CN115462900A - Vertebral plate grinding track planning method of spinal surgery robot - Google Patents
Vertebral plate grinding track planning method of spinal surgery robot Download PDFInfo
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- 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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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
- A61B34/10—Computer-aided planning, simulation or modelling of surgical operations
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
- A61B34/10—Computer-aided planning, simulation or modelling of surgical operations
- A61B2034/107—Visualisation of planned trajectories or target regions
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- 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
- A61B2034/2046—Tracking techniques
- A61B2034/2065—Tracking using image or pattern recognition
Abstract
The invention discloses a vertebral plate grinding track planning method of a spinal surgery robot, which comprises the following steps: s1, three-dimensional reconstruction and preparation of artificial vertebrae; s1 comprises the substeps of: s11, three-dimensional reconstruction is carried out on the vertebra in the operated area by adopting MC and MS algorithms; s12, processing and analyzing the vertebral bone surface model based on Geomagic; s13, 3D printing preparation of the artificial vertebra; s2, obtaining a grinding track of the artificial vertebral plate by a doctor operating the spinal surgery robot; s2 comprises the substeps of: s21, establishing a track space mapping relation; s22, acquiring and preprocessing robot grinding track point cloud data; s23, generating a grinding track; and S3, registering the artificial vertebrae of the operation space with the operation object, and planning the grinding track of the vertebral plate of the actual operation object. The invention realizes the planning of the vertebral plate grinding track of the vertebral plate surgical robot, not only can ensure the grinding quality, but also can improve the high efficiency and the safety in the operation, reduce the wound to the bone tissue of a patient and improve the precision and the efficiency of the vertebral plate grinding formation.
Description
Technical Field
The invention relates to the technical field of orthopedic surgery robots, in particular to a vertebral plate grinding track planning method of a spinal surgery robot.
Background
Spinal disorders are mostly due to spinal nerve compression, and therefore, laminectomy nerve decompression is the most important task in spinal surgery. In performing a laminectomy, grinding of the vertebral lamina is one of the most important tasks, which requires grinding of the vertebrae by a grinding tool to a specific shape in preparation for the next treatment.
At present, doctors mainly know the operated area of a patient through CT scanning images without preparing personalized artificial vertebra models, the CT images can only be observed from two-dimensional angles and cannot be observed from any three-dimensional angles, and the space shape of the spine of the patient cannot be intuitively known, so that the subsequent operation route and the use of instruments are influenced. Because the spine form of each patient always has slight difference, and the degree that the vertebral plate grinding needs to be carried out to the patient is also different, it is difficult to make different grinding track strategies to different patients when the surgical robot carries out vertebral plate grinding. The personalized artificial vertebra model is prepared by the 3D printing technology, so that a doctor observes the artificial vertebra model, performs operations such as tool setting and grinding on the artificial vertebra model, and performs an operation on a patient by the robot, and therefore the method can not only combine the operation experience of the doctor, but also have the characteristics of accuracy and stability of the robot. Therefore, it is important for the surgical robot to simulate the grinding track of the doctor to perform the surgery on the patient.
When the orthopedic robot performs surgical operation, the traditional orthopedic robot mostly adopts a CT image navigation system to perform preoperative planning, and is not intuitive enough for high-risk cases, the robot track planning is too stylized, preoperative cutting simulation for personalized individuals is lacked, a personalized grinding track is difficult to form, skills of doctors for performing surgical operation are not learned, and abundant surgical experience of the doctors and the characteristics of the robot, such as accuracy and stability, cannot be combined. It can be seen that it is difficult for conventional planning methods to ensure the accuracy of preoperative diagnosis of high-risk orthopedic surgery and the grinding accuracy and safety of intraoperative robots.
Disclosure of Invention
In order to solve the problems, the invention provides a vertebral plate grinding track planning method of a spinal surgery robot, which is reasonable in design, overcomes the defects of the prior art and has a good effect.
In order to realize the purpose of the invention, the following technical scheme is adopted:
a vertebral plate grinding track planning method of a spinal surgery robot comprises the following steps:
s1, three-dimensional reconstruction and preparation of artificial vertebrae, which specifically comprises the following substeps: s11, three-dimensional reconstruction is carried out on the vertebra in the operated area by adopting MC and MS algorithms; s12, processing and analyzing the vertebral bone surface model based on Geomagic; s13, 3D printing and preparing the artificial vertebra;
s2, obtaining a grinding track of the artificial vertebral plate of the spine surgery robot controlled by the doctor, and specifically comprising the following substeps: s21, establishing a track space mapping relation; s22, acquiring and preprocessing robot grinding track point cloud data; s23, generating a grinding track;
s3, planning a grinding track of the vertebral plate of the actual operation object by the spinal operation robot, and specifically comprises the following substeps: s31, registering the artificial vertebrae of the operation space and the operation object; and S32, obtaining a grinding track of the spinal surgery robot on the vertebrae of the surgical object.
