CN114396900A - Robot calibration method and system based on plane constraint - Google Patents

Robot calibration method and system based on plane constraint Download PDF

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Publication number
CN114396900A
CN114396900A CN202210056099.1A CN202210056099A CN114396900A CN 114396900 A CN114396900 A CN 114396900A CN 202210056099 A CN202210056099 A CN 202210056099A CN 114396900 A CN114396900 A CN 114396900A
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robot
module
cost function
coordinate system
iron block
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夏子涛
郭震
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Shanghai Jingwu Trade Technology Development Co Ltd
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Shanghai Jingwu Trade Technology Development Co Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
    • G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
    • G01B21/042—Calibration or calibration artifacts

Abstract

The invention provides a robot calibration method and system based on plane constraint, comprising the following steps: step S1: collecting the joint angle of the robot; step S2: constructing a robot parameter model; step S3: constructing a cost function based on a robot parameter model; step S4: iteratively optimizing a cost function by using the collected joint angles of the robot until the cost function value is minimum; when the cost function value is minimum, the parameter value of the robot is optimal. The method reduces the complexity of data acquisition, and only needs the tail end sharp needle of the robot to touch the surface of the iron block in different postures, so that the calibration process is simplified.

Description

Robot calibration method and system based on plane constraint
Technical Field
The invention relates to the technical field of robots, in particular to a robot calibration method and system based on plane constraint.
Background
The pose accuracy of the robot has repeatability accuracy and absolute positioning accuracy, wherein the repeatability accuracy refers to an error of the robot repeating the same joint parameter to reach an actual pose, and the absolute positioning accuracy refers to an error between the actual pose reached by the robot and the pose given according to the kinematic model. Most robots are controlled by kinematic models, but due to the influence of machining errors and assembly errors, the DH parameters of a robot design model and the DH parameters of an actual model have deviations, so that the absolute accuracy error of the robot is generally larger. Robots in many industrial applications require high absolute accuracy to perform critical tasks such as aerospace manufacturing and metrology inspection, and calibration of the DH parameters of the robot is a very important task. However, calibration of the robot usually requires expensive measuring equipment, such as laser measuring trackers, three-coordinate measuring machines. The invention provides a method for calibrating the robot by using simple equipment, and the complexity of robot calibration is reduced.
Patent document CN104608129B (application number: 201410711022.9) discloses a robot calibration method based on plane constraint, which specifically includes the following steps: establishing a robot kinematic model by using a DH and MDH combined method; establishing a robot tail end position error model based on a differential transformation principle; establishing a position calibration model of the robot based on plane constraint; calibrating the position and pose of the block; teaching and recording a theoretical pose of the tail end of the robot; calibrating kinematic parameters of the robot; and comparing by using the calibration result, and re-calibrating if the precision requirement is not met. The invention overcomes the limitation of various conditions in the calibration process in the prior art, such as: in the patent, the calibration block needs to be correctly placed in the working space of the robot, and the normal vectors of three planes which are perpendicular to each other on the calibration block are ensured to be parallel to the polar coordinate system axis of the robot. The actual operation can not be realized, and the base coordinates of the robot can not be seen and touched.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a robot calibration method and system based on plane constraint.
The invention provides a robot calibration method based on plane constraint, which comprises the following steps:
step S1: collecting the joint angle of the robot;
step S2: constructing a robot parameter model;
step S3: constructing a cost function based on a robot parameter model;
step S4: iteratively optimizing a cost function by using the collected joint angles of the robot until the cost function value is minimum; when the cost function value is minimum, the parameter value of the robot is optimal.
Preferably, the step S1 adopts:
step S1.1: placing a machining iron block in a preset working area of the robot;
step S1.2: the robot is set in a teaching mode, a tip needle at the tail end of the robot touches the upper surface of an iron block in different postures, and the angles of 6 joints of the robot in different postures are collected respectively.
