A vertebral lamina grinding trajectory planning method for spinal surgery robot

Abstract

The present invention discloses a method for planning the grinding trajectory of vertebral plates by a spinal surgery robot, and the steps are as follows: S1, three-dimensional reconstruction and preparation of artificial vertebrae; S1 includes sub-steps: S11, three-dimensional reconstruction of the vertebrae in the surgical area by using MC and MS algorithms; S12, processing and analyzing the surface model of the vertebrae based on Geomagic; S13, 3D printing preparation of artificial vertebrae; S2, obtaining the grinding trajectory of the artificial vertebral plates by the doctor controlling the spinal surgery robot; S2 includes sub-steps: S21, establishing a trajectory space mapping relationship; S22, obtaining and preprocessing the point cloud data of the robot grinding trajectory; S23, generating a grinding trajectory; S3, registering the artificial vertebrae in the surgical space with the surgical object, and planning the grinding trajectory of the vertebral plates of the actual surgical object. The present invention realizes the planning of the grinding trajectory of the vertebral plates of the spinal surgery robot, which can not only ensure the grinding quality, but also improve the efficiency and safety in the operation, reduce the trauma to the patient's bone tissue, and improve the accuracy and efficiency of vertebral plate grinding and forming.

Description

Technical Field

[0001] The invention relates to the technical field of orthopedic surgical robots, and in particular to a vertebral plate grinding trajectory planning method for a spinal surgical robot. Background Art

[0002] Most spinal diseases are caused by compression of spinal nerves. Therefore, the most important task in spinal surgery is to remove the nerves and decompress the laminectomy. During laminectomy, laminectomy is the most important task. It requires the use of grinding tools to grind the vertebrae into a specific shape in preparation for the next step of treatment.

[0003] At present, doctors mainly understand the surgical area of ​​patients through CT scan images. Without the preparation of personalized artificial vertebral models, CT images can only be observed from a two-dimensional perspective, and cannot be observed from any three-dimensional angle. Since the spatial shape of the patient's spine cannot be intuitively understood, this will affect the future surgical route and the use of instruments. Since there are always subtle differences in the spinal morphology of each patient, and the degree of lamina grinding required for each patient is also different, it is difficult to make different grinding trajectory strategies for different patients when the surgical robot performs lamina grinding. Through the preparation of personalized artificial vertebral models by 3D printing technology, doctors can first observe, calibrate, grind and other operations on the artificial vertebral model, and then the robot can perform surgery on the patient. This can not only combine the doctor's surgical experience, but also have the characteristics of precision and stability of the robot. Therefore, it is particularly important for the surgical robot to imitate the doctor's grinding trajectory to perform surgery on the patient.

[0004] When orthopedic robots perform surgical operations, traditional orthopedic robots mostly use CT image navigation systems for preoperative planning. For high-risk cases, it is still not intuitive enough. The robot trajectory planning is too programmed, lacks preoperative cutting simulation for personalized individuals, and is difficult to form personalized grinding trajectories. It does not learn the skills of doctors in performing surgical operations, and fails to combine the rich surgical experience of doctors with the precise and stable characteristics of robots. It can be seen that conventional planning methods are difficult to ensure the accuracy of preoperative diagnosis of high-risk orthopedic surgeries and the grinding accuracy and safety of robots during operations. Summary of the invention

[0005] In order to solve the above problems, the present invention provides a vertebral plate grinding trajectory planning method for a spinal surgery robot, which has a reasonable design, solves the shortcomings of the prior art, and has good effects.

[0006] In order to achieve the purpose of the invention, the following technical solutions are adopted:

[0007] A method for planning a vertebral plate grinding trajectory of a spinal surgery robot comprises the following steps:

[0008] S1. 3D reconstruction and preparation of artificial vertebrae, specifically including sub-steps: S11. 3D reconstruction of the vertebrae in the surgical area using MC and MS algorithms; S12. Processing and analysis of the vertebrae surface model based on Geomagic; S13. 3D printing preparation of artificial vertebrae;

[0009] S2, obtaining the grinding trajectory of the artificial vertebral plate by the doctor controlling the spinal surgery robot, specifically including sub-steps: S21, establishing a trajectory space mapping relationship; S22, obtaining and preprocessing the robot grinding trajectory point cloud data; S23, generating a grinding trajectory;

[0010] S3, the spinal surgery robot plans the grinding trajectory of the vertebral plate of the actual surgical object, which specifically includes sub-steps: S31, alignment of the artificial vertebrae in the surgical space and the surgical object; S32, obtaining the grinding trajectory of the spinal surgery robot on the vertebrae of the surgical object.

[0011] Furthermore, S21 includes the following sub-steps:

[0012] S211. Establish a robot lamina grinding trajectory measurement system, which consists of a laser tracker, a target ball and a spinal surgery robot, and the target ball is fixed at the end of the robot;

[0013] Establish the flange coordinate system {E}, base coordinate system {B} and tool coordinate system {T} of the spinal surgery robot. The transformation relationship between the flange coordinate system {E} and the base coordinate system {B} is expressed by the matrix B T E express:

[0014]

[0015] in, B R E Represents the rotation matrix of the robot flange coordinate system {E} relative to the robot base coordinate system {B}, including three direction vectors B n E , B o E and B a E , used to represent the direction cosines of the three unit principal vectors of {E} relative to {B};

[0016] B p E It is represented as the position vector of {E} relative to {B};

[0017] matrix B T T It can also be used to represent the transformation relationship between the tool coordinate system {T} of the spine surgery robot and the base coordinate system {B}. E T TTo express the transformation relationship between the tool coordinate system {T} of the spinal surgery robot and the flange coordinate system {E}, the end tool grinding head of the robot is fixed on the end of the robot, so E T T It is fixed and is derived from the structure when the terminal is designed;

[0018] At the same time, the formula is obtained:

[0019] B T E · E T T = B T T ; (2)

[0020] The position of the target ball P in the robot flange coordinate system {E} is obtained by the above method, and the position of the target ball center in the robot base coordinate system {B} is obtained. Then, the coordinates of the target ball center P in the laser tracker coordinate system {M} are directly obtained by the laser tracker. The conversion between the laser tracker and the robot base coordinate system is realized according to the common point conversion.

[0021] S212, calibration of tool coordinate system and acquisition of space transformation matrix;

[0022] The position of the target ball center P in the robot base coordinate system {B} is expressed by formula (3):

[0023]

[0024] in, B T E represents the transformation matrix of the spine surgery robot flange coordinate system {E} in the robot base coordinate system {B}, P E represents the position of the target ball P in the flange coordinate system {E}, and N represents the number of positions. By moving the robot, two different positions m and n are obtained, and their deviation in the robot base coordinate system is:

[0025]

[0026] The deviation of the target sphere center P in the laser tracker coordinate system {M} is:

[0027]

[0028] The distance between the two target balls at different positions, m and n, is the same in the laser tracker and the robot base coordinates, that is:

[0029]

[0030] Substituting equations (4) and (5) into the equation, we obtain:

[0031]

[0032] In the above formula, Can be read directly in the robot teaching box, is the result of the laser tracker measurement; according to formula (7), the coordinate P of the target ball center P in the robot flange coordinate system {E} is obtained by the least squares method. E ;

[0033] The position P of the target sphere center P in the flange coordinate system {E} is obtained by the above formula E , then move the robot to more than 4 positions, and record the flange end pendant reading and the position of the target ball center in the laser tracker coordinate system {M} at each position; the positions of all target ball centers in the robot base coordinate system can be obtained by formula (3), and the transformation matrix between the robot base coordinate system and the laser tracker coordinate system {M} can be obtained by formula (18) M T B :

[0034] P B =P E B T E =P M M T B (8).

[0035] Further, S22 includes the following sub-steps:

[0036] S221, obtaining point cloud data;

[0037] Place the laser tracker in a place with good lighting conditions, and use the computer to control the point selection to ensure that the position of the target ball is not blocked during the entire grinding process; the end of the handheld robot grinds the vertebral lamina of the 3D printed spine, and the laser tracker records the point cloud of the path;

[0038] S222: Filter the point cloud data to remove outliers in the point cloud data.

[0039] Further, S23 includes the following sub-steps:

[0040] S231, NURBS curve fitting of point cloud data;

[0041] The fitting formula of NURBS curve is:

[0042] Among them, B i,3 represents the cubic B-spline basis function, W i represents the weight factor, D irepresents the control vertex, u represents the parameter value; B i,3 The calculation formula is:

[0043]

[0044] Among them, u i Represents the parameter value of the i-th node;

[0045] Let the weight factor W i =1, the B-spline basis function satisfies:

[0046]

[0047] Transform formula (9) into:

[0048]

[0049] For any discrete point p j , there is a point p(u j ) corresponds to:

[0050]

[0051] Among them, u j represents the corresponding parameter value, and the deviation between the discrete point and the curve is |P(u j )-p j |, optimize it to get the control vertex, so that the total deviation of the fitting curve to all discrete points is minimized, and the functional relationship between the total deviation and the control vertex is:

[0052]

[0053] Where m represents the number of discrete points before NURBS curve fitting;

[0054] From formula (12) to formula (14), the vertex value of any control point is obtained, and the fitting equation is obtained;

[0055] After fitting is completed, the spacing between adjacent points is determined according to the accuracy requirements in actual lamina grinding, and the NURBS curve is discretized into a straight line point cloud to eliminate the slight fluctuations of the original data and obtain a smooth line point cloud;

[0056] S232, estimating a normal vector for the point cloud data;

[0057] S233, generating a grinding trajectory;

[0058] The robot grinding trajectory is generated to determine the tool contact point and tool position data. The method to obtain the tool contact point and tool position data is as follows: take a point in the point cloud set P as the current tool contact point, its position vector is represented by p, and its normal vector is represented by v nIndicates that the line connecting this point and the next point is the tangent vector v t , let v c =v t ·v n ; Construct the knife contact point as the coordinate origin, v c , v n , v t is the coordinate system of the coordinate axis; the transformation matrix of this coordinate system relative to the robot base coordinate system B p t for:

[0059]

[0060] B p t Indicates the tool position data corresponding to the tool contact point;

[0061] The conversion relationship between coordinate systems is:

[0062]

[0063] I is the identity matrix, It is known from the calibration of the tool coordinate system, so the robot's pose matrix can be expressed as:

[0064]

[0065] After solving the inverse kinematics of the spinal surgery robot, a series of robot joint angles are obtained, so that the robot can reach the desired knife contact point positions in sequence, and the knife contact points are connected in series to form a processing trajectory planning.

[0066] Further, S31 includes the following sub-steps:

[0067] S311, establishing a surgical space registration coordinate system;

[0068] Establishing the robot base coordinate system {B} and the laser tracker coordinate system {M}, using the probe on the laser tracker to measure the point set of the artificial vertebrae coordinates {P} and the actual vertebrae coordinates {V};

[0069] S312, corresponding point set registration;

[0070] At least four registration points are selected on the artificial vertebra and the actual patient vertebra, and the coordinates of a set of points under the artificial vertebra are set to P = {p i}, the point set coordinates corresponding to each of them under the actual patient's vertebrae are V = {v i}, where i = 1, 2, ..., n, n represents the number of registration points;

[0071] S313, find an optimal matrix VT P , let the transformed coordinate p i closest to coordinate v i .

[0072] Furthermore, the specific process of S313 is as follows:

[0073] The transformation matrix is ​​represented by four rotation parameters V T P The rotation transformation in the translation transformation is represented by three translation parameters. The four rotation parameters and three translation parameters are put into a vector q = [q R ,q T ]middle, V T P =q, where q R Represents the rotation matrix obtained by the quaternion, q T represents the obtained translation vector;

[0074] The mathematical problem becomes the problem of finding the minimum value of the objective function f(q):

[0075]

[0076] Find the centroid p of point sets P and V 0 and v 0 :

[0077]

[0078] Solve the covariance matrix C of point sets P and V:

[0079]

[0080] Construct a symmetric matrix E from matrix C:

[0081]

[0082] Where tr(C) represents the trace of the covariance matrix C, that is, the sum of the diagonal elements of the matrix C;

[0083] Solve the eigenvalues ​​and eigenvectors of the symmetric matrix E. If the quaternion Q(q 0 ,q x ,q y ,q z ) is the same as the eigenvector corresponding to the maximum eigenvalue of the symmetric matrix E, the rotation transformation matrix q represented by the quaternion R Make the value of the objective function f(q) minimum;

[0084] Using quaternions to find the rotation matrix q R The solution formula is as follows:

[0085]

[0086] According to the centroid p of point sets P and V 0 and v 0 , can be obtained by q R Calculate the translation vector q T :

[0087] q T =v 0 -q R p 0 ; (19)

[0088] Get the spatial transformation matrix from the artificial vertebra to the actual patient vertebra V T P .

[0089] The present invention has the following beneficial effects:

[0090] The present invention realizes the planning of the vertebral plate grinding trajectory of the spinal surgery robot, which can not only ensure the grinding quality, but also improve the efficiency and safety during the operation, reduce the trauma to the patient's bone tissue, and improve the accuracy and efficiency of vertebral plate grinding. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 This is a flow chart of a vertebral plate grinding trajectory planning method of a spinal surgery robot of the present invention;

[0092] Figure 2 This is a schematic diagram of the structure of a spinal surgery robot in one embodiment of the present invention;

[0093] Figure 3 It is a schematic diagram of a robot lamina grinding trajectory measurement system in one embodiment of the present invention;

[0094] Figure 4 is an original point cloud data graph in one embodiment of the present invention;

[0095] Figure 5 is a point cloud data graph after filtering in one embodiment of the present invention;

[0096] Figure 6 is a schematic diagram of a grinding trajectory after fitting in one embodiment of the present invention;

[0097] Figure 7 (a) is a schematic diagram of a robot tracking grinding trajectory in one embodiment of the present invention;

[0098] Figure 7 (b) is a schematic diagram of a real grinding trajectory in one embodiment of the present invention; DETAILED DESCRIPTION

[0099] The specific implementation of the present invention is further described below in conjunction with specific embodiments:

[0100] A spine surgery robot lamina grinding trajectory planning method, such as Figure 1 As shown, the following steps are included:

[0101] S1. Three-dimensional reconstruction and preparation of artificial vertebrae;

[0102] S1 includes the following sub-steps:

[0103] S11, MC and MS algorithms are used to perform three-dimensional reconstruction of the spine in the operated area;

[0104] The present invention uses VTK as a development tool, and applies MC and MS algorithms to achieve three-dimensional reconstruction of CT scan images. The tool is a document-view MFC program. Import the CT image into VTK, find the position of the bone tissue to be reconstructed in the two-dimensional image, calculate the spatial coordinates of its position and the position index of the image pixel, and then the threshold of the bone tissue can be obtained. By selecting the reconstructed tissue with the mouse, the two-dimensional coordinates of the reconstructed tissue can be obtained. This coordinate is in pixels and can be converted into three-dimensional physical coordinates through the perspective projection function in the program. When selecting the threshold for reconstructing the tissue, use the MS algorithm to determine whether the contour of the contour line matches the contour of the tissue to be reconstructed to make a choice. When the contour line selection is good, use the threshold for three-dimensional reconstruction. If the contour line selection is not good, change the position and replace the reconstruction threshold.

[0105] In this embodiment, a lumbar L2 segment vertebral entity model is selected for CT scanning, and a threshold value of 1050 is obtained by using the MS algorithm.

[0106] S12. Processing and analysis of vertebral surface model based on Geomagic;

[0107] Through S11, the patient's spine was reconstructed in three dimensions based on the MC and MS algorithms. However, the data obtained after fitting cannot be directly used for 3D printing because the surface of the three-dimensional reconstructed model is rough and uneven, and it needs to be processed through reverse engineering.

[0108] The present invention selects Geomagic Quick Surface to process the model, which mainly includes the following aspects:

[0109] ① Based on the processing of Geomagic studio model polygon and shape stage;

[0110] ②Surface treatment based on Geomagic fashion;

[0111] S13. 3D printing preparation of artificial vertebrae: Use 3D printing technology to provide a 1:1 model of the patient's spine.

[0112] S2, obtaining the grinding trajectory of the artificial vertebral plate by the doctor controlling the spinal surgery robot;

[0113] S2 includes sub-steps:

[0114] S21, establishing trajectory space mapping relationship;

[0115] S21 includes the following sub-steps:

[0116] S211. This embodiment uses a 6-DOF serial robot to replace manual surgical instruments to complete the grinding of the vertebral plate. The overall structure of the robot is as follows: Figure 2 As shown; establish a robot lamina grinding trajectory measