CN111515955A - Method and device for inhibiting residual shaking of flexible joint mechanical arm - Google Patents

Method and device for inhibiting residual shaking of flexible joint mechanical arm Download PDF

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CN111515955A
CN111515955A CN202010399907.5A CN202010399907A CN111515955A CN 111515955 A CN111515955 A CN 111515955A CN 202010399907 A CN202010399907 A CN 202010399907A CN 111515955 A CN111515955 A CN 111515955A
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joint
mechanical arm
inertia
elbow joint
elbow
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CN111515955B (en
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杨跞
汪晓姗
王成刚
周飞
许楠
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Siasun 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
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1635—Programme controls characterised by the control loop flexible-arm control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1607—Calculation of inertia, jacobian matrixes and inverses

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Abstract

The application provides a method and a device for inhibiting residual jitter of a flexible joint mechanical arm, wherein the method for inhibiting the residual jitter comprises the following steps: calculating dynamic parameters of the mechanical arm, wherein the dynamic parameters comprise natural frequency and structural damping of each joint of the mechanical arm; calculating pulse parameters of a time-varying input shaper according to the kinetic parameters, wherein the pulse parameters comprise pulse amplitude and time; convolving the shaping pulse of the time-varying input shaper with the command signal to obtain a convolved signal; and inputting the convolved signal into a second-order system as an input signal of the second-order system to obtain an output response with zero residual jitter, and finishing the inhibition of the residual jitter of the flexible joint mechanical arm. The method and the device can adapt to the natural frequency and damping of a time-varying system, complete the suppression of the residual vibration of the flexible joint mechanical arm, and have a good residual vibration suppression effect.

Description

Method and device for inhibiting residual shaking of flexible joint mechanical arm
Technical Field
The application belongs to the technical field of mechanical arm control, and particularly relates to a method and a device for inhibiting residual shaking of a flexible joint mechanical arm.
Background
The light-weight cooperative mechanical arm is driven by the harmonic reducer, and the rigidity of the harmonic reducer is low, so that the joint of the mechanical arm is flexible. Especially when the robot arm is started or stopped, the residual shaking caused by the flexible joint is very obvious.
In the prior art, one usually employs an open-loop vibration suppression algorithm to suppress the residual jitter. Input shaping is an effective open-loop vibration suppression algorithm, which designs a series of pulse signals to be convolved with a reference signal to generate a shaped signal. The shaping signal is used as a feedforward control signal of the system, and the jitter of the joint output end can be eliminated. The system has time-varying dynamics because the joint angle and load of the mechanical arm vary with time, resulting in a time-varying mass distribution of the system. The traditional input shaping vibration suppression algorithm cannot adapt to the natural frequency and the damping of a time-varying system, so that the vibration suppression effect is limited.
Disclosure of Invention
In order to overcome the problems in the related art at least to a certain extent, the application provides a method and a device for inhibiting the residual shaking of the flexible joint mechanical arm.
According to a first aspect of embodiments of the present application, there is provided a method for suppressing residual shake of a flexible joint manipulator, including:
calculating dynamic parameters of the mechanical arm, wherein the dynamic parameters comprise natural frequency and structural damping of each joint of the mechanical arm;
calculating pulse parameters of a time-varying input shaper according to the kinetic parameters, wherein the pulse parameters comprise pulse amplitude and time;
convolving the shaping pulse of the time-varying input shaper with the command signal to obtain a convolved signal;
and inputting the convolved signal into a second-order system as an input signal of the second-order system to obtain an output response with zero residual jitter, and finishing the inhibition of the residual jitter of the flexible joint mechanical arm.
In the method for suppressing residual vibration of a flexible joint mechanical arm, when the mechanical arm includes 6 rotary joints and a plurality of rods connected to the rotary joints, where the 6 rotary joints include a shoulder joint, a first elbow joint, a second elbow joint, a first wrist joint, a second wrist joint, and a third wrist joint, the step of calculating the kinetic parameters of the mechanical arm includes:
simplifying the configuration of the mechanical arm so as to reserve a shoulder joint, a first elbow joint and a second elbow joint which have large influence on the whole inertia change of the mechanical arm, and omit a first wrist joint, a second wrist joint and a third wrist joint which have large influence on the whole inertia change of the mechanical arm;
kinetic parameters of the shoulder joint, the first elbow joint and the second elbow joint are calculated.
Further, the specific process of calculating the kinetic parameters of the shoulder joint, the first elbow joint and the second elbow joint in the steps is as follows:
the shoulder joint, the first elbow joint and the second elbow joint are all regarded as double-inertia models, and a dynamic equation from a motor end to a load end in the double-inertia models corresponding to the shoulder joint, the first elbow joint and the second elbow joint is obtained;
obtaining the natural frequencies of the shoulder joint, the first elbow joint and the second elbow joint according to a kinetic equation from a motor end to a load end in the double-inertia model;
obtaining that the vibration of the tail end of the mechanical arm mainly depends on the shoulder joint according to the relation between the natural frequency of the shoulder joint, the first elbow joint and the second elbow joint and the corresponding inertia item;
according to the relation between the natural frequency of the shoulder joint and the load end angle in the double-inertia model, the expression of the natural frequency of the shoulder joint with respect to the length from the center of the end tool of the mechanical arm to the origin of the base coordinate system in the horizontal direction is obtained as follows:
Figure BDA0002489002880000021
in the formula, ω1(M, t) denotes the natural frequency of the shoulder joint, xe(t) represents the length from the center of the tool at the tail end of the mechanical arm to the origin of the base coordinate system in the horizontal direction, M represents the tail end load mass of the mechanical arm, and the coefficients a, b, c and d are obtained through experimental fitting.
Furthermore, the dynamic equation from the motor end to the load end in the dual inertia model corresponding to the shoulder joint, the first elbow joint and the second elbow joint is as follows:
Figure BDA0002489002880000031
Figure BDA0002489002880000032
Figure BDA0002489002880000033
Figure BDA0002489002880000034
Figure BDA0002489002880000035
Figure BDA0002489002880000036
wherein θ is ═ θ1θ2θ3]T，
Figure BDA0002489002880000037
Moment, G, representing the Coriolis force and the centrifugal force of the i-th jointi(θ) represents a gravitational moment; kTiRepresenting the spring rate, r, of the ith joint in a dual inertia modeliThe expression represents the reduction ratio, θ, of the reduction gear in the dual inertia modelmiRepresenting the motor angle, θ, in a model representing the dual inertiaiRepresenting load end angles in a representation dual-inertia model; mij(θ) represents an inertia term; c. CmiCoefficient representing the viscous damping present at each joint motor, ciCoefficient representing the viscous damping present at each joint, ckiRepresenting the coefficient of viscous damping present at each torsion spring.
Further, the natural frequencies of the shoulder joint, the first elbow joint, and the second elbow joint are:
Figure BDA0002489002880000038
in the formula, KTiIs a constant; m(2i)(2i)(θ) represents an inertia term;
when i is 1, the natural frequency ω of the shoulder joint1(M, t) is with respect to the inertia term M22Expression of (theta), and inertia term M22(theta) end angle theta with load2And theta3(ii) a change;
when i is 2, the natural frequency ω of the first elbow joint2(M, t) is with respect to the inertia term M44Expression of (theta), and inertia term M44(θ) is a constant;
when i is 3, the natural frequency ω of the second elbow joint3(M, t) is with respect to the inertia term M66Expression of (theta), and inertia term M66(θ) is a constant.
Further, in the step of calculating the pulse parameters of the time-varying input shaper according to the kinetic parameters, the pulse parameters of the time-varying input shaper are:
Figure BDA0002489002880000041
in the formula, A1And t1Respectively representing the amplitude and input time of the first pulse, A2And t2Respectively representing the amplitude and input time of the second pulse, A3And t3Respectively representing the amplitude and input time of the third pulse; zeta denotes the structural damping, M denotes the end load mass of the robot arm, omega1(M, t) represents the natural frequency of the shoulder joint.
Further, the step of convolving the shaped pulse of the time-varying input shaper with the command signal to obtain a convolved signal, where the convolved signal is:
Figure BDA0002489002880000042
in the formula, thetad(t) represents a command signal.
According to a second aspect of the embodiments of the present application, there is also provided a flexible joint mechanical arm residual jitter suppression device based on a time-varying input shaper, including:
a memory and a processor, wherein the processor is capable of,
the processor is configured to execute any of the flexible joint manipulator residual jitter suppression methods described above based on instructions stored in the memory.
According to a third aspect of embodiments of the present application, there is also provided a computer storage medium having a computer program stored thereon, the computer program, when executed by a processor, implementing the flexible joint robot residual-shaking suppressing method of any one of the above.
According to the above embodiments of the present application, at least the following advantages are obtained: the method for suppressing the residual jitter of the flexible joint mechanical arm calculates the dynamic parameters of the mechanical arm, calculates the pulse parameters of the time-varying input shaper according to the dynamic parameters, and convolves the shaping pulse of the time-varying input shaper with an instruction signal to obtain a convolved signal; the convolved signal is input into a second-order system as an input signal of the second-order system to obtain an output response with zero residual jitter.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the scope of the invention, as claimed.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of the specification of the application, illustrate embodiments of the application and together with the description, serve to explain the principles of the application.
Fig. 1 is a flowchart of a method for suppressing residual shaking of a flexible joint robot arm according to an embodiment of the present disclosure.
Fig. 2 is a schematic structural diagram of a robot arm configuration according to an embodiment of the present disclosure.
Fig. 3 is a schematic diagram of a dual inertia model of a joint according to an embodiment of the present application.
Fig. 4 is a schematic diagram of joint jitter control based on a time-varying input shaper according to an embodiment of the present application.
Fig. 5 is a schematic diagram of input shaping provided in an embodiment of the present application.
Detailed Description
For the purpose of promoting a clear understanding of the objects, aspects and advantages of the embodiments of the present application, reference will now be made to the accompanying drawings and detailed description, wherein like reference numerals refer to like elements throughout.
The illustrative embodiments and descriptions of the present application are provided to explain the present application and not to limit the present application. Additionally, the same or similar numbered elements/components used in the drawings and the embodiments are used to represent the same or similar parts.
As used herein, "first," "second," …, etc., are not specifically intended to mean in a sequential or chronological order, nor are they intended to limit the application, but merely to distinguish between elements or operations described in the same technical language.
With respect to directional terminology used herein, for example: up, down, left, right, front or rear, etc., are simply directions with reference to the drawings. Accordingly, the directional terminology used is intended to be illustrative and is not intended to be limiting of the present teachings.
As used herein, the terms "comprising," "including," "having," "containing," and the like are open-ended terms that mean including, but not limited to.
As used herein, "and/or" includes any and all combinations of the described items.
References to "plurality" herein include "two" and "more than two"; reference to "multiple sets" herein includes "two sets" and "more than two sets".
As used herein, the terms "substantially", "about" and the like are used to modify any slight variation in quantity or error that does not alter the nature of the variation. In general, the range of slight variations or errors that such terms modify may be 20% in some embodiments, 10% in some embodiments, 5% in some embodiments, or other values. It should be understood by those skilled in the art that the aforementioned values can be adjusted according to actual needs, and are not limited thereto.
Certain words used to describe the present application are discussed below or elsewhere in this specification to provide additional guidance to those skilled in the art in describing the present application.
Fig. 1 shows a flowchart of a method for suppressing residual shaking of a flexible joint manipulator according to the present application.
