CN113843804A - Robot kinematics calibration method and system based on plane constraint - Google Patents

Robot kinematics calibration method and system based on plane constraint Download PDF

Info

Publication number
CN113843804A
CN113843804A CN202111222380.XA CN202111222380A CN113843804A CN 113843804 A CN113843804 A CN 113843804A CN 202111222380 A CN202111222380 A CN 202111222380A CN 113843804 A CN113843804 A CN 113843804A
Authority
CN
China
Prior art keywords
robot
coordinate system
plane
laser
tool
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202111222380.XA
Other languages
Chinese (zh)
Other versions
CN113843804B (en
Inventor
王永超
郭震
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shanghai Jingwu Intelligent Technology Co Ltd
Original Assignee
Shanghai Jingwu Intelligent Technology Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Shanghai Jingwu Intelligent Technology Co Ltd filed Critical Shanghai Jingwu Intelligent Technology Co Ltd
Priority to CN202111222380.XA priority Critical patent/CN113843804B/en
Publication of CN113843804A publication Critical patent/CN113843804A/en
Application granted granted Critical
Publication of CN113843804B publication Critical patent/CN113843804B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert 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
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • 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
    • B25J9/1679—Programme controls characterised by the tasks executed
    • B25J9/1692—Calibration of manipulator

Abstract

The invention provides a robot kinematics calibration method and system based on plane constraint, comprising the following steps: establishing a base coordinate system, a flange coordinate system and a tool coordinate system; operating the robot to move, and recording the degree of the laser displacement sensor and the angle of the robot joint; establishing a kinematic model of the robot, and obtaining the position of a laser point on a plane in a coordinate system according to the reading of the laser displacement sensor; calculating a normal vector of the plane according to the position of the laser point on the plane, and establishing a calibration equation of a single plane; and repeating the steps in the working space of the robot until the error vectors of the kinematic parameters and the tool parameters are full-rank equations, and calculating the error vectors of the kinematic parameters and the tool parameters. The invention can correct the kinematic parameters of the robot and improve the absolute positioning precision of the work of the robot. The invention has non-contact measurement and higher precision; the laser displacement sensor and the calibration plane are used, so that the cost is low, the operation is simple and convenient, the laser displacement sensor can be widely applied to medium and small enterprises, and the feasibility is good in practice.

