CN111590570A - Contour control method for synchronous cross-coupling robot - Google Patents

Contour control method for synchronous cross-coupling robot Download PDF

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CN111590570A
CN111590570A CN202010412932.2A CN202010412932A CN111590570A CN 111590570 A CN111590570 A CN 111590570A CN 202010412932 A CN202010412932 A CN 202010412932A CN 111590570 A CN111590570 A CN 111590570A
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contour
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CN111590570B (en
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王瑜瑜
刘少军
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Xian Aeronautical Polytechnic Institute
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    • 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

Abstract

The invention discloses a contour control method for a synchronous cross-coupling robot, which comprises the following steps: obtaining a workspace desired position xd、ydPerforming inverse kinematics calculation to output the desired joint space position theta1d、θ2d(ii) a The joint is related to the actual position theta of the joint space1a、θ2aAfter difference operation is carried out, joint space x-axis tracking error E is output1Joint space y-axis tracking error E2(ii) a x-axis joint space tracking error E1Y-axis joint space tracking error E2The motor is driven to operate after the operation of the PD controller; meanwhile, according to the space tracking error E of the x-axis joint1Y-axis joint space tracking error E2Separately calculating contour errorscSynchronous errorsError in profilecSynchronous errorsAfter the operation is respectively carried out by the contour controller and the synchronous controller, the position ring of the working space and the speed ring of the joint space are respectively compensated by combining the corresponding gains. Can further reduce the profile error and improve the controlAnd the effect is controlled, so that the tracking precision of the robot system is ensured.

Description

Contour control method for synchronous cross-coupling robot
Technical Field
The invention belongs to the technical field of robot control methods, and relates to a contour control method for a synchronous cross-coupling robot.
Background
With the rapid development of robot control technology and the increasingly perfect functions of robots, more and more robots are widely applied to the processing and manufacturing fields such as grinding, spraying and the like, and the requirements on the motion control precision of the robots are also higher and higher. In this case, the design of the robot system controller must take the contour error as an important performance index for the measurement system in addition to the original position tracking error, which determines that the size of the contour error must be considered in the controller design. However, the conventional contour control method is generally applicable to an orthogonal structure system or a numerical control machine tool system, and the research on the contour control method of the industrial robot system is very rare, and the nonlinearity of the motion relationship of the system further limits the direct application range of the conventional cross-coupling control.
Disclosure of Invention
The invention aims to provide a contour control method of a synchronous cross-coupling robot, which solves the problem that the traditional cross-coupling control in the prior art cannot be applied to an industrial robot system.
The technical scheme adopted by the invention is that the contour control method of the synchronous cross-coupling robot comprises the following steps:
step 1, obtaining a working space expected position xd、ydFor the desired position x of the workspaced、ydPerforming inverse kinematics solution operation to output joint space expected position theta1d、θ2d；
Step 2, obtaining the expected position theta of the joint space1d、θ2dWith the actual position theta in the joint space1a、θ2aAfter difference operation is carried out, joint space x-axis tracking error E is output1Joint space y-axis tracking error E2；
Step 3, x-axis joint space tracking error E1Y-axis joint space tracking error E2After the operation of the PD controller, the driving motor operates, and meanwhile, the tracking error E is obtained according to the space of the x-axis joint1Y-axis joint space tracking error E2Calculating contour errorcSeparately calculating contour errorscSynchronous errorsError in profilecAfter the operation of the profile controller, the synchronous error is compensated to the position ring of the working space by combining the corresponding gainsAfter operation by the synchronous controller, the corresponding gain is combined to compensateVelocity ring of joint space.
