CN113843804B - Robot kinematics calibration method and system based on plane constraint - Google Patents
Robot kinematics calibration method and system based on plane constraint Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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- B25J9/00—Programme-controlled manipulators
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- B—PERFORMING OPERATIONS; TRANSPORTING
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- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
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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 a plane according to the position of a laser point on the plane, and establishing a calibration equation of a single plane; repeating the steps in the robot working space 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
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 to be carried out by expensive precise measuring instruments such as a laser tracker, a three-coordinate measuring machine, a ball bar instrument and the like, and needs to be operated by professional personnel.
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 calibration cost and improve calibration efficiency.
Patent document CN104608129B (application number: CN 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. 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, and the implementation difficulty is higher; 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: CN 201810196264.7) 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) driving the robot to measure the constraint planes respectively; (5) identifying kinematic parameters of the robot; and (6) verifying the 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: CN 201711264644.1) discloses a method for calibrating a link parameter of an industrial robot based on a terminal point plane constraint, which includes 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: CN 201810374769.8) 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 attitude 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: CN 201810303734.5) 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 an optical axis of the camera is parallel to the vertical direction; mounting a calibration tool on the robotic tool, a geometric center point of a calibration feature on the calibration tool being aligned vertically with a 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;
and 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;
and 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 in the robot working space 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.
Preferably, in the step S1:
the robot base establishes a base coordinate system 0, the center of a robot flange establishes a flange coordinate system n, 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 superposed with the laser emission point of the laser displacement sensor, the Z direction of the tool coordinate system is superposed 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 robot i Changing 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 the error vectors of the kinematic parameters and the tool parameters are full-rank equations.
Preferably, in the step S3:
a kinematic model of the robot is established by adopting a D-H method, and a homogeneous transformation matrix from a connecting rod coordinate system i-1 to a connecting rod coordinate system i is expressed as
The robot end flange coordinate system n is relative to the robot base coordinate system nA homogeneous transformation matrix of system 0
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, l,1 ]] T Wherein 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:
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;
indicating the position offset of the laser emitting point in the flange coordinate system, and working together with the kinematic error of the robotFor the calibrated error, the nominal position p of the laser point on the plane in the robot base coordinate system n Comprises the following steps:
p n ＝f(θ i ，l)
considering the kinematic error of the robot and the deviation of the tool coordinate system, the actual position p of the laser point on the plane in the robot base coordinate system is:
p＝p n +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 obtained i Comprises the following steps:
p i ＝p i n +J i *σ，i＝1，2...，n
p i n is the nominal position of the ith point; j. the design is a square i A 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
(p i+2 -p 1 )×(p i+1 -p 1 )
＝(p i+2 n -p 1 n +J i+2 *σ-J 1 *σ)×(p i+1 n -p 1 n +J i+1 *σ-J 1 *σ)，
Wherein i =1,2,. Cndot.n-2;
is unfolded to obtain
(p i+2 -p 1 )×(p i+1 -p 1 )＝M i +N i *σ，i＝1，2，...，n-2
Wherein
M i ＝(p i+2 n -p 1 n )×(p i+1 n -p 1 n )
N i ＝(p i+2 n -p 1 n )×(J i+1 -J 1 )+(J i+2 -J 1 )(p i+1 n -p 1 n )
The quadratic term of σ is ignored; m i 、N i For 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:
M 1 ×M i+1 ＝-(M 1 ×N i+1 +N 1 ×M i+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:
y i ＝b i *σ，i＝1，2...，n-3
y i ＝M 1 ×M i+1
b i ＝-(M 1 ×N i+1 +N 1 ×M i+1 )
y i 、b i for the sake of brevity;
establishing a calibration equation of a single plane:
Y＝B*σ
wherein, the first and the second end of the pipe are connected with each other,
Y＝[y 1 ，y 2 ，...，y n-3 ] T ，B＝[b 1 ，b 2 ，...，b n-3 ] T
Y、B、y n 、b n all 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 of the kth plane be y k，i Expressed, then the calibration equation for k planes is:
wherein:
calculating a kinematic parameter and a tool parameter error vector sigma according to a least square method:
the invention provides a robot kinematics calibration system based on plane constraint, which comprises:
a module M1: establishing a base coordinate system, a flange coordinate system and a tool coordinate system;
a module M2: the robot is operated to move, and the degree of the laser displacement sensor and the angle of the robot joint are recorded;
a 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;
a module M4: calculating a normal vector of a plane according to the position of a laser point on the plane, and establishing a calibration equation of a single plane;
the modules M2-M4 are repeated in the robot workspace until the kinematic parameter and tool parameter error vectors are full rank equations, and the kinematic parameter and tool parameter error vectors are calculated.
