CN113040910B - Calibration method of tracer on tail end of surgical navigation robot - Google Patents
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- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
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- A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
- A61B34/20—Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
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- A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
- A61B34/20—Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
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- A61B2034/2055—Optical tracking systems
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- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
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- A61B34/20—Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
- A61B2034/2068—Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis using pointers, e.g. pointers having reference marks for determining coordinates of body points
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- A61B34/30—Surgical robots
- A61B2034/305—Details of wrist mechanisms at distal ends of robotic arms
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Abstract
A calibration method for a tracer on the tail end of a surgical navigation robot belongs to the technical field of medical assistance, and comprises the steps of directly reading the coordinates of the tracer on the tail end of the robot under a coordinate system of an optical tracker by using the optical tracker, and calculating the coordinates of the tracer on the tail end of the robot by recording the coordinates of 3 different positions under the optical tracker respectively.
Description
Technical Field
The invention belongs to the technical field of medical assistance, relates to a calibration method of a tracer on the tail end of a surgical navigation robot, and particularly relates to position calibration of a marker arranged on the tracer on the tail end of the surgical navigation robot.
Background
With the widespread application of minimally invasive surgery and the increasing requirement on the positioning precision of instruments or internal implants in surgery in recent years, auxiliary positioning or surgery navigation systems based on medical image guidance have been greatly developed.
Such systems are generally divided into several large components: a CTCB machine, an optical tracker and a navigation robot; the CTCB machine is used for establishing three-dimensional medical images, the optical tracker tracks the positions of the robot and the patient through a specific tracer, and the navigation robot is used for finishing the final operation. To complete the surgery, registration is first performed, i.e., coordinate transformation relationships between the CTCB machine, the optical tracker, and the navigation robot are established. And then planning the operation, namely planning the operation path by the doctor according to the three-dimensional medical image model established by the CTCB machine. And finally, a surgical implementation part is carried out, namely, a planned surgical path is placed on the surgical path through a handheld surgical guide or an executing mechanism such as a control robot positions the guide on the surgical path, and a doctor completes surgical operation or implantation of the implant through the aid of the guide.
The most central one of the above steps is to establish a system coordinate transformation relationship, namely registration, and finally realize the connection between the operation target and the executing mechanism, and finally the executing mechanism can position the path through the planned path in the three-dimensional image. With the great improvement of the precision of the optical tracker, a high-precision navigation system registration scheme is generally adopted, a coordinate conversion relation between a CTCB machine (with consistent surgical target coordinates) and the optical tracker is established, then the coordinate conversion relation between the optical tracker and a navigation robot is established, and finally the coordinates of the surgical target and the navigation robot are established.
Further, to establish the coordinate transformation relationship between the optical tracker and the navigation robot, a special tracer with more than 3 markers is required to be installed at the end of the navigation robot, and the markers on the tracer have coordinates under the coordinate system of the optical tracker and the coordinate system of the navigation robot. The marker on the tracer can be directly identified by the optical tracker and the coordinates under the coordinate system of the optical tracker are calculated, while the coordinates of the navigation robot are calculated by the position of the marker relative to the tail end of the robot, and the position of the marker relative to the tail end of the robot is difficult to directly measure, and the corresponding coordinates are generally calculated according to the design size of the tracer.
In the prior art, when the coordinates of the tracer marker in the terminal coordinate system of the robot are required to be acquired, one method is to use a special positioning and ranging instrument which is very expensive and cannot be popularized in hospitals, and the other method is to rely on the machining and assembling precision of the robot, so that once a tracer with the precision which does not meet the specified requirement is installed, the precision of the whole system is difficult to guarantee, and the consequence is very serious.