Description

Robot kinematics calibration method and system based on plane constraint
Technical Field
The invention relates to the field of robot calibration, in particular to a robot kinematics calibration method and system based on plane constraint.
Background
With the wide application of the robot technology in various industries, the requirements on the repeated positioning accuracy and the absolute positioning accuracy of the robot are higher and higher. At present, the repeated positioning precision of the robot is high, the absolute positioning precision is low, and the difference of each robot is large, so that the application range of the robot is severely limited. The robot kinematics calibration generally comprises four steps of modeling, measurement, error identification and compensation. At present, data measurement generally needs expensive precision measuring instruments such as a laser tracker, a three-coordinate measuring machine, a ball arm instrument and the like, and needs professional personnel to operate.
The invention provides a kinematics calibration method of an industrial robot, aiming at the technical problems of expensive existing kinematics calibration equipment, complex operation and the like, and the kinematics calibration method can reduce the calibration cost and improve the calibration efficiency.
Patent document CN104608129B (application number: CN201410711022.9) 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. However, the invention differs from the calibration block of the invention: the calibration block of the invention is provided with three mutually vertical planes, n points are taught on the three planes respectively, and the invention is different from the invention; this invention differs from the error model of the invention: the method establishes an error model by the difference value of the position errors of any two points at the tail end of the robot in the plane normal direction being equal to the difference value of the theoretical coordinate values of the two points; the invention needs to ensure that three mutually perpendicular normal vectors are parallel to a robot base coordinate system, thereby having higher implementation difficulty; the invention needs to control the robot to be in contact with the calibration block for teaching, and has larger implementation error.
Patent document CN108406771B (application number: CN201810196264.7) discloses a robot self-calibration method, which includes the following steps: (1) establishing a robot kinematics model; (2) establishing a robot tail end position error model; (3) establishing a plane constraint error model; (4) the robot is driven to measure the constraint planes respectively; (5) identifying kinematic parameters of the robot; (6) and verifying a calibration result. The invention needs to know the theory secondary transformation matrix of the coordinate system OcXcYcZc at the angular point of the calibration block of the robot base coordinate system, and the invention respectively establishes the coordinate systems of three planes by measuring the calibration block and establishes an error model according to the position errors of the three planes.
Patent document CN107972071B (application number: CN201711264644.1) discloses a method for calibrating link parameters of an industrial robot based on plane constraint of end points, which comprises the following steps: 1) establishing a connecting rod coordinate system and a tool coordinate system of the industrial robot to obtain the terminal position coordinate of the industrial robot; 2) carrying out plane constraint on the terminal point to establish an industrial robot connecting rod parameter error identification model; 3) changing the pose state of the industrial robot, recording joint values of joint variables and the length of a laser beam, and calculating initial parameters of a plane equation according to position coordinates of the three poses; 4) carrying out error identification on the parameters of the connecting rod of the industrial robot; 5) and correcting the parameters to be corrected in sequence, and verifying the precision of the industrial robot after correction. The method needs to calculate the initial parameters of a plane equation, and has measurement errors; the motion range of the robot is limited by the plane placing position, and the robot cannot be calibrated in a larger working space of the robot.
Patent document CN108731591B (application number: CN201810374769.8) discloses a robot tool coordinate system calibration method based on plane constraint, which includes setting a motion mode of a robot; establishing a base coordinate system B, a terminal coordinate system E and a tool coordinate system T; establishing a plane constraint condition; ensuring that the irradiation point is always on the marble platform, keeping the posture of the terminal coordinate system E unchanged, and controlling the position of the terminal coordinate system E to move for six times; ensuring that the irradiation point is always on the marble platform, keeping the position of the terminal coordinate system E unchanged, and controlling the posture of the terminal coordinate system E to change for three times; and solving an illumination point coordinate equation. But the plane of the invention is fixed and the calibration tool coordinate system is used.
Patent document CN110340881A (application number: CN201810303734.5) discloses a calibration method and a calibration system for a robot tool. The calibration method comprises the following steps: providing a calibration tool and a camera, wherein the calibration tool is provided with a calibration feature with a regular geometric shape, and the optical axis of the camera is parallel to the vertical direction; mounting a calibration tool on the robotic tool, the geometric center point of the calibration feature on the calibration tool being vertically aligned with the center point of the robotic tool; identifying an initial position of a geometric center point of the calibration feature with the camera; driving the robotic tool to rotate about a vertical axis by a predetermined angle; identifying an end position of a geometric center point of the calibration feature with the camera; calculating the offset distance of the central point of the robot tool relative to the central point of the end flange plate according to the initial position, the termination position and the preset angle; and calibrating the central point of the robot tool according to the offset distance. However, the plane of the robot is fixed and cannot be calibrated in a larger working space of the robot.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a robot kinematics calibration method and system based on plane constraint.
The invention provides a robot kinematics calibration method based on plane constraint, which comprises the following steps:
step S1: establishing a base coordinate system, a flange coordinate system and a tool coordinate system;
step S2: operating the robot to move, and recording the degree of the laser displacement sensor and the angle of the robot joint;
step S3: establishing a kinematic model of the robot, and obtaining the position of a laser point on a plane in a coordinate system according to the reading of the laser displacement sensor;
step S4: calculating a normal vector of the plane according to the position of the laser point on the plane, and establishing a calibration equation of a single plane;
repeating steps S2-S4 within the robot workspace until the kinematic parameter and tool parameter error vectors are full rank equations, calculating the kinematic parameter and tool parameter error vectors.
Preferably, in the step S1:
the robot base establishes a base coordinate system 0, a flange coordinate system n is established at the center of a robot flange, the robot flange is provided with a laser displacement sensor, the laser sensor establishes a tool coordinate system T, the origin of the tool coordinate system is coincided with the laser emission point of the laser displacement sensor, the Z direction of the tool coordinate system is coincided with the laser irradiation direction, and the direction of the tool coordinate system is the same as the direction of the flange coordinate system;
a plane is fixed in the robot working space, and the planeness grade is more than 00 grade;
preferably, in the step S2:
operating the robot to move, enabling the laser beam of the laser displacement sensor to strike on a plane, recording the reading l of the laser displacement sensor and recording the joint angle theta of the robotiChanging the pose of the robot, repeatedly measuring n times of data, wherein n depends on the number of errors to be calibrated, and ensuring that kinematic parameters and tool parameter error vectors are full-rank equations.