As shown in fig. 1, a method for suppressing residual shaking of a flexible joint manipulator provided in an embodiment of the present application includes the following steps:
and S1, calculating dynamic parameters of the mechanical arm, wherein the dynamic parameters comprise the natural frequency and the structural damping of each joint.
Since the structural damping of each joint does not change much during the operation of the robot arm, the structural damping of each joint is usually set to be constant. Since the flexibility of the joints is considered to be a main source of mechanical arm vibration, the calculation of the kinetic parameters is mainly to calculate the natural frequency of each joint.
S11, simplifying the configuration of the mechanical arm;
before calculating the dynamic parameters of the mechanical arm, the configuration of the mechanical arm needs to be simplified, and a part of the mechanical arm which has small influence on calculation is omitted.
Fig. 2 is a schematic diagram of a robot arm configuration. The mechanical arm comprises 6 rotary joints and a plurality of rod pieces connected with the rotary joints. The 6 rotary joints are shoulder Joint joints respectively1First elbow Joint Joint2And a second elbow Joint3And a first wrist Joint4Second wrist Joint Joint5And a third wrist Joint6。
As shown in FIG. 2, ● represents a revolute pair, ○ represents a center of mass of a rod, and joint variables of the mechanical arm are rotation angles of the joints around the axes of the revolute pair in the coordinate system of the mechanical arm, corresponding to the revolute joints, and the rotation angles are theta1、θ2、θ3、θ4、θ5And theta6。
Because the influence of the wrist Joint of the mechanical arm on the integral inertia change of the mechanical arm is small, when the dynamic parameters of each Joint are deduced, the Joint of the wrist Joint can be used4、Joint5And Joint6As a quality point, only the shoulder Joint is calculated1And a first elbow Joint2And a second elbow Joint3And the 3 joints are subjected to jitter suppression based on the input shaper.
S12, calculating the dynamic parameters of the shoulder joint and the elbow joint;
each single joint of the robotic arm may be considered a dual inertia model as shown in fig. 3. In the dual inertia model, the spring rate of the ith joint is set to KTiThe reduction ratio of the speed reducer is riAngle of the motor being thetamiThe load end angle is thetai。
Suppose that there is a coefficient c at the i-th joint motormiWith a coefficient of presence c at each jointiWith a coefficient of c at each torsion springkiViscous damping of (2); motor end inertia is JmiThe inertia of the joint is JliTorque at motor end τiOf the transmission torque taulmiTorque at the load end τliFor a single joint:
a motor end:
Figure BDA0002489002880000071
a load end:
Figure BDA0002489002880000072
wherein,
Figure BDA0002489002880000073
a transmission link:
Figure BDA0002489002880000081
then for shoulder Joint1First elbow Joint Joint2And a second elbow Joint3In other words, the following kinetic equations exist:
Figure BDA0002489002880000082
Figure BDA0002489002880000083
Figure BDA0002489002880000084
Figure BDA0002489002880000085
Figure BDA0002489002880000086
Figure BDA0002489002880000087
in formulae (1) to (6), θ ═ θ1θ2θ3]T，
Figure BDA0002489002880000088
Moment, G, representing the Coriolis force and the centrifugal force of the i-th jointi(θ) represents the gravitational moment.