Further, S21 includes the following substeps:
s211, establishing a robot vertebral plate grinding track measuring system, wherein the system consists of a laser tracker, a target ball and a spinal surgery robot, and the target ball is fixed at the tail end of the robot;
establishing a matrix for a conversion relation between a vertebral disc coordinate system { E }, a base coordinate system { B } and a tool coordinate system { T }, the vertebral disc coordinate system { E } and the base coordinate system { B }, and establishing a vertebral disc operation robot flange coordinate system { E }, a base coordinate system { B }, and a tool coordinate system { T }, wherein the base coordinate system { B } is different from the vertebral disc coordinate system { E }, and the vertebral disc coordinate system { E } is different from the base coordinate system { B } B T E Represents:
wherein the content of the first and second substances, B R E a rotation matrix representing the robot flange coordinate system { E } relative to the robot base coordinate system { B } and including three direction vectors B n E 、 B o E And B a E the directional cosines of the three unit principal vectors used to represent { E } relative to { B }; B p E expressed as a vector of { E } positions relative to { B };
matrix array B T E Can also be used for representing the conversion relation of the coordinate system { T } of the spinal surgery robot tool relative to the coordinate system { B } of the base coordinate system E T T To show the conversion relation of the coordinate system { T } of the tool of the spinal surgery robot relative to the coordinate system { E } of the flange, the grinding head of the tool at the end of the robot is fixed on the end of the robot, so that E T T Is fixed and invariable and is obtained by the structure when the tail end is designed;
at the same time, the formula is derived:
B T E · E T T ＝ B T T ； (2)
obtaining the position of the target ball P in the robot flange plate coordinate system { E } by the method, obtaining the position of the center of the target ball in the robot base coordinate system { B }, then directly obtaining the coordinate of the center of the target ball P under the laser tracker coordinate system { M } by the laser tracker, and realizing the conversion between the laser tracker and the robot base coordinate system according to the common point conversion;
s212, calibrating a tool coordinate system and acquiring a spatial transformation matrix;
the position of the target ball center P under the robot-based coordinate system { B } is represented by equation (3):
wherein, the first and the second end of the pipe are connected with each other, E T B represents a conversion matrix, P, of a vertebral flange coordinate system { E } of the spinal surgery robot under a robot base coordinate system { B } E The position of the target ball P in the flange coordinate system { E } is represented, and N represents the position number; two different positions m and n are obtained through the mobile robot, and the deviation of the two positions m and n under the robot base coordinate system is as follows:
the deviation of the target ball center P under the laser tracker coordinate system { M } is:
two target balls in different positions, the distance between the two balls is the same in the laser tracker and robot base coordinates, namely:
substituting formula (3) to obtain:
in the above-mentioned formula, the compound of formula,
can be read directly in the robot teach pendant,
is the result of the laser tracker measurement; obtaining the center of the target ball by a least square method according to the formula (7)P coordinate P in robot flange coordinate system { E } E ；
The position P of the center P of the target ball in the flange coordinate system { E } is obtained by the formula E Then the robot is moved to more than 4 positions, and the reading of the flange end demonstrator in each position and the position of the center of the target ball in a coordinate system { M } of the laser tracker are recorded simultaneously; the positions of all the target ball centers in the robot base coordinate system can be obtained through the formula (3), and the conversion matrix between the robot base coordinate system and the laser tracker coordinate system { M } can be obtained through calculation of the formula (18) M T B ：
P B ＝P E E T B ＝P M M T B (8)。
Further, S22 comprises the following substeps:
s221, point cloud data are obtained;
the laser tracker is placed at a place with good lighting conditions, and the computer is used for controlling point taking through SA software, so that the position of a target ball is not shielded in the whole grinding process; the tail end of the handheld robot carries out vertebral plate grinding on 3D printed vertebra, and point cloud of a path is recorded through a laser tracker;
s222, filtering the point cloud data to remove outliers in the point cloud data.
Further, S23 includes the following sub-steps:
s231, carrying out NURBS curve fitting on the point cloud data;
the fitting formula for NURBS curves is:
wherein, B i,3 Representing a cubic B-spline odd function, W i Represents a weight factor, D i Representing control vertices, u represents curve nodes;
B i,3 the calculation formula of (c) is:
wherein u is k Representing a node;
weighting factor W i =1,b spline basis function satisfies:
converting formula (9) to:
for any discrete point p j All points p (u) on the fitting curve j ) Correspondingly, the method comprises the following steps:
wherein u is j The deviation of the discrete point from the curve is | P (u) representing the corresponding parameter value j )-p j And I, optimizing the control vertex to obtain a control vertex, and minimizing the total deviation from the fitting curve to all the discrete points, wherein the functional relation between the total deviation and the control vertex is as follows:
wherein m represents the number of discrete points before NURBS curve fitting;
obtaining the vertex value of any control point from the formula (12) to the formula (14), and solving a fitting equation;
after the fitting is finished, determining the distance between adjacent points according to the precision requirement in actual vertebral plate grinding, dispersing the NURBS curve into a linear point cloud, eliminating the fine fluctuation of original data, and obtaining a smooth linear point cloud;
s232, carrying out normal vector estimation on the point cloud data;
s233, generating a grinding track;
the method for generating the grinding track of the robot to determine the knife contact and the knife position point data and obtain the knife contact and the knife position point data comprises the following steps: taking one point in the point cloud set P as the current contact point, the position vector is represented by P, and the normal vector is represented by v n Indicating that the line connecting this point with the next point is taken as tangent vector v t V is provided c ＝v t ·v n (ii) a Construction with the tool contact as origin of coordinates, v c ，v n ，v t A coordinate system being a coordinate axis; transformation matrix of the coordinate system relative to the robot base coordinate system B p t Comprises the following steps:
B p t representing the knife position data corresponding to the knife contact;
the conversion relationship between the coordinate systems is:
after the solution is carried out through the inverse kinematics of the spinal surgery robot, joint corners of a series of robots are obtained, the robots sequentially reach expected knife contact positions, and the knife contacts are connected in series to form a processing track so as to finish the whole vertebral plate grinding process.
