CN109974584B - Calibration system and calibration method for auxiliary laser osteotomy robot - Google Patents

Calibration system and calibration method for auxiliary laser osteotomy robot Download PDF

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CN109974584B
CN109974584B CN201910293683.7A CN201910293683A CN109974584B CN 109974584 B CN109974584 B CN 109974584B CN 201910293683 A CN201910293683 A CN 201910293683A CN 109974584 B CN109974584 B CN 109974584B
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CN109974584A (en
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宋锐
王莉娟
赵赫
袁宏祥
李倩倩
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Shandong Shanda Science And Technology Park Development Co ltd
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    • G01—MEASURING; TESTING
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Abstract

The invention discloses a calibration system and a calibration method for an auxiliary laser osteotomy robot, which are used for acquiring a transfer matrix of a mechanical arm tail end coordinate system relative to a robot base coordinate system and a transfer matrix of a tracking device coordinate system relative to a camera coordinate system; solving a translation vector of the tool coordinate system relative to the mechanical arm tail end coordinate system, establishing a transfer matrix of the tool coordinate system relative to the mechanical arm tail end coordinate system, obtaining a transfer matrix of the tool coordinate system relative to the robot base coordinate system, and realizing tool calibration of the robot; and solving the translation vector of the tool coordinate system relative to the tracking device coordinate system, acquiring two groups of three-dimensional point sets of the tool coordinate system origin, and solving the transfer matrix of the robot base coordinate system relative to the camera coordinate system to realize the hand-eye calibration of the robot.

Description

Calibration system and calibration method for auxiliary laser osteotomy robot
Technical Field
The disclosure relates to the field of robot calibration, in particular to a calibration system and a calibration method for an auxiliary laser osteotomy robot.
Background
In recent years, surgical robotics has become more and more widely used in clinical settings. An auxiliary laser osteotomy robot is an autonomous surgical robot which can help doctors to automatically complete osteotomy according to preoperative planning during operation. Compared with the traditional osteotomy surgical instrument, the osteotomy surgical instrument has the advantages of accuracy, controllability, small damage to surrounding tissues and the like. Tool calibration and hand-eye calibration are important steps before the auxiliary osteotomy operation robot is installed and operated, and directly determine the positioning precision and the operation effect of the robot.
The inventor finds that the traditional calibration method mostly depends on advanced measuring equipment in the research and development process, the calibration process is complex, the cost of the measuring equipment is high, and the measurement precision depends on the precision of the measuring equipment to a great extent, so that the method is difficult to effectively apply in actual operation. The existing calibration methods such as the four-point method and the six-point method are complex in operation process and poor in stability, and cannot meet the requirements of clinical operations. On the other hand, in the auxiliary laser osteotomy robot system, the calibration of the laser tool is the calibration of a suspended point in the space of the laser effective ablation point, belongs to the non-contact tool calibration, and improves the difficulty of system calibration.
Disclosure of Invention
In order to overcome the defects of the prior art, the present disclosure provides a calibration system and a calibration method for assisting a laser osteotomy robot, which can automatically and effectively realize the tool and hand-eye calibration of the laser osteotomy robot, and improve the calibration precision.
The technical scheme adopted by the disclosure is as follows:
a calibration method for an auxiliary laser osteotomy robot comprises the following steps:
establishing a coordinate system of the robot, the tail end of the mechanical arm, the camera, the tracking device and a tool positioned at the tail end of the mechanical arm;
acquiring a transfer matrix of a mechanical arm tail end coordinate system relative to a robot base coordinate system and a transfer matrix of a tracking device coordinate system relative to a camera coordinate system when tool emitted laser vertically irradiates each plane of a calibration device and passes through the center of the calibration device;
solving a translation vector of the tool coordinate system relative to the mechanical arm tail end coordinate system, and establishing a transfer matrix of the tool coordinate system relative to the mechanical arm tail end coordinate system;
multiplying a transfer matrix of the robot arm tail end coordinate system relative to the robot base coordinate system by a transfer matrix of the tool coordinate system relative to the robot arm tail end coordinate system to obtain a transfer matrix of the tool coordinate system relative to the robot base coordinate system, and realizing tool calibration of the robot;
and solving the translation vector of the tool coordinate system relative to the tracking device coordinate system, acquiring two groups of three-dimensional point sets of the tool coordinate system origin, and solving the transfer matrix of the robot base coordinate system relative to the camera coordinate system to realize the hand-eye calibration of the robot.