Preferably, in the step S3:
establishing a kinematic model of the robot by adopting a D-H method, and expressing a homogeneous transformation matrix from a connecting rod coordinate system i-1 to a connecting rod coordinate system i as
Figure BDA0003313087610000031
The homogeneous transformation matrix of the robot end flange coordinate system n relative to the robot base coordinate system 0 is
Figure BDA0003313087610000032
Figure BDA0003313087610000033
A homogeneous transformation matrix of a robot tail end flange coordinate system n relative to a robot base coordinate system 0 is provided, the flange coordinate system is established for the center of a robot flange by n,
Figure BDA0003313087610000034
is a homogeneous transformation matrix of the N-bar relative to the N-1 bar,
Figure BDA0003313087610000035
is a rotation matrix of a robot end flange coordinate system n relative to a robot base coordinate system 0,
Figure BDA0003313087610000036
a position matrix of a robot tail end flange coordinate system n relative to a robot base coordinate system 0, R is a rotation matrix, and p is a position matrix;
according to the reading of the laser displacement sensor, the position of the laser point on the plane under the tool coordinate system is [0,0, l,1 ]]TWherein l is the reading of the laser displacement sensor;
the positions of the laser points on the plane under the robot base coordinate system are as follows:
Figure BDA0003313087610000041
p is a position matrix of a laser point on a plane under a robot base coordinate system, I is a unit rotation matrix, and t is a tool coordinate system;
Figure BDA0003313087610000042
the position offset of the laser emission point under the flange coordinate system is represented, the position offset and the robot kinematic error are taken as calibrated error, and the nominal position p of the laser point on the plane in the robot base coordinate systemnComprises the following steps:
pn＝f(θi，l)
considering the robot kinematic error and the tool coordinate system deviation, the actual position p of the laser point on the plane in the robot base coordinate system is:
p＝pn+J*σ
wherein J is a calibrated Jacobian matrix, and σ is a kinematic parameter and tool parameter error vector.
Preferably, in the step S4:
for n groups of measured data, the actual position p of the ith point is obtainediComprises the following steps:
pi＝pi n+Ji*σ，i＝1，2...，n
pi nis the nominal position of the ith point; j. the design is a squareiA Jacobian matrix for the ith position point;
calculating the normal vector of the plane by taking two points on the measured plane and measuring the first point of the n points
(pi+2-p1)×(pi+1-p1)
＝(pi+2 n-p1 n+Ji+2*σ-J1*σ)×(pi+1 n-p1 n+Ji+1*σ-J1*σ)，
Wherein, i is 1,2,. and n-2;
is unfolded to obtain
(pi+2-p1)×(pi+1-p1)＝Mi+Ni*σ，i＝1，2，...，n-2
Wherein
Mi＝(pi+2 n-p1 n)×(pi+1 n-p1 n)
Ni＝(pi+2 n-p1 n)×(Ji+1-J1)+(Ji+2-J1)(pi+1 n-p1 n)
The quadratic term of σ is ignored; mi、NiFor the sake of brevity;
the normal vectors of the actual plane are parallel, the cross multiplication between the normal vectors is 0, and the first normal vector and any normal vector are cross-multiplied to obtain:
M1×Mi+1＝-(M1×Ni+1+N1×Mi+1)*σ，i＝1，2...，n-3；
the first normal vector refers to a normal vector calculated by 3 points in front of a measuring plane;
unfolding to obtain:
yi＝bi*σ，i＝1，2...，n-3
yi＝M1×Mi+1
bi＝-(M1×Ni+1+N1×Mi+1)
yi、bifor the sake of brevity;
establishing a calibration equation of a single plane:
Y＝B*σ
wherein the content of the first and second substances,
Y＝[y1，y2，...，yn-3]T，B＝[b1，b2，...，bn-3]T
Y、B、yn、bnall the expressions are corresponding expressions in brief description.
Preferably, moving the plane in the working space of the robot, repeating the steps S2-S4k times, wherein k depends on the number of errors to be calibrated, and ensuring that the error vectors of the kinematic parameters and the tool parameters are full-rank equations;
let the calibration equation for the kth plane be yk，iExpressed, then the calibration equation for k planes is:
Figure BDA0003313087610000051
wherein:
Figure BDA0003313087610000052
Figure BDA0003313087610000053
Figure BDA0003313087610000054
is prepared from,
Figure BDA0003313087610000055
Is, yk，n-3B isk，n-3All are corresponding expressions which are briefly expressed;
calculating a kinematic parameter and tool parameter error vector sigma according to a least square method:
Figure BDA0003313087610000056
the invention provides a robot kinematics calibration system based on plane constraint, which comprises:
module M1: establishing a base coordinate system, a flange coordinate system and a tool coordinate system;
module M2: operating the robot to move, and recording the degree of the laser displacement sensor and the angle of the robot joint;
module M3: establishing a kinematic model of the robot, and obtaining the position of a laser point on a plane in a coordinate system according to the reading of the laser displacement sensor;
module M4: calculating a normal vector of the plane according to the position of the laser point on the plane, and establishing a calibration equation of a single plane;
the modules M2-M4 are repeated within the robot workspace until the kinematic parameter and tool parameter error vectors are full rank equations, the kinematic parameter and tool parameter error vectors are calculated.
Preferably, in said module M1:
the robot base establishes a base coordinate system 0, a flange coordinate system n is established at the center of a robot flange, the robot flange is provided with a laser displacement sensor, the laser sensor establishes a tool coordinate system T, the origin of the tool coordinate system is coincided with the laser emission point of the laser displacement sensor, the Z direction of the tool coordinate system is coincided with the laser irradiation direction, and the direction of the tool coordinate system is the same as the direction of the flange coordinate system;
a plane is fixed in the robot working space, and the planeness grade is more than 00 grade;
preferably, in said module M2:
operating the robot to move, enabling the laser beam of the laser displacement sensor to strike on a plane, recording the reading l of the laser displacement sensor and recording the joint angle theta of the robotiChanging the pose of the robot, repeatedly measuring n times of data, wherein n depends on the number of errors to be calibrated, and ensuringThe kinematic parameter and tool parameter error vectors are full rank equations.
Preferably, in said module M3:
establishing a kinematic model of the robot by adopting a D-H method, and expressing a homogeneous transformation matrix from a connecting rod coordinate system i-1 to a connecting rod coordinate system i as
Figure BDA0003313087610000061
The homogeneous transformation matrix of the robot end flange coordinate system n relative to the robot base coordinate system 0 is
Figure BDA0003313087610000062
Figure BDA0003313087610000063
A homogeneous transformation matrix of a robot tail end flange coordinate system n relative to a robot base coordinate system 0 is provided, the flange coordinate system is established for the center of a robot flange by n,
Figure BDA0003313087610000064
is a homogeneous transformation matrix of the N-bar relative to the N-1 bar,
Figure BDA0003313087610000065
is a rotation matrix of a robot end flange coordinate system n relative to a robot base coordinate system 0,
Figure BDA0003313087610000066
a position matrix of a robot tail end flange coordinate system n relative to a robot base coordinate system 0, R is a rotation matrix, and p is a position matrix;
according to the reading of the laser displacement sensor, the position of the laser point on the plane under the tool coordinate system is [0,0, l,1 ]]TWherein l is the reading of the laser displacement sensor;
the positions of the laser points on the plane under the robot base coordinate system are as follows:
Figure BDA0003313087610000067
p is a position matrix of a laser point on a plane under a robot base coordinate system, I is a unit rotation matrix, and t is a tool coordinate system;
Figure BDA0003313087610000068
the position offset of the laser emission point under the flange coordinate system is represented, the position offset and the robot kinematic error are taken as calibrated error, and the nominal position p of the laser point on the plane in the robot base coordinate systemnComprises the following steps:
pn＝f(θi，l)
considering the robot kinematic error and the tool coordinate system deviation, the actual position p of the laser point on the plane in the robot base coordinate system is:
p＝pn+J*σ
wherein J is a calibrated Jacobian matrix, and σ is a kinematic parameter and tool parameter error vector.
Preferably, in said module M4:
for n groups of measured data, the actual position p of the ith point is obtainediComprises the following steps:
pi＝pi n+Ji*σ，i＝1，2...，n
pi nis the nominal position of the ith point; j. the design is a squareiA Jacobian matrix for the ith position point;
calculating the normal vector of the plane by taking two points on the measured plane and measuring the first point of the n points
(pi+2-p1)×(pi+1-p1)
＝(pi+2 n-p1 n+Ji+2*σ-J1*σ)×(pi+1 n-p1 n+Ji+1*σ-J1*σ)，
Wherein, i is 1,2,. and n-2;
is unfolded to obtain
(pi+2-p1)×(pi+1-p1)＝Mi+Ni*σ，i＝1，2，...，n-2
Wherein
Mi＝(pi+2 n-p1 n)×(pi+1 n-p1 n)
Ni＝(pi+2 n-p1 n)×(Ji+1-J1)+(Ji+2-J1)(pi+1 n-p1 n)
The quadratic term of σ is ignored; mi、NiFor the sake of brevity;
the normal vectors of the actual plane are parallel, the cross multiplication between the normal vectors is 0, and the first normal vector and any normal vector are cross-multiplied to obtain:
M1×Mi+1＝-(M1×Ni+1+N1×Mi+1)*σ，i＝1，2...，n-3；
the first normal vector refers to a normal vector calculated by 3 points in front of a measuring plane;
unfolding to obtain:
yi＝bi*σ，i＝1，2...，n-3
yi＝M1×Mi+1
bi＝-(M1×Ni+1+N1×Mi+1)
yi、bifor the sake of brevity;
establishing a calibration equation of a single plane:
Y＝B*σ
wherein Y ═ Y1，y2，...，yn-3]T，B＝[b1，b2，...，bn-3]T
Y、B、yn、bnAll the expressions are corresponding expressions in brief description.
Preferably, the plane is moved in the working space of the robot, and the modules M2-M4k times are repeated, wherein k depends on the number of errors to be calibrated, so that the kinematic parameter and tool parameter error vectors are full-rank equations;
let the calibration equation for the kth plane be yk，iExpressed, then the calibration equation for k planes is:
Figure BDA0003313087610000071
wherein:
Figure BDA0003313087610000072
Figure BDA0003313087610000073
Figure BDA0003313087610000074
is prepared from,
Figure BDA0003313087610000075
Is, yk，n-3B isk，n-3All are corresponding expressions which are briefly expressed;
calculating a kinematic parameter and tool parameter error vector sigma according to a least square method:
Figure BDA0003313087610000081
compared with the prior art, the invention has the following beneficial effects:
1. the kinematics calibration device and the kinematics calibration method for the robot can correct the kinematics parameters of the robot, improve the absolute positioning precision of the work of the robot, realize non-contact measurement and have higher precision;
2. the invention uses the laser displacement sensor and the calibration plane, has low cost and simple and convenient operation, and can be widely applied to medium-sized and small enterprises;
3. the components or equipment adopted by the device can be selected from the existing mature commercial products, and the device has good feasibility in practice;
4. the invention has no limitation of the movement range by the plane placing position and can be calibrated in a larger working space of the robot.
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 calibration;
fig. 2 is a calibration flow chart.
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:
according to the robot kinematics calibration method based on plane constraint provided by the invention, as shown in fig. 1-2, the method comprises the following steps:
step S1: establishing a base coordinate system, a flange coordinate system and a tool coordinate system;
step S2: operating the robot to move, and recording the degree of the laser displacement sensor and the angle of the robot joint;
step S3: establishing a kinematic model of the robot, and obtaining the position of a laser point on a plane in a coordinate system according to the reading of the laser displacement sensor;
step S4: calculating a normal vector of the plane according to the position of the laser point on the plane, and establishing a calibration equation of a single plane;
repeating steps S2-S4 within the robot workspace until the kinematic parameter and tool parameter error vectors are full rank equations, calculating the kinematic parameter and tool parameter error vectors.
Specifically, in the step S1:
the robot base establishes a base coordinate system 0, a flange coordinate system n is established at the center of a robot flange, the robot flange is provided with a laser displacement sensor, the laser sensor establishes a tool coordinate system T, the origin of the tool coordinate system is coincided with the laser emission point of the laser displacement sensor, the Z direction of the tool coordinate system is coincided with the laser irradiation direction, and the direction of the tool coordinate system is the same as the direction of the flange coordinate system;
a plane is fixed in the robot working space, and the planeness grade is more than 00 grade;
specifically, in the step S2:
operating the robot to move, enabling the laser beam of the laser displacement sensor to strike on a plane, recording the reading l of the laser displacement sensor and recording the joint angle theta of the robotiChanging the pose of the robot, repeatedly measuring n times of data, wherein n depends on the number of errors to be calibrated, and ensuring that kinematic parameters and tool parameter error vectors are full-rank equations.
Specifically, in the step S3:
establishing a kinematic model of the robot by adopting a D-H method, and expressing a homogeneous transformation matrix from a connecting rod coordinate system i-1 to a connecting rod coordinate system i as
Figure BDA0003313087610000091
The homogeneous transformation matrix of the robot end flange coordinate system n relative to the robot base coordinate system 0 is
Figure BDA0003313087610000092
Figure BDA0003313087610000093
A homogeneous transformation matrix of a robot tail end flange coordinate system n relative to a robot base coordinate system 0 is provided, the flange coordinate system is established for the center of a robot flange by n,
Figure BDA0003313087610000094
is a homogeneous transformation matrix of the N-bar relative to the N-1 bar,
Figure BDA0003313087610000095
is a rotation matrix of a robot end flange coordinate system n relative to a robot base coordinate system 0,
Figure BDA0003313087610000096
a position matrix of a robot tail end flange coordinate system n relative to a robot base coordinate system 0, R is a rotation matrix, and p is a position matrix;
according to the reading of the laser displacement sensor, the position of the laser point on the plane under the tool coordinate system is [0,0, l,1 ]]TWherein l is the reading of the laser displacement sensor;
the positions of the laser points on the plane under the robot base coordinate system are as follows:
Figure BDA0003313087610000097
p is a position matrix of a laser point on a plane under a robot base coordinate system, I is a unit rotation matrix, and t is a tool coordinate system;
Figure BDA0003313087610000098
the position offset of the laser emission point under the flange coordinate system is represented, the position offset and the robot kinematic error are taken as calibrated error, and the nominal position p of the laser point on the plane in the robot base coordinate systemnComprises the following steps:
pn＝f(θi，l)
considering the robot kinematic error and the tool coordinate system deviation, the actual position p of the laser point on the plane in the robot base coordinate system is:
p＝pn+J*σ
wherein J is a calibrated Jacobian matrix, and σ is a kinematic parameter and tool parameter error vector.
Specifically, in the step S4:
for n sets of data measured, obtainActual position p of the ith pointiComprises the following steps:
pi＝pi n+Ji*σ，i＝1，2...，n
pi nis the nominal position of the ith point; j. the design is a squareiA Jacobian matrix for the ith position point;
calculating the normal vector of the plane by taking two points on the measured plane and measuring the first point of the n points
(pi+2-p1)×(pi+1-p1)
＝(pi+2 n-p1 n+Ji+2*σ-J1*σ)×(pi+1 n-p1 n+Ji+1*σ-J1*σ)，
Wherein, i is 1,2,. and n-2;
is unfolded to obtain
(pi+2-p1)×(pi+1-p1)＝Mi+Ni*σ，i＝1，2，...，n-2
Wherein
Mi＝(pi+2 n-p1 n)×(pi+1 n-p1 n)
Ni＝(pi+2 n-p1 n)×(Ji+1-J1)+(Ji+2-J1)(pi+1 n-p1 n)
The quadratic term of σ is ignored; mi、NiFor the sake of brevity;
the normal vectors of the actual plane are parallel, the cross multiplication between the normal vectors is 0, and the first normal vector and any normal vector are cross-multiplied to obtain:
M1×Mi+1＝-(M1×Ni+1+N1×Mi+1)*σ，i＝1，2...，n-3；
