CN111283676B - Tool coordinate system calibration method and calibration device of three-axis mechanical arm - Google Patents

Tool coordinate system calibration method and calibration device of three-axis mechanical arm Download PDF

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CN111283676B
CN111283676B CN201811497332.XA CN201811497332A CN111283676B CN 111283676 B CN111283676 B CN 111283676B CN 201811497332 A CN201811497332 A CN 201811497332A CN 111283676 B CN111283676 B CN 111283676B
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coordinate system
mechanical arm
tool
calibration
circle
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CN111283676A (en
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颜良益
张鑫
伍蒙
张曼
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Delta Electronics (Jiangsu) Ltd.
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DELTA ELECTRONICS (JIANGSU) Ltd
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • 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
    • B25J9/1653—Programme controls characterised by the control loop parameters identification, estimation, stiffness, accuracy, error analysis

Abstract

The invention provides a calibration method and a calibration device for a tool coordinate system of a triaxial mechanical arm, wherein the calibration method comprises the following steps: based on the same circular marker, the mechanical arm performs n times of shooting according to a plurality of different posturesShooting in a first posture, shooting in a second posture when the end part of the calibration jig reaches the circle center position in the ith shooting action, shooting in a jth shooting action, and recording a coordinate O corresponding to the tail end of the mechanical arm in the shooting action respectively when the end part of the calibration jig reaches the circle center position in the jth shooting actionE iAnd OE jAnd establishing an equation to solve, and finally obtaining the horizontal distance W from the tail end of the mechanical arm to the end part of the calibration jig and the included angle theta between the connecting line of the tail end of the mechanical arm and the central point of the tool and the X-axis direction of the coordinate system at the tail end of the mechanical arm.

Description

Tool coordinate system calibration method and calibration device of three-axis mechanical arm
Technical Field
The invention relates to the field of tool coordinate system calibration, in particular to a tool coordinate system calibration method and a calibration device of a three-axis mechanical arm.
Background
In an industrial production line, special parts are usually fixed at the end of a robot arm of an industrial robot as tools, such as a jig, a welding gun, etc., and a coordinate system, a so-called tool coordinate system, is usually established at a fixed position on the tools. The trajectory planning of the robot is usually performed for a certain Point of the Tool after adding the Tool as described above, and this Point is usually called a Tool Center Point (TCP). In general, the origin of the tool coordinate system is TCP, and after the tool is mounted on the end of the mechanical arm of the robot, the relation of the tool coordinate system with respect to the robot end coordinate system (i.e. the flange coordinate system) is fixed and unchanged unless the mounting position of the tool is changed artificially. The correct tool coordinate system calibration has a significant impact on the trajectory planning of the robot, and the tool of the robot may need to be changed frequently for different application scenarios.
Triaxial arm is changed by four-axis arm evolution and comes, and four-axis arm has four degrees of freedom of motion: x, Y, Z translational degree of freedom and RZ rotational degree of freedom, the three-axis mechanical arm only has X, Y, Z translational degree of freedom and can not rotate; the tool coordinate system calibration method is different from the four-axis mechanical arm. The tool coordinate system is calibrated by a conventional method, the calibration is manually performed by an operator, the precision is difficult to guarantee, the calculation result with the minimum error is usually required to be obtained through multiple times of calibration, a large amount of time and energy are consumed, the calibration process has certain technical threshold requirements on the operator, and the on-site application is not facilitated, so that the rapid, accurate and automatic calibration method for the three-axis mechanical arm tool coordinate system is urgently needed in practical application.
In view of this, the present invention provides a method and a device for calibrating a tool coordinate system of a three-axis robot arm.
Disclosure of Invention
Aiming at the problems in the prior art, the invention aims to provide a tool coordinate system calibration method and a calibration device of a three-axis mechanical arm, which overcome the difficulties in the prior art, can automatically complete the processes of matching, position teaching, switching a hand system, calculating a tool coordinate system and the like, greatly simplifies the calibration process, and ensures the calibration precision due to the use of vision.