As a further technical solution of the present disclosure, the method for acquiring the transfer matrix of the robot arm end coordinate system with respect to the robot base coordinate system includes:
measuring the distance from a tool to the center of an external sphere of the calibration device when the tool at the tail end of the mechanical arm emits laser to vertically irradiate a first plane of the calibration device and pass through the center of the calibration device;
when the measured distance is equal to the sum of the effective laser ablation distance and the external sphere radius of the calibration device, the position and posture information of the central point of the end tool of the mechanical arm relative to the base coordinate system of the robot is obtained, and a first transfer matrix of the end coordinate system { E } of the mechanical arm relative to the base coordinate system { B } of the robot is formed
Figure GDA0002308571790000021
Repeating the steps until a second transfer matrix of the coordinate system { E } of the tail end of the mechanical arm relative to the base coordinate system { B } of the robot is obtained
Figure GDA0002308571790000031
Third transition matrix
Figure GDA0002308571790000032
And a fourth transfer matrix
Figure GDA0002308571790000033
As a further technical solution of the present disclosure, the method for acquiring the transfer matrix of the tracking device coordinate system with respect to the camera coordinate system includes:
measuring the distance from a tool to the center of an external sphere of the calibration device when the tool at the tail end of the mechanical arm emits laser to vertically irradiate a first plane of the calibration device and pass through the center of the calibration device;
when the measured distance is equal to the sum of the effective laser ablation distance and the external sphere radius of the calibration device, acquiring the position and posture information of the tracking device coordinate system relative to the camera coordinate system to form a first transfer matrix of the tracking device coordinate system { D } relative to the camera coordinate system { C }
Figure GDA0002308571790000034
Repeating the above steps until a second tracking device coordinate system { D } is obtained relative to the camera coordinate system { C }, andtransfer matrix
Figure GDA0002308571790000035
Third transition matrix
Figure GDA0002308571790000036
And a fourth transfer matrix
Figure GDA0002308571790000037
As a further technical solution of the present disclosure, the method for solving the translation vector of the tool coordinate system relative to the robot arm end coordinate system includes:
establishing conversion relations of a tool coordinate system { T }, a mechanical arm end coordinate system { E }, and a robot base coordinate system { B };
transfer matrix of robot end coordinate system { E } relative to robot base coordinate system { B }
Figure GDA0002308571790000038
Substituting the obtained conversion relation into the obtained conversion relation to obtain an incompatibility equation set;
solving the optimal least square solution of the incompatible equation set by using a singular value decomposition method to obtain a translation vector of the tool coordinate system { T } relative to the mechanical arm terminal coordinate system { E }
Figure GDA0002308571790000039
Combining the rotation matrix invariant principle of the translation relation between the tool coordinate system { T } and the robot end coordinate system { E }, obtaining the transfer matrix of the tool coordinate system { T } relative to the robot end coordinate system { E }
Figure GDA00023085717900000310
Transfer matrix relating tool coordinate system { T } to robot end coordinate system { E }
Figure GDA0002308571790000041
Transfer matrix from the robot arm end coordinate system { E } relative to the robot base coordinate system { B }
Figure GDA0002308571790000042
Multiplying to obtain a transfer matrix of the tool coordinate system { T } relative to the robot base coordinate system { B }
Figure GDA0002308571790000043
Transfer matrix according to tool coordinate system { T } relative to robot base coordinate system { B }
Figure GDA0002308571790000044
And adjusting the position and posture information of the tool center point at the tail end of the mechanical arm relative to the robot base coordinate system to realize the calibration of the robot system tool.
As a further technical solution of the present disclosure, the method for solving the translation vector of the tool coordinate system relative to the tracking device coordinate system comprises:
establishing conversion relations of a tool coordinate system { T }, a tracking device coordinate system { D }, and a camera coordinate system { C };
transfer matrix of tracking device coordinate system { D } relative to camera coordinate system { C }
Figure GDA0002308571790000045
Substituting the obtained conversion relation into the obtained conversion relation to obtain an incompatibility equation set;
solving the optimal least square solution of the incompatible equation set by using a singular value decomposition method to obtain a translation vector of the tool coordinate system { T } relative to the tracking device coordinate system { D }, wherein
Figure GDA0002308571790000046
As a further technical solution of the present disclosure, the step of obtaining two sets of three-dimensional point sets of the tool coordinate system origin includes:
translation vector according to tool coordinate system { T } relative to tracking device coordinate system { D }
Figure GDA0002308571790000047
Translating the tracking coordinate system origin to the tool coordinate system origin；
And acquiring two groups of three-dimensional point sets of the tool coordinate system origin positioned at any position in space under the robot base coordinate system and the camera coordinate system.
As a further technical solution of the present disclosure, the step of solving the transfer matrix of the robot base coordinate system with respect to the camera coordinate system includes:
defining a function F between the rotation matrix of the robot base coordinate system and the camera coordinate system and the two three-dimensional point sets of the tool coordinate system origin under the robot base coordinate system and the camera coordinate system;
solving the maximum value of the function F by adopting a least square method based on singular value decomposition to obtain a rotation matrix of the robot coordinate system relative to the camera coordinate system;
calculating the translation component of the robot base coordinate system relative to the camera coordinate system according to the transformation mapping relation of the tool coordinate system origin from the robot base coordinate system to the camera coordinate system;
obtaining a transfer matrix of the robot base coordinate system and the camera coordinate system based on a rotation matrix of the robot base coordinate system relative to the camera coordinate system and a translation component of the robot base coordinate system relative to the camera coordinate system;
and controlling a tool arranged at the tail end of the mechanical arm to move according to a set track according to the transfer matrix of the robot base coordinate system and the camera coordinate system, and simultaneously acquiring pose information of the tool relative to the camera coordinate system to realize the hand-eye calibration of the system.