Further, S31 includes the following substeps:
s311, establishing an operation space registration coordinate system;
establishing a robot base coordinate system { B } and a laser tracker coordinate system { M }, and measuring a point set of an artificial vertebra coordinate { P } and an actual operated vertebra coordinate { V } by using a probe on the laser tracker;
s312, registering the corresponding point set;
selecting at least 4 registration points on the artificial vertebra and the actual patient vertebra, and enabling the coordinates of a set of points under the artificial vertebra to be P = { P = { (P) } i With a set of points corresponding to one of the actual patient vertebrae, V = { V = i Where i =1,2, \8230, n, n denotes the number of registration points;
s313, finding an optimal matrix V T P Let pass the converted coordinate p i Closest to the coordinate v i 。
Further, the specific process of S313 is:
representing a transformation matrix using four rotation parameters V T P The rotational transformation in (1) represents the translational transformation by using three translational parameters, and the four rotational parameters and the three translational parameters are put into a vector q = [ q ] R ,q T ]In the step (1), the first step, V T P = q, wherein q R A rotation matrix obtained by expressing a quaternion, q T Representing the obtained translation vector;
the mathematical problem becomes the minimum problem of the objective function f (q):
solving the centroid P of the point sets P and V 0 And v 0 ：
Solving covariance matrix C of point sets P and V:
constructing a symmetric matrix E from the matrix C:
where tr (C) represents the trace of the covariance matrix C, i.e., the sum of the diagonal elements of the matrix C;
solving the eigenvalue and eigenvector of the symmetric matrix E if quaternion Q (Q) 0 ,q x ,q y ,q z ) A rotation transformation matrix q represented by a quaternion when the eigenvector corresponding to the maximum eigenvalue of the symmetric matrix E is the same R Minimizing the value of f (q) of the objective function;
rotation matrix q is obtained by quaternion R The solution equation of (a) is as follows:
centroid W from point sets W and M 0 And m 0 From q can be R Calculating a translation vector q T ：
q T ＝v 0 -q R p 0 ； (19)
Obtaining a spatial transformation matrix of the artificial vertebrae to the actual patient V T P 。
The invention has the beneficial effects that:
the invention realizes the planning of the vertebral plate grinding track of the vertebral plate surgical robot, not only can ensure the grinding quality, but also can improve the high efficiency and the safety in the operation, reduce the wound to the bone tissue of a patient and improve the precision and the efficiency of the vertebral plate grinding formation.
Drawings
FIG. 1 is a flow chart of a vertebral plate grinding trajectory planning method of a spinal surgery robot according to the present invention;
FIG. 2 is a schematic view of a spinal surgical robot according to an embodiment of the present invention;
FIG. 3 is a schematic view of a robotic lamina grinding trajectory measurement system in accordance with an embodiment of the present invention;
FIG. 4 is a diagram of raw point cloud data in accordance with an embodiment of the present invention;
FIG. 5 is a diagram of point cloud data after filtering in one embodiment of the present invention;
FIG. 6 is a schematic illustration of a fitted grinding trajectory in an embodiment of the present invention;
FIG. 7 (a) is a schematic diagram of a robot tracking a grinding trajectory in an embodiment of the present invention;
FIG. 7 (b) is a schematic diagram of a true grinding trajectory in one embodiment of the present invention;
Detailed Description
The following description will further illustrate embodiments of the present invention with reference to specific examples:
a vertebral plate grinding track planning method for a spinal surgery robot, as shown in fig. 1, comprising the following steps:
s1, three-dimensional reconstruction and preparation of artificial vertebrae;
s1 comprises the substeps of:
s11, performing three-dimensional reconstruction on the vertebra in the operated area by adopting MC and MS algorithms;
the invention uses VTK as a development tool, applies MC and MS algorithm to realize the three-dimensional reconstruction of CT scanning images, and the tool is a MFC program in a document-view mode. The threshold value of the bone tissue can be obtained by introducing the CT image into the VTK, finding the position of the bone tissue to be reconstructed in the two-dimensional image, and calculating the spatial coordinates of the position and the position index of the image pixel. The two-dimensional coordinates of the reconstructed tissue can be obtained by selecting the reconstructed tissue through a mouse, the coordinates take a pixel as a unit, and the pixels can be converted into three-dimensional physical coordinates through a perspective projection function in a program. When the reconstruction tissue threshold is selected, whether the contour of the contour line is matched with the contour of the tissue to be reconstructed is judged by using an MS algorithm to select a choice, when the contour line is well selected, the threshold is used for three-dimensional reconstruction, and when the contour line is not well selected, a position is changed, and the reconstruction threshold is changed;
in the embodiment, a solid model of lumbar vertebra L2 is selected for CT scanning, and the threshold obtained by using the MS algorithm is 1050.