Preferably, the step S2 adopts:
step S2.1: according to the improved D-H modeling method, the coordinate transformation relation of the joint coordinate system { i } relative to the previous joint coordinate system { i-1 }:
Figure BDA0003476288890000021
step S2.2: the transformation matrix of the robot tip with respect to the robot base is:
Figure BDA0003476288890000022
step S2.3: knowing that the x, y and z offsets of the robot tip relative to the 6-axis coordinate system are pt _ x, pt _ y and pt _ z, respectively, the coordinate system of the tip relative to the 6-axis coordinate system is:
Figure BDA0003476288890000023
step S2.4: the transformation matrix of the tail end needle point of the robot relative to the robot base coordinate system is as follows:
Figure BDA0003476288890000024
step S2.5: joint angle Q based on nth touch iron block surface acquisitionnThe coordinate transformation relationship of the joint coordinate system { i } with respect to the previous joint coordinate system { i-1 }:
Figure BDA0003476288890000025
Figure BDA0003476288890000031
step S2.6: association
Figure BDA0003476288890000032
To
Figure BDA0003476288890000033
Obtaining the pose of the tail end needle point of the robot
Figure BDA0003476288890000034
Step S2.7: calculating the position of the needle tip according to the robot model:
Figure BDA0003476288890000035
preferably, the step S3 adopts:
step S3.1: defining an iron block plane equation as Z ═ a × X + b × Y + c, wherein Z, X and Y respectively represent three-dimensional coordinates of the needle tip, and a, b and c are coefficients;
step S3.2: fitting the P1.. Pn coordinate points using a least squares method, solving equation coefficients:
Figure BDA0003476288890000036
wherein Zn, Xn and Yn represent three-dimensional coordinate values of the needle tip calculated by touching the iron block for the nth time according to the robot model;
step S3.3: respectively substituting the X and Y coordinates of n points into the plane equation of the iron block to obtain the values on the plane
Figure BDA0003476288890000037
Let Z and
Figure BDA0003476288890000038
with minimum error therebetween, defining a cost function Fcost：
Figure BDA0003476288890000039
Preferably, the step S4 adopts: iteratively optimizing a cost function by utilizing the collected robot joint angles through a particle swarm algorithm until the cost function value is minimum; when the cost function value is minimum, the parameter value of the robot is optimal.
The invention provides a robot calibration system based on plane constraint, which comprises:
module M1: collecting the joint angle of the robot;
module M2: constructing a robot parameter model;
module M3: constructing a cost function based on a robot parameter model;
module M4: iteratively optimizing a cost function by using the collected joint angles of the robot until the cost function value is minimum; when the cost function value is minimum, the parameter value of the robot is optimal.
Preferably, the module M1 employs:
module M1.1: placing a machining iron block in a preset working area of the robot;
module M1.2: the robot is set in a teaching mode, a tip needle at the tail end of the robot touches the upper surface of an iron block in different postures, and the angles of 6 joints of the robot in different postures are collected respectively.
Preferably, the module M2 employs:
module M2.1: according to the improved D-H modeling method, the coordinate transformation relation of the joint coordinate system { i } relative to the previous joint coordinate system { i-1 }:
Figure BDA0003476288890000041
module M2.2: the transformation matrix of the robot tip with respect to the robot base is:
Figure BDA0003476288890000042
module M2.3: knowing that the x, y and z offsets of the robot tip relative to the 6-axis coordinate system are pt _ x, pt _ y and pt _ z, respectively, the coordinate system of the tip relative to the 6-axis coordinate system is:
Figure BDA0003476288890000043
module M2.4: the transformation matrix of the tail end needle point of the robot relative to the robot base coordinate system is as follows:
Figure BDA0003476288890000044
module M2.5: joint angle Q based on nth touch iron block surface acquisitionnThe coordinate transformation relationship of the joint coordinate system { i } with respect to the previous joint coordinate system { i-1 }:
Figure BDA0003476288890000045
Figure BDA0003476288890000046
module M2.6: association
Figure BDA0003476288890000047
To
Figure BDA0003476288890000048
Obtaining the pose of the tail end needle point of the robot
Figure BDA0003476288890000049
Module M2.7: calculating the position of the needle tip according to the robot model:
Figure BDA00034762888900000410
preferably, the module M3 employs:
module M3.1: defining an iron block plane equation as Z ═ a × X + b × Y + c, wherein Z, X and Y respectively represent three-dimensional coordinates of the needle tip, and a, b and c are coefficients;
module M3.2: fitting the P1.. Pn coordinate points using a least squares method, solving equation coefficients:
Figure BDA00034762888900000411
wherein Zn, Xn and Yn represent three-dimensional coordinate values of the needle tip calculated by touching the iron block for the nth time according to the robot model;
module M3.3: respectively substituting the X and Y coordinates of n points into the plane equation of the iron block to obtain the values on the plane
Figure BDA00034762888900000412
Let Z and
Figure BDA00034762888900000413
with minimum error therebetween, defining a cost function Fcost：
Figure BDA0003476288890000051
Preferably, the module M4 employs: iteratively optimizing a cost function by utilizing the collected robot joint angles through a particle swarm algorithm until the cost function value is minimum; when the cost function value is minimum, the parameter value of the robot is optimal.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention provides high absolute precision of the robot by calibrating the joint zero position of the mechanical arm and the length of the connecting rod;
2. the invention replaces expensive measuring equipment with a simple machining iron block, so that the aim of calibrating the robot is fulfilled in a cheap way;
3. the method reduces the complexity of data acquisition, and only needs the tail end sharp needle of the robot to touch the surface of the iron block in different postures, so that the calibration process is simplified.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
fig. 1 is a schematic diagram of a robot tip touching an iron block.