Disclosure of Invention
The invention provides a calibration method of a tracer at the tail end of a surgical navigation robot, aiming at the problem that the position of the tracer at the tail end of the surgical navigation robot is difficult to measure at present, and the coordinates of the tracer at the tail end of the surgical navigation robot can be accurately calibrated without expensive instruments.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows: a calibration method for a tracer on the tail end of a surgical navigation robot is characterized in that an optical tracker is utilized to directly read the coordinates of the tracer on the tail end of the robot under the coordinate system of the optical tracker, and the coordinates of the tracer on the tail end of the robot under the tail end of the robot are finally calculated by recording the coordinates of 3 different positions under the optical tracker, and comprises the following steps:
the method comprises the following steps of presetting a coordinate system G of a robot base, a coordinate system E of a robot tail end flange, a coordinate system C of an optical tracker, installing markers capable of reflecting infrared light on a tracer, setting the number of the markers to be n, wherein n is more than or equal to 3, fixing the tracer on the robot tail end flange, and enabling the robot to be a 6-axis robot, wherein the method comprises the following specific steps:
step 1: and moving the robot to a specific position, wherein the direction of the z-axis of a flange coordinate system E at the tail end of the robot is required to be consistent with or opposite to the direction of the z-axis of a robot base coordinate system G, the direction of the 5 th axis of the robot is required to be the same as the direction of the y-axis under the E coordinate system, and the position of the marker on the tracer at the moment relative to the robot base coordinate system G is 0.
Step 2: the optical tracker is moved so that the robot end flange is within the visible range of the optical tracker.
And step 3: and rotating the 6 th axis theta angle of the robot to enable infrared light reflected by the marker on the tracer to be received by the optical tracker, wherein the position of the marker on the tracer relative to the robot base coordinate system G at the moment of marking is 1, and recording the coordinates of the marker on the tracer under the optical tracker coordinate system C by using the optical tracker.
And 4, step 4: rotating the 6 th axis by an angle alpha within a range of 20-90 degrees, wherein the tracer is required to be within the visible range of the optical tracker after being rotated, translating the length of L in the Z axis upwards or downwards, and moving the L not to exceed the visible range of the optical tracker, wherein the position of the marker on the tracer at the moment relative to the robot base coordinate system G is 2, and the optical tracker is used for recording the coordinates of the marker on the tracer under the optical tracker coordinate system C.
And 5: returning to the position 1, rotating the 5 th axis by an angle beta within the range of 20-90 degrees, wherein the tracer is required to be within the visible range of the optical tracker after rotation, marking the position of the marker on the tracer at the moment relative to the robot base coordinate system G to be 3, and recording the coordinates of the marker on the tracer under the optical tracker coordinate system C by using the optical tracker.
Step 6: and calculating the coordinates of the marker on the tracer in the space of the robot tail end coordinate system E through the coordinates of the marker under the optical tracker coordinate system C recorded at the positions 1, 2, and 3 on the optical tracker and the position transformation matrix of the robot.
In the above step, let the coordinate transformation matrix of the robot end coordinate system E from position 1 to position 0 beThe matrix is a 4x4 homogeneous matrix, and is specifically represented as
Further, let a coordinate transformation matrix of the robot end coordinate system E from position 2 to position 1 beAssuming that the step 4 is offset by a along the Z axis, if a is equal to L in the same direction as the Z axis, and if a is equal to L in the opposite direction, the matrix is a 4x4 homogeneous matrix, specifically denoted as
Further, let a coordinate transformation matrix of the robot end coordinate system E from position 3 to position 1 beAssuming that the shortest distance from the center point of the end flange to the center line of the 5 th axis is b, unit mm, the matrix is a 4x4 homogeneous matrix, which is specifically shown as
Further, at position 1, the transformation matrix from the optical tracker coordinate system C to the robot end coordinate system E is B, denoted as B
Setting any marker P point of the tracer, and reading homogeneous coordinate P by the optical tracker at the position 1C1=[PC1x PC1y PC1z 1]TAt position 2, the homogeneous coordinate read by the optical tracker is PC2=[PC2x PC2y PC2z 1]TThe homogeneous coordinate read by the optical tracker at position 3 is PC3=[PC3x PC3y PC3z 1]TThen there is
The above two equations are written as a general expression
B·[x'y'z'1]T=A·B·[x y z 1]T (3)
And performing matrix operation on the matrixes A and B, wherein the final result is as follows:
let matrix X ═ B11,B12,B13,B14,B21,B22,B23,B24,B31,B32,B33,B34]TThe above can be expressed as a matrix
Substituting the variables in the formula (1) into the formula (3) specifically as follows:
[x' y' z' 1]T=PC2=[PC2x PC2y PC2z 1]T,
[x y z 1]T=PC1=[PC1x PC1y PC1z 1]T
by equation (4), 3 equations can be derived for each marker on the tracer, for a total of n markers, 3n equations can be derived,
also, 3n equations can be obtained by substituting the variables in equation (2) into equation (3). That is, there are 6n equations in total, and the unknown variable is only X ═ B11,B12,B13,B14,B21,B22,B23,B24,B31,B32,B33,B34]T. Finally obtaining X ═ B through Singular Value Decomposition (SVD)11,B12,B13,B14,B21,B22,B23,B24,B31,B32,B33,B34]TI.e. the values of the matrix B are obtained.
