started; if the signal is on, the next step is carried out, and if the signal is not on, the step is carried out to S8; s3, judging whether the single vibration suppression is started or not; if the signal is on, the next step is carried out, and if the signal is not on, the step is carried out to S6; s4, measuring the first vibration frequency and the first damping ratio, and calculating the related ZVD shaper coefficient AiAnd ti(ii) a S5, obtaining shaping position information through calculation and outputting the shaping position information; s6, measuring a second vibration frequency and a second damping ratio, and calculating a related ZVD shaper coefficient AiAnd ti(ii) a S7, obtaining shaping position information through calculation and outputting the shaping position information; and S8, ending. The invention has good inhibition effect aiming at the ubiquitous terminal shake of the robot, reduces the positioning time and improves the efficiency.

Description

Robot tail end jitter suppression method and system based on ZVD shaper
Technical Field
The invention relates to the field of robot control, in particular to a robot tail end jitter suppression method and system based on a ZVD shaper.
Background
In China, the number of robots increases exponentially, the annual growth rate of the robots reaches about 30% in three years, and by 2017, the number of the robots sold is estimated to be 15 thousands; in the future, more and more Chinese robot suppliers enter the market, the competition between foreign resources and Chinese native robot suppliers is more and more intense, and the growth potential of the Chinese market robots in the future is huge.
At present, the robot control technology generally has the problem of inaccuracy caused by terminal jitter, the problem is the key technology for robot development, many enterprises also need to urgently solve the problem, and the market demand is large.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a robot end jitter suppression method and a system thereof based on a ZVD shaper.
In order to achieve the purpose, the invention adopts the following technical scheme:
the robot end jitter suppression method based on the ZVD shaper comprises the following steps of;
s1, obtaining a position instruction;
s2, judging whether the terminal shaking function is started; if the signal is on, the next step is carried out, and if the signal is not on, the step is carried out to S8;
s3, judging whether the single vibration suppression is started or not; if the signal is on, the next step is carried out, and if the signal is not on, the step is carried out to S6;
s4, measuring the first vibration frequency and the first damping ratio, and calculating the related ZVD shaper coefficient AiAnd ti；
S5, obtaining shaping position information through calculation and outputting the shaping position information;
s6, measuring a second vibration frequency and a second damping ratio, and calculating a related ZVD shaper coefficient AiAnd ti；
S7, obtaining shaping position information through calculation and outputting the shaping position information;
and S8, ending.
The further technical scheme is as follows: in S1, the position command is obtained through 62.5us of control cycles according to the position loop.
The further technical scheme is as follows: and the step S1 is that the position command is output through the ZVD shaper, the position loop P is adjusted, the position feedforward outputs a given speed, and PI adjustment of a speed loop and a current loop is carried out to control the operation of the motor.
The further technical scheme is as follows: the S4 includes:
s41, obtaining a first vibration frequency and a first damping ratio according to the position feedback waveform of the virtual oscilloscope;
s42, calculating the related ZVD shaper coefficient A according to the first vibration frequency and the first damping ratioiAnd ti。
The further technical scheme is as follows: in S5, by the first difference equation,calculating output shaping position information with a first difference equation of
Figure BDA0001748720060000021
The further technical scheme is as follows: the S6 includes:
s61, measuring a second vibration frequency and a second damping ratio by using a virtual oscilloscope;
s62, calculating related ZVD shaper coefficient A in a cascade mode according to the first vibration frequency, the second vibration frequency, the first damping ratio and the second damping ratioiAnd ti。
The further technical scheme is as follows: in S7, calculating output shaping position information by a second difference equation; the second difference equation is
Figure BDA0001748720060000031
Robot end shake suppression system based on ZVD shaper includes:
a location unit for obtaining a location instruction;
the jitter judging unit is used for judging whether the terminal jitter function is started or not;
the vibration suppression judging unit is used for judging whether single vibration suppression is started or not;
a measurement calculation unit for measuring the vibration frequency and damping ratio and calculating the related ZVD shaper coefficient AiAnd ti；
And the calculation output unit is used for calculating and outputting the shaping position information.