Preferably, in said module M1:
the robot base establishes a base coordinate system 0, the center of a robot flange establishes a flange coordinate system n, 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 superposed with the laser emission point of the laser displacement sensor, the Z direction of the tool coordinate system is superposed 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 working space of the robot, and the planeness grade is more than 00 grade;
preferably, in said module M2:
the robot is operated to move, so that the laser beam of the laser displacement sensor is projected on a plane, the reading l of the laser displacement sensor is recorded, and the angle theta of the joint of the robot is recorded i Changing 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 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
The homogeneous transformation matrix of the robot end flange coordinate system n with respect to the robot base coordinate system 0 is
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, l,1 ] can be obtained] T Wherein 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:
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;
the position offset of the laser emission point under the flange coordinate system is represented, and the position offset and the kinematic error of the robot are taken as calibrated errors, and the nominal position p of the laser point on the plane in the robot base coordinate system n Comprises the following steps:
p n ＝f(θ i ，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＝p n +J*σ
where J is the nominal Jacobian matrix and σ is the kinematic parameters and tool parameter error vectors.
Preferably, in said module M4:
for n groups of measured data, the actual position p of the ith point is obtained i Comprises the following steps:
p i ＝p i n +J i *σ，i＝1，2...，n
p i n is the nominal position of the ith point; j is a unit of i A 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
(p i+2 -p 1 )×(p i+1 -p 1 )
＝(p i+2 n -p 1 n +J i+2 *σ-J 1 *σ)×(p i+1 n -p 1 n +J i+1 *σ-J 1 *σ)，
Wherein i =1,2,. N-2;
is unfolded to obtain
(p i+2 -p 1 )×(p i+1 -p 1 )＝M i +N i *σ，i＝1，2，...，n-2
Wherein
M i ＝(p i+2 n -p 1 n )×(p i+1 n -p 1 n )
N i ＝(p i+2 n -p 1 n )×(J i+1 -J 1 )+(J i+2 -J 1 )(p i+1 n -p 1 n )
The quadratic term of σ is ignored; m is a group of i 、N i For 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:
M 1 ×M i+1 ＝-(M 1 ×N i+1 +N 1 ×M i+1 )*σ，i＝1，2...，n-3；
the first normal vector refers to a normal vector calculated at 3 points in front of a measuring plane;
unfolding to obtain:
y i ＝b i *σ，i＝1，2...，n-3
y i ＝M 1 ×M i+1
b i ＝-(M 1 ×N i+1 +N 1 ×M i+1 )
y i 、b i for the sake of brevity;
establishing a calibration equation of a single plane:
Y＝B*σ
wherein Y = [ Y = 1 ，y 2 ，...，y n-3 ] T ，B＝[b 1 ，b 2 ，...，b n-3 ] T
Y、B、y n 、b n All the expressions are corresponding expressions in brief description.
Preferably, moving the plane in the 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 of the kth plane be y k，i Expressed, then the calibration equation for k planes is:
wherein:
calculating a kinematic parameter and a tool parameter error vector sigma according to a least square method:
compared with the prior art, the invention has the following beneficial effects:
1. the kinematics calibration device and method for the robot can correct the kinematics parameters of the robot, improve the absolute positioning precision of the work of the robot, and realize non-contact measurement and 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;
and 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;
and step S4: calculating a normal vector of a plane according to the position of a laser point on the plane, and establishing a calibration equation of a single plane;
and repeating the steps S2-S4 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.
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:
the robot is operated to move, so that the laser beam of the laser displacement sensor is projected on a plane, the reading l of the laser displacement sensor is recorded, and the angle theta of the joint of the robot is recorded i Changing 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:
a kinematic model of the robot is established by adopting a D-H method, and a homogeneous transformation matrix from a connecting rod coordinate system i-1 to a connecting rod coordinate system i is expressed as
The homogeneous transformation matrix of the robot end flange coordinate system n relative to the robot base coordinate system 0 is
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, l,1 ] can be obtained] T Wherein 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:
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;
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 system n Comprises the following steps:
p n ＝f(θ i ，l)
considering the kinematic error of the robot and the deviation of the tool coordinate system, the actual position p of the laser point on the plane in the robot base coordinate system is:
p＝p n +J*σ
where J is the nominal Jacobian matrix and σ is the kinematic parameters and tool parameter error vectors.