Fig. 2 is a schematic diagram of the robot tip touching the iron block.
Fig. 3 is a schematic view of a robot joint.
FIG. 4 is a schematic diagram of an improved DH model.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
Example 1
The invention relates to calibration of a mechanical arm, which comprises a machined iron block, wherein the precision of the machined iron block is determined according to the precision requirement of a robot, and the size of the machined iron block is determined according to the working space of the mechanical arm. In this example, the surface roughness of the processed iron block is required to be of sub-millimeter level accuracy, with a length of 600mm, a width of 600mm and a thickness of 10 mm. The end of the arm is fitted with a sharp needle which is used to touch the surface of the block as shown in figure 2.
According to the robot calibration method based on plane constraint provided by the invention, as shown in fig. 1, the method comprises the following steps:
step S1: collecting the joint angle of the robot;
step S2: constructing a robot parameter model;
step S3: constructing a cost function based on a robot parameter model;
step S4: iteratively optimizing a cost function by using the collected joint angles of the robot until the cost function value is minimum; when the cost function value is minimum, the parameter value of the robot is optimal.
Preferably, the step S1 adopts:
step S1.1: placing the machining iron block in a main working area of the robot, such as right in front of the robot;
step S1.2: the robot is set in a teaching mode, a sharp needle at the tail end is made to touch the upper surface of an iron block by dragging the tail end of the robot, and the angles of 6 joints of the robot at the moment are collected; this acquisition process is repeated many times, but the tip of the end of the robot touches the upper surface of the iron block in different postures, i.e. at different angles. Collecting n groups of robot joint angles Q for n times (n is more than 30 is recommended)1,Q2,...Qn；
Figure BDA0003476288890000061
And the sharp needle at the tail end of the robot touches the upper surface of the iron block in different postures, and the angles of 6 joints of the robot in different postures are respectively collected.
Preferably, the step S2 adopts:
step S2.1: according to the improved D-H modeling method, the coordinate transformation relationship of the joint coordinate system { i } relative to the previous joint coordinate system { i-1} is as shown in FIG. 4:
Figure BDA0003476288890000062
wherein, ai-1Represents along Xi-1Axis from Zi-1Move to ZiThe distance of (d); alpha is alphai-1Represents around Xi-1Axis from Zi-1Rotate to ZiThe angle of (d); diRepresents along ZiAxis from Xi-1The shaft being moved to XiThe distance of (d); thetaiRepresents around ZiAxis from Xi-1The shaft being rotated to XiThe angle of (d);
the joint coordinate system { i } is ordered in sequence from the base to the end with respect to the previous joint coordinate system { i-1} as shown in FIG. 3;
step S2.2: the transformation matrix of the robot tip with respect to the robot base is:
Figure BDA0003476288890000063
as shown in fig. 3, the 6-axis joint mechanical arm is sequentially sorted backwards from the base of the mechanical arm to the tail end of the mechanical arm, wherein 1\2\3\4\5\6, and 0 represents a base coordinate system;
step S2.3: knowing that the x, y and z offsets of the robot tip relative to the 6-axis coordinate system are pt _ x, pt _ y and pt _ z, respectively, the coordinate system of the tip relative to the 6-axis coordinate system is:
Figure BDA0003476288890000071
step S2.4: the transformation matrix of the tail end needle point of the robot relative to the robot base coordinate system is as follows:
Figure BDA0003476288890000072
the position of the robot end coordinate is contained in the transformation matrix, and the transformation matrix is a transformation matrix of a tool coordinate system of the mechanical arm relative to a robot base coordinate system;
the robot to be calibrated in the invention has a similar configuration as the ur robot, and the MDH nominal parameter table is as follows, wherein the parameter to be calibrated is d1 d4 d5 d6 a3 a4 θ1 θ2 θ3 θ4 θ5 θ6
Link di(mm) ai(mm) αi(degrees) θi(degrees)
1 d 1 0 0 θ1
2 0 0 -90 θ2-90
3 0 a3 0 θ3+90
4 d4 a4 0 θ4-90
5 d5 0 -90 θ5
6 d6 0 -90 θ6
Step S2.5: theta is a variable and is based on the joint angle Q acquired by touching the surface of the iron block for the nth timenThe coordinate transformation relationship of the joint coordinate system { i } with respect to the previous joint coordinate system { i-1 }:
Figure BDA0003476288890000073
Figure BDA0003476288890000074
step S2.6: association
Figure BDA0003476288890000075
To
Figure BDA0003476288890000076
Substituting the pose into the formula (5) to obtain the pose of the tail end needle point of the robot
Figure BDA0003476288890000077
Step S2.7: calculating the position of the needle tip according to the robot model:
Figure BDA0003476288890000078
wherein the content of the first and second substances,
Figure BDA0003476288890000079
to represent
Figure BDA00034762888900000710
The numerical values of the 1 st row and the 4 th column in the matrix;
Figure BDA00034762888900000711
to represent
Figure BDA00034762888900000712
The 2 nd row and 4 th column values in the matrix;
Figure BDA00034762888900000713
to represent
Figure BDA00034762888900000714
The values in the 3 rd row and the 4 th column in the matrix;
therefore, the position of the tip of the robot and the joint parameters are defined as the following functions, wherein the function f and the MDH parameter d1 d4 d5 d6a3 a4 θ1 θ2 θ3 θ4 θ5 θ6And (4) correlating.
Pn＝f(Qn) (8)
Preferably, the step S3 adopts:
step S3.1: defining an iron block plane equation as Z ═ a × X + b × Y + c, wherein Z, X and Y respectively represent three-dimensional coordinates of the needle tip, and a, b and c are coefficients;
step S3.2: fitting the P1.. Pn coordinate points by using a least square method, solving the plane equation coefficient of the iron block:
Figure BDA0003476288890000081
wherein Zn, Xn and Yn represent three-dimensional coordinate values of the needle tip calculated by touching the iron block for the nth time according to the robot model;
step S3.3: respectively substituting the X and Y coordinates of n points into the plane equation of the iron block to obtain the values on the plane
Figure BDA0003476288890000082
Let Z and
Figure BDA0003476288890000083
with minimum error therebetween, defining a cost function Fcost：
Figure BDA0003476288890000084
Preferably, the step S4 adopts: iteratively optimizing a cost function by utilizing the collected robot joint angles through a particle swarm algorithm until the cost function value is minimum; when the cost function value is minimum, the parameter value of the robot is optimal.
MDH parameter d to be calibrated by using particle swarm optimization1 d4 d5 d6 a3 a4 θ1 θ2 θ3 θ4 θ5 θ6The 12-dimensional variables are optimized, and the fitness function uses the cost function F mentioned abovecost. The algorithm searching boundary is obtained by adding a certain offset to the nominal MDH parameter, and a proper offset is selected according to the machining precision of the robot.
In this example, the rod length variable is set to be offset by 5mm up and down, and the angle is set to be offset by 2.5 degrees up and down. The iteration times of the algorithm are set to 300 generations, and the population size of the particle swarm is set to 200.
The invention provides a robot calibration system based on plane constraint, which comprises:
module M1: collecting the joint angle of the robot;
module M2: constructing a robot parameter model;
module M3: constructing a cost function based on a robot parameter model;
module M4: iteratively optimizing a cost function by using the collected joint angles of the robot until the cost function value is minimum; when the cost function value is minimum, the parameter value of the robot is optimal.