The invention is also characterized in that:
error in contourcSynchronous errorsThe calculation method comprises the following steps:
spatial tracking error E of x-axis joint1Y-axis joint space tracking error E2Performing kinematics positive solution operation and outputting the actual position x of the working spacea、ya；
The actual position x of the working spacea、yaAnd the expected position x of the working spaced、ydDifferencing to obtain x-axis tracking error ExY-axis tracking error Ey；
Error of tracking according to x-axis ExY-axis tracking error EyCalculating to obtain the contour errorcSynchronous errors。
Error in contourcCalculated according to the following formula:
c＝-ExCx+EyCy+ (1)；
in the above equation, the contour error compensation term is used.
When the profile shape is a linear straight line,
Figure BDA0002493953970000021
the profile error compensation term is 0.
When the profile shape is a curve, the profile error can be calculated according to the following equation:
Figure BDA0002493953970000022
in the above formula, R is the radius of the osculating circle, and theta is the included angle between the tangent vector of a certain point of the osculating circle and the x-axis;
then the x-axis gain CxY-axis gain CyComprises the following steps:
Figure BDA0002493953970000031
＝c-a，
Figure BDA0002493953970000032
error in contourcAfter the operation of the contour controller, compensating to a position ring of a working space by combining corresponding gain; the method specifically comprises the following steps: error in contourcAfter being calculated by a contour controller, the X-axis gain C is multiplied by the X-axis gain C respectivelyxY-axis gain CyCompensating to the desired position x of the working spaced、yd。
Synchronization errorsCalculated according to the following formula:
s＝Ex-Ey(9)；
assuming synchronization errorsSpace tracking error E of joint with x axis1Y-axis joint space tracking error E2The relationship is linear:
s＝C1E1+C2E2(10)；
in the above formula, C1For x-axis synchronous error gain, C2Is the y-axis synchronization error gain;
knowing the expected positions x and y of the working space, solving the joint space position theta according to the inverse kinematics1、θ2：
Figure BDA0002493953970000033
At the actual position (x) of the working space0,y0) Treating:
Figure BDA0002493953970000034
Figure BDA0002493953970000041
the four coefficients in the above formula are: a. the1＝f′1x(x0，y0)，B1＝f′1y(x0,y0)，A2＝f′2x(x0,y0)，B2＝f′2y(x0,y0)。
Synchronization errorsAfter the operation of the synchronous controller, the speed loop compensated to the joint space by combining the corresponding gain is specifically as follows: synchronization errorsAfter the calculation of the synchronous controller, the X-axis synchronous error gains C are respectively multiplied1Y-axis synchronous error gain C2Compensating to a desired position theta in joint space1d、θ2d。
The invention has the beneficial effects that:
according to the contour control method of the synchronous cross-coupling robot, the traditional cross-coupling control and PD control are combined, and the working space position and the joint space position of the robot are compensated in real time through the contour error and the synchronous error, so that the cross-coupling control method suitable for the system contour of the industrial robot is obtained; the contour error can be further reduced, the control effect is improved, and the tracking precision of the robot system is further ensured.
Drawings
FIG. 1 is a flow chart of a method for contour control of a synchronous cross-coupled robot according to the present invention;
FIG. 2a is a diagram illustrating the control effect of an embodiment of a contour control method for a position cross-coupling robot;
FIG. 2b is a diagram illustrating the control effect of an embodiment of the contour control method for a synchronous cross-coupled robot according to the present invention;
FIG. 3a is a diagram of the control effect of another embodiment of the contour control method of the position cross-coupling robot;
FIG. 3b is a diagram illustrating the control effect of another embodiment of the contour control method for a synchronous cross-coupled robot according to the present invention;
FIG. 4a is a diagram of the control effect of a third embodiment of the contour control method for a position cross-coupling robot;
fig. 4b is a control effect diagram of a contour control method for a synchronous cross-coupled robot according to a third embodiment of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
A contour control method for a synchronous cross-coupled robot, as shown in fig. 1, includes the following steps:
step 1, obtaining a working space expected position xd、ydFor the desired position x of the workspaced、ydPerforming inverse kinematics solution operation to output joint space expected position theta1d、θ2d(ii) a Workspace desired location xd、ydOutputting through an interpolator;
step 2, obtaining the expected position theta of the joint space1d、θ2dThe actual position theta of the joint space obtained by the feedback of the motor encoder1a、θ2aAfter difference operation is carried out, joint space x-axis tracking error E is output1Joint space y-axis tracking error E2；
Step 3, x-axis joint space tracking error E1Y-axis joint space tracking error E2After the operation of the PD controller, the driving motor operates, and meanwhile, the tracking error E is obtained according to the space of the x-axis joint1Y-axis joint space tracking error E2Separately calculating contour errorscSynchronous errorsError in profilecAfter being calculated by a contour controller, the X-axis gain C is multiplied by the X-axis gain C respectivelyxY-axis gain CyCompensated to (position loop of workspace) workspace desired position xd、yd(ii) a Synchronization errorsAfter the calculation of the synchronous controller, the X-axis synchronous error gains C are respectively multiplied1Y-axis synchronous error gain C2Compensated to (velocity ring of joint space) desired position θ of joint space1d、θ2d. The synchronization error reflects the coordination among all the motion axes of the system, and the smaller the error value is, the higher the coordination between the x axis and the y axis is, and the more positive the mutual response is.
In particular, profile errorscSynchronous errorsThe calculation method comprises the following steps:
will be carried through the PD controllerCalculated x-axis joint space tracking error E1Y-axis joint space tracking error E2Performing kinematics positive solution operation and outputting the actual position x of the working spacea、ya；
The actual position x of the working spacea、yaAnd the expected position x of the working spaced、ydDifferencing to obtain x-axis tracking error ExY-axis tracking error Ey；
Error of tracking according to x-axis ExY-axis tracking error EyCalculating to obtain the contour errorcSynchronous errors。
Further, profile errorcCalculated according to the following formula:
c＝-ExCx+EyCy+ (1)；
error in contourcThe calculation of (1) includes a linear straight line and a curved line, and when the contour shape is a linear straight line, the contour errorcCalculated by the following formula:
c＝-Exsinθ+Eycosθ (2)；
in the above formula, θ is an included angle between the linear straight line profile and the positive direction of the x axis;
comparing formula (2) with formula (1) gives:
Figure BDA0002493953970000061
the profile error compensation term is 0.
When the contour shape is a curve, the contour errorcCalculated by the following formula:
Figure BDA0002493953970000062
in the above formula, R is the radius of the osculating circle, and theta is the included angle between the tangent vector of a certain point of the osculating circle and the x-axis;
the formula (4) is developed in taylor to obtain:
Figure BDA0002493953970000063
the high order infinitesimal omission and then simplification in equation (5) can be:
Figure BDA0002493953970000064
similarly, comparing equation (5) with equation (1) can be:
Figure BDA0002493953970000071
the profile compensation error is obtained by subtracting equation (10) from equation (5): is ═ ic-a。
Synchronization errorsCalculated according to the following formula:
s＝Ex-Ey(9)；
synchronization errorsControl of (2) is critically the synchronous error gain C1、C2And (4) determining. Since the synchronous error feedback compensation is in the joint space, the relation between the synchronous error and the tracking error of each motion axis in the joint space is determined, and the synchronous error is assumedsSpace tracking error E of joint with x axis1Y-axis joint space tracking error E2The relationship is linear:
s＝C1E1+C2E2(10)；
knowing the workspace position x, y, i.e. the workspace desired position xd、ydSolving the joint space position theta according to the inverse kinematics1、θ2：
Figure BDA0002493953970000072
The above formula is arranged at the position (x) of the working space0,y0) Where, i.e. the actual position x of the workspacea、yaUsing taylor series expansion, we can obtain:
Figure BDA0002493953970000073
due to (x)0,y0) Representing the actual position and (x, y) the desired position, then: e1＝f1(x,y)-f1(x0,y0)，E2＝f2(x,y)-f2(x0,y0)；Ex＝x-x0，Ey＝y-y0Equation (12) may become:
Figure BDA0002493953970000074
the four coefficients are respectively: a. the1＝f′1x(x0,y0)，B1＝f′1y(x0，y0)，A2＝f′2x(x0，y0)，B2＝f′2y(x0，y0)；
From formulas (9) and (10):
Ex-Ey＝C1E1+C2E2(14)；
solving equations (13) and (14) simultaneously yields:
Figure BDA0002493953970000081
examples
The invention selects a plane five-rod parallel robot system as an experimental platform, and the rod length parameters are shown in the following table 1. The system is driven by 2 AC servo motors to operate, the rotating speed ratio is 30:1, the sampling time of the controller is 10ms, and the output voltage is limited to +/-10V. And circular and elliptical profile tracks are respectively selected for the position loop cross coupling robot profile control method and the synchronous cross coupling robot profile control method for carrying out comparison experiments.