The further technical scheme is as follows: the measurement calculation unit comprises a measurement module and a calculation module;
the measuring module is used for measuring the vibration frequency and the damping ratio;
a calculation module for calculating the related ZVD shaper coefficient AiAnd ti。
Compared with the prior art, the invention has the beneficial effects that: aiming at the ubiquitous terminal shake of the robot, the robot has a good inhibition effect, the positioning time is shortened, and the efficiency is improved.
The invention is further described below with reference to the accompanying drawings and specific embodiments.
Drawings
FIG. 1 is a flow chart of a robot end jitter suppression method based on a ZVD shaper according to the present invention;
FIG. 2 is a diagram illustrating a dithering cycle of FIG. 1;
FIG. 3 is a schematic diagram of the operation of the robot end jitter suppression method based on the ZVD shaper according to the present invention;
fig. 4 is a block diagram of the robot end-shaking suppression system based on the ZVD shaper according to the present invention.
10 position unit 20 shake determination unit
30 vibration suppression determination unit 40 measurement calculation unit
41 measurement module 42 calculation module
50 calculation output unit
Detailed Description
In order to more fully understand the technical content of the present invention, the technical solution of the present invention will be further described and illustrated with reference to the following specific embodiments, but not limited thereto.
The specific embodiments shown in fig. 1 to 4, wherein, as shown in fig. 1 to 3, the invention discloses a robot end jitter suppression method based on a ZVD shaper, comprising the following steps:
s1, obtaining a position instruction;
s2, judging whether the terminal shaking function is started; if the signal is on, the next step is carried out, and if the signal is not on, the step is carried out to S8;
s3, judging whether the single vibration suppression is started or not; if the signal is on, the next step is carried out, and if the signal is not on, the step is carried out to S6;
s4, measuring the first vibration frequency and the first damping ratio, and calculating the related ZVD shaper coefficient AiAnd ti；
S5, obtaining shaping position information through calculation and outputting the shaping position information;
s6, measuring a second vibration frequency and a second damping ratio, and calculating a related ZVD shaper coefficient AiAnd ti；
S7, obtaining shaping position information through calculation and outputting the shaping position information;
and S8, ending.
As shown in fig. 2, in S1, the position command is obtained according to the control cycle 62.5us of the position loop.
Specifically, as shown in fig. 3, S1 further includes that the position command is output through the ZVD shaper, the position loop P adjustment and the position feedforward output to set the speed, and the PI adjustment of the speed loop and the current loop is performed to control the operation of the motor.
Wherein S4 includes:
s41, obtaining a first vibration frequency and a first damping ratio according to the position feedback waveform of the virtual oscilloscope;
s42, calculating the related ZVD shaper coefficient A according to the first vibration frequency and the first damping ratioiAnd ti。
In S5, the output shaping position information is calculated by the first difference equation of
Figure BDA0001748720060000051
Wherein S6 includes:
s61, measuring a second vibration frequency and a second damping ratio by using a virtual oscilloscope;
s62, calculating related ZVD shaper coefficient A in a cascade mode according to the first vibration frequency, the second vibration frequency, the first damping ratio and the second damping ratioiAnd ti。
In S7, calculating output shaping position information by using a second difference equation; the second difference equation is
Figure BDA0001748720060000061
The ZVD input shaper is another strategy for passively eliminating buffeting besides a filtering mode, belongs to open-loop control, and is often used for eliminating buffeting at the tail end of a flexible system such as a mechanical arm and the like; based on the physical resonance characteristics of the equipment, but different from the control idea of filtering a specific resonance frequency by a filtering scheme, the input shaping technology starts from the modal analysis of a mechanical system, the part of the jitter of the command excitation tail end of a servo control system is eliminated by self, and the command directly followed by the servo does not contain the characteristic frequency any more, so that the elastic jitter is restrained.
Wherein, the principle of the ZVD input shaper is as follows: like the notch filter, the input shaper also performs certain processing on the position command before the position command enters the servo driver, so that the position command cannot excite the whole servo drive control new system, and therefore the position command is positioned between the position command virtual oscilloscope and the servo tracking drive system like the notch filter; the basic idea of the input shaper is to decompose the original position command into a series of pulse signals, which are input into the system in sequence, i.e. to achieve the purpose of eliminating the end jitter by shaping the command into a form that does not cause residual vibration of the system.