Preferably, the module M1 employs:
module M1.1: placing the machining iron block in a main working area of the robot, such as right in front of the robot;
module M1.2: the robot is set in a teaching mode, a sharp needle at the tail end is made to touch the upper surface of an iron block by dragging the tail end of the robot, and the angles of 6 joints of the robot at the moment are collected; this acquisition process is repeated many times, but the tip of the end of the robot touches the upper surface of the iron block in different postures, i.e. at different angles. Collecting n groups of robot joint angles Q for n times (n is more than 30 is recommended)1,Q2,...Qn；
Figure BDA0003476288890000091
And the sharp needle at the tail end of the robot touches the upper surface of the iron block in different postures, and the angles of 6 joints of the robot in different postures are respectively collected.
Preferably, the module M2 employs:
module M2.1: according to the improved D-H modeling method, the coordinate transformation relationship of the joint coordinate system { i } relative to the previous joint coordinate system { i-1} is as shown in FIG. 4:
Figure BDA0003476288890000092
wherein, ai-1Represents along Xi-1Axis from Zi-1Move to ZiThe distance of (d); alpha is alphai-1Represents around Xi-1Axis from Zi-1Rotate to ZiThe angle of (d); diRepresents along ZiAxis from Xi-1The shaft being moved to XiThe distance of (d); thetaiRepresents around ZiAxis from Xi-1The shaft being rotated to XiThe angle of (d);
the joint coordinate system { i } is ordered in sequence from the base to the end with respect to the previous joint coordinate system { i-1} as shown in FIG. 3;
module M2.2: the transformation matrix of the robot tip with respect to the robot base is:
Figure BDA0003476288890000093
as shown in fig. 3, the 6-axis joint mechanical arm is sequentially sorted backwards from the base of the mechanical arm to the tail end of the mechanical arm, wherein 1\2\3\4\5\6, and 0 represents a base coordinate system;
module M2.3: knowing that the x, y and z offsets of the robot tip relative to the 6-axis coordinate system are pt _ x, pt _ y and pt _ z, respectively, the coordinate system of the tip relative to the 6-axis coordinate system is:
Figure BDA0003476288890000094
module M2.4: the transformation matrix of the tail end needle point of the robot relative to the robot base coordinate system is as follows:
Figure BDA0003476288890000095
the position of the robot end coordinate is contained in the transformation matrix, and the transformation matrix is a transformation matrix of a tool coordinate system of the mechanical arm relative to a robot base coordinate system;
the robot to be calibrated in the invention has a similar configuration as the ur robot, and the MDH nominal parameter table is as follows, wherein the parameter to be calibrated is d1 d4 d5 d6 a3 a4 θ1 θ2 θ3 θ4 θ5 θ6
Link di(mm) ai(mm) αi(degrees) θi(degrees)
1 d 1 0 0 θ1
2 0 0 -90 θ2-90
3 0 a3 0 θ3+90
4 d4 a4 0 θ4-90
5 d5 0 -90 θ5
6 d6 0 -90 θ6
Module M2.5: theta is a variable and is based on the joint angle Q acquired by touching the surface of the iron block for the nth timenThe coordinate transformation relationship of the joint coordinate system { i } with respect to the previous joint coordinate system { i-1 }:
Figure BDA0003476288890000101
Figure BDA0003476288890000102
module M2.6: association
Figure BDA0003476288890000103
To
Figure BDA0003476288890000104
Substituting the pose into the formula (5) to obtain the pose of the tail end needle point of the robot
Figure BDA0003476288890000105
Module M2.7: calculating the position of the needle tip according to the robot model:
Figure BDA0003476288890000106
wherein the content of the first and second substances,
Figure BDA0003476288890000107
to represent
Figure BDA0003476288890000108
The numerical values of the 1 st row and the 4 th column in the matrix;
Figure BDA0003476288890000109
to represent
Figure BDA00034762888900001010
The 2 nd row and 4 th column values in the matrix;
Figure BDA00034762888900001011
to represent
Figure BDA00034762888900001012
The values in the 3 rd row and the 4 th column in the matrix;
therefore, the position of the tip of the robot and the joint parameters are defined as the following functions, wherein the function f and the MDH parameter d1 d4 d5 d6a3 a4 θ1 θ2 θ3 θ4 θ5 θ6And (4) correlating.
Pn＝f(Qn) (8)
Preferably, the module M3 employs:
module M3.1: defining an iron block plane equation as Z ═ a × X + b × Y + c, wherein Z, X and Y respectively represent three-dimensional coordinates of the needle tip, and a, b and c are coefficients;
module M3.2: fitting the P1.. Pn coordinate points by using a least square method, solving the plane equation coefficient of the iron block:
Figure BDA00034762888900001013
wherein Zn, Xn and Yn represent three-dimensional coordinate values of the needle tip calculated by touching the iron block for the nth time according to the robot model;
module M3.3: respectively substituting the X and Y coordinates of n points into the plane equation of the iron block to obtain the values on the plane
Figure BDA0003476288890000111
Let Z and
Figure BDA0003476288890000112
with minimum error therebetween, defining a cost function Fcost：
Figure BDA0003476288890000113
Preferably, the module M4 employs: iteratively optimizing a cost function by utilizing the collected robot joint angles through a particle swarm algorithm until the cost function value is minimum; when the cost function value is minimum, the parameter value of the robot is optimal.
MDH parameter d to be calibrated by using particle swarm optimization1 d4 d5 d6 a3 a4 θ1 θ2 θ3 θ4 θ5 θ6The 12-dimensional variables are optimized, and the fitness function uses the cost function F mentioned abovecost. The algorithm searching boundary is obtained by adding a certain offset to the nominal MDH parameter, and a proper offset is selected according to the machining precision of the robot.
In this example, the rod length variable is set to be offset by 5mm up and down, and the angle is set to be offset by 2.5 degrees up and down. The iteration times of the algorithm are set to 300 generations, and the population size of the particle swarm is set to 200.
Those skilled in the art will appreciate that, in addition to implementing the systems, apparatus, and various modules thereof provided by the present invention in purely computer readable program code, the same procedures can be implemented entirely by logically programming method steps such that the systems, apparatus, and various modules thereof are provided in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Therefore, the system, the device and the modules thereof provided by the present invention can be considered as a hardware component, and the modules included in the system, the device and the modules thereof for implementing various programs can also be considered as structures in the hardware component; modules for performing various functions may also be considered to be both software programs for performing the methods and structures within hardware components.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.

Claims (10)

1. A robot calibration method based on plane constraint is characterized by comprising the following steps:
step S1: collecting the joint angle of the robot;
step S2: constructing a robot parameter model;
step S3: constructing a cost function based on a robot parameter model;
step S4: iteratively optimizing a cost function by using the collected joint angles of the robot until the cost function value is minimum; when the cost function value is minimum, the parameter value of the robot is optimal.
2. The method for calibrating a robot based on planar constraints according to claim 1, wherein the step S1 comprises:
step S1.1: placing a machining iron block in a preset working area of the robot;
step S1.2: the robot is set in a teaching mode, a tip needle at the tail end of the robot touches the upper surface of an iron block in different postures, and the angles of 6 joints of the robot in different postures are collected respectively.
3. The method for calibrating a robot based on planar constraints according to claim 1, wherein the step S2 comprises:
step S2.1: according to the improved D-H modeling method, the coordinate transformation relation of the joint coordinate system { i } relative to the previous joint coordinate system { i-1 }:
Figure FDA0003476288880000011
step S2.2: the transformation matrix of the robot tip with respect to the robot base is:
Figure FDA0003476288880000012
step S2.3: knowing that the x, y and z offsets of the robot tip relative to the 6-axis coordinate system are pt _ x, pt _ y and pt _ z, respectively, the coordinate system of the tip relative to the 6-axis coordinate system is:
Figure FDA0003476288880000013
step S2.4: the transformation matrix of the tail end needle point of the robot relative to the robot base coordinate system is as follows:
Figure FDA0003476288880000014
step S2.5: joint angle Q based on nth touch iron block surface acquisitionnThe coordinate transformation relationship of the joint coordinate system { i } with respect to the previous joint coordinate system { i-1 }:
Figure FDA0003476288880000021
Figure FDA0003476288880000022
step S2.6: association
Figure FDA0003476288880000027
To
Figure FDA0003476288880000028
Obtaining the pose of the tail end needle point of the robot
Figure FDA0003476288880000026
Step S2.7: calculating the position of the needle tip according to the robot model:
Figure FDA0003476288880000023
4. the method for calibrating a robot based on planar constraints according to claim 1, wherein the step S3 comprises:
step S3.1: defining an iron block plane equation as Z ═ a × X + b × Y + c, wherein Z, X and Y respectively represent three-dimensional coordinates of the needle tip, and a, b and c are coefficients;
step S3.2: fitting the P1.. Pn coordinate points using a least squares method, solving equation coefficients:
Figure FDA0003476288880000024
wherein Zn, Xn and Yn represent three-dimensional coordinate values of the needle tip calculated by touching the iron block for the nth time according to the robot model;
step S3.3: respectively substituting the X and Y coordinates of n points into the plane equation of the iron block to obtain the values on the plane
Figure FDA0003476288880000029
Let Z and
Figure FDA00034762888800000210
with minimum error therebetween, defining a cost function Fcost：
Figure FDA0003476288880000025
5. The method for calibrating a robot based on planar constraints according to claim 1, wherein the step S4 comprises: iteratively optimizing a cost function by utilizing the collected robot joint angles through a particle swarm algorithm until the cost function value is minimum; when the cost function value is minimum, the parameter value of the robot is optimal.