S12, processing and analyzing the vertebral bone surface model based on Geomagic;
through S11, three-dimensional reconstruction is completed on the vertebra of the operated patient based on MC and MS algorithms. However, the obtained data cannot be directly used for 3D printing after fitting is completed, because the three-dimensional reconstructed model has rough and uneven surface and needs to be processed by reverse engineering.
The invention selects the Geomagic rapid curved surface to process the model, and mainly comprises the following aspects:
(1) processing the polygon and shape stages based on the Geomagic studio model;
(2) surface treatment based on Geomagic washion;
s13, 3D printing preparation of the artificial vertebra: using 3D printing techniques to provide 1:1, preparing a model.
S2, obtaining a grinding track of the artificial vertebral plate by a doctor for controlling the spine surgery robot;
s2 comprises the substeps of:
s21, establishing a track space mapping relation;
s21 includes the following substeps:
s211, the 6-DOF type serial robot is adopted to replace a manual operation instrument to finish grinding of the vertebral plate, and the overall structure of the robot is shown in figure 2; establishing a robot vertebral plate grinding track measuring system, wherein the system consists of a laser tracker, a target ball, a spinal surgery robot, a six-axis force sensor and a spherical grinding tool, and the target ball is fixed at the tail end of the robot as shown in figure 3; the laser tracker is a Leica-AT960 laser tracker;
establishing a vertebral operation robot flange plate coordinate system { E }, a base coordinate system { B } and a tool coordinate system { T }, using a homogeneous transformation matrix to express a conversion relation between the coordinate systems, and using the matrix for the conversion relation between the vertebral operation robot flange plate coordinate system { E } and the base coordinate system { B } B T E Represents:
wherein, the first and the second end of the pipe are connected with each other, B R E a rotation matrix representing the robot flange coordinate system { E } relative to the robot base coordinate system { B } and including three direction vectors B n E 、 B o E And B a E the directional cosines of the three unit principal vectors used to represent { E } relative to { B }; B p E expressed as a vector of { E } positions relative to { B };
matrix array B T E Can also be used for representing the conversion relation of the coordinate system { T } of the vertebral operation robot tool relative to the coordinate system { B }, and can be used for E T T To show the conversion relationship between the coordinate system { T } of the tool of the spine surgery robot and the coordinate system { E } of the flange, and the grinding head of the tool at the end of the robot is fixed on the end of the robot, therefore E T T Is fixed and is obtained by the structure when the tail end is designed;
at the same time, the formula is derived:
B T E · E T T ＝ B T T ； (2)
obtaining the position of the target ball P in a robot flange plate coordinate system { E } through the method, obtaining the position of the center of the target ball in a robot base coordinate system { B }, then directly obtaining the coordinate of the center of the target ball P under the coordinate system of the laser tracker through the laser tracker, and realizing the conversion between the laser tracker and the robot base coordinate system according to the common point conversion;
s212, calibrating a tool coordinate system and acquiring a spatial transformation matrix;
the position of the target ball center P under the robot base coordinate system { B } is represented by equation (3):
wherein, the first and the second end of the pipe are connected with each other, E T B represents a conversion matrix, P, of a vertebral flange coordinate system { E } of the spinal surgery robot under a robot base coordinate system { B } E The representation represents the position of the target ball P in a flange coordinate system { E }, and N represents the position number; two different positions m and n are obtained by the mobile robot, and the deviation of the two positions m and n under the robot base coordinate system is as follows:
the deviation of the target ball center P under the coordinate system of the laser tracker is as follows:
two target balls in different positions, although their displayed coordinates in the robot-based coordinate system and the laser tracker coordinate system are different, the distance between them is the same in the laser tracker and the robot-based coordinate system, i.e.:
substituting formula (4) to obtain:
in the above-mentioned formula, the compound of formula,
can be read directly in the robot teach pendant,
is the result of the laser tracker measurement; obtaining the coordinate P of the center P of the target ball in the robot flange plate coordinate system { E } by a least square method according to the formula (7) E ；
The method obtains the target ball center P on the flange seatPosition P in the system { E } E Then, the robot is moved to more than 4 positions, and the reading of the flange tail end demonstrator of each position and the position of the center of the target ball in the coordinate system of the laser tracker are recorded simultaneously; the positions of all target ball centers in the robot base coordinate system can be obtained through the formula (3), and the conversion matrix between the robot base coordinate system and the laser tracker coordinate system can be obtained through the calculation of the formula (8) M T B ：
P B ＝P E E T B ＝P M M T B ； (8)
P M Is the coordinate of the target ball center P under the laser tracker coordinate system { M };
during the experiment, the relative positions of the laser tracker and the spine surgery robot must be kept unchanged. In the process of solving, three unknowns exist in the equation, but due to the existence of errors, the fewer coordinate points are used, the lower the accuracy of the solution is, and therefore, 6 unknowns are selected for solving. The point coordinates measured by the laser tracker are shown in table 1.