The invention provides a tool coordinate system calibration method of a three-axis mechanical arm, which comprises the following steps:
establishing a geodetic coordinate system based on a mechanical arm base, a terminal coordinate system (namely a flange coordinate system) based on the tail end of the mechanical arm and a tool coordinate system generated based on a camera, and setting the origin of the tool coordinate system as a tool center point;
based on the same circular marker, the mechanical arm carries out shooting actions for n times according to a plurality of different postures, wherein n is more than or equal to 2, and the shooting actions comprise: moving the mechanical arm to reach the upper part of the circular marker and shooting at least one part of the circular marker, obtaining the circle center position of the circular marker in the tool coordinate system through a circle center fitting algorithm, moving the mechanical arm to drive the end part of the calibration jig to reach the circle center position, and recording the position of the calibration jigWith the coordinate O of the tip in the geodetic coordinate systemE(XE,YE) A first included angle theta between a first axis of the mechanical arm in the geodetic coordinate system and the X-axis direction of the geodetic coordinate system1A second included angle theta between a second shaft of the mechanical arm and the X-axis direction of the geodetic coordinate system2(ii) a The position of the tail end of the mechanical arm under the geodetic coordinate system is set as OE(px,py) Establishing a matrix expressing the coordinates of the tool center point in the geodetic coordinate system
Figure BDA0001897217300000021
Wherein d isxAs the origin O of the tool coordinate systemTAnd the origin O of the terminal coordinate systemEDifference in X-axis direction of the terminal coordinate system, dyAs the origin O of the tool coordinate systemTAnd the origin O of the terminal coordinate systemEThe difference in the Y-axis direction of the terminal coordinate system, beta is a first included angle theta1And a second angle theta2Summing;
shooting in a first posture, when shooting for the ith time, the end part of the calibration jig reaches the circle center position, shooting in a second posture, when shooting for the jth time, the end part of the calibration jig reaches the circle center position, and respectively recording a coordinate O of the tail end corresponding to the shooting action under a geodetic coordinate systemE iAnd OE jAnd the equation is established:
Figure BDA0001897217300000022
solving for dxAnd dy；
Solving the horizontal distance W from the tail end of the mechanical arm to the end part of the calibration jig,
Figure BDA0001897217300000031
and the included angle theta between the connecting line of the tail end of the mechanical arm and the central point of the tool and the X-axis direction of the tail end coordinate system,
Figure BDA0001897217300000032
wherein the X-axis direction of the terminal coordinate system is parallel to the second axis direction.
Preferably, the circular marker is composed of a plurality of concentric circles.
Preferably, the step of obtaining the position of the center of the circle of the circular marker in the tool coordinate system comprises:
let the center coordinate of a circle be (x)0,y0) And the radius is R, the equation of the circle is
(x-x0)2+(y-y0)2＝R2；
Three points are taken on the circle, and the coordinates of the three points are respectively set as (x)1,y1)，(x2,y2)，(x3,y3) Then, there are:
Figure BDA0001897217300000033
the formula (1) (2) is subtracted, and the formula (1) (3) is simplified to obtain:
Figure BDA0001897217300000034
Figure BDA0001897217300000035
wherein x0，y0The only condition for a solution is that the coefficient determinant is not equal to 0:
Figure BDA0001897217300000036
the formula after transformation is as follows:
Figure BDA0001897217300000037
namely, the coordinates of the selected three points cannot be collinear;
setting: a ═ x1-x2；b＝y1-y2；c＝x1-x3；d＝x1-y3；
Figure BDA0001897217300000038
The coordinates (x) of the circle center can be calculated0,y0) Comprises the following steps:
Figure BDA0001897217300000041
preferably, the center coordinates (x) are calculated from0,y0) Substituting the formula (1), namely calculating a radius value R of a circle, judging whether the radius value R is equal to a preset radius of any circle in concentric circles, and if so, moving the mechanical arm to enable the end part of the calibration jig to reach the position of the circle center; if not, the mechanical arm translates the default distance, and the shooting action is executed again.