Further, taking two pulses as an example, for a servo control system under one elastic connection system, at the time when T is 0s, the pulse a1 may excite the system response to generate a jitter phenomenon, the jitter period of the system is T, if the pulse a2 is added to the system at the time when T is T/2, the system response may also be excited to generate a jitter phenomenon, the jitter period of the system response is T, the two phases are different by a half cycle, and if the amplitudes of the pulses a1 and a2 can be further controlled to match, the jitters excited by the pulses a1 and a2 can be cancelled out, so as to achieve the effect of suppressing the end jitter.
The response characteristic of most systems is determined by a pair of dominant poles, and the transfer function is:
Figure BDA0001748720060000062
wherein, ω isnIs the natural frequency, and ε is the damping ratio.
The input shaping technique is a process: convolving a command loaded by a system with a specified pulse time-lag signal to obtain the passing of a shaping signal; when 0< epsilon <1, the system shows under damping and the unit pulse of the system is output;
Figure BDA0001748720060000071
wherein
Figure BDA0001748720060000072
Is the natural frequency of a second order system.
The input shaper formed by N pulses is expressed as:
Figure BDA0001748720060000073
Figure BDA0001748720060000074
the input shaper is generally placed in front of the whole closed-loop system, and the whole controlled system belongs to open-loop control at the moment; in case the unit pulse output of the controlled object is ω (t) and the unit pulse output of the input shaper is f (t), the unit pulse output of the system can be expressed as:
Figure BDA0001748720060000075
when the number of pulses is n, the response is formed by the superposition of n pulse response formulas, namely, a unit pulse signal forms a pulse sequence after being input into a shaper, then a second-order system receives the command, and the response of the system is formed by the sum of the outputs caused by the n pulse time-lag sequences. The system is formed by superposing sinusoidal signals with the same frequency, and can be simplified by a trigonometric function, so that the system response of a plurality of pulses is as follows:
Figure BDA0001748720060000076
by taking the ratio of the above amplitude values, a unitless residual vibration expression can be obtained, that is:
Figure BDA0001748720060000081
if the system has no end jitter phenomenon, it must satisfy:
Figure BDA0001748720060000082
since the calculation result of the system of equations is of infinite order, an infinite number of input shapers are obtained, so that the system presents a finite impulse response. If the constraint condition on the performance of the input shaper is increased, a unique solution can be obtained, and the obtained input shaper has a specific performance index.
Firstly, the amplitude is defined, and the gain is ensured to have the same amplitude before and after shaping, namely:
Figure BDA0001748720060000083
if overshoot does not occur in the system, the amplitudes should all be equal to positive numbers, i.e.:
Ai＞0
the input shaper is a targeted time-lag implanted system, and in order to improve the response speed of the system, the time is required to be as small as possible, so that the first pulse is specified to be realized at the zero moment, namely:
t1＝0
if the input shaper is required to implement, i >1, then:
ti＞0
the Zero Vibration Differential (ZVD) input shaper consists of three pulses, the concrete representation of which can be written as:
Figure BDA0001748720060000084
such a shaper not only requires zero amplitude of the vibrations in the system response, but also zero amplitude of the variations of the vibrations, meaning a stronger suppression and robustness to vibrations.
Figure BDA0001748720060000091
According to the above conditions, the correlation coefficient in step three can be obtained:
Figure BDA0001748720060000092
wherein T is the period of the controlled object:
Figure BDA0001748720060000093
Figure BDA0001748720060000094
discretizing treatment: let ti＝niTs，TsFor a sampling period, f(s) performs Z-transform:
Figure BDA0001748720060000095
the difference equation is then:
y(n)＝A1x(n-n1)+A2x(n-n2)+A3x(n-n3)
since n is10, can be simplified as:
y(n)＝A1x(n)+A2x(n-n2)+A3x(n-n3)
if the sampling frequency is 16384hz and the vibration frequency is detected to be more than 4hz, the number of sampling points is 16384/4-4096; from n toi＝ti/Ts＝tifsN can be determinediThe value of (c) actually corresponds to a FIR filter.
The parameters are related to the natural frequency and the damping ratio, and the natural frequency is determined by measuring and calculating the vibration period and the oscillation frequency according to the waveform fed back by the display position of the virtual oscilloscope, so that the natural frequency and the damping ratio can be obtained.