Table 1 calibration point laser tracker measurement coordinates
The pose data of the tail end of the flange plate read by the robot teaching box corresponding to the 6 calibration points are shown in the table 2, and then the pose data can be obtained E T B 。
TABLE 2 robot Flange end pose parameters
The calibration of the tool coordinate system by the method described above enables the position of the target ball in the end flange coordinate system (22.451, 47.792, 34.618) to be obtained. The coordinates of these 6 calibration points in the robot base coordinate system are then calculated as shown in table 3.
TABLE 3 coordinates P of the calibration points in the robot base coordinate system B
According to formula P B ＝P E E T B ＝P M M T B Can obtain a homogeneous transformation matrix of the base coordinate system of the spinal surgery robot relative to the coordinate system of the laser tracker M T B Comprises the following steps:
s22, acquiring and preprocessing robot grinding track point cloud data;
s22 includes the following substeps:
s221, point cloud data are obtained;
the laser tracker is placed at a place with good lighting conditions, and the computer is used for controlling point taking through SA software, so that the position of a target ball is not shielded in the whole grinding process; the vertebral plate grinding is carried out on the 3D printed vertebra by the tail end of the handheld robot, and the point cloud of the path is recorded through the laser tracker, as shown in fig. 4;
however, when the laser tracker is used for measuring the grinding track of a doctor, the laser tracker is influenced by various factors, such as vibration generated when the grinding head grinds the artificial vertebra, the fixing degree of the target ball, the scanning speed of the laser tracker, the angle between the laser plane and the measuring plane and the like. Due to these effects, the obtained point cloud data is inaccurate, and furthermore, due to the limitation of the measurement method, a measurement blind area may be generated. Therefore, before the spinal surgery robot obtains the grinding path, it is necessary to perform preprocessing such as filtering on the obtained point cloud to enhance the reliability of the point cloud data.
And S222, filtering the point cloud data to remove outliers in the point cloud data.
Firstly, mean filtering is adopted to perform data processing, as shown in fig. 5, outliers in point cloud data are removed, and the adopted method is as follows: the average distance between each point and the neighboring point is calculated, since the distance is far from the target, the distance is far. Discrete points can then be deleted by deleting long-distance data points, and significant outliers can be removed when the average distance of three times all distance values is deleted
And S23, generating a grinding track.
S231, carrying out NURBS curve fitting on the point cloud data;
the fitting formula for NURBS curves is:
wherein, B i,3 Represents a cubic B-spline odd function, W i Representing a weight factor, D i Representing control vertices, u represents curve segments
Point; b is i,3 The calculation formula of (2) is as follows:
wherein u is k Representing a node;
fitting of NURBS curves requires three parameters: control vertex, node vector, weight factor. Of these parameters, the control vertex has the most significant effect on the quality of the curve, and the shape of the curve may vary considerably as the position and number of the control vertex changes.
Let weight factor W i =1,b spline basis function satisfying:
converting formula (24) to:
for any discrete point p j All points p (u) on the fitting curve j ) Correspondingly, the method comprises the following steps:
wherein u is j The deviation of the discrete point from the curve is | P (u) representing the corresponding parameter value j )-p j And I, optimizing the control vertex to obtain a control vertex, and minimizing the total deviation from the fitting curve to all the discrete points, wherein the functional relation between the total deviation and the control vertex is as follows:
wherein m represents the number of discrete points before NURBS curve fitting;
obtaining the vertex value of any control point from the formula (12) to the formula (14), and solving a fitting equation;
after the fitting is finished, determining the distance between adjacent points according to the precision requirement in actual vertebral plate grinding, dispersing the NURBS curve into linear point cloud, eliminating the fine fluctuation of the original data, and obtaining smooth line point cloud, as shown in FIG. 6;
s232, carrying out normal vector estimation on point cloud data;
set point cloud set as P = { l = 1 ,l 2 ,…,l n H, point cloud of each line segment is l i ＝{p i1 ,p i2 ,…,p in }，p ij Is the current calculation point. Searching the point cloud set P to find out the point cloud set P ij P on the same line ij-1 And p ij+1 Then find out the P nearest to P on two adjacent lines i-1j And p i+1j Then it can be obtained as { p } ij ,p ij+1 ,p i-1j }，{p ij ,p i-1j ,p ij-1 }，{p ij ,p ij-1 ,p i+1j }， {p ij ,p i+1j ,p ij+1 Four triangles with vertices, which are aligned in order to meet the right-hand rule. And respectively assigning coordinate values of all vertexes of all the triangles to a, b and c, wherein:
a＝(x a ,y a ,z a ) T b＝(x b ,y b ,z b ) T ，c＝(x c ,y c ,z c ) T ；
the normal vector of the triangular patch can be calculated using equation (15):
by using the expressions (15) - (17), n is the four normal vectors of the four triangles 1 ，n 2 ，n 3 ，n 4 Taking the weighted average of the normal vectors of the four triangles as the common vertex p ij Normal vector n of ij ＝(n x ,n y ,n z ) T The weight coefficient is determined by the area of each triangle.