the first normal vector refers to a normal vector calculated by 3 points in front of a measuring plane;
unfolding to obtain:
yi＝bi*σ，i＝1，2...，n-3
yi＝M1×Mi+1
bi＝-(M1×Ni+1+N1×Mi+1)
yi、bifor the sake of brevity;
establishing a calibration equation of a single plane:
Y＝B*σ
wherein the content of the first and second substances,
Y＝[y1，y2，...，yn-3]T，B＝[b1，b2，...，bn-3]T
Y、B、yn、bnall the expressions are corresponding expressions in brief description.
Specifically, moving a plane in a robot working space, repeating the steps S2-S4k times, wherein k depends on the number of errors to be calibrated, and ensuring that kinematic parameters and tool parameter error vectors are full-rank equations;
let the calibration equation for the kth plane be yk，iExpressed, then the calibration equation for k planes is:
Figure BDA0003313087610000111
wherein:
Figure BDA0003313087610000112
Figure BDA0003313087610000113
Figure BDA0003313087610000114
is prepared from,
Figure BDA0003313087610000115
Is, yk，n-3B isk，n-3All are corresponding expressions which are briefly expressed;
calculating a kinematic parameter and tool parameter error vector sigma according to a least square method:
Figure BDA0003313087610000116
example 2:
example 2 is a preferred example of example 1, and the present invention will be described in more detail.
The robot kinematics calibration method based on plane constraint provided by the invention can be understood as a specific implementation manner of the robot kinematics calibration system based on plane constraint by those skilled in the art, that is, the robot kinematics calibration system based on plane constraint can be realized by executing the step flow of the robot kinematics calibration method based on plane constraint.
The invention provides a robot kinematics calibration system based on plane constraint, which comprises:
module M1: establishing a base coordinate system, a flange coordinate system and a tool coordinate system;
module M2: operating the robot to move, and recording the degree of the laser displacement sensor and the angle of the robot joint;
module M3: establishing a kinematic model of the robot, and obtaining the position of a laser point on a plane in a coordinate system according to the reading of the laser displacement sensor;
module M4: calculating a normal vector of the plane according to the position of the laser point on the plane, and establishing a calibration equation of a single plane;
the modules M2-M4 are repeated within the robot workspace until the kinematic parameter and tool parameter error vectors are full rank equations, the kinematic parameter and tool parameter error vectors are calculated.
Specifically, in the module M1:
the robot base establishes a base coordinate system 0, a flange coordinate system n is established at the center of a robot flange, the robot flange is provided with a laser displacement sensor, the laser sensor establishes a tool coordinate system T, the origin of the tool coordinate system is coincided with the laser emission point of the laser displacement sensor, the Z direction of the tool coordinate system is coincided with the laser irradiation direction, and the direction of the tool coordinate system is the same as the direction of the flange coordinate system;
a plane is fixed in the robot working space, and the planeness grade is more than 00 grade;
specifically, in the module M2:
operating the robot to move, enabling the laser beam of the laser displacement sensor to strike on a plane, recording the reading 1 of the laser displacement sensor and recording the joint angle theta of the robotiChanging the pose of the robot, repeatedly measuring n times of data, wherein n depends on the number of errors to be calibrated, and ensuring that kinematic parameters and tool parameter error vectors are full-rank equations.
Specifically, in the module M3:
establishing a kinematic model of the robot by adopting a D-H method, and expressing a homogeneous transformation matrix from a connecting rod coordinate system i-1 to a connecting rod coordinate system i as
Figure BDA0003313087610000121
The homogeneous transformation matrix of the robot end flange coordinate system n relative to the robot base coordinate system 0 is
Figure BDA0003313087610000122
Figure BDA0003313087610000123
A homogeneous transformation matrix of a robot tail end flange coordinate system n relative to a robot base coordinate system 0 is provided, the flange coordinate system is established for the center of a robot flange by n,
Figure BDA0003313087610000124
is a homogeneous transformation matrix of the N-bar relative to the N-1 bar,
Figure BDA0003313087610000125
is a rotation matrix of a robot end flange coordinate system n relative to a robot base coordinate system 0,
Figure BDA0003313087610000126
a position matrix of a robot tail end flange coordinate system n relative to a robot base coordinate system 0, R is a rotation matrix, and p is a position matrix;
according to the reading of the laser displacement sensor, the position of the laser point on the plane under the tool coordinate system is [0,0, l,1 ]]TWherein l is the reading of the laser displacement sensor;
the positions of the laser points on the plane under the robot base coordinate system are as follows:
Figure BDA0003313087610000127
p is a position matrix of a laser point on a plane under a robot base coordinate system, I is a unit rotation matrix, and t is a tool coordinate system;
Figure BDA0003313087610000128
the position offset of the laser emission point under the flange coordinate system is represented, the position offset and the robot kinematic error are taken as calibrated error, and the nominal position p of the laser point on the plane in the robot base coordinate systemnComprises the following steps:
pn＝f(θi，l)
considering the robot kinematic error and the tool coordinate system deviation, the actual position p of the laser point on the plane in the robot base coordinate system is:
p＝pn+J*σ
wherein J is a calibrated Jacobian matrix, and σ is a kinematic parameter and tool parameter error vector.
Specifically, in the module M4:
for n groups of measured data, the actual position p of the ith point is obtainediComprises the following steps:
pi＝pi n+Ji*σ，i＝1，2...，n
pi nis the nominal position of the ith point; j. the design is a squareiA Jacobian matrix for the ith position point;
calculating the normal vector of the plane by taking two points on the measured plane and measuring the first point of the n points
(pi+2-p1)×(pi+1-p1)
＝(pi+2 n-p1 n+Ji+2*σ-J1*σ)×(pi+1 n-p1 n+Ji+1*σ-J1*σ)，
Wherein, i is 1,2,. and n-2;
is unfolded to obtain
(pi+2-p1)×(pi+1-p1)＝Mi+Ni*σ，i＝1，2，...，n-2
Wherein
Mi＝(pi+2 n-p1 n)×(pi+1 n-p1 n)
Ni＝(pi+2 n-p1 n)×(Ji+1-J1)+(Ji+2-J1)(pi+1 n-p1 n)
The quadratic term of σ is ignored; mi、NiFor the sake of brevity;
the normal vectors of the actual plane are parallel, the cross multiplication between the normal vectors is 0, and the first normal vector and any normal vector are cross-multiplied to obtain:
M1×Mi+1＝-(M1×Ni+1+N1×Mi+1)*σ，i＝1，2...，n-3；
the first normal vector refers to a normal vector calculated by 3 points in front of a measuring plane;
unfolding to obtain:
yi＝bi*σ，i＝1，2...，n-3
yi＝M1×Mi+1
bi＝-(M1×Ni+1+N1×Mi+1)
yi、bifor the sake of brevity;
establishing a calibration equation of a single plane:
Y＝B*σ
wherein Y ═ Y1，y2，...，yn-3]T，B＝[b1，b2，...，bn-3]T
Y、B、yn、bnAll the expressions are corresponding expressions in brief description.
Specifically, moving a plane in a robot working space, repeating the modules M2-M4k times, wherein k depends on the number of errors to be calibrated, and ensuring that kinematic parameters and tool parameter error vectors are full-rank equations;
let the calibration equation for the kth plane be yk，iExpressed, then the calibration equation for k planes is:
Figure BDA0003313087610000131
wherein:
Figure BDA0003313087610000132
Figure BDA0003313087610000141
Figure BDA0003313087610000142
is prepared from,
Figure BDA0003313087610000143
Is, yk，n-3B isk，n-3All are corresponding expressions which are briefly expressed;
calculating a kinematic parameter and tool parameter error vector sigma according to a least square method:
Figure BDA0003313087610000144
example 3:
example 3 is a preferred example of example 1, and the present invention will be described in more detail.
The robot kinematics calibration method measures plane point coordinates by using a laser displacement sensor, obtains a calibration equation according to constraint conditions of plane normal vector parallel behavior formed by three points in a plane, and solves kinematics parameters by using a least square method. Comprises the following steps:
(1) the robot base establishes a base coordinate system 0, a flange coordinate system n is established at the center of a robot flange, the robot flange is provided with a laser displacement sensor, the laser sensor establishes a tool coordinate system T, the origin of the tool coordinate system is coincided with the laser emission point of the laser displacement sensor, the Z direction of the tool coordinate system is coincided with the laser irradiation direction, and the direction of the tool coordinate system is the same as the direction of the flange coordinate system;
(2) a plane is fixed in the robot working space and can be made of marble, iron blocks and the like, and the planeness grade is 00 or above.
(3) Operating the robot to move, enabling the laser beam of the laser displacement sensor to strike on a plane, recording the reading l of the laser displacement sensor, and simultaneously recording the joint angle theta of the robotiAnd changing the pose of the robot and repeatedly measuring the data for n times.
(4) Establishing a kinematic model of the robot by adopting a D-H method, and expressing a homogeneous transformation matrix from a connecting rod coordinate system i-1 to a connecting rod coordinate system i as
Figure BDA0003313087610000145
The homogeneous transformation matrix of the robot end flange coordinate system n relative to the robot base coordinate system 0 is
Figure BDA0003313087610000146
According to the reading of the laser displacement sensor, the position of the laser point on the plane under the tool coordinate system is [0,0, l,1 ]]TAnd l is the reading of the laser displacement sensor. The position of the laser point on the plane under the robot base coordinate system is
Figure BDA0003313087610000147
Wherein
Figure BDA0003313087610000148
The position offset of the laser emission point in the flange coordinate system can be used as a calibrated error amount together with the robot kinematic error amount. The nominal position of the laser point on the plane in the robot base coordinate system is
pn＝f(θi，l)
Considering the kinematic error of the robot and the deviation of the tool coordinate system, the actual position of the laser point on the plane on the robot base coordinate system is
p＝pn+J*σ
Wherein J is a calibrated Jacobian matrix, and σ is a kinematic parameter and tool parameter error vector.
(5) For the n groups of data measured in step 3), the actual position of the ith point can be obtained from step 4)
pi＝pi n+Ji*σ，i＝1，2...，n
Calculating normal vector of plane by taking two points of plane and first point
(pi+2-p1)×(pi+1-p1)
＝(pi+2 n-p1 n+Ji+2*σ-J1*σ)×(pi+1 n-p1 n+Ji+1*σ-J1*σ)，
Wherein, i is 1,2,. and n-2;
is unfolded to obtain
(pi+2-p1)×(pi+1-p1)＝Mi+Ni*σ，i＝1，2，...，n-2
Wherein
Mi＝(pi+2 n-p1 n)×(pi+1 n-p1 n)
Ni＝(pi+2 n-p1 n)×(Ji+1-J1)+(Ji+2-J1)(pi+1 n-p1 n)
The quadratic term of a is ignored,
the normal vectors of the actual plane are parallel, the cross multiplication between the normal vectors is 0, and the first normal vector and any normal vector are cross-multiplied to obtain
M1×Mi+1＝-(M1×Ni+1+N1×Mi+1)*σ，i＝1，2...，n-3；
Unfolding to obtain:
yi＝bi*σ，i＝1，2...，n-3
yi＝M1×Mi+1
bi＝-(M1×Ni+1+N1×Mi+1)
establishing a calibration equation of a single plane: y ═ B · σ
Wherein Y is ═ Y1，y2，...，yn-3]T，B＝[b1，b2，...，bn-3]T
(6) Moving the plane in the working space of the robot, repeating the step 3), the step 4), the step 5) k times, and setting a calibration equation y of the kth planek，iExpressed, then the calibration equation for k planes is:
Figure BDA0003313087610000151
wherein
Figure BDA0003313087610000152
Figure BDA0003313087610000153
Calculating kinematic parameter and tool parameter error vectors according to least squares
Figure BDA0003313087610000154
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 kinematics calibration method based on plane constraint is characterized by comprising the following steps:
step S1: establishing a base coordinate system, a flange coordinate system and a tool coordinate system;
step S2: operating the robot to move, and recording the degree of the laser displacement sensor and the angle of the robot joint;
step S3: establishing a kinematic model of the robot, and obtaining the position of a laser point on a plane in a coordinate system according to the reading of the laser displacement sensor;
step S4: calculating a normal vector of the plane according to the position of the laser point on the plane, and establishing a calibration equation of a single plane;
repeating steps S2-S4 within the robot workspace until the kinematic parameter and tool parameter error vectors are full rank equations, calculating the kinematic parameter and tool parameter error vectors.
2. The robot kinematics calibration method based on plane constraint according to claim 1, wherein:
in the step S1:
the robot base establishes a base coordinate system 0, a flange coordinate system n is established at the center of a robot flange, the robot flange is provided with a laser displacement sensor, the laser sensor establishes a tool coordinate system T, the origin of the tool coordinate system is coincided with the laser emission point of the laser displacement sensor, the Z direction of the tool coordinate system is coincided with the laser irradiation direction, and the direction of the tool coordinate system is the same as the direction of the flange coordinate system;
a plane is fixed in the robot working space, and the planeness grade is more than 00 grade;
in the step S2:
operating the robot to move, enabling the laser beam of the laser displacement sensor to strike on a plane, recording the reading l of the laser displacement sensor and recording the joint angle theta of the robotiChanging the pose of the robot, repeatedly measuring n times of data, wherein n depends on the number of errors to be calibrated, and ensuring that kinematic parameters and tool parameter error vectors are full-rank equations.
3. The method for robot kinematics calibration according to claim 1, wherein in step S3:
establishing a kinematic model of the robot by adopting a D-H method, and expressing a homogeneous transformation matrix from a connecting rod coordinate system i-1 to a connecting rod coordinate system i as
Figure FDA0003313087600000011
The homogeneous transformation matrix of the robot end flange coordinate system n relative to the robot base coordinate system 0 is
Figure FDA0003313087600000012
Figure FDA0003313087600000013
A homogeneous transformation matrix of a robot tail end flange coordinate system n relative to a robot base coordinate system 0 is provided, the flange coordinate system is established for the center of a robot flange by n,
Figure FDA0003313087600000014
is a homogeneous transformation matrix of the N-bar relative to the N-1 bar,
Figure FDA0003313087600000015
is a rotation matrix of a robot end flange coordinate system n relative to a robot base coordinate system 0,
Figure FDA0003313087600000016
a position matrix of a robot tail end flange coordinate system n relative to a robot base coordinate system 0, R is a rotation matrix, and p is a position matrix;
according to the reading of the laser displacement sensor, the position of the laser point on the plane under the tool coordinate system is [0,0, l,1 ]]TWherein l is the reading of the laser displacement sensor;
the positions of the laser points on the plane under the robot base coordinate system are as follows:
Figure FDA0003313087600000021
p is a position matrix of a laser point on a plane under a robot base coordinate system, I is a unit rotation matrix, and t is a tool coordinate system;
Figure FDA0003313087600000022
the position offset of the laser emission point under the flange coordinate system is represented, the position offset and the robot kinematic error are taken as calibrated error, and the nominal position p of the laser point on the plane in the robot base coordinate systemnComprises the following steps:
pn＝f(θi,l)
considering the robot kinematic error and the tool coordinate system deviation, the actual position p of the laser point on the plane in the robot base coordinate system is:
p＝pn+J*σ
wherein J is a calibrated Jacobian matrix, and σ is a kinematic parameter and tool parameter error vector.
4. The method for robot kinematics calibration according to claim 1, wherein in step S4:
for n groups of measured data, the actual position p of the ith point is obtainediComprises the following steps:
pi＝pi n+Ji*σ,i＝1,2…,n
pi nis the nominal position of the ith point; j. the design is a squareiA Jacobian matrix for the ith position point;
calculating the normal vector of the plane by taking two points on the measured plane and measuring the first point of the n points
(pi+2-p1)×(pi+1-p1)
＝(pi+2 n-p1 n+Ji+2*σ-J1*σ)×(pi+1 n-p1 n+Ji+1*σ-J1*σ),
Wherein i is 1,2, …, n-2;
is unfolded to obtain
(pi+2-p1)×(pi+1-p1)＝Mi+Ni*σ,i＝1,2,…,n-2
Wherein
Mi＝(pi+2 n-p1 n)×(pi+1 n-p1 n)
Ni＝(pi+2 n-p1 n)×(Ji+1-J1)+(Ji+2-J1)(pi+1 n-p1 n)
The quadratic term of σ is ignored; mi、NiFor the sake of brevity;
the normal vectors of the actual plane are parallel, the cross multiplication between the normal vectors is 0, and the first normal vector and any normal vector are cross-multiplied to obtain:
M1×Mi+1＝-(M1×Ni+1+N1×Mi+1)*σ，i＝1,2…,n-3；
the first normal vector refers to a normal vector calculated by 3 points in front of a measuring plane;
unfolding to obtain:
yi＝bi*σ，i＝1,2…,n-3
yi＝M1×Mi+1
bi＝-(M1×Ni+1+N1×Mi+1)
yi、bifor the sake of brevity;
establishing a calibration equation of a single plane:
Y＝B*σ
wherein the content of the first and second substances,
Y＝[y1,y2,…,yn-3]T,B＝[b1,b2,…,bn-3]T
Y、B、yn、bnall the expressions are corresponding expressions in brief description.
5. The robot kinematics calibration method based on plane constraint according to claim 1, wherein:
moving the plane in the working space of the robot, repeating the steps S2-S4k times, wherein k depends on the number of errors to be calibrated, and ensuring that kinematic parameters and tool parameter error vectors are full-rank equations;
let the calibration equation for the kth plane be yk,iExpressed, then the calibration equation for k planes is:
Figure FDA0003313087600000031
wherein:
Figure FDA0003313087600000032
Figure FDA0003313087600000033
Figure FDA0003313087600000034
is prepared from,
Figure FDA0003313087600000035
Is, yk,n-3B isk,n-3All are corresponding expressions which are briefly expressed;
calculating a kinematic parameter and tool parameter error vector sigma according to a least square method:
Figure FDA0003313087600000036
6. a robot kinematics calibration system based on plane constraint is characterized by comprising:
module M1: establishing a base coordinate system, a flange coordinate system and a tool coordinate system;
module M2: operating the robot to move, and recording the degree of the laser displacement sensor and the angle of the robot joint;
module M3: establishing a kinematic model of the robot, and obtaining the position of a laser point on a plane in a coordinate system according to the reading of the laser displacement sensor;
module M4: calculating a normal vector of the plane according to the position of the laser point on the plane, and establishing a calibration equation of a single plane;
the modules M2-M4 are repeated within the robot workspace until the kinematic parameter and tool parameter error vectors are full rank equations, the kinematic parameter and tool parameter error vectors are calculated.
7. The planar constraint-based robot kinematics calibration system according to claim 6, wherein:
in the module M1:
the robot base establishes a base coordinate system 0, a flange coordinate system n is established at the center of a robot flange, the robot flange is provided with a laser displacement sensor, the laser sensor establishes a tool coordinate system T, the origin of the tool coordinate system is coincided with the laser emission point of the laser displacement sensor, the Z direction of the tool coordinate system is coincided with the laser irradiation direction, and the direction of the tool coordinate system is the same as the direction of the flange coordinate system;
a plane is fixed in the robot working space, and the planeness grade is more than 00 grade;
in the module M2:
operating the robot to move, enabling the laser beam of the laser displacement sensor to strike on a plane, recording the reading l of the laser displacement sensor and recording the joint angle theta of the robotiChanging the pose of the robot, repeatedly measuring n times of data, wherein n depends on the number of errors to be calibrated, and ensuring that kinematic parameters and tool parameter error vectors are full-rank equations.
8. Robot kinematics calibration system according to claim 6, wherein in said module M3:
establishing a kinematic model of the robot by adopting a D-H method, and expressing a homogeneous transformation matrix from a connecting rod coordinate system i-1 to a connecting rod coordinate system i as
Figure FDA0003313087600000041
The homogeneous transformation matrix of the robot end flange coordinate system n relative to the robot base coordinate system 0 is
Figure FDA0003313087600000042
Figure FDA0003313087600000043
A homogeneous transformation matrix of a robot tail end flange coordinate system n relative to a robot base coordinate system 0 is provided, the flange coordinate system is established for the center of a robot flange by n,
Figure FDA0003313087600000044
is a homogeneous transformation matrix of the N-bar relative to the N-1 bar,
Figure FDA0003313087600000045
is a rotation matrix of a robot end flange coordinate system n relative to a robot base coordinate system 0,
Figure FDA0003313087600000046
a position matrix of a robot tail end flange coordinate system n relative to a robot base coordinate system 0, R is a rotation matrix, and p is a position matrix;
according to the reading of the laser displacement sensor, the position of the laser point on the plane under the tool coordinate system is [0,0, l,1 ]]TWherein l is the reading of the laser displacement sensor;
the positions of the laser points on the plane under the robot base coordinate system are as follows:
Figure FDA0003313087600000047
p is a position matrix of a laser point on a plane under a robot base coordinate system, I is a unit rotation matrix, and t is a tool coordinate system;
Figure FDA0003313087600000048
the position offset of the laser emission point under the flange coordinate system is represented, the position offset and the robot kinematic error are taken as calibrated error, and the nominal position p of the laser point on the plane in the robot base coordinate systemnComprises the following steps:
pn＝f(θi,l)
considering the robot kinematic error and the tool coordinate system deviation, the actual position p of the laser point on the plane in the robot base coordinate system is:
p＝pn+J*σ
wherein J is a calibrated Jacobian matrix, and σ is a kinematic parameter and tool parameter error vector.
9. Robot kinematics calibration system according to claim 6, wherein in said module M4:
for n groups of measured data, the actual position p of the ith point is obtainediComprises the following steps:
pi＝pi n+Ji*σ,i＝1,2…,n
pi nis the nominal position of the ith point; j. the design is a squareiA Jacobian matrix for the ith position point;
calculating the normal vector of the plane by taking two points on the measured plane and measuring the first point of the n points
(pi+2-p1)×(pi+1-p1)
＝(pi+2 n-p1 n+Ji+2*σ-J1*σ)×(pi+1 n-p1 n+Ji+1*σ-J1*σ),
Wherein i is 1,2, …, n-2;
is unfolded to obtain
(pi+2-p1)×(pi+1-p1)＝Mi+Ni*σ,i＝1,2,…,n-2
Wherein
Mi＝(pi+2 n-p1 n)×(pi+1 n-p1 n)
Ni＝(pi+2 n-p1 n)×(Ji+1-J1)+(Ji+2-J1)(pi+1 n-p1 n)
The quadratic term of σ is ignored; mi、NiFor the sake of brevity;
the normal vectors of the actual plane are parallel, the cross multiplication between the normal vectors is 0, and the first normal vector and any normal vector are cross-multiplied to obtain:
M1×Mi+1＝-(M1×Ni+1+N1×Mi+1)*σ，i＝1,2…,n-3；
the first normal vector refers to a normal vector calculated by 3 points in front of a measuring plane;
unfolding to obtain:
yi＝bi*σ，i＝1,2…,n-3
yi＝M1×Mi+1
bi＝-(M1×Ni+1+N1×Mi+1)
yi、bifor the sake of brevity;
establishing a calibration equation of a single plane:
Y＝B*σ
wherein Y ═ Y1,y2,…,yn-3]T,B＝[b1,b2,…,bn-3]T
Y、B、yn、bnAll the expressions are corresponding expressions in brief description.
10. The planar constraint-based robot kinematics calibration system according to claim 6, wherein:
moving a plane in a robot working space, repeating the modules M2-M4k times, wherein k depends on the number of errors to be calibrated, and ensuring that kinematic parameters and tool parameter error vectors are full-rank equations;
let the calibration equation for the kth plane be yk,iExpressed, then the calibration equation for k planes is:
Figure FDA0003313087600000061
wherein:
Figure FDA0003313087600000062
Figure FDA0003313087600000063
Figure FDA0003313087600000064
is prepared from,
Figure FDA0003313087600000065
Is, yk,n-3B isk,n-3All are corresponding expressions which are briefly expressed;
calculating a kinematic parameter and tool parameter error vector sigma according to a least square method:
Figure FDA0003313087600000066
CN202111222380.XA 2021-10-20 2021-10-20 Robot kinematics calibration method and system based on plane constraint Active CN113843804B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111222380.XA CN113843804B (en) 2021-10-20 2021-10-20 Robot kinematics calibration method and system based on plane constraint