In formulae (1) to (6)Term of inertia Mij(theta) directly affects the natural frequency, and if the rod section is uniform and symmetrical, the inertia term M is obtained according to the equations (1) to (6)ij(θ) is:
M11(θ)＝Jm1(7)
M22(θ)＝(malga2+Ja+Jc)C22+(mblgb 2+Jb+Jd)C32+mc(lbC3-
lgcC2)2+md(lcC2+lgdC3)2+M(lcC2+(la+lb)C3)2(8)
M33(θ)＝Jm2(9)
M44(θ)＝malga 2+Ja+mclgc 2+Jc+mdla 2+Mla 2(10)
M46(θ)＝M64(θ)＝mdlalgaC23-mclblgcC23+Mld(ld-lb)C23 (11)
M55(θ)＝Jm3(12)
M66(θ)＝mblgb 2+Jb+mclb 2+mdlgb 2+Jd+M(ld-lb)2(13)
in the formulae (7) to (13), lk(k ═ a, b, c, d) denotes the corresponding rod length, lgk(k ═ a, b, c, d) denotes the distance of the centroid of the corresponding bar to the joint, mk(k ═ a, b, c, d) denotes the mass of the rod, Jk(k ═ a, b, c, d) denotes inertia of the rod, Jmi(i ═ 1, 2, 3) denotes inertia of the motor, M denotes end load mass, and C2 denotes cos θ2And C3 represents cos θ3And C23 denotes cos (. theta.) (2-θ3)。
The natural frequency of the ith joint can be expressed as:
Figure BDA0002489002880000091
in the formula (14), KTiIs a constant.
As can be seen from equation (14), when i is 1, the natural frequency ω of the shoulder joint is1(M, t) is with respect to the inertia term M22(θ); and as can be seen from equation (8), the inertia term M22(theta) end angle theta with load2And theta3And (4) changing.
As can be seen from equation (14), when i is 2, the first elbow Joint2Natural frequency of (omega)2(M, t) is with respect to the inertia term M44The expression of (theta), and as can be seen from the expression (10), the inertia term M44(θ) is a constant.
As can be seen from equation (14), when i is 3, the second elbow Joint3Natural frequency of (omega)3(M, t) is with respect to the inertia term M66The expression of (θ), and as can be seen from the expression (13), the inertia term M66(θ) is a constant.
More importantly, the inertia term M22(θ) relative, inertia term M44(theta) and M66The value of (theta) is smaller, and therefore, the first elbow Joint Joint2And a second elbow Joint3The corresponding natural frequency is higher and the amplitude is smaller, so that the first elbow Joint2And a second elbow Joint3The influence on the amplitude of the tail end is smaller, and the vibration of the tail end of the mechanical arm is mainly determined by Joint of the shoulder Joint1. Therefore, only the shoulder Joint needs to be calculated1Time-varying kinetic parameter ω1(M, t) and designing a corresponding time-varying shaper to restrain shoulder Joint1Jitter of (2).
For an i-2, 3 case, the natural frequency ω of the first elbow joint need not be taken into account2(M, t) and omega of the first elbow joint3(M, t) changes along with time, and the first elbow Joint can be restrained only by designing a shaper with unchanged corresponding dynamic parameters2And a second elbow Joint3Jitter of (2).
Therefore, when i is 1, the load end angle θ is measured in real time2(t) and θ3(t) calculating the natural frequency ω of the shoulder joint1(M, t) is the key to designing the time varying shaper.
Since controllers of industrial robots or robot arms require higher computational efficiency, it is necessary to simplify equations (8) and (14). For convenience of simplification, physical quantity x is introducedeAs shown in fig. 3. Xe(t) represents the length in the horizontal direction from the center of the end-of-arm-tool to the origin of the base coordinate system.
Natural frequency omega of shoulder joint1(M, t) and an inertia term M22(θ), equivalent mass meConstant K and physical quantity xeThe relationship between (t) is:
Figure BDA0002489002880000101
the natural frequency ω of the shoulder joint can be obtained from the formula (14)1(M, t) term of inertia M22Expression of (θ):
Figure BDA0002489002880000102
in combination with formula (15) to yield:
M22(θ)＝mexe(t)2+C (16)
in the formula (16), C is a constant since mexe(t)2Larger, and therefore the constant C can be neglected, in combination with the natural frequency omega of the shoulder joint1(M, t) term of inertia M22(θ) to obtain:
Figure BDA0002489002880000103
the natural frequency period T of the shoulder joint1(M, t) satisfies:
T1(M，t)∝axe(t)+b
wherein a and b are constants, physical quantity xe(t) angle of load end θ2(t) and θ3(t) related, physical quantities xeThe value of (t), i.e. the length from the center of the end tool of the arm in the horizontal direction to the origin of the base coordinate system, can be read in real time.