A calibration system for an auxiliary laser osteotomy robot comprises a robot system, a vision system, a calibration device and a processor;
the robot system is used for operating the mechanical arm to enable the tool to emit laser to vertically irradiate each plane of the calibration device and pass through the center of the calibration device, acquiring a transfer matrix of a mechanical arm tail end coordinate system relative to a robot base coordinate system, and uploading the transfer matrix to the processor;
the vision system is used for acquiring a transfer matrix of a tracking device coordinate system relative to a camera coordinate system when the tool emission laser vertically irradiates each plane of the calibration device and passes through the center of the calibration device, and uploading the transfer matrix to the processor;
the processor comprises a transfer matrix establishing module, a robot tool calibration module and a robot eye calibration module; wherein:
the transfer matrix establishing module is used for judging whether the distance from the tool to the external sphere center of the calibration device meets the sum of the effective laser ablation distance and the external sphere radius of the calibration device, and if so, acquiring a transfer matrix of the tail end coordinate system of the mechanical arm relative to the robot base coordinate system and a transfer matrix of the coordinate system of the tracking device relative to the camera coordinate system;
the robot tool calibration module is used for solving a translation vector of a tool coordinate system relative to a mechanical arm tail end coordinate system and establishing a transfer matrix of the tool coordinate system relative to the mechanical arm tail end coordinate system; multiplying a transfer matrix of the robot arm tail end coordinate system relative to the robot base coordinate system by a transfer matrix of the tool coordinate system relative to the robot arm tail end coordinate system to obtain a transfer matrix of the tool coordinate system relative to the robot base coordinate system, and realizing tool calibration of the robot;
the robot hand-eye calibration module is used for solving the translation vector of the tool coordinate system relative to the tracking device coordinate system, acquiring two groups of three-dimensional point sets of the tool coordinate system origin according to the translation vector of the tool coordinate system relative to the tracking device coordinate system, and solving the transfer matrix of the robot base coordinate system relative to the camera coordinate system, so as to realize the robot hand-eye calibration.
As a further technical scheme of the disclosure, the calibration device is a regular four-surface marker, the four vertex angles of the regular four-surface marker are provided with tracking devices, and the centers of the four planes of the regular four-surface marker are provided with small holes for light passing.
Through above-mentioned technical scheme, this disclosed beneficial effect is:
(1) the calibration device is designed specially for effective laser ablation points by combining system characteristics of a laser osteotomy robot, and simultaneously realizes calibration of a non-contact tool under a robot coordinate system and a camera coordinate system, so that the calibration precision of the robot can be greatly improved; the calibration device is simple and easy to operate, and the cost is greatly reduced;
(2) the calibration method provided by the disclosure overcomes the problems of complex operation process and poor stability of the traditional method, improves the automation degree of the calibration process, and reduces unnecessary errors such as manual operation;
(3) the robot system is suitable for assisting the laser osteotomy operation robot system, can effectively and accurately realize tool calibration and hand-eye calibration, and improves the automation degree of the robot.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this disclosure, are included to provide a further understanding of the disclosure, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the disclosure and together with the description serve to explain the application and not to limit the disclosure.
FIG. 1 is a schematic representation of a regular tetrahedron tag according to an embodiment;
FIG. 2 is a flowchart of a calibration method of the laser osteotomy robot according to the second embodiment;
FIG. 3 is a schematic diagram of a three-coordinate system structure according to an embodiment.
Detailed Description
The present disclosure is further described with reference to the following drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The noun explains:
(1) TCP, Tool Center Point.
Example one
The embodiment provides a calibration system of an auxiliary laser osteotomy robot, wherein the calibration device comprises a robot system, a vision system, a calibration device and a processor, the robot system adopts the existing auxiliary laser osteotomy robot system technical structure, and the robot system mainly comprises a six-degree-of-freedom mechanical arm, a laser tool arranged at the tail end of the mechanical arm and the like. The vision system comprises an infrared stereo camera, and the calibration device is a regular tetrahedron marker.
Referring to fig. 1, the calibration device is a regular tetrahedral marker, a tracking device of an infrared reflective sphere is respectively mounted at four vertices of the regular tetrahedral marker, four planes of the regular tetrahedral marker are respectively made of a transparent material, a central calibration point of the four planes of the marking tool is respectively provided with a light through hole, laser can penetrate through the light through hole on one plane and irradiate on an opposite vertex angle perpendicular to the plane, and the distance from a laser emission position to the vertex angle opposite to the one plane of the marking tool is controlled, so that the laser effective ablation points of a plurality of sets of calibration points are ensured to coincide with the center of the regular tetrahedral marker.
The regular tetrahedron marker of the embodiment is of a special symmetrical structure of a regular tetrahedron, so that the posture of the robot can be adjusted to the maximum extent while the calibration points are uniformly distributed, and the self-calibration precision is improved.
And controlling the robot to operate the mechanical arm to enable the laser emitted by the laser source to irradiate a top angle opposite to the plane from the light-transmitting small hole in the center of the first plane of the marking tool, so that the laser vertically irradiates the plane and passes through the center of the marking tool.
The robot system is used for operating the mechanical arm to enable the tool to emit laser to vertically irradiate each plane of the calibration device and pass through the center of the calibration device, obtaining the position and posture information of the tail end tcp of the mechanical arm relative to the base coordinate system of the robot, forming a transfer matrix of the tail end coordinate system of the mechanical arm relative to the base coordinate system of the robot, and uploading the transfer matrix to the processor.
And the vision system is used for acquiring the position and posture information of the tracking device relative to the camera coordinate system when the tool-emitted laser vertically irradiates each plane of the calibration device and passes through the center of the calibration device, forming a transfer matrix of the tracking device coordinate system relative to the camera coordinate system, and uploading the transfer matrix to the processor.