Preferably, the n-time photographing actions are based on either one of a right-handed system and a left-handed system.
Preferably, the ith shooting motion and the jth shooting motion are each based on one of a right-handed system and a left-handed system.
Preferably, said solution dxAnd dyThe method comprises the following steps:
based on
Figure BDA0001897217300000042
Deducing:
Figure BDA0001897217300000043
the method is simplified as follows: a. theij·X＝Bij
Wherein the content of the first and second substances,
Figure BDA0001897217300000044
Figure BDA0001897217300000045
namely: a. X ═ B
Wherein
Figure BDA0001897217300000046
The solution matrix equation is as follows:
Figure BDA0001897217300000047
to obtain dxAnd dy。
The invention also provides a tool coordinate system calibration device of the triaxial mechanical arm, which comprises a mechanical arm base, a first shaft, a second shaft, a calibration jig and a camera, and the tool coordinate system calibration method of the mechanical arm is realized.
Preferably, the camera imaging plane of the camera is parallel to the plane of the circular marker.
Preferably, the circular marker is located within reach of the camera based on both left-handed and right-handed movements.
In view of this, the tool coordinate system calibration method and the calibration device of the three-axis mechanical arm can automatically complete the processes of matching, position teaching, switching a hand system, calculating a tool coordinate system and the like, greatly simplify the calibration process, and ensure the calibration precision due to the use of vision; when the position of the camera changes, the recalibration of the tool coordinate system can be quickly realized, and the method is stable, reliable and strong in repeatability; the tail end coordinate system of the second shaft or third shaft additional tool of the three-shaft mechanical arm can be calibrated by using the lower vision, and the reproducibility is strong; the method greatly reduces the correction time of the coordinate system of the camera tool of the three-axis mechanical arm, improves the calibration precision, reduces the operation threshold, and is a great improvement on the traditional manual teaching method.
Drawings
Other features, objects and advantages of the present invention will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, with reference to the accompanying drawings.
FIG. 1 is a schematic flow chart of a tool coordinate system calibration method of a tri-axial robotic arm of the present invention;
FIG. 2 is a schematic view of the tool coordinate system calibration arrangement of the tri-axial robotic arm of the present invention;
FIG. 3 is a schematic view of a circular marker for use in the present invention;
FIG. 4 is a schematic diagram of the circle center fitting process in the tool coordinate system calibration method of the three-axis robot arm of the present invention;
FIG. 5 is a reference diagram of the geodetic coordinate system and the tool coordinate system in the tool coordinate system calibration method of the three-axis robot arm according to the present invention;
FIG. 6 is a schematic diagram of a first pose imaging by the tool coordinate system calibration method of the three-axis robot arm of the present invention;
fig. 7 is a schematic diagram of the second posture photographing performed by the tool coordinate system calibration method of the three-axis robot arm in the invention.
Reference numerals
1 mechanical arm base
2 first axis
3 second axis
4 pick-up head
5 circular marker
6 third shaft
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. The same reference numerals in the drawings denote the same or similar structures, and thus their repetitive description will be omitted.