6. A robot calibration system based on plane constraint is characterized by comprising:
module M1: collecting the joint angle of the robot;
module M2: constructing a robot parameter model;
module M3: constructing a cost function based on a robot parameter model;
module M4: iteratively optimizing a cost function by using the collected joint angles of the robot until the cost function value is minimum; when the cost function value is minimum, the parameter value of the robot is optimal.
7. The plane constraint-based robot calibration system of claim 6, wherein the module M1 adopts:
module M1.1: placing a machining iron block in a preset working area of the robot;
module M1.2: the robot is set in a teaching mode, a tip needle at the tail end of the robot touches the upper surface of an iron block in different postures, and the angles of 6 joints of the robot in different postures are collected respectively.
8. The plane constraint-based robot calibration system of claim 6, wherein the module M2 adopts:
module M2.1: according to the improved D-H modeling method, the coordinate transformation relation of the joint coordinate system { i } relative to the previous joint coordinate system { i-1 }:
Figure FDA0003476288880000031
module M2.2: the transformation matrix of the robot tip with respect to the robot base is:
Figure FDA0003476288880000032
module M2.3: knowing that the x, y and z offsets of the robot tip relative to the 6-axis coordinate system are pt _ x, pt _ y and pt _ z, respectively, the coordinate system of the tip relative to the 6-axis coordinate system is:
Figure FDA0003476288880000033
module M2.4: the transformation matrix of the tail end needle point of the robot relative to the robot base coordinate system is as follows:
Figure FDA0003476288880000034
module M2.5: joint angle Q based on nth touch iron block surface acquisitionnThe coordinate transformation relationship of the joint coordinate system { i } with respect to the previous joint coordinate system { i-1 }:
Figure FDA0003476288880000035
Figure FDA0003476288880000036
module M2.6: association
Figure FDA00034762888800000310
To
Figure FDA0003476288880000039
Obtaining the pose of the tail end needle point of the robot
Figure FDA00034762888800000311
Module M2.7: calculating the position of the needle tip according to the robot model:
Figure FDA0003476288880000037
9. the plane constraint-based robot calibration system of claim 6, wherein the module M3 adopts:
module M3.1: defining an iron block plane equation as Z ═ a × X + b × Y + c, wherein Z, X and Y respectively represent three-dimensional coordinates of the needle tip, and a, b and c are coefficients;
module M3.2: fitting the P1.. Pn coordinate points using a least squares method, solving equation coefficients:
Figure FDA0003476288880000041
wherein Zn, Xn and Yn represent three-dimensional coordinate values of the needle tip calculated by touching the iron block for the nth time according to the robot model;
module M3.3: respectively substituting the X and Y coordinates of n points into the plane equation of the iron block to obtain the values on the plane
Figure FDA0003476288880000043
Let Z and
Figure FDA0003476288880000044
with minimum error therebetween, defining a cost function Fcost：
Figure FDA0003476288880000042
10. The plane constraint-based robot calibration system of claim 6, wherein the module M4 adopts: iteratively optimizing a cost function by utilizing the collected robot joint angles through a particle swarm algorithm until the cost function value is minimum; when the cost function value is minimum, the parameter value of the robot is optimal.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114932551A (en) * 2022-05-25 2022-08-23 上海景吾酷租科技发展有限公司 Zero calibration method, system and medium for mechanical arm

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114932551A (en) * 2022-05-25 2022-08-23 上海景吾酷租科技发展有限公司 Zero calibration method, system and medium for mechanical arm

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