The processor comprises a transfer matrix establishing module, a robot tool calibration module and a robot eye calibration module; wherein:
the transfer matrix establishing module is used for judging whether the distance from the tool to the external sphere center of the calibration device meets the sum of the effective laser ablation distance and the external sphere radius of the calibration device, and if so, acquiring a transfer matrix of the tail end coordinate system of the mechanical arm relative to the robot base coordinate system and a transfer matrix of the coordinate system of the tracking device relative to the camera coordinate system;
the robot tool calibration module is used for solving a translation vector of a tool coordinate system relative to a mechanical arm tail end coordinate system and establishing a transfer matrix of the tool coordinate system relative to the mechanical arm tail end coordinate system; multiplying a transfer matrix of the robot arm tail end coordinate system relative to the robot base coordinate system by a transfer matrix of the tool coordinate system relative to the robot arm tail end coordinate system to obtain a transfer matrix of the tool coordinate system relative to the robot base coordinate system, and realizing tool calibration of the robot;
the robot hand-eye calibration module is used for solving the translation vector of the tool coordinate system relative to the tracking device coordinate system, acquiring two groups of three-dimensional point sets of the tool coordinate system origin according to the translation vector of the tool coordinate system relative to the tracking device coordinate system, and solving the transfer matrix of the robot base coordinate system relative to the camera coordinate system, so as to realize the robot hand-eye calibration.
In this embodiment, the robot system is specifically configured to:
aiming at a first calibration point at the center of a first plane of the calibration device, laser emitted by the end tool passes through a small hole at the center of the first plane of the regular tetrahedron calibration body through a mechanical arm of the robot system, and the distance d measured by laser ranging meets the relation: d ═ l + r, and the end of the arm tcp at this time is taken relative toThe position and the attitude information of the robot base coordinate system form a transfer matrix of the robot arm end coordinate system { E } relative to the robot base coordinate system { B }
Figure GDA0002308571790000091
In the same way, for the other three calibration points, the position and posture information of the end tool relative to the robot base coordinate system is obtained through the robot system, and the transfer matrix of the mechanical arm end coordinate system { E } relative to the robot base coordinate system { B } is obtained
Figure GDA0002308571790000101
In particular, the vision system is particularly configured to:
aiming at a first calibration point at the center of a first plane of the calibration device, laser emitted by the end tool passes through a small hole at the center of the first plane of the regular tetrahedron calibration body through a mechanical arm of the robot system, and the distance d measured by laser ranging meets the relation: d + r, and acquiring the position and posture information of the tracking device relative to the camera coordinate system at the moment to form a transfer matrix of the tracking device coordinate system { D } relative to the camera coordinate system { C }, wherein
Figure GDA0002308571790000102
In the same way, for the other three calibration points, the position and posture information of the tracking device relative to the camera coordinate system is obtained through the infrared stereo camera of the vision system, and the transfer matrix of the tracking device coordinate system { D } relative to the camera coordinate system { C } is obtained
Figure GDA0002308571790000103
In particular, the robot tool calibration module is specifically configured to:
a transfer matrix of the mechanical arm end coordinate system { E } of the 4 marking points obtained by the robot system relative to the robot base coordinate system { B }
Figure GDA0002308571790000104
Substituting into the conversion relation calibrated by the robot tool to obtain an incompatible equation set, solving the most probable approximate solution of the equation set in the least square sense by using a Singular Value Decomposition (SVD) method to obtain a translation vector of a tool coordinate system { T } relative to a mechanical arm terminal coordinate system { E }
Figure GDA0002308571790000105
Combining the rotation matrix invariant principle of translation relation, and based on the translation vector of the tool coordinate system { T } relative to the robot end coordinate system { E }, the method is characterized in that
Figure GDA0002308571790000106
Obtaining a transfer matrix of the tool coordinate system { T } relative to the robot end coordinate system { E }
Figure GDA0002308571790000107
Transfer matrix of robot end coordinate system { E } relative to robot base coordinate system { B }
Figure GDA0002308571790000108
And a transfer matrix of the tool coordinate system { T } relative to the robot end coordinate system { E }
Figure GDA0002308571790000109
Multiplying to obtain a transfer matrix of the tool coordinate system { T } relative to the robot base coordinate system { B }
Figure GDA00023085717900001010
And the tool calibration of the robot is realized.
The robot hand-eye calibration module is specifically configured to:
transfer matrix of tracking device coordinate system { D } of 4 mark points obtained by robot system relative to camera coordinate system { C }
Figure GDA0002308571790000111
Substituting into the conversion relation calibrated by robot tool to obtain incompatible equation set, and solving by Singular Value Decomposition (SVD)Solving the most probable approximate solution of the equation system in the least square sense to obtain a translation vector of the tool coordinate system { T } relative to the tracking device coordinate system { D }, and obtaining a translation vector of the tool coordinate system { T } relative to the tracking device coordinate system { D }
Figure GDA0002308571790000112
Translation vector according to tool coordinate system { T } relative to tracking device coordinate system { D }
Figure GDA0002308571790000113
Translating the origin of the tracking device acquired by the infrared stereo camera to the origin of the tool coordinate system, so that the camera can directly read the position information of the origin of the tool coordinate system.
Operating the mechanical arm to make the laser tool pick up points randomly in the space and obtaining a point set P of the tool coordinate system origin under the robot coordinate systemi(i ═ 1.. n) and a set of points P in the camera coordinate systemi'。
And realizing hand-eye calibration through least square solution fitting of two groups of three-dimensional point sets.
Example two
The embodiment provides a calibration method of an auxiliary laser osteotomy robot, which is realized based on the calibration device of the auxiliary laser osteotomy robot.
Referring to fig. 2, the calibration method of the auxiliary laser osteotomy robot includes the following steps:
and S101, setting a calibration device and a tracking device for assisting the laser osteotomy robot, and adjusting the laser emission distance.
Let the robot base coordinate system be { B }, the robot arm end coordinate system be { E }, the camera coordinate system be { C }, the tracking device coordinate system be { D }, the laser tool coordinate system be { T } (hereinafter simply referred to as the tool coordinate system), and { T } be the coordinate system established with the laser ablation effective point as the origin, please refer to fig. 3.