TABLE 1 pole length parameter table
Figure BDA0002493953970000082
Example 1
The contour track is oval, the radius of the desired circle center contour track is set to be 8cm, the initial position (0.02, 0.35) of the end effector is set, the setting of the initial position of the end effector ensures that the robot is always located in a working space in the motion process, and the specific track equation is as follows:
Figure BDA0002493953970000083
the angular velocity ω of the circular trajectory is executed to set two cases of low speed and medium speed, respectively, and firstly, a low speed state where ω is 0.02rad/s is set, and the obtained motion profile error change and experimental data are respectively shown in fig. 2a, fig. 2b and table 2:
TABLE 2 Low speed circular trajectory experimental data
Figure BDA0002493953970000091
The comparison experiment result shows that the contour error of synchronous cross coupling control is obviously reduced, the maximum error of the contour is reduced by 3.12 mu m, and the root mean square value is reduced by 1.63 mu m.
Then, the tracking angular velocity is set to a medium speed, i.e., ω is 0.04rad/s, and the motion profile error variation and experimental data are obtained in the same manner as shown in fig. 3a, fig. 3b, and table 3, respectively:
TABLE 3 Medium speed circular trajectory experimental data
Figure BDA0002493953970000092
The results of the medium-speed comparison experiment show that the maximum error of the profile controlled by the synchronous cross coupling adopted by the control system of the ring cross coupling in a position is reduced by 1.96 mu m, and the root mean square value is reduced by 1.48 mu m.
Therefore, under the conditions of low speed or medium speed, the synchronous cross coupling control effect is obviously superior to that of position loop cross coupling control.
Example 2
The contour track is oval, the long radius of the expected circle center contour track is set to be 8cm, the short radius is set to be 4cm, the initial position (0.02 and 0.35) of the end effector effectively ensures the motion process of the system in the working space, and the specific track equation is as follows:
Figure BDA0002493953970000101
the motion profile error variation and experimental data obtained by setting ω to 0.02rad/s are shown in fig. 4a, 4b and table 4, respectively, as follows:
TABLE 4 Low-speed elliptical trajectory Experimental data
Figure BDA0002493953970000102
Similarly, the result of an oval outline comparison experiment shows that the maximum error of the outline is reduced by 6.21 μm and the root mean square value is reduced by 1.11 μm compared with the outline adopting synchronous cross coupling control in position loop cross coupling control.
Therefore, for the oval outline with a more complex shape, the synchronous cross coupling control effect still has a better control effect than the position ring cross coupling control, and the tracking precision of the system is greatly improved.
Through the mode, the contour control method of the synchronous cross-coupling robot can compensate the working space position and the joint space position of the robot in real time through the contour error and the synchronous error, can further reduce the contour error, improves the control effect and further ensures the tracking precision of a robot system.