Fig. 1 is a schematic flow chart of a tool coordinate system calibration method of a three-axis robot arm according to the present invention. Fig. 2 is a schematic diagram of the tool coordinate system calibration apparatus of the tri-axial robot arm of the present invention. As shown in fig. 1 and 2, the present invention provides a method for calibrating a tool coordinate system of a three-axis robot arm, the three-axis robot arm used in the present invention includes a robot arm base 1, a first axis 2, a second axis 3, and a camera 4, and the tool coordinate system calibration is performed based on a circular marker 5. The three-axis mechanical arm in the embodiment comprises a base and the mechanical arm, the end flange is not rotatable, and other joints can move to enable the mechanical arm to reach the marker. The machine vision of the three-axis mechanical arm comprises a vision controller, a camera 4 and the like; the camera is arranged on the first shaft 2 or the second shaft 3, and the imaging plane of the camera is parallel to the flange surface of the three-shaft mechanical arm. The circular markers 5 are composed of concentric circles with different radiuses, the selection of the density of the circles is related to the visual field range, and the radius of each circle in the circular markers 5 is known. The marker needs to be pasted on a machine table below the mechanical arm and is parallel to the imaging plane of the camera, and the pasting position ensures that the camera can shoot the outermost round edge after the left-right hand system is switched. The invention aims to simplify the calibration process of a machine tool coordinate system on a three-axis mechanical arm and realize a one-key high-precision high-speed calibration tool coordinate system. The tool coordinate system calibration method of the three-axis mechanical arm comprises the following steps:
s101, establishing a geodetic coordinate system based on the mechanical arm base 1, a terminal coordinate system (namely a flange coordinate system) based on the mechanical arm terminal, and a tool coordinate system generated based on the camera 4, and setting the origin of the tool coordinate system as a tool center point.
S102, referring to fig. 3, based on the same circular marker 5, the robot arm performs n times of photographing operations according to a plurality of different postures, where n is equal to or greater than 2, and the photographing operations include: after moving the robot arm to reach above the circular marker 5 and capturing at least a part of the circular marker 5, for example: transferring the position of the origin of the pixel coordinates of the camera view field from the default upper left corner of the display to the view field center; and selecting a proper lens, and adjusting the focal length, the light incoming quantity and the like to clearly present the circular marker in the field of view. The inching manipulator (hands are selected) moves to the upper part of the circular marker, so that the edge of the circular marker can be displayed in the visual field without being adjusted to the center of the visual field. Then, the position of the center of the circular marker 5 in the tool coordinate system is obtained through a center fitting algorithm.
Referring to fig. 4, in the present embodiment, the step of obtaining the center position of the circular marker 5 in the tool coordinate system is as follows, but not limited thereto:
let the center coordinate of a circle be (x)0,y0) And the radius is R, the equation of the circle is
(x-x0)2+(y-y0)2＝R2；
Three points are taken on the circle, and the coordinates of the three points are respectively set as (x)1,y1)，(x2,y2)，(x3,y3) Then, there are:
Figure BDA0001897217300000071
the formula (1) (2) is subtracted, and the formula (1) (3) is simplified to obtain:
Figure BDA0001897217300000072
Figure BDA0001897217300000073
wherein x0，y0The only condition for a solution is that the coefficient determinant is not equal to 0:
Figure BDA0001897217300000074
the formula after transformation is as follows:
Figure BDA0001897217300000075
namely, the coordinates of the selected three points cannot be collinear;
setting: a ═ x1-x2；b＝y1-y2；c＝x1-x3；d＝x1-y3；
Figure BDA0001897217300000081
The coordinates (x) of the circle center can be calculated0,y0) Comprises the following steps:
Figure BDA0001897217300000082
preferably, the center coordinates (x) are calculated from0,y0) Substituting the formula (1), calculating a radius value R of the circle, judging whether the radius value R is equal to a preset radius of any circle in the concentric circles, and if so, moving the mechanical arm to enable the end part of the calibration jig to reach the position of the circle center; if not, the mechanical arm translates for the default distance, and the shooting action is executed again.
Subsequently, referring to fig. 5, the mobile mechanical arm drives the end of the calibration jig to reach the circle center position, and records the coordinate O of the tail end of the calibration jig in the geodetic coordinate systemE(XE,YE) A first included angle theta between the first axis 2 of the mechanical arm in the geodetic coordinate system and the X-axis direction of the geodetic coordinate system1A second included angle theta between the second shaft 3 of the mechanical arm and the X-axis direction of the geodetic coordinate system2(ii) a The position of the tail end of the mechanical arm under the geodetic coordinate system is set as OE(px,py) Establishing a matrix expressing the coordinates of the tool center point in the geodetic coordinate system
Figure BDA0001897217300000083
Wherein d isxAs the origin O of the tool coordinate systemTAnd the origin O of the terminal coordinate systemEDifference in X-axis direction of the terminal coordinate system, dyAs the origin O of the tool coordinate systemTAnd the origin O of the terminal coordinate systemEThe difference in the Y-axis direction of the terminal coordinate system, beta is a first included angle theta1And a second angle theta2And (4) summing.