Specifically, in the step S4:
for n groups of measured data, the actual position p of the ith point is obtained i Comprises the following steps:
p i ＝p i n +J i *σ，i＝1，2...，n
p i n is the nominal position of the ith point; j. the design is a square i A 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 n points
(p i+2 -p 1 )×(p i+1 -p 1 )
＝(p i+2 n -p 1 n +J i+2 *σ-J 1 *σ)×(p i+1 n -p 1 n +J i+1 *σ-J 1 *σ)，
Wherein i =1,2,. N-2;
is unfolded to obtain
(p i+2 -p 1 )×(p i+1 -p 1 )＝M i +N i *σ，i＝1，2，...，n-2
Wherein
M i ＝(p i+2 n -p 1 n )×(p i+1 n -p 1 n )
N i ＝(p i+2 n -p 1 n )×(J i+1 -J 1 )+(J i+2 -J 1 )(p i+1 n -p 1 n )
The quadratic term of σ is ignored; m i 、N i For 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:
M 1 ×M i+1 ＝-(M 1 ×N i+1 +N 1 ×M i+1 )*σ，i＝1，2...，n-3；
the first normal vector refers to a normal vector calculated at 3 points in front of a measuring plane;
unfolding to obtain:
y i ＝b i *σ，i＝1，2...，n-3
y i ＝M 1 ×M i+1
b i ＝-(M 1 ×N i+1 +N 1 ×M i+1 )
y i 、b i for 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＝[y 1 ，y 2 ，...，y n-3 ] T ，B＝[b 1 ，b 2 ，...，b n-3 ] T
Y、B、y n 、b n all 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 y k，i Expressed, then the calibration equation for k planes is:
wherein:
calculating a kinematic parameter and tool parameter error vector sigma according to a least square method:
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 implemented 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:
a module M1: establishing a base coordinate system, a flange coordinate system and a tool coordinate system;
a module M2: operating the robot to move, and recording the degree of the laser displacement sensor and the angle of the robot joint;
a 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;
a module M4: calculating a normal vector of a plane according to the position of a laser point on the plane, and establishing a calibration equation of a single plane;
the modules M2-M4 are repeated in the robot workspace until the kinematic parameter and tool parameter error vectors are full rank equations, and 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;
in particular, in said module M2:
the robot is operated to move, so that the laser beam of the laser displacement sensor is projected on a plane, the reading 1 of the laser displacement sensor is recorded, and the angle theta of the joint of the robot is recorded i Changing 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.
In particular, in said module M3:
a kinematic model of the robot is established by adopting a D-H method, and a homogeneous transformation matrix from a connecting rod coordinate system i-1 to a connecting rod coordinate system i is expressed as
Robot end flangeThe homogeneous transformation matrix of the coordinate system n relative to the robot base coordinate system 0 is
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, l,1 ]] T Wherein 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:
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;
indicating the position offset of the laser emission point in the flange coordinate system, andthe kinematic error of the robot is taken as a calibrated error, and the laser point on the plane is at a nominal position p of the robot base coordinate system n Comprises the following steps:
p n ＝f(θ i ，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＝p n +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 obtained i Comprises the following steps:
p i ＝p i n +J i *σ，i＝1，2...，n
p i n is the nominal position of the ith point; j. the design is a square i A 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
(p i+2 -p 1 )×(p i+1 -p 1 )
＝(p i+2 n -p 1 n +J i+2 *σ-J 1 *σ)×(p i+1 n -p 1 n +J i+1 *σ-J 1 *σ)，
Wherein i =1,2,. N-2;
is unfolded to obtain
(p i+2 -p 1 )×(p i+1 -p 1 )＝M i +N i *σ，i＝1，2，...，n-2
Wherein
M i ＝(p i+2 n -p 1 n )×(p i+1 n -p 1 n )
N i ＝(p i+2 n -p 1 n )×(J i+1 -J 1 )+(J i+2 -J 1 )(p i+1 n -p 1 n )
The quadratic term of σ is ignored; m i 、N i For 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:
M 1 ×M i+1 ＝-(M 1 ×N i+1 +N 1 ×M i+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:
y i ＝b i *σ，i＝1，2...，n-3
y i ＝M 1 ×M i+1
b i ＝-(M 1 ×N i+1 +N 1 ×M i+1 )
y i 、b i for the sake of brevity;
establishing a calibration equation of a single plane:
Y＝B*σ
wherein Y = [ Y = 1 ，y 2 ，...，y n-3 ] T ，B＝[b 1 ，b 2 ，...，b n-3 ] T
Y、B、y n 、b n All the expressions are corresponding expressions in brief description.