Claims (8)

1. A contour control method for a synchronous cross-coupling robot is characterized by comprising the following steps:
step 1, obtaining a working space expected position xd、ydFor the desired position x of the workspaced、ydPerforming inverse kinematics solution operation to output joint space expected position theta1d、θ2d；
Step 2, obtaining the expected position theta of the joint space1d、θ2dWith the actual position theta in the joint space1a、θ2aAfter difference operation is carried out, joint space x-axis tracking error E is output1Joint space y-axis tracking error E2；
Step 3, tracking error E of x-axis joint space1Y-axis joint space tracking error E2The motor is driven to operate after the operation of the PD controller; meanwhile, according to the space tracking error E of the x-axis joint1Y-axis joint space tracking error E2Separately calculating contour errorscSynchronous errorsThe contour errorcAfter the operation of the profile controller, the synchronous error is compensated to a position ring of a working space by combining the corresponding gainsAfter the calculation of the synchronous controller, the speed loop of the joint space is compensated by combining the corresponding gain.
2. The method of claim 1, wherein the contour error is a contour error of a synchronous cross-coupled robotcSynchronous errorsThe calculation method comprises the following steps:
spatial tracking error E of x-axis joint1Y-axis joint space tracking error E2Performing kinematics positive solution operation and outputting the actual position x of the working spacea、ya；
The actual position x of the working space is measureda、yaAnd the expected position x of the working spaced、ydDifferencing to obtain x-axis tracking error ExY-axis tracking error Ey；
According to the x-axis tracking error ExY-axis tracking error EyCalculating to obtain the contour errorcSynchronous errors。
3. The method of claim 2, wherein the contour error is a contour error of a synchronous cross-coupled robotcCalculated according to the following formula:
c＝-ExCx+EyCy+ (1)；
in the above equation, the contour error compensation term is used.
4. The contour control method for the synchronous cross-coupled robot according to claim 3, wherein when the contour shape is a linear straight line,
Figure FDA0002493953960000021
the profile error compensation term is 0.
5. The method as claimed in claim 3, wherein when the contour shape is a curve, the contour error is calculated according to the following formula:
Figure FDA0002493953960000022
in the above formula, R is the radius of the osculating circle, and theta is the included angle between the tangent vector of a certain point of the osculating circle and the x-axis;
then the x-axis gain CxY-axis gain CyComprises the following steps:
Figure FDA0002493953960000023
＝c-a，
Figure FDA0002493953960000024
6. the method of claim 3, wherein the profile error is a profile error of a synchronous cross-coupled robotcAfter the operation of the contour controller, compensating to a position ring of a working space by combining corresponding gain; the method specifically comprises the following steps: the contour errorcAfter being calculated by a contour controller, the X-axis gain C is multiplied by the X-axis gain C respectivelyxY-axis gain CyCompensating to the desired position x of the working spaced、yd。
7. The method of claim 2, wherein the synchronization error is a synchronization errorsCalculated according to the following formula:
s＝Ex-Ey(9)；
assuming synchronization errorsSpace tracking error E of joint with x axis1Y-axis joint space tracking error E2The relationship is linear:
s＝C1E1+C2E2(10)；
in the above formula, C1For x-axis synchronous error gain, C2Is the y-axis synchronization error gain;
knowing the expected positions x and y of the working space, solving the joint space position theta according to the inverse kinematics1、θ2：
Figure FDA0002493953960000031
At the actual position (x) of the working space0,y0) Treating:
Figure FDA0002493953960000032
Figure FDA0002493953960000033
the four coefficients in the above formula are: a. the1＝f′1x(x0,y0)，B1＝f′1y(x0，y0)，A2＝f′2x(x0,y0)，B2＝f′2y(x0,y0)。
8. The method of claim 7, wherein the synchronization error is a synchronization errorsAfter the calculation of the synchronous controller, compensating to a velocity ring of a joint space by combining corresponding gains; the method specifically comprises the following steps: the synchronization errorsAfter the calculation of the synchronous controller, the X-axis synchronous error gains C are respectively multiplied1Y-axis synchronous error gain C2Compensating to a desired position theta in joint space1d、θ2d。
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