In this embodiment, the circular marker 5 is composed of a plurality of concentric circles, but not limited thereto.
S103, referring to fig. 6, the photographing is performed in the first posture, in this embodiment, the photographing operation based on the right-hand system is taken as the first posture, and after the end of the calibration jig reaches the center position in the ith photographing operation, the geodetic coordinate O of the end corresponding to the photographing operation is recordedE i。
Referring to fig. 7, the second posture is taken as the second posture, the end of the calibration jig reaches the center of the circle in the jth shooting operation, and the geodetic coordinates O of the corresponding end of the shooting operation are recordedE iAnd OE jAnd the equation is established:
Figure BDA0001897217300000091
solving for dxAnd dy。
Preferably, solving for dxAnd dyThe method comprises the following steps:
based on
Figure BDA0001897217300000092
Deducing:
Figure BDA0001897217300000093
the method is simplified as follows: a. theij·X＝Bij
Wherein the content of the first and second substances,
Figure BDA0001897217300000094
Figure BDA0001897217300000095
namely: a. X ═ B
Wherein
Figure BDA0001897217300000096
The solution matrix equation is as follows:
Figure BDA0001897217300000097
to obtain dxAnd dy。
With continued reference to fig. 5, in the present embodiment, the displacement amount of the origin of the terminal coordinate system in the geodetic coordinate system based on the robot arm base 1 with respect to the origin of the tool coordinate system generated based on the camera 4 is established as
Figure BDA0001897217300000098
In a preferred embodiment, the n photographing operations are based on any one of a right-handed system and a left-handed system, but not limited thereto.
In a preferred embodiment, the ith shooting motion and the jth shooting motion are based on one of a right-handed system and a left-handed system, but not limited thereto.
The invention adopts more gestures to shoot so as to obtain new coordinates or adopts different right-hand systems/left-hand systems to shoot for multiple times so as to obtain new coordinates, which is helpful to obtain more accurate origin O in the tool coordinate systemTAnd the origin O of the terminal coordinate systemEDifference d in X-axis direction of terminal coordinate systemxAt the origin O of the tool coordinate systemTAnd the origin O of the terminal coordinate systemEDifference d in the Y-axis direction of the end coordinate systemyThe conversion accuracy between the tool coordinate system and the geodetic coordinate system is improved.
S104, with continued reference to fig. 5, finally obtaining two parameters required for the conversion from the tool coordinate system to the geodetic coordinate system: width (Width), Angle (Angle). Solving the horizontal distance W from the tail end of the mechanical arm to the end part of the calibration jig,
Figure BDA0001897217300000101
and the included angle theta between the connecting line of the tail end of the mechanical arm and the central point of the tool and the X-axis direction of the tail end coordinate system,
Figure BDA0001897217300000102
wherein the X-axis direction of the terminal coordinate system is parallel to the second axis direction.
After the width and angle information required by the conversion of the tool coordinate system is obtained, a special instruction in the mechanical arm can be called, and a new tool coordinate system center is set.
Referring to fig. 2, the present invention further provides a tool coordinate system calibration device for a three-axis robot arm, including a robot arm base 1, a first axis 2, a second axis 3, a third axis 6, a calibration fixture, and a camera 4, so as to implement the tool coordinate system calibration method for the robot arm, which is not described herein again.
In a preferred embodiment, the camera imaging plane of the camera 4 is parallel to the plane of the circular marker 5, but not limited thereto.
In a preferred embodiment, the circular marker 5 is located within reach of the camera 4 based on both left-handed and right-handed movements, but not limited thereto.