The natural frequency is the reciprocal of the vibration period, the empirically obtained damping ratio has a corresponding relationship with the oscillation period, and the oscillation period number represents the number of oscillation periods that the load experiences when the controlled object is finally stabilized at the target position (as shown in the following table).
Number of oscillation cycles 1 2 3 4 5
Damping ratio 0.4 0.3 0.2 0.15 0.13
Number of oscillation cycles 6 7 8 9 10
Damping ratio 0.11 0.1 0.09 0.07 0.06
Number of oscillation cycles 11 12 13 14 15
Damping ratio 0.05 0.046 0.043 0.04 0.035
The system often has more than one vibration mode, and if one group of shapers cannot completely eliminate the jitter, a plurality of shapers need to be arranged in a cascade manner, taking two groups of shapers as an example:
Figure BDA0001748720060000101
Figure BDA0001748720060000102
convolving the two formulas to set the amplitude value as A1，A2,A3；B1,B2，B3The parameters of the input shaper for both modes are:
Figure BDA0001748720060000103
as shown in fig. 4, the present invention also discloses a robot end jitter suppression system based on the ZVD shaper, which includes:
a position unit 10 for obtaining a position instruction;
a jitter judging unit 20 for judging whether the terminal jitter function is on;
a vibration suppression judgment unit 30 for judging whether the single vibration suppression is on;
a measurement calculation unit 40 for measuring the vibration frequency and damping ratio and calculating the related ZVD shaper coefficient AiAnd ti；
And a calculation output unit 50 for calculating and outputting the shaping position information.
Wherein, the measurement calculation unit 40 includes a measurement module 41 and a calculation module 42;
a measuring module 41 for measuring the vibration frequency and the damping ratio;
a calculating module 42 for calculating the related ZVD shaper coefficient aiAnd ti。
The invention has good inhibition effect aiming at the ubiquitous terminal shake of the robot, reduces the positioning time and improves the efficiency.
The technical contents of the present invention are further illustrated by the examples only for the convenience of the reader, but the embodiments of the present invention are not limited thereto, and any technical extension or re-creation based on the present invention is protected by the present invention. The protection scope of the invention is subject to the claims.

Claims (5)

1. The robot end jitter suppression method based on the ZVD shaper is characterized by comprising the following steps of:
s1, obtaining a position instruction;
s2, judging whether the terminal shaking function is started; if the signal is on, the next step is carried out, and if the signal is not on, the step is carried out to S8;
s3, judging whether the single vibration suppression is started or not; if the signal is on, the next step is carried out, and if the signal is not on, the step is carried out to S6;
s4, measuring the first vibration frequency and the first damping ratio, and calculating the related ZVD shaper coefficient AiAnd ti；
S5, obtaining shaping position information through calculation and outputting the shaping position information;
s6, measuring a second vibration frequency and a second damping ratio, and calculating a related ZVD shaper coefficient AiAnd ti；
S7, obtaining shaping position information through calculation and outputting the shaping position information;
s8, ending;
in S1, the position command is obtained according to the control cycle of the position loop of 62.5 us; the step S1 is that the position instruction is output by a ZVD shaper, the position loop P adjustment and the position feedforward output give speed, and PI adjustment of a speed loop and a current loop is carried out to control the operation of the motor; taking two pulses as an example, for a servo control system under an elastic connection system, at the time when T is 0s, the pulse a1 can excite the system to respond to the jitter phenomenon, the jitter period of the system is T, if the pulse a2 is added to the system at the time when T is T/2, the pulse a1 can also excite the system to respond to the jitter phenomenon, the jitter period of the system is T, the phase difference between the two is half a period, and if the amplitude of the pulses a1 and a2 can be further controlled to cooperate, the jitters excited by the pulses a1 and a2 can be mutually cancelled, so that the effect of suppressing the end jitter is achieved;
the response characteristic of most systems is determined by a pair of dominant poles, and the transfer function is:
Figure FDA0003293167370000021
wherein, ω isnIs the natural frequency, epsilon is the damping ratio;
the input shaping technique is a process: convolving a command loaded by a system with a specified pulse time-lag signal to obtain the passing of a shaping signal; when 0< epsilon <1, the system shows under damping and the unit pulse of the system is output;
Figure FDA0003293167370000022
wherein
Figure FDA0003293167370000023