Specifically, in step 101, the specific implementation manner of adjusting the laser emission distance is as follows:
and measuring the distance of the laser emitted by the end tool from the central light-passing small hole of one plane of the calibration device to the top angle opposite to the plane. If the distance measured by the tail end laser tool is d, the effective laser ablation distance l and the external spherical radius r of the calibration device satisfy the relationship: d ═ l + r. And judging whether the measured distance is equal to d or not, and if not, controlling the mechanical arm to adjust the distance of the tail end tool for emitting the laser to meet d.
S102, acquiring data information of four calibration points on the calibration device, wherein the data information comprises a transfer matrix of a robot arm terminal coordinate system { E } relative to a robot base coordinate system { B }
Figure GDA0002308571790000121
Transfer matrix of tracking device coordinate system { D } relative to camera coordinate system { C }
Figure GDA0002308571790000122
Specifically, for a first calibration point at the center of a first plane of the calibration device, laser emitted by the end tool is made to pass through a small hole at the center of the first plane of the regular tetrahedron body by a mechanical arm of the robot system, and the distance d measured by laser ranging satisfies the relationship: and d + r, acquiring the position and posture information of the tail end tcp of the mechanical arm relative to the base coordinate system of the robot at the moment, and obtaining a transfer matrix of the tail end coordinate system { E } of the mechanical arm relative to the base coordinate system { B } of the robot
Figure GDA0002308571790000123
Acquiring the position and posture information of the tracking device relative to a camera coordinate system through an infrared stereo camera of a vision system to obtain a transfer matrix of the coordinate system { D } of the tracking device relative to a camera coordinate system { C }
Figure GDA0002308571790000124
In the same way, for the other three calibration points, the position and posture information of the end tool relative to the robot base coordinate system is obtained through the robot system, and the transfer matrix of the mechanical arm end coordinate system { E } relative to the robot base coordinate system { B } is obtained
Figure GDA0002308571790000125
Acquiring the position and posture information of the tracking device relative to a camera coordinate system through an infrared stereo camera of a vision system to obtain a transfer matrix of the coordinate system { D } of the tracking device relative to a camera coordinate system { C }
Figure GDA0002308571790000126
S103, solving the translation vector of the tool coordinate system { T } relative to the mechanical arm end coordinate system { E }
Figure GDA0002308571790000127
And a translation vector of the tool coordinate system { T } relative to the tracking device coordinate system { D }
Figure GDA0002308571790000128
Specifically, a transfer matrix of a robot arm end coordinate system { E } of 4 marking points obtained by the robot system relative to a robot base coordinate system { B }, is obtained
Figure GDA0002308571790000129
Substituting into the conversion relation calibrated by the robot tool to obtain an incompatible equation set, solving the most probable approximate solution of the equation set in the least square sense by using a Singular Value Decomposition (SVD) method to obtain a translation vector of a tool coordinate system { T } relative to a mechanical arm terminal coordinate system { E }
Figure GDA0002308571790000131
Specifically, in step 103, the translation vector of the tool coordinate system { T } relative to the robot end coordinate system { E } is solved
Figure GDA0002308571790000132
The specific process is as follows:
the transfer matrix of the tool coordinate system { T } relative to the robot base coordinate system { B } is represented as
Figure GDA0002308571790000133
Due to the laser tool and the heel of the robotThe tracking device is fixedly connected with the tail end connecting rod of the robot operation mechanical arm, so that the pose relation of a tool coordinate system { T } relative to a tail end connecting rod coordinate system { E }
Figure GDA0002308571790000134
Is constant, i.e. has a rotational component
Figure GDA0002308571790000135
And translation vector
Figure GDA0002308571790000136
And is not changed.
The transfer matrix of the tracking device coordinate system { D } relative to the camera coordinate system { C } is represented as
Figure GDA0002308571790000137
Since the calibration tool is also fixedly connected to the tracking device, the transfer matrix of the tool coordinate system { T } relative to the tracking device coordinate system { D }, is
Figure GDA0002308571790000138
Is constant, i.e. has a rotational component
Figure GDA0002308571790000139
And translation vector
Figure GDA00023085717900001310
And is not changed.
The default tool coordinate system { T } is translated from the end of arm coordinate system { E }, and the tool coordinate system pose is the same as the end of arm coordinate system pose. Completing the calibration of the robot tool coordinate system by only requiring the translation vector of the transfer matrix of the tool coordinate system and the mechanical arm tail end coordinate system
Figure GDA00023085717900001311
The tool coordinate system { T }, the arm end coordinate system { E }, and the robot base coordinate system { B } coordinate system satisfy the following transformation relations:
Figure GDA00023085717900001312
converting the coordinate system of the tail end of the mechanical arm of the ith calibration point obtained in the step 102 into a robot base coordinate system
Figure GDA00023085717900001313
Can be substituted by the formula (1)
Figure GDA00023085717900001314
The write composition block form is:
Figure GDA00023085717900001315
let the 4 th column calculated on both sides of the equation be equal to each other, then:
Figure GDA0002308571790000141
for each calibration point, the position vector of the tool coordinate system origin relative to the robot base coordinate system { B }
Figure GDA0002308571790000142
Remain unchanged. Then, for all index points:
Figure GDA0002308571790000143
written in matrix form as:
Figure GDA0002308571790000144
the above formula is an incompatible equation system, and the translation vector can be obtained
Figure GDA0002308571790000145
The optimal least squares solution of.