Then the homogeneous coordinate P of any marker in the robot end coordinate system EE=[PEx PEy PEz 1]Can be represented by formula
PE=B·PC1
And (6) calculating.
Compared with the prior art, the calibration method of the tracer at the tail end of the surgical navigation robot provided by the invention can accurately calculate the coordinates of the marker without using a professional measuring instrument, avoids errors caused by processing precision, improves the precision of the whole surgical navigation system, and is simple in operation, low in cost and convenient to popularize.
Drawings
FIG. 1 is a schematic representation of a marker position 1 according to the present invention;
FIG. 2 is a schematic view of a marker position 2 of the present invention;
FIG. 3 is a schematic view of a marker position 3 of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and specific examples.
As shown in fig. 1 to fig. 3, in the calibration method for the tracer at the distal end of the surgical navigation robot provided in this embodiment, the optical tracker is used to directly read the coordinates of the tracer at the distal end of the robot in the coordinate system of the optical tracker, and the coordinates of the tracer at the distal end of the robot are calculated by recording the coordinates of 3 different positions respectively under the optical tracker.
Wherein 1 is the robot, 2 is the tracer, 3 is the optical tracker, 11 is the robot base, 12 is the terminal flange of robot, 13 is the 5 th axle of robot, 14 is the 6 th axle of robot, 21 is the marker. The tracer 2 is fixed to the robot end flange 12 and the optical tracker 3 can read the coordinates of the markers 21 on the tracer 2 with 4 markers 21 on the tracer 2.
Presetting a coordinate system G of a robot base 11, a coordinate system E of a flange 12 at the tail end of a robot 1, a coordinate system C of an optical tracker 3 and a 6-axis robot 1, and specifically comprising the following steps:
step 1: the robot is moved to the position shown in fig. 1, where the end coordinate system E is shown, where the z-axis of the coordinate system E of the robot end flange 12 is in the opposite direction to the z-axis of the coordinate system B of the robot base 11, the x-axis of the coordinate system E is the same as the x-axis of the coordinate system B, and the y-axis of the coordinate system E is opposite to the y-axis of the coordinate system B.
And 2, step: the optical tracker 3 is moved so that the robot end flange 12 is within the visual range of the optical tracker 3.
And step 3: the 6 th axis θ is rotated by an angle θ, where θ is 0, so that the infrared light reflected by the marker 21 on the tracer 2 is received by the optical tracker 3, the position of the marker 21 on the tracer 2 relative to the robot base coordinate system G at the time of marking is 1, and the coordinates of the marker 21 on the tracer 2 in the optical tracker 3 coordinate system C are recorded by the optical tracker 3.
And 4, step 4: the 6 th axis of rotation α is 30 degrees and the Z axis is translated upwards by 20mm, marking the position of the marker 21 on the tracer 2 at this time with respect to the robot base coordinate system G by 2, and the coordinates of the marker 21 on the tracer 2 in the optical tracker 3 coordinate system C are recorded by the optical tracker 3.
And 5: returning to position 1, the 5 th axis β is rotated by 30 degrees, the position of the marker 21 on the tracer 2 at this time is marked as 3 with respect to the robot base coordinate system G, and the coordinates of the marker 21 on the tracer 2 in the optical tracker 3 coordinate system C are recorded by the optical tracker 3.
Step 6: the coordinates of the marker 21 on the tracer 2 in the space of the robot end coordinate system E are calculated from the coordinates of the marker 21 recorded on the optical tracker 3 at positions 1, 2, 3 in the coordinate system C of the optical tracker 3 and the position transformation matrix of the robot 1.
The robot 1 in the step is a 6-axis robot.
In the above steps, a coordinate transformation matrix of the robot end flange coordinate system E from the position 1 to the position 0 is set asThe matrix is a 4x4 homogeneous matrix, specifically expressed as (current θ ═ 0)
Further, let the coordinate transformation matrix of robot end flange coordinate system E from position 2 to position 1 beWhen a is-20The matrix is a 4x4 homogeneous matrix, specifically denoted as (in this case, 30)
Further, let a coordinate conversion matrix of the robot end flange coordinate system E from position 3 to position 1 beThe shortest distance from the center point of the robot end flange 12 to the center line of the 5 th axis used in this example is 94, mm, which is a 4x4 homogeneous matrix, specifically denoted as (in this case, 30)
Further, at position 1, the transformation matrix from the optical tracker coordinate system C to the robot end flange coordinate system E is B, denoted as B
Let any marker 21 of the tracer 2 be point P, and the homogeneous coordinate read by the optical tracker 3 at position 1 be point PC1=[PC1x PC1y PC1z 1]TAt position 2, the homogeneous coordinate read by optical tracker 3 is PC2=[PC2x PC2y PC2z 1]TAt position 3, the homogeneous coordinate read by the optical tracker 3 is PC3=[PC3x PC3y PC3z 1]TThen there is
The above two equations are written as a general expression
B·[x' y' z'1]T=A·B·[x y z 1]T (3)
Wherein the matrix A is represented as
And carrying out matrix operation on the matrixes A and B, wherein the final result is as follows:
let matrix X ═ B11,B12,B13,B14,B21,B22,B23,B24,B31,B32,B33,B34]TThe above can be expressed as a matrix
Substituting the variables in the formula (1) into the formula (3) specifically as follows:
[x' y' z'1]T=PC2=[PC2x PC2y PC2z 1]T,
[x y z 1]T=PC1=[PC1x PC1y PC1z 1]T
from equation (4), 3 equations can be derived for each marker 21 on the tracer 2, for a total of 4 markers, 12 equations can be derived,
also according to the variable in the formula (2), substituting into the formula(3) In (2), 12 equations can also be derived. That is, there are 24 equations in total, and the unknown variable is only X ═ B11,B12,B13,B14,B21,B22,B23,B24,B31,B32,B33,B34]T. Finally obtaining X ═ B through Singular Value Decomposition (SVD)11,B12,B13,B14,B21,B22,B23,B24,B31,B32,B33,B34]TI.e. the values of the matrix B are obtained.
Then the homogeneous coordinate P of any marker 21 in the robot end flange coordinate system EE=[PEx PEy PEz 1]Can be represented by
PE=B·PC1
It is calculated that the coordinates of the 4 markers 21 on the tracer 2 of this example in space at the end E of the robot are finally calculated.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical idea proposed by the present invention fall within the protection scope of the claims of the present invention. The technology not related to the invention can be realized by the prior art.