Compared with the prior art, the method has the following remarkable advantages and beneficial effects:
in the existing practice, to complete the matching between the center of a circle of a logo and the central position of a field of view, the actual distance and the pixel fluctuation difference are large, and the matching cannot be completed manually, so that the mechanical arm needs to have a micro-distance inching condition. In view of the above, matching the center of the logo and the center of the field of view is a difficult point in the current practice. The method realizes the purpose of automatically matching the center of a circle and the central position of a view field through the concentric circular marker map with different radiuses, and can automatically complete the processes of matching, position teaching, switching a hand system, calculating a tool coordinate system and the like as long as the initial position vision can obtain the edge of the marker map, thereby greatly simplifying the calibration process and ensuring the calibration precision by using the vision.
The method can automatically complete the calibration of the camera tool coordinate system only by adjusting the position of the mechanical arm once initially, can quickly realize the recalibration of the tool coordinate system when the position of the camera is changed, and is stable, reliable and strong in repeatability.
The method can be derived to the calibration of other tool coordinate systems of the three-axis mechanical arm, the calibration of the terminal coordinate system (such as the tool coordinate system) of the tool additionally arranged on the second axis or the third axis 6 (see figure 2) of the three-axis mechanical arm can be carried out by utilizing the lower vision, and the reproducibility is strong.
The method greatly reduces the correction time of the coordinate system of the camera tool of the three-axis mechanical arm, improves the calibration precision, reduces the operation threshold, and is a great improvement on the traditional manual teaching method.
In conclusion, the tool coordinate system calibration method and the calibration device of the three-axis mechanical arm can automatically complete the processes of matching, position teaching, switching a hand system, calculating a tool coordinate system and the like, greatly simplify the calibration process, and ensure the calibration precision due to the use of vision; when the position of the camera changes, the recalibration of the tool coordinate system can be quickly realized, and the method is stable, reliable and strong in repeatability; the terminal coordinate system of the second or third shaft additional tool of the three-shaft mechanical arm can be calibrated under the installation of vision, and the reproducibility is strong; the method greatly reduces the correction time of the coordinate system of the camera tool of the three-axis mechanical arm, improves the calibration precision, reduces the operation threshold, and is a great improvement on the traditional manual teaching method.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (9)

1. A method for tool coordinate system calibration of a tri-axial robotic arm, the method comprising:
establishing a geodetic coordinate system based on a mechanical arm base, a terminal coordinate system based on the mechanical arm terminal and a tool coordinate system generated based on a camera, and setting the origin of the tool coordinate system as a tool center point;
based on the same circular marker, the circular marker is composed of a plurality of concentric circles, the mechanical arm carries out shooting actions for n times according to a plurality of different postures, n is greater than or equal to 2, and the shooting actions comprise:after the mechanical arm is moved to reach the upper part of the circular marker and at least one part of the circular marker is shot, the circle center position of a circle in the circular marker in the tool coordinate system is obtained through a circle center fitting algorithm, the radius value R of the circle is obtained through the circle center position, when the radius value R is equal to the preset radius of any circle in the concentric circles, the mechanical arm is moved to drive the end part of the calibration jig to reach the circle center position, and the coordinate O of the tail end of the calibration jig in the earth coordinate system is recordedE(XE,YE) A first included angle theta between a first axis of the mechanical arm in the geodetic coordinate system and the X-axis direction of the geodetic coordinate system1A second included angle theta between a second shaft of the mechanical arm and the X-axis direction of the geodetic coordinate system2(ii) a The position of the tail end of the mechanical arm under the geodetic coordinate system is set as OE(px,py) Establishing a matrix expressing the coordinates of the tool center point in the geodetic coordinate system
Figure FDA0003209116570000011
Wherein d isxAs the origin O of the tool coordinate systemTAnd the origin O of the terminal coordinate systemEDifference in X-axis direction of the terminal coordinate system, dyAs the origin O of the tool coordinate systemTAnd the origin O of the terminal coordinate systemEThe difference in the Y-axis direction of the terminal coordinate system, beta is a first included angle theta1And a second angle theta2Summing;
shooting in a first posture, when shooting for the ith time, the end part of the calibration jig reaches the circle center position, shooting in a second posture, when shooting for the jth time, the end part of the calibration jig reaches the circle center position, and respectively recording a coordinate O of the tail end corresponding to the shooting action under a geodetic coordinate systemE iAnd OE jAnd the equation is established:
Figure FDA0003209116570000012
solving for dxAnd dy；
Solving the horizontal distance W from the tail end of the mechanical arm to the end part of the calibration jig,
Figure FDA0003209116570000021
and the included angle theta between the connecting line of the tail end of the mechanical arm and the central point of the tool and the X-axis direction of the tail end coordinate system,
Figure FDA0003209116570000022
wherein the X-axis direction of the terminal coordinate system is parallel to the second axis direction.