Is the natural frequency of the second order system;
the input shaper formed by N pulses is expressed as:
Figure FDA0003293167370000024
Figure FDA0003293167370000025
the input shaper is generally placed in front of the whole closed-loop system, and the whole controlled system belongs to open-loop control at the moment; in case the unit pulse output of the controlled object is ω (t) and the unit pulse output of the input shaper is f (t), the unit pulse output of the system can be expressed as:
Figure FDA0003293167370000026
when the number of pulses is n, the response is formed by the superposition of n pulse response types, namely, a unit pulse signal forms a pulse sequence after being input into a shaper, then a second-order system receives the command, the response of the system is formed by the sum of the outputs caused by the n pulse time-delay sequences, the response is formed by the superposition of sinusoidal signals with the same frequency, the response can be simplified by a trigonometric function, and the system response of a plurality of pulses is as follows:
Figure FDA0003293167370000031
by taking the ratio of the above amplitude values, a unitless residual vibration expression can be obtained, that is:
Figure FDA0003293167370000032
if the system has no end jitter phenomenon, it must satisfy:
Figure FDA0003293167370000033
because the calculation result of the equation set is infinite order, an infinite number of input shapers are obtained, so that the system presents finite impulse response; if the constraint condition for the performance of the input shaper is increased, a unique solution can be obtained, and the obtained input shaper has a specific performance index;
firstly, the amplitude is defined, and the gain is ensured to have the same amplitude before and after shaping, namely:
Figure FDA0003293167370000034
if overshoot does not occur in the system, the amplitudes should all be equal to positive numbers, i.e.:
Ai＞0
the input shaper is a targeted time-lag implanted system, and in order to improve the response speed of the system, the time is required to be as small as possible, so that the first pulse is specified to be realized at the zero moment, namely:
t1＝0
if the input shaper is required to implement, i >1, then:
ti＞0
the zero-vibration differential input shaper consists of three pulses, a concrete representation of which can be written as:
Figure FDA0003293167370000041
the shaper not only requires the vibration amplitude in the system response to be zero, but also requires the vibration variation amplitude to be zero, which means that the shaper has stronger suppression effect and robustness on the vibration;
Figure FDA0003293167370000042
according to the above conditions, the correlation coefficient in step three can be obtained:
Figure FDA0003293167370000043
wherein T is the period of the controlled object:
Figure FDA0003293167370000044
Figure FDA0003293167370000045
discretizing treatment: let ti＝niTs，TsFor a sampling period, f(s) performs Z-transform:
Figure FDA0003293167370000046
the difference equation is then:
y(n)＝A1x(n-n1)+A2x(n-n2)+A3x(n-n3)
since n is10, can be simplified as:
y(n)＝A1x(n)+A2x(n-n2)+A3x(n-n3)
if the sampling frequency is 16384hz and the vibration frequency is detected to be more than 4hz, the number of sampling points is 16384/4-4096; from n toi＝ti/Ts＝tifsN can be determinediA value of (a), effectively corresponding to a FIR filter;
the parameters are related to the natural frequency and the damping ratio, and the natural frequency is determined by measuring and calculating the vibration period and the oscillation frequency according to the waveform fed back by the display position of the virtual oscilloscope, so that the natural frequency and the damping ratio can be obtained.
2. The ZVD shaper-based robot end jitter suppression method according to claim 1, wherein said S4 comprises:
s41, obtaining a first vibration frequency and a first damping ratio according to the position feedback waveform of the virtual oscilloscope;
s42, calculating the related ZVD shaper coefficient A according to the first vibration frequency and the first damping ratioiAnd ti。
3. The ZVD shaper-based robot end shake suppression method according to claim 1, wherein in S5, output shaping position information is calculated by a first difference equation; the first difference equation is
Figure FDA0003293167370000051
4. The ZVD shaper-based robot end jitter suppression method according to claim 1, wherein said S6 comprises:
s61, measuring a second vibration frequency and a second damping ratio by using a virtual oscilloscope;
s62, calculating related ZVD shaper coefficient A in a cascade mode according to the first vibration frequency, the second vibration frequency, the first damping ratio and the second damping ratioiAnd ti。
5. The ZVD shaper-based robot end shake suppression method according to claim 1, wherein in S7, output shaping position information is calculated by a second difference equation; the second difference equation is
Figure FDA0003293167370000052
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