As can be seen from the above derivation process, equations (8) and (14) can be simplified to equation (17), thereby increasing the natural frequency ω of the shoulder joint1Efficiency of calculation of (M, t).
Because the end load mass M of the mechanical arm is different under different working conditions and tasks, the frequency changes along with the end load mass M. The following can be obtained through experiments:
Figure BDA0002489002880000111
the natural frequency period T of the shoulder joint1(M, t) satisfies:
T1(M，t)∝cM+d
obtained from formula (17) and formula (18):
T1(M，t)＝axe(t)+b+cM+d，
the natural frequency omega of the shoulder joint1(M, t) with respect to the physical quantity XeThe expression of (t) is:
Figure BDA0002489002880000112
the coefficients a, b, c, d in equation (19) were obtained by experimental fitting.
S2, calculating pulse parameters of the shaper according to the dynamic parameters of the mechanical arm;
input shaping creates a new system input by convolving the original input of the system with a set of pulses determined based on the dynamics of the system to modify the original input of the system. The new input does not excite the system dither resonance mode, but suppresses the system dither.
The working principle of the shaper is as follows: for a single joint dual inertia model, it can be considered as a linear second-order system, with a natural frequency ω (M, t) and a damping constant ζ.
For a linear second order system, the impulse response is:
Figure BDA0002489002880000113
in the formula (20), A is the pulse amplitude, t is the time, t0Is the pulse input time.
When multiple pulses are applied in a linear dithering system, the response of the system to the pulses is superimposed. As shown in FIG. 5, the first amplitude is A1After passing through the system, a first impulse response is generated. t is t2After time, the second amplitude is A2The first impulse response is cancelled by the impulse response generated by the system, and the amplitude of the resultant response of the system is zero. Thus, if the system is to generate a dynamic response to a first pulsed input, the dynamic response generated by the first pulsed input can be cancelled by applying a second pulse of appropriate magnitude to the system at the appropriate time.
The process of finding the input shaper is to find when the system is inputting pulses of large amplitude. Inputting new pulses to the original system, namely performing convolution calculation on the new pulses and the original system input, so that the responses of the new pulses and the original system input are synthesized into zero after the new pulses and the original system input pass through the system, wherein the parameter solving principle is as follows:
the original input of the system is x (t), the input after convolution with the shaper (namely a series of pulses) through the input shaper is
x*(t)＝(x*I)(t)
For shoulder Joint1Which is a second order linear system, x*(t) after passing through a linear second-order system, the resultant impulse response is:
Figure BDA0002489002880000121
in equation (21), the input time of the ith pulse of the system is tiAmplitude of Ai。
Generally, taking N to 3, the residual jitter percentage of the system is:
Figure BDA0002489002880000122
since it is expected that the residual jitter is completely eliminated to zero, according to the zero-oscillation elimination method, the following conditions are satisfied:
Figure BDA0002489002880000131
and (3) calculating the formula (23) to obtain the pulse parameters of the shaper, wherein the pulse parameters of the shaper comprise: amplitude A of the first pulse1And an input time t1Amplitude A of the second pulse2And an input time t2Amplitude of the third pulse A3And an input time t3The pulse parameters are respectively as follows:
Figure BDA0002489002880000132
s3, convolving the shaper with the input signal to obtain a convolved signal;
for shoulder Joint1As shown in fig. 4, the shaped pulse obtained in step S2 and the system arbitrary command signal θ are usedd(t) performing convolution, wherein the signal after convolution is as follows:
Figure BDA0002489002880000133
and S4, inputting the convolved signal into a second-order system as an input signal of the second-order system to obtain an output response with zero residual jitter.
Joint through shoulder Joint1The output response of the second-order system is theta (t), and the residual jitter V (omega) is output1And (M, t) and zeta are zero, so that the vibration is eliminated, and the aim of inhibiting the residual vibration of the mechanical arm is fulfilled.