2. The method of calibrating a tool coordinate system of a tri-axial robotic arm of claim 1, wherein the step of obtaining the location of the center of the circle of the circular marker in the tool coordinate system comprises:
let the center coordinate of a circle be (x)0,y0) And the radius is R, the equation of the circle is
(x-x0)2+(y-y0)2＝R2；
Three points are taken on the circle, and the coordinates of the three points are respectively set as (x)1,y1)，(x2,y2)，(x4,y4) Then, there are:
Figure FDA0003209116570000023
the formula (1) (2) is subtracted, and the formula (1) (3) is simplified to obtain:
Figure FDA0003209116570000024
Figure FDA0003209116570000025
wherein x0，y0The only condition for a solution is that the coefficient determinant is not equal to 0:
Figure FDA0003209116570000026
the formula after transformation is as follows:
Figure FDA0003209116570000027
namely, the coordinates of the selected three points cannot be collinear;
setting: a ═ x1-x2；b＝y1-y2；c＝x1-x4；d＝x1-y4；
Figure FDA0003209116570000028
The coordinates (x) of the circle center can be calculated0,y0) Comprises the following steps:
Figure FDA0003209116570000031
3. the tool coordinate system calibration method of a tri-axial robot arm as claimed in claim 2, wherein the center coordinates (x) are calculated from the center coordinates (x)0,y0) Substituting the formula (1), namely calculating a radius value R of a circle, judging whether the radius value R is equal to a preset radius of any circle in concentric circles, and if so, moving the mechanical arm to enable the end part of the calibration jig to reach the position of the circle center; if not, the mechanical arm translates the default distance, and the shooting action is executed again.
4. The tool coordinate system calibration method of a three-axis robot arm according to claim 1, wherein the n photographing actions are based on any one of a right-handed system and a left-handed system.
5. The tool coordinate system calibration method of a triaxial robot arm according to claim 1, wherein the ith photographing action and the jth photographing action are each based on one of a right-handed system and a left-handed system.
6. The method for tool coordinate system calibration of a tri-axial robotic arm of claim 1, wherein said solving for dxAnd dyThe method comprises the following steps:
based on
Figure FDA0003209116570000032
Deducing:
Figure FDA0003209116570000033
the method is simplified as follows: a. theij·X＝Bij
Wherein the content of the first and second substances,
Figure FDA0003209116570000034
Figure FDA0003209116570000035
namely: a. X ═ B
Wherein
Figure FDA0003209116570000036
The solution matrix equation is as follows:
Figure FDA0003209116570000041
to obtain dxAnd dy。
7. A tool coordinate system calibration device of a three-axis mechanical arm is characterized by comprising a mechanical arm base, a first axis, a second axis, a calibration jig and a camera, and realizing the tool coordinate system calibration method of the mechanical arm as claimed in any one of claims 1 to 6.
8. The apparatus for calibrating a tool coordinate system of a tri-axial robotic arm as defined in claim 7, wherein the camera imaging plane of the camera is parallel to the plane of the circular marker.
9. The apparatus of claim 7, wherein the circular marker is within reach of the camera based on both left-handed and right-handed motions.
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