All points in the point cloud are traversed by the above method, i.e., i =1,2, \8230, n and j =1,2, \8230, n, and then normal vectors of all points are obtained.
S233, generating a grinding track;
the grinding track of the robot is mainly generated by determining the tool contact point and tool position point data.
The method of obtaining the knife contact and the knife position point data is as follows. Taking one point in the point cloud set P as the current contact point, the position vector of the point cloud set P is represented by P, and the normal vector is represented by v n Indicating that the line connecting this point with the next point is taken as tangent vector v t V is given c ＝v t ·v n (ii) a Construction with the tool contact as origin of coordinates, v c ，v n ，v t A coordinate system being a coordinate axis; transformation matrix of the coordinate system relative to the robot base coordinate system B p t Comprises the following steps:
B p t representing the cutter point data corresponding to the cutter contact;
the conversion relationship between the coordinate systems is:
after the solution is carried out through the inverse kinematics of the spinal surgery robot, joint corners of a series of robots are obtained, the robots sequentially reach expected knife contact positions, and the knife contacts are connected in series to form a processing track so as to finish the whole vertebral plate grinding process. Comparing the point cloud data of the robot motion recorded by the laser tracker with the point cloud data of the real grinding as shown in fig. 7, it can be seen that the robot well replicates the grinding track of the vertebral plate.
S3, planning a grinding track of a vertebral plate of an actual operation object by the spinal operation robot;
s3 comprises the substeps of:
s31, registering the artificial vertebrae of the operation space and the operation object;
the robot obtains the grinding track of the artificial vertebra space, the grinding track of the artificial vertebra space is transferred to the actual patient space through the robot vertebral plate grinding operation, and therefore the artificial vertebra space and the actual patient space need to be registered, and the position in the artificial vertebra space and the position in the actual operated patient vertebra are guaranteed to correspond to each other.
S31 includes the following substeps:
s311, establishing an operation space registration coordinate system;
establishing a robot base coordinate system { B } and a laser tracker coordinate system { M }, and measuring a point set of an artificial vertebra coordinate { P } and an actual operated vertebra coordinate { V } by using a probe on the laser tracker;
s312, registering the corresponding point set;
selecting 5 registration points on the artificial vertebra and the actual patient vertebra, and enabling the coordinates of a group of point sets under the artificial vertebra to be P = { P = { (P) } i And a coordinate of a point set corresponding to one of the points under the actual patient's vertebrae is V = { V } i Wherein i =1,2, \8230 }, n, n denotes the number of registration points; in order to eliminate random errors as much as possible, 10 sets of data were taken by the probe for each coordinate, and the average of the 10 sets of coordinates was taken as the coordinate value of each point, as shown in table 4.
TABLE 4 registration of artificial vertebrae to actual vertebrae to be operated on
S313, finding an optimal matrix V T P Let pass the converted coordinate p i Closest to the coordinate v i 。
Further, the specific process of S313 is:
representing a transformation matrix using four rotation parameters V T P The rotational transformation in (1) represents the translational transformation by using three translational parameters, and the four rotational parameters and the three translational parameters are put into a vector q = [ q ] R ,q T ]In (1), V T P = q, wherein q R Representing a rotation matrix obtained by quaternion, q T Representing the obtained translation vector;
the mathematical problem becomes the problem of minimizing the objective function f (q):
solving the centroid P of the point sets P and V 0 And v 0 ：
Solving a covariance matrix C of the point sets P and V:
constructing a symmetric matrix E from the matrix C:
where tr (C) represents the trace of the covariance matrix C, i.e., the sum of the diagonal elements of the matrix C;
solving the eigenvalue and eigenvector of the symmetric matrix E, and using the Berthold theory if quaternion Q (Q) 0 ,q x ,q y ,q z ) A rotation transformation matrix q represented by a quaternion when the eigenvector corresponding to the maximum eigenvalue of the symmetric matrix E is the same R Minimizing the value of f (q) of the objective function;
rotation matrix q is obtained by quaternion R Solution ofThe formula is as follows:
centroid W from point sets W and M 0 And m 0 From q can be R Calculating a translation vector q T ：
q T ＝v 0 -q R p 0 ； (21)
Substituting the five groups of data in the table 4 into the formulas (20) and (21) to obtain the space transformation matrix from the artificial vertebra to the actual patient V T P ：
And S32, obtaining a grinding track of the spine surgical robot on the actual surgical object vertebra through the matrix transformation relation.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.