Specifically, a plane is moved in a robot working space, the modules are repeated for M2-M4k times, k depends on the number of errors to be calibrated, and the kinematic parameters and tool parameter error vectors are ensured to be full-rank equations;
let the calibration equation for the kth plane be y k，i Expressed, then the calibration equation for the k planes is:
wherein:
calculating a kinematic parameter and tool parameter error vector sigma according to a least square method:
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 of the invention uses a laser displacement sensor to measure the coordinates of plane points, obtains a calibration equation according to the constraint condition of plane normal vector parallel formed by three points in a plane, and uses a least square method to solve kinematics parameters. 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 robot i And 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
The homogeneous transformation matrix of the robot end flange coordinate system n relative to the robot base coordinate system 0 is
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, l,1 ] can be obtained] T Wherein 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
Wherein
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
p n ＝f(θ i ，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＝p n +J*σ
Wherein J is a calibrated Jacobian matrix, and σ is a kinematic parameter and tool parameter error vector.
(5) For n groups of data measured in step 3), the actual position of the ith point can be obtained from step 4)
p i ＝p i n +J i *σ，i＝1，2...，n
Calculating the normal vector of the plane by taking two points of the plane and the first point
(p i+2 -p 1 )×(p i+1 -p 1 )
＝(p i+2 n -p 1 n +J i+2 *σ-J 1 *σ)×(p i+1 n -p 1 n +J i+1 *σ-J 1 *σ)，
Wherein i =1,2,. Cndot.n-2;
is unfolded to obtain
(p i+2 -p 1 )×(p i+1 -p 1 )＝M i +N i *σ，i＝1，2，...，n-2
Wherein
M i ＝(p i+2 n -p 1 n )×(p i+1 n -p 1 n )
N i ＝(p i+2 n -p 1 n )×(J i+1 -J 1 )+(J i+2 -J 1 )(p i+1 n -p 1 n )
The quadratic term of sigma 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
M 1 ×M i+1 ＝-(M 1 ×N i+1 +N 1 ×M i+1 )*σ，i＝1，2...，n-3；
Unfolding to obtain:
y i ＝b i *σ，i＝1，2...，n-3
y i ＝M 1 ×M i+1
b i ＝-(M 1 ×N i+1 +N 1 ×M i+1 )
establishing a calibration equation of a single plane: y = B σ
Wherein Y = [ Y = 1 ，y 2 ，...，y n-3 ] T ，B＝[b 1 ，b 2 ，...，b n-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 plane k，i Expressed, then the calibration equation for the k planes is:
wherein
Calculating kinematic parameter and tool parameter error vectors according to least squares
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 apparatus, and the modules thereof provided by the present invention may be considered as a hardware component, and the modules included in the system, the apparatus, and the modules for implementing various programs may 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 (2)
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 reading of the laser displacement sensor and the angle of the robot joint;
and 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;
and 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 the steps S2-S4 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;
in the step S4:
for n groups of measured data, the actual position p of the ith point is obtained i Comprises the following steps:
p i ＝p i n +J i *σ，i＝1，2…，n
p i n is the nominal position of the ith point; j. the design is a square i A 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
(p i+2 -p 1 )×(p i+1 -p 1 )
＝(p i+2 n -p 1 n +J i+2 *σ-J 1 *σ)×(p i+1 n -p 1 n +J i+1 *σ-J 1 *σ)，
Wherein i =1,2,. N-2;
is unfolded to obtain
(p i+2 -p 1 )×(p i+1 -p 1 )＝M i +N i *σ，i＝1，2，…，n-2
Wherein
M i ＝(p i+2 n -p 1 n )×(p i+1 n -p 1 n )
N i ＝(p i+2 n -p 1 n )×(J i+1 -J 1 )+(J i+2 -J 1 )(p i+1 n -p 1 n )
The quadratic term of σ is ignored; m i 、N i For 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:
M 1 ×M i+1 ＝-(M 1 ×N i+1 +N 1 ×M i+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:
y i ＝b i *σ，i＝1，2…，n-3
y i ＝M 1 ×M i+1
b i ＝-(M 1 ×N i+1 +N 1 ×M i+1 )
y i 、b i for 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＝[y 1 ，y 2 ，...，y n-3 ] T ，B＝[b 1 ，b 2 ，...，b n-3 ] T
Y、B、y n 、b n all are corresponding expressions which are briefly expressed;
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 displacement sensor establishes a tool coordinate system T, the origin of the tool coordinate system is superposed with the laser emission point of the laser displacement sensor, the Z direction of the tool coordinate system is superposed 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 robot i Changing 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; theta i The ith joint angle of the robot;
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
The homogeneous transformation matrix of the robot end flange coordinate system n relative to the robot base coordinate system 0 is