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111222380.XA CN113843804B (en) 2021-10-20 2021-10-20 Robot kinematics calibration method and system based on plane constraint

Publications (2)

Publication Number Publication Date
CN113843804A true CN113843804A (en) 2021-12-28
CN113843804B CN113843804B (en) 2023-03-17

Family

ID=78982403

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111222380.XA Active CN113843804B (en) 2021-10-20 2021-10-20 Robot kinematics calibration method and system based on plane constraint

Country Status (1)

Country Link
CN (1) CN113843804B (en)

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104608129A (en) * 2014-11-28 2015-05-13 江南大学 Planar constraint based robot calibration method
US20160346932A1 (en) * 2014-02-11 2016-12-01 Tyco Electronics (Shanghai) Co. Ltd. Automatic Calibration Method For Robot Systems Using a Vision Sensor
CN107525472A (en) * 2017-10-11 2017-12-29 北京航空航天大学 A kind of laser displacement sensor site error scaling method
CN109304730A (en) * 2017-07-28 2019-02-05 华中科技大学 A kind of robot kinematics' parameter calibration method based on laser range finder
CN111590588A (en) * 2020-06-03 2020-08-28 南京埃斯顿机器人工程有限公司 Non-contact tool coordinate system calibration method for welding robot

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20160346932A1 (en) * 2014-02-11 2016-12-01 Tyco Electronics (Shanghai) Co. Ltd. Automatic Calibration Method For Robot Systems Using a Vision Sensor
CN104608129A (en) * 2014-11-28 2015-05-13 江南大学 Planar constraint based robot calibration method
CN109304730A (en) * 2017-07-28 2019-02-05 华中科技大学 A kind of robot kinematics' parameter calibration method based on laser range finder
CN107525472A (en) * 2017-10-11 2017-12-29 北京航空航天大学 A kind of laser displacement sensor site error scaling method
CN111590588A (en) * 2020-06-03 2020-08-28 南京埃斯顿机器人工程有限公司 Non-contact tool coordinate system calibration method for welding robot

Also Published As

Publication number Publication date
CN113843804B (en) 2023-03-17

Similar Documents

Publication Publication Date Title
CN109773786B (en) Industrial robot plane precision calibration method
CN110193829B (en) Robot precision control method for coupling kinematics and rigidity parameter identification
CN111203861B (en) Calibration method and calibration system for robot tool coordinate system
CN108731591B (en) Robot tool coordinate system calibration method based on plane constraint
US4831549A (en) Device and method for correction of robot inaccuracy
CN106777656B (en) Industrial robot absolute accuracy calibration method based on PMPSD
CN110815206B (en) Kinematics calibration method for Stewart parallel robot
CN109176505B (en) Ball arm instrument-based six-axis joint industrial robot spatial error calibration method
CN103231375A (en) Industrial robot calibration method based on distance error models
CN104608129A (en) Planar constraint based robot calibration method
CN112318498B (en) Industrial robot calibration method considering parameter coupling
KR101797122B1 (en) Method for Measurement And Compensation of Error on Portable 3D Coordinate Measurement Machine
CN111168719B (en) Robot calibration method and system based on positioning tool
CN104890013A (en) Pull-cord encoder based calibration method of industrial robot
CN111055273A (en) Two-step error compensation method for robot
CN107053216A (en) The automatic calibration method and system of robot and end effector
Qiao et al. A novel calibration method for multi-robots system utilizing calibration model without nominal kinematic parameters
CN104833324A (en) Robot calibration method based on measuring head
JPH06131032A (en) Robot device and teaching method for robot device
Fan et al. A vision-based fast base frame calibration method for coordinated mobile manipulators
CN113211436B (en) Six-degree-of-freedom series robot error calibration method based on genetic algorithm
Yang et al. Simultaneous base and tool calibration for self-calibrated parallel robots
CN113843804B (en) Robot kinematics calibration method and system based on plane constraint
Mei et al. Calibration of a 6-DOF industrial robot considering the actual mechanical structures and CNC system
CN113878586B (en) Robot kinematics calibration device, method and system

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
CB02 Change of applicant information
CB02 Change of applicant information

Address after: 311231 building 3, No. 477, Hongxing Road, Qiaonan block, economic and Technological Development Zone, Xiaoshan District, Hangzhou City, Zhejiang Province

Applicant after: Hangzhou Jingwu Intelligent Technology Co.,Ltd.

Address before: Room 12, 3rd floor, No.2 Lane 1446, Yunguan Road, Lingang New District, Pudong New Area pilot Free Trade Zone, Shanghai, 201306

Applicant before: Shanghai Jingwu Intelligent Technology Co.,Ltd.

GR01 Patent grant
GR01 Patent grant