Claims (6)
1. A vertebral plate grinding track planning method of a spinal surgery robot is characterized by comprising the following steps:
s1, three-dimensional reconstruction and preparation of artificial vertebrae, which specifically comprises the following substeps: s11, three-dimensional reconstruction is carried out on the vertebra in the operated area by adopting MC and MS algorithms; s12, processing and analyzing the vertebral bone surface model based on Geomagic; s13, 3D printing and preparing the artificial vertebra;
s2, obtaining a grinding track of the artificial vertebral plate of the spine surgery robot controlled by the doctor, and specifically comprising the following substeps: s21, establishing a track space mapping relation; s22, acquiring and preprocessing robot grinding track point cloud data; s23, generating a grinding track;
s3, the spine surgical robot carries out grinding track planning on the vertebral plate of the actual surgical object, and the method specifically comprises the following substeps: s31, registering the artificial vertebrae of the operation space and the operation object; and S32, obtaining a grinding track of the vertebral plate of the operation object by the spinal operation robot.
2. The method of claim 1, wherein the step S21 comprises the following substeps:
s211, establishing a robot vertebral plate grinding track measuring system, wherein the system consists of a laser tracker, a target ball and a spinal surgery robot, and the target ball is fixed at the tail end of the robot;
establishing a matrix for a conversion relation among a vertebral disc coordinate system { E }, a base coordinate system { B }, a tool coordinate system { T }, the vertebral disc coordinate system { E } and the base coordinate system { B }, and establishing a vertebral disc operation robot flange coordinate system { E }, a base coordinate system { B }, and a tool coordinate system { T }, wherein the vertebral disc coordinate system { E } and the base coordinate system { B } are in a conversion relation B T E Represents:
wherein the content of the first and second substances, B R E a rotation matrix representing the robot flange coordinate system { E } relative to the robot base coordinate system { B } and including three direction vectors B n E 、 B o E And B a E three unit principal vectors used to represent { E } are direction cosines with respect to { B }; B p E expressed as a vector of { E } positions relative to { B };
matrix array B T E Can also be used for representing the conversion relation of the coordinate system { T } of the spinal surgery robot tool relative to the coordinate system { B } of the base coordinate system E T T To show the conversion relation of the coordinate system { T } of the tool of the spinal surgery robot relative to the coordinate system { E } of the flange, the grinding head of the tool at the end of the robot is fixed on the end of the robot, so that E T T Is fixed and invariable and is obtained by the structure when the tail end is designed;
meanwhile, the formula is obtained:
B T E · E T T ＝ B T T ； (2)
obtaining the position of the target ball P in a robot flange coordinate system { E } and the position of the center of the target ball in a robot base coordinate system { B } by the method, then directly obtaining the coordinate of the center of the target ball P under the coordinate system { M } of the laser tracker by the laser tracker, and realizing the conversion between the laser tracker and the robot base coordinate system according to the common point conversion;
s212, calibrating a tool coordinate system and acquiring a spatial transformation matrix;
the position of the target ball center P under the robot-based coordinate system { B } is represented by equation (3):
wherein the content of the first and second substances, E T B representing a transformation matrix, P, of a vertebral flange coordinate system { E } of the spinal surgery robot under a robot base coordinate system { B } E The representation represents the position of the target ball P in a flange coordinate system { E }, and N represents the position number; two different positions m and n are obtained through the mobile robot, and the deviation of the two positions m and n under the robot base coordinate system is as follows:
the deviation of the target ball center P under the coordinate system { M } of the laser tracker is as follows:
two target balls in different positions, the distance between the two target balls is the same in the laser tracker and the robot-based coordinates, namely:
substituting formula (3) to obtain:
in the above-mentioned formula, the reaction mixture,
can be read directly in the robot teach pendant,
is the result of the laser tracker measurement; obtaining the coordinate P of the center P of the target ball in the robot flange coordinate system { E } by a least square method according to the formula (7) E ；
The position P of the center P of the target ball in the flange coordinate system { E } is obtained by the formula E Then, the robot is moved to more than 4 positions, and the reading of the flange end demonstrator of each position and the position of the center of the target ball in the coordinate system { M } of the laser tracker are recorded simultaneously; the positions of all target ball centers in the robot base coordinate system can be obtained through the formula (3), and the conversion matrix between the robot base coordinate system and the laser tracker coordinate system { M } can be obtained through the calculation of the formula (8) M T B ：
P B ＝P E E T B ＝P M M T B (8)。
3. The method for planning a laminectomy track of a spinal surgical robot according to claim 1, wherein the step S22 comprises the substeps of:
s221, point cloud data are obtained;
the laser tracker is placed at a place with good lighting conditions, and the computer is used for controlling point taking through SA software, so that the position of a target ball is not shielded in the whole grinding process; the tail end of the handheld robot carries out vertebral plate grinding on 3D printed vertebra, and point cloud of a path is recorded through a laser tracker;
and S222, filtering the point cloud data to remove outliers in the point cloud data.
4. The method of claim 1, wherein the step S23 comprises the following substeps:
s231, carrying out NURBS curve fitting on the point cloud data;
the fitting formula for NURBS curves is:
wherein, B i,3 Representing a cubic B-spline odd function, W i Representing a weight factor, D i Representing control vertices, u represents curve nodes;
B i,3 the calculation formula of (2) is as follows:
wherein u is k Representing a node;
weighting factor W i =1,b spline basis function satisfies:
converting formula (9) to:
for any discrete point p j All points p (u) on the fitting curve j ) Correspondingly:
wherein，u j The deviation of the discrete point from the curve is | P (u) representing the corresponding parameter value j )-p j And I, optimizing the control vertex to obtain a control vertex, and minimizing the total deviation from the fitting curve to all the discrete points, wherein the functional relation between the total deviation and the control vertex is as follows:
wherein m represents the number of discrete points before NURBS curve fitting;
obtaining the vertex value of any control point from the formula (12) to the formula (14), and solving a fitting equation;
after the fitting is finished, determining the distance between adjacent points according to the precision requirement in actual vertebral plate grinding, dispersing a NURBS curve into linear point cloud, eliminating the fine fluctuation of original data, and obtaining smooth line point cloud;
s232, carrying out normal vector estimation on point cloud data;
s233, generating a grinding track;
the method for generating the grinding track of the robot to determine the knife contact and the knife position point data and obtain the knife contact and the knife position point data comprises the following steps: taking one point in the point cloud set P as the current contact point, the position vector is represented by P, and the normal vector is represented by v n Showing that the line connecting this point and the next point is taken as tangent vector v t V is provided c ＝v t ·v n (ii) a Construction with the tool contact as origin of coordinates, v c ，v n ，v t A coordinate system being a coordinate axis; transformation matrix of the coordinate system relative to the robot base coordinate system B p t Comprises the following steps:
B p t representing the cutter point data corresponding to the cutter contact;
the conversion relationship between the coordinate systems is:
after the solution is carried out through the inverse kinematics of the spinal surgery robot, joint corners of a series of robots are obtained, the robots sequentially reach expected knife contact positions, and the knife contacts are connected in series to form a processing track so as to finish the whole vertebral plate grinding process.
5. The method for planning a laminectomy track of a spinal surgical robot according to claim 1, wherein the step S31 comprises the substeps of:
s311, establishing an operation space registration coordinate system;
establishing a robot base coordinate system { B } and a laser tracker coordinate system { M }, and measuring a point set of an artificial vertebra coordinate { P } and an actual operated vertebra coordinate { V } by using a probe on the laser tracker;
s312, registering the corresponding point set;
selecting at least 4 registration points on the artificial vertebra and the actual patient vertebra, and enabling the coordinates of a set of points under the artificial vertebra to be P = { P = { (P) } i And a coordinate of a point set corresponding to one of the points under the actual patient's vertebrae is V = { V } i Where i =1,2, \8230, n, n denotes the number of registration points;
s313, finding an optimal matrix V T P Let pass the converted coordinate p i Closest to the coordinate v i 。
6. The method for planning a laminectomy grinding track of a spinal surgical robot according to claim 5, wherein the specific process of S313 comprises:
representing a transformation matrix using four rotation parameters V T P The translation transformation in (1) is represented by three translation parameters, and the four rotation parameters and the three translation parameters are put into a vector q = [ q ] = R ,q T ]In (1), V T P = q, wherein q R A rotation matrix obtained by expressing a quaternion, q T Representing the obtained translation vector;
the mathematical problem becomes the minimum problem of the objective function f (q):
solving the centroid P of the point sets P and V 0 And v 0 ：
Solving a covariance matrix C of the point sets P and V:
constructing a symmetric matrix E from the matrix C:
where tr (C) represents the trace of the covariance matrix C, i.e., the sum of the diagonal elements of the matrix C;
solving the eigenvalue and eigenvector of the symmetric matrix E if quaternionQ(q 0 ,q x ,q y ,q z ) A rotation transformation matrix q represented by a quaternion when the eigenvector corresponding to the maximum eigenvalue of the symmetric matrix E is the same R Minimizing the value of f (q) of the objective function;
rotation matrix q is obtained by quaternion R The solution equation of (a) is as follows:
centroid W from point sets W and M 0 And m 0 From q can be R Calculating a translation vector q T ：
q T ＝v 0 -q R p 0 ； (19)
Obtaining a spatial transformation matrix of the artificial vertebrae to the actual patient V T P 。
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| CN116712168B (en) * | 2023-08-10 | 2023-11-21 | 鑫君特(苏州)医疗科技有限公司 | Vertebral plate grinding control method and surgical robot system |
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