In an exemplary embodiment, the present application further provides a flexible joint robot residual jitter suppression apparatus based on a time-varying input shaper, which includes a memory and a processor, wherein the processor is configured to execute the flexible joint robot residual jitter suppression method in any one of the embodiments of the present application based on instructions stored in the memory.
The memory may be a system memory, a fixed nonvolatile storage medium, or the like, and the system memory may store an operating system, an application program, a boot loader, a database, other programs, and the like.
In an exemplary embodiment, the present application further provides a computer storage medium, which is a computer readable storage medium, for example, a memory including a computer program, which is executable by a processor to perform the flexible joint robot residual jitter suppression method in any one of the embodiments of the present application.
The embodiments of the present application described above may be implemented in various hardware, software code, or a combination of both. For example, the embodiments of the present application may also represent program codes for executing the above-described methods in a Digital Signal Processor (DSP). The present application may also relate to a variety of functions performed by a computer processor, digital signal processor, microprocessor, or Field Programmable Gate Array (FPGA). The processor described above may be configured in accordance with the present application to perform certain tasks by executing machine-readable software code or firmware code that defines certain methods disclosed herein. Software code or firmware code may be developed to represent different programming languages and different formats or forms. Different target platforms may also be represented to compile the software code. However, different code styles, types, and languages of software code and other types of configuration code for performing tasks according to the present application do not depart from the spirit and scope of the present application.
The foregoing represents only exemplary embodiments of the present application and all equivalent changes and modifications made by those skilled in the art without departing from the spirit and principles of the present application should fall within the scope of the present application.

Claims (9)

1. A method for suppressing residual jitter of a flexible joint mechanical arm is characterized by comprising the following steps:
calculating dynamic parameters of the mechanical arm, wherein the dynamic parameters comprise natural frequency and structural damping of each joint of the mechanical arm;
calculating pulse parameters of a time-varying input shaper according to the kinetic parameters, wherein the pulse parameters comprise pulse amplitude and time;
convolving the shaping pulse of the time-varying input shaper with the command signal to obtain a convolved signal;
and inputting the convolved signal into a second-order system as an input signal of the second-order system to obtain an output response with zero residual jitter, and finishing the inhibition of the residual jitter of the flexible joint mechanical arm.
2. The method of suppressing residual jitter of a flexible joint robot arm according to claim 1, wherein when the robot arm includes 6 rotational joints including a shoulder joint, a first elbow joint, a second elbow joint, and a first wrist joint, a second wrist joint, and a third wrist joint, and a plurality of rods connected to the rotational joints, the step of calculating the kinetic parameters of the robot arm includes:
simplifying the configuration of the mechanical arm so as to reserve a shoulder joint, a first elbow joint and a second elbow joint which have large influence on the whole inertia change of the mechanical arm, and omit a first wrist joint, a second wrist joint and a third wrist joint which have large influence on the whole inertia change of the mechanical arm;
kinetic parameters of the shoulder joint, the first elbow joint and the second elbow joint are calculated.
3. The method for suppressing the residual vibration of the flexible joint mechanical arm according to claim 2, wherein the specific process of calculating the dynamic parameters of the shoulder joint, the first elbow joint and the second elbow joint is as follows:
the shoulder joint, the first elbow joint and the second elbow joint are all regarded as double-inertia models, and a dynamic equation from a motor end to a load end in the double-inertia models corresponding to the shoulder joint, the first elbow joint and the second elbow joint is obtained;
obtaining the natural frequencies of the shoulder joint, the first elbow joint and the second elbow joint according to a kinetic equation from a motor end to a load end in the double-inertia model;
obtaining that the vibration of the tail end of the mechanical arm mainly depends on the shoulder joint according to the relation between the natural frequency of the shoulder joint, the first elbow joint and the second elbow joint and the corresponding inertia item;
according to the relation between the natural frequency of the shoulder joint and the load end angle in the double-inertia model, the expression of the natural frequency of the shoulder joint with respect to the length from the center of the end tool of the mechanical arm to the origin of the base coordinate system in the horizontal direction is obtained as follows:
Figure FDA0002489002870000021
in the formula, ω1(M, t) denotes the natural frequency of the shoulder joint, xe(t) represents the length from the center of the tool at the tail end of the mechanical arm to the origin of the base coordinate system in the horizontal direction, M represents the tail end load mass of the mechanical arm, and the coefficients a, b, c and d are obtained through experimental fitting.