Specifically, the Singular Value Decomposition (SVD) method is used to solve the most likely approximate solution of the above incompatible equation system (5) in the least square sense, and the specific implementation process is as follows:
order to
Figure GDA0002308571790000146
SVD A is carried out, and A is U lambda VTThe generalized inverse matrix A of A can be obtained+＝VΛ+UTWherein
Figure GDA0002308571790000147
Finally using A+Solving least squares solutions of incompatible equations, i.e.
Figure GDA0002308571790000148
Transfer matrix of tracking device coordinate system { D } relative to camera coordinate system { C } for 4 marker points obtained by vision system
Figure GDA0002308571790000149
The translation vector of the tool coordinate system { T } relative to the tracking device coordinate system { D } is solved in the same manner as described above
Figure GDA00023085717900001410
Are not described in detail in this application.
S104, combining the rotation matrix invariant principle of the translation relation, and based on the translation vector of the tool coordinate system { T } relative to the mechanical arm terminal coordinate system { E }, the rotation matrix invariant principle is adopted
Figure GDA0002308571790000151
Obtaining a transfer matrix of the tool coordinate system { T } relative to the robot end coordinate system { E }
Figure GDA0002308571790000152
In this embodiment, the tool coordinate system { T } is translated from the end of arm coordinate system { E }, and the tool coordinate system is then oriented in the same manner as the end of arm coordinate system. Combined with a translational relationshipThe rotation matrix invariant principle can obtain the transfer matrix of the tool coordinate system { T } relative to the robot end coordinate system { E }
Figure GDA0002308571790000153
S105, a transfer matrix of the coordinate system { E } of the tail end of the mechanical arm relative to the base coordinate system { B } of the robot
Figure GDA0002308571790000154
And a transfer matrix of the tool coordinate system { T } relative to the robot end coordinate system { E }
Figure GDA0002308571790000155
Multiplying to obtain a transfer matrix of the tool coordinate system { T } relative to the robot base coordinate system { B }
Figure GDA0002308571790000156
The robot system transfers matrices according to a tool coordinate system { T } relative to a robot base coordinate system { B }
Figure GDA0002308571790000157
And adjusting the position and posture information of the tool center point at the tail end of the mechanical arm relative to the robot base coordinate system to realize the calibration of the robot system tool.
In particular, a transfer matrix of the tool coordinate system { T } relative to a robot base coordinate system { B }
Figure GDA0002308571790000158
The calculation formula of (2) is as follows:
Figure GDA0002308571790000159
the robot system obtains a transfer matrix of the tool coordinate system { T } relative to the robot base coordinate system { B }, based on the obtained transfer matrix
Figure GDA00023085717900001510
And operating the mechanical arm to adjust the position and the posture of the tail end tool so as to realize the tool calibration of the robot.
And S106, acquiring two sets of three-dimensional information of the tool coordinate system origin.
Specifically, in step 106, the specific implementation process of obtaining two sets of three-dimensional information of the tool coordinate system origin is as follows:
translation vector according to tool coordinate system { T } relative to tracking device coordinate system { D }
Figure GDA00023085717900001511
Translating the origin of the tracking device acquired by the infrared stereo camera to the origin of the tool coordinate system, so that the camera can directly read the position information of the origin of the tool coordinate system.
Operating the mechanical arm to make the laser tool pick up point randomly in space and obtain the three-dimensional information P of the tool coordinate system origin under the robot coordinate systemi(i ═ 1.. n) and a set of points P in the camera coordinate systemi'。
And S107, realizing hand-eye calibration through least square solution fitting of two groups of three-dimensional point sets.
Specifically, in step 107, a specific process of implementing the hand-eye calibration by least squares solution fitting of two sets of three-dimensional point sets is as follows:
(1) the two sets of three-dimensional information about the origin of the tool coordinate system obtained in step 106 are respectively set P of points in the robot coordinate systemiAnd point set P under camera coordinate systemi', the two sets of point sets satisfy the following relationship:
Pi'＝RPi+t+ni(7)
wherein R is a rotation matrix of a robot coordinate system and a camera coordinate system, t is a translation vector, niIs a noise vector.
R and t are obtained so as to satisfy:
Figure GDA0002308571790000161
(2) assuming a rotation matrix of a least squares solution of
Figure GDA0002308571790000162
Translation directionMeasured as
Figure GDA0002308571790000163
The centers of the two sets of point sets are respectively
Figure GDA0002308571790000164
Is provided with
Figure GDA0002308571790000165
Then { Pi' } and { Pi"} have the same center, i.e., P' ═ P".
Order to
Figure GDA0002308571790000166
Then there is
Figure GDA0002308571790000171
(3) Requires min δ2Is equivalent to
Figure GDA0002308571790000172
Defining functions
Figure GDA0002308571790000173
Wherein
Figure GDA0002308571790000174
SVD H (singular value decomposition) H-ULambda VTLet X be VUT(3X 3 orthogonal matrix) then
XH＝VUTUΛVT＝VΛVT(13)
For any 3 x 3 orthogonal matrix B there is Trace (XH) ≧ Trace (BXH).
Wherein, if det (X) ═ 1, then
Figure GDA0002308571790000175
If det (X) is-1, then the algorithm does not apply (this isThis rarely occurs). In all 3X 3 orthogonal matrices, X maximizes F, i.e., δ2And minimum.