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, l,1 ] can be obtained] T Wherein 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:
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 is a tool coordinate system;
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 system n Comprises the following steps:
p n ＝f(θ i ，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＝p n +J*σ
wherein J is a Jacobian matrix, and sigma is a kinematic parameter and a tool parameter error vector;
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 y k，i Expressed, then the calibration equation for k planes is:
wherein:
calculating a kinematic parameter and tool parameter error vector sigma according to a least square method:
2. a robot kinematics calibration system based on plane constraint is characterized by comprising:
a module M1: establishing a base coordinate system, a flange coordinate system and a tool coordinate system;
a module M2: operating the robot to move, and recording the reading of the laser displacement sensor and the angle of the robot joint;
a 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;
a module M4: calculating a normal vector of a plane according to the position of a laser point on the plane, and establishing a calibration equation of a single plane;
repeating the modules M2-M4 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;
in said module M4:
for n groups of measured data, the actual position p of the ith point is obtained i Comprises the following steps:
p i ＝p i n +J i *σ，i＝1，2…，n
p i n is the nominal position of the ith point; j is a unit of i A 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 n points
(p i+2 -p 1 )×(p i+1 -p 1 )
＝(p i+2 n -p 1 n +J i+2 *σ-J 1 *σ)×(p i+1 n -p 1 n +J i+1 *σ-J 1 *σ)，
Wherein i =1,2,. Cndot.n-2;
is unfolded to obtain
(p i+2 -p 1 )×(p i+1 -p 1 )＝M i +N i *σ，i＝1，2，...，n-2
Wherein
M i ＝(p i+2 n -p 1 n )×(p i+1 n -p 1 n )
N i ＝(p i+2 n -p 1 n )×(J i+1 -J 1 )+(J i+2 -J 1 )(p i+1 n -p 1 n )
The quadratic term of σ is ignored; m is a group of i 、N i For 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:
M 1 ×M i+1 ＝-(M 1 ×N i+1 +N 1 ×M i+1 )*σ，i＝1，2…，n-3；
the first normal vector refers to a normal vector calculated at 3 points in front of a measuring plane;
unfolding to obtain:
y i ＝b i *σ，i＝1，2...，n-3
y i ＝M 1 ×M i+1
b i ＝-(M 1 ×N i+1 +N 1 ×M i+1 )
y i 、b i for the sake of brevity;
establishing a calibration equation of a single plane:
Y＝B*σ
wherein Y = [ Y = 1 ，y 2 ，...，y n-3 ] T ，B＝[b 1 ，b 2 ，...，b n-3 ] T
Y、B、y n 、b n All are corresponding generations which are briefly described;
in the module M1:
the robot base establishes a base coordinate system 0, the center of a robot flange establishes a flange coordinate system n, the robot flange is provided with a laser displacement sensor, the laser displacement sensor establishes a tool coordinate system T, the origin of the tool coordinate system is superposed with the laser emission point of the laser displacement sensor, the Z direction of the tool coordinate system is superposed 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 working space of the robot, and the planeness grade is more than 00 grade;
in said module M2:
the robot is operated to move, so that the laser beam of the laser displacement sensor is projected on a plane, the reading l of the laser displacement sensor is recorded, and the angle theta of the joint of the robot is recorded i Changing 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 the error vectors of the kinematic parameters and the tool parameters are full-rank equations; theta.theta. i The ith joint angle of the robot is set;
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
The homogeneous transformation matrix of the robot end flange coordinate system n with respect to the robot base coordinate system 0 is
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, l,1 ]] T Wherein 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 as follows:
p is a position matrix of a laser point on the plane under a robot base coordinate system, I is a unit rotation matrix and is a tool coordinate system;
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 system n Comprises the following steps:
p n ＝f(θ i ，l)
considering the kinematic error of the robot and the deviation of the tool coordinate system, the actual position p of the laser point on the plane in the robot base coordinate system is:
p＝p n +J*σ
wherein J is a Jacobian matrix, and sigma is a kinematic parameter and a tool parameter error vector;
moving a plane in a robot working space, repeating the modules for 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 y k，i Expressed, then the calibration equation for k planes is:
wherein:
calculating a kinematic parameter and tool parameter error vector sigma according to a least square method:
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