4. The method for suppressing the residual vibration of the flexible joint mechanical arm according to claim 3, wherein the dynamic equation from the motor end to the load end in the double inertia model corresponding to the shoulder joint, the first elbow joint and the second elbow joint is as follows:
Figure FDA0002489002870000022
Figure FDA0002489002870000023
Figure FDA0002489002870000024
Figure FDA0002489002870000025
Figure FDA0002489002870000026
Figure FDA0002489002870000027
wherein θ is ═ θ1θ2θ3]T，
Figure FDA0002489002870000028
Figure FDA0002489002870000029
Moment, G, representing the Coriolis force and the centrifugal force of the i-th jointi(θ) represents a gravitational moment; kTiRepresenting the spring rate, r, of the ith joint in a dual inertia modeliThe expression represents the reduction ratio, θ, of the reduction gear in the dual inertia modelmiRepresenting the motor angle, θ, in a model representing the dual inertiaiRepresenting load end angles in a representation dual-inertia model; mij(θ) represents an inertia term; c. CmiCoefficient representing the viscous damping present at each joint motor, ciCoefficient representing the viscous damping present at each joint, ckiRepresenting the coefficient of viscous damping present at each torsion spring.
5. The method for suppressing residual jitter of a flexible joint robot arm according to claim 3, wherein the natural frequencies of the shoulder joint, the first elbow joint and the second elbow joint are:
Figure FDA0002489002870000031
in the formula, KTiIs a constant; m(2i)(2i)(θ) represents an inertia term;
when i is 1, the natural frequency ω of the shoulder joint1(M, t) is with respect to the inertia term M22Expression of (theta), andmeasure M22(theta) end angle theta with load2And theta3(ii) a change;
when i is 2, the natural frequency ω of the first elbow joint2(M, t) is with respect to the inertia term M44Expression of (theta), and inertia term M44(θ) is a constant;
when i is 3, the natural frequency ω of the second elbow joint3(M, t) is with respect to the inertia term M66Expression of (theta), and inertia term M66(θ) is a constant.
6. The method for suppressing the residual jitter of the flexible joint mechanical arm according to claim 2, wherein in the step of calculating the pulse parameters of the time-varying input shaper according to the kinetic parameters, the pulse parameters of the time-varying input shaper are as follows:
Figure FDA0002489002870000032
in the formula, A1And t1Respectively representing the amplitude and input time of the first pulse, A2And t2Respectively representing the amplitude and input time of the second pulse, A3And t3Respectively representing the amplitude and input time of the third pulse; zeta denotes the structural damping, M denotes the end load mass of the robot arm, omega1(M, t) represents the natural frequency of the shoulder joint.
7. The method for suppressing the residual jitter of the flexible joint mechanical arm according to claim 6, wherein the step of convolving the shaping pulse of the time-varying input shaper with the command signal obtains a convolved signal, and the convolved signal is:
Figure FDA0002489002870000041
in the formula, thetad(t) represents a command signal.
8. A flexible joint mechanical arm residual jitter suppression device based on a time-varying input shaper is characterized by comprising:
a memory and a processor, wherein the processor is capable of,
the processor is configured to execute the flexible joint mechanical arm residual jitter suppression method according to any one of claims 1 to 7 based on instructions stored in the memory.
9. A computer storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method for suppressing residual shake of a flexible joint robot arm according to any one of claims 1 to 7.
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