Claims (7)
1. A calibration method of a tracer on the tail end of a surgical navigation robot is characterized by comprising the following steps: directly reading the coordinates of a marker on a tracer at the tail end of the robot under an optical tracker coordinate system by using an optical tracker, and calculating the coordinates of the marker in a flange coordinate system space at the tail end of the robot by recording the coordinates of 3 different positions under the optical tracker coordinate system and a position transformation matrix of the robot;
the specific method comprises the following steps: presetting a coordinate system G of a robot base, a coordinate system E of a robot tail end flange and a coordinate system C of an optical tracker, wherein markers capable of reflecting infrared light are installed on the tracers, the number of the markers is n, n is more than or equal to 3, the tracers are fixed on the robot tail end flange, the robot is a 6-axis robot, and the method comprises the following steps:
step 1: fixing the robot, setting the direction of the z axis of the robot end flange coordinate system E to be consistent with or opposite to the direction of the z axis of the robot base coordinate system G, setting the direction of the 5 th axis of the robot to be the same as the direction of the y axis under the robot end flange coordinate system E, and marking the position of the marker relative to the robot base coordinate system G at the moment to be 0;
step 2: fixing the optical tracker such that the robot end flange is within a visible range of the optical tracker;
and step 3: rotating the 6 th axis theta angle of the robot to enable infrared light reflected by the rotated marker to be received by the optical tracker, marking the position of the marker relative to the robot base coordinate system G at the moment to be 1, and recording the coordinates of the marker in the optical tracker coordinate system C by using the optical tracker;
and 4, step 4: rotating the 6 th axis alpha of the robot by an angle so that infrared light reflected by the rotated marker can be received by the optical tracker, translating the robot end flange coordinate system E upwards or downwards by an L length along the Z axis, and keeping the moved position within the visible range of the optical tracker, wherein the position of the marker relative to the robot base coordinate system G at the moment is 2, and recording the coordinates of the marker in the optical tracker coordinate system C by the optical tracker;
and 5: returning to the position 1, rotating the 5 th axis beta of the robot by an angle so that the infrared light reflected by the marker can be received by the optical tracker, marking the position of the marker relative to the robot base coordinate system G at the moment as 3, and recording the coordinates of the marker in the optical tracker coordinate system C by the optical tracker;
step 6: and calculating the coordinates of the marker in the robot end flange coordinate system E space through the coordinates of the marker in the optical tracker coordinate system C recorded at the positions 1, 2 and 3 on the optical tracker and the position transformation matrix of the robot.
3. a method for calibrating a tracer according to claim 1, wherein: setting a coordinate transformation matrix of a robot tail end flange coordinate system E from a position 2 to a position 1 asAssuming that the offset of step 4 along the Z axis is a, if the offset direction is the same as the Z axis, a is L, and if the offset direction is opposite to the Z axis, a is L, the matrix is a 4x4 homogeneous matrix, which is specifically expressed as:
4. the method for calibrating a tracer according to claim 1, wherein: setting a coordinate transformation matrix of a robot tail end flange coordinate system E from a position 3 to a position 1 asAssuming that the shortest distance from the center point of the end flange to the center line of the 5 th axis is b, unit mm, the matrix is a 4x4 homogeneous matrix, which is specifically shown as:
6. a method for calibrating a tracer according to claim 5, wherein: if the marker is a point P, the homogeneous coordinate read by the optical tracker at the position 1 is PC1=[PC1x PC1y PC1z 1]TAt said position 2 the homogeneous coordinate read by the optical tracker is PC2=[PC2x PC2y PC2z 1]TAt said position 3 the homogeneous coordinate read by the optical tracker is
PC3=[PC3x PC3y PC3z 1]TThen, there are:
the two equations of the formulas (1) and (2) are written as a general expression, and are:
B·[x' y' z' 1]T=A·B·[x y z 1]T (3)
where matrix A is represented as:
and carrying out matrix operation on the matrixes A and B, wherein the final result is as follows:
let matrix X ═ B11,B12,B13,B14,B21,B22,B23,B24,B31,B32,B33,B34]TThen, the result of the above matrix budget can be expressed as:
7. method for calibrating a tracer according to claim 6, characterized in that: substituting the variables in the formula (1) into the formula (3) specifically as follows:
[x' y' z' 1]T=PC2=[PC2x PC2y PC2z 1]T,
[x y z 1]T=PC1=[PC1x PC1y PC1z 1]T
by the formula (4), each marker on the tracer can obtain 3 equations, and if n markers exist, 3n equations can be obtained;
when the variables in equation (2) are substituted into equation (3), 3n equations can be similarly obtained, there are 6n equations in total, and the unknown variable is only X ═ 2 [, ]B11,B12,B13,B14,B21,B22,B23,B24,B31,B32,B33,B34]T(ii) a Obtaining the value of X through singular value decomposition to obtain the value of a matrix B, and obtaining the homogeneous coordinate P of the marker in a robot end flange coordinate system EE=[PEx PEy PEz 1]Can be calculated by the formula:
PE=B·PC1。
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