(4) From SVD method and orthogonal matrix properties, solving
Figure GDA0002308571790000176
The translation component can then be found to be
Figure GDA0002308571790000177
Obtaining a transfer matrix of a robot base coordinate system and a camera coordinate system as follows:
Figure GDA0002308571790000178
the robot system is based on a transfer matrix of the robot base coordinate system { B } relative to the camera coordinate system { C }
Figure GDA0002308571790000181
When the robot system controls a tool arranged at the tail end of the mechanical arm to move according to a set track, the camera of the vision system acquires pose information of the tool and feeds the pose information back to the robot system in real time, and hand-eye calibration of the robot system is achieved.
The calibration method provided by the embodiment overcomes the problems of complex operation process and poor stability of the traditional method, improves the automation degree of the calibration process, and reduces unnecessary errors such as manual operation and the like; meanwhile, the calibration of the non-contact tool under a robot coordinate system and a three-dimensional camera coordinate system is realized, and the calibration precision of the robot can be improved; the calibration device is simple and easy to operate, and the cost is greatly reduced; the laser osteotomy robot system is suitable for assisting the laser osteotomy robot system, can effectively and accurately realize the calibration of tools under a robot coordinate system and a camera coordinate system, and improves the automation degree of the robot.
Although the present disclosure has been described with reference to specific embodiments, it should be understood that the scope of the present disclosure is not limited thereto, and those skilled in the art will appreciate that various modifications and changes can be made without departing from the spirit and scope of the present disclosure.

Claims (8)

1. A calibration method for an auxiliary laser osteotomy robot is characterized by comprising the following steps:
establishing a coordinate system of the robot, the tail end of the mechanical arm, the camera, the tracking device and a tool positioned at the tail end of the mechanical arm;
acquiring a transfer matrix of a mechanical arm tail end coordinate system relative to a robot base coordinate system and a transfer matrix of a tracking device coordinate system relative to a camera coordinate system when tool emitted laser vertically irradiates each plane of a calibration device and passes through the center of the calibration device;
solving a translation vector of the tool coordinate system relative to the mechanical arm tail end coordinate system, and establishing a transfer matrix of the tool coordinate system relative to the mechanical arm tail end coordinate system;
multiplying a transfer matrix of the robot arm tail end coordinate system relative to the robot base coordinate system by a transfer matrix of the tool coordinate system relative to the robot arm tail end coordinate system to obtain a transfer matrix of the tool coordinate system relative to the robot base coordinate system, and realizing tool calibration of the robot;
solving a translation vector of a tool coordinate system relative to a tracking device coordinate system, acquiring two groups of three-dimensional point sets of an original point of the tool coordinate system, and solving a transfer matrix of a robot base coordinate system relative to a camera coordinate system to realize hand-eye calibration of the robot;
the calibration device is a regular four-surface marker, four vertex angles of the regular four-surface marker are provided with tracking devices, and the centers of four planes of the regular four-surface marker are provided with small holes for light to pass through.
2. The calibration method of the auxiliary laser osteotomy robot of claim 1, wherein the acquisition method of the transfer matrix of the robot arm end coordinate system relative to the robot base coordinate system comprises:
measuring the distance from a tool to the center of an external sphere of the calibration device when the tool at the tail end of the mechanical arm emits laser to vertically irradiate a first plane of the calibration device and pass through the center of the calibration device;
when the measured distance is equal to the sum of the effective laser ablation distance and the external sphere radius of the calibration device, the position and posture information of the central point of the end tool of the mechanical arm relative to the base coordinate system of the robot is obtained, and a first transfer matrix of the end coordinate system { E } of the mechanical arm relative to the base coordinate system { B } of the robot is formed
Figure FDA0002308571780000021
Repeating the steps until a second transfer matrix of the coordinate system { E } of the tail end of the mechanical arm relative to the base coordinate system { B } of the robot is obtained
Figure FDA0002308571780000022
Third transition matrix
Figure FDA0002308571780000023
And a fourth transfer matrix
Figure FDA0002308571780000024
3. The calibration method of the auxiliary laser osteotomy robot of claim 1, wherein the acquisition method of the transfer matrix of the tracking device coordinate system relative to the camera coordinate system comprises:
measuring the distance from a tool to the center of an external sphere of the calibration device when the tool at the tail end of the mechanical arm emits laser to vertically irradiate a first plane of the calibration device and pass through the center of the calibration device;
when the measured distance is equal to the sum of the effective laser ablation distance and the external sphere radius of the calibration device, acquiring the position and posture information of the tracking device coordinate system relative to the camera coordinate system to form a first transfer matrix of the tracking device coordinate system { D } relative to the camera coordinate system { C }
Figure FDA0002308571780000025
Repeating the above steps until a second transition matrix of the tracking device coordinate system { D } relative to the camera coordinate system { C } is obtained
Figure FDA0002308571780000026
Third transition matrix
Figure FDA0002308571780000027
And a fourth transfer matrix
Figure FDA0002308571780000028
4. The method for calibrating the robot for assisting laser osteotomy according to claim 1, wherein the solution of the translation vector of the tool coordinate system relative to the robot arm tip coordinate system is:
establishing conversion relations of a tool coordinate system { T }, a mechanical arm end coordinate system { E }, and a robot base coordinate system { B };
transfer matrix of robot end coordinate system { E } relative to robot base coordinate system { B }
Figure FDA0002308571780000029
Substituting the obtained conversion relation into the obtained conversion relation to obtain an incompatibility equation set;
solving the optimal least square solution of the incompatible equation set by using a singular value decomposition method to obtain a translation vector of the tool coordinate system { T } relative to the mechanical arm terminal coordinate system { E }
Figure FDA00023085717800000210
Combining the rotation matrix invariant principle of the translation relation between the tool coordinate system { T } and the robot end coordinate system { E }, obtaining the transfer matrix of the tool coordinate system { T } relative to the robot end coordinate system { E }
Figure FDA0002308571780000031
Transfer matrix relating tool coordinate system { T } to robot end coordinate system { E }
Figure FDA0002308571780000032
Transfer matrix from the robot arm end coordinate system { E } relative to the robot base coordinate system { B }
Figure FDA0002308571780000033
Multiplying to obtain a transfer matrix of the tool coordinate system { T } relative to the robot base coordinate system { B }
Figure FDA0002308571780000034
Transfer matrix according to tool coordinate system { T } relative to robot base coordinate system { B }
Figure FDA0002308571780000035
And adjusting the position and posture information of the tool center point at the tail end of the mechanical arm relative to the robot base coordinate system to realize the calibration of the robot system tool.
5. The calibration method of an assisted laser osteotomy robot of claim 1, wherein said translation vector of said tool coordinate system relative to said tracking device coordinate system is solved by:
establishing conversion relations of a tool coordinate system { T }, a tracking device coordinate system { D }, and a camera coordinate system { C };
transfer matrix of tracking device coordinate system { D } relative to camera coordinate system { C }
Figure FDA0002308571780000036
Substituting the obtained conversion relation into the obtained conversion relation to obtain an incompatibility equation set;
solving the optimal least square solution of the incompatible equation set by using a singular value decomposition method to obtain a translation vector of the tool coordinate system { T } relative to the tracking device coordinate system { D }, wherein
Figure FDA0002308571780000037
6. The method for calibrating a robot for assisted laser osteotomy surgery of claim 1, wherein said step of obtaining two sets of three-dimensional points of an origin of a tool coordinate system comprises:
translation vector according to tool coordinate system { T } relative to tracking device coordinate system { D }
Figure FDA0002308571780000038
Translating the origin of the tracking coordinate system to the origin of the tool coordinate system;
and acquiring two groups of three-dimensional point sets of the tool coordinate system origin positioned at any position in space under the robot base coordinate system and the camera coordinate system.
7. The method for calibrating an assisted laser osteotomy robot of claim 1, wherein said step of solving a transfer matrix of a robot base coordinate system relative to a camera coordinate system comprises:
defining a function F between the rotation matrix of the robot base coordinate system and the camera coordinate system and the two three-dimensional point sets of the tool coordinate system origin under the robot base coordinate system and the camera coordinate system;
solving the maximum value of the function F by adopting a least square method based on singular value decomposition to obtain a rotation matrix of the robot coordinate system relative to the camera coordinate system;
calculating the translation component of the robot base coordinate system relative to the camera coordinate system according to the transformation mapping relation of the tool coordinate system origin from the robot base coordinate system to the camera coordinate system;
obtaining a transfer matrix of the robot base coordinate system and the camera coordinate system based on a rotation matrix of the robot base coordinate system relative to the camera coordinate system and a translation component of the robot base coordinate system relative to the camera coordinate system;
and controlling a tool arranged at the tail end of the mechanical arm to move according to a certain track according to the transfer matrix of the robot base coordinate system and the camera coordinate system, and acquiring pose information of the tool relative to the camera coordinate system to realize the hand-eye calibration of the robot system.
8. A calibration system for assisting a laser osteotomy robot is characterized by comprising a robot system, a vision system, a calibration device and a processor;
the robot system is used for operating the mechanical arm to enable the tool to emit laser to vertically irradiate each plane of the calibration device and pass through the center of the calibration device, acquiring a transfer matrix of a mechanical arm tail end coordinate system relative to a robot base coordinate system, and uploading the transfer matrix to the processor;
the vision system is used for acquiring a transfer matrix of a tracking device coordinate system relative to a camera coordinate system when the tool emission laser vertically irradiates each plane of the calibration device and passes through the center of the calibration device, and uploading the transfer matrix to the processor;
the processor comprises a transfer matrix establishing module, a robot tool calibration module and a robot eye calibration module; wherein:
the transfer matrix establishing module is used for judging whether the distance from the tool to the external sphere center of the calibration device meets the sum of the effective laser ablation distance and the external sphere radius of the calibration device, and if so, acquiring a transfer matrix of the tail end coordinate system of the mechanical arm relative to the robot base coordinate system and a transfer matrix of the coordinate system of the tracking device relative to the camera coordinate system;
the robot tool calibration module is used for solving a translation vector of a tool coordinate system relative to a mechanical arm tail end coordinate system and establishing a transfer matrix of the tool coordinate system relative to the mechanical arm tail end coordinate system; multiplying a transfer matrix of the robot arm tail end coordinate system relative to the robot base coordinate system by a transfer matrix of the tool coordinate system relative to the robot arm tail end coordinate system to obtain a transfer matrix of the tool coordinate system relative to the robot base coordinate system, and realizing tool calibration of the robot;
the robot hand-eye calibration module is used for solving the translation vector of the tool coordinate system relative to the tracking device coordinate system, acquiring two groups of three-dimensional point sets of the tool coordinate system origin according to the translation vector of the tool coordinate system relative to the tracking device coordinate system, and solving the transfer matrix of the robot base coordinate system relative to the camera coordinate system to realize the robot hand-eye calibration;
the calibration device is a regular four-surface marker, four vertex angles of the regular four-surface marker are provided with tracking devices, and the centers of four planes of the regular four-surface marker are provided with small holes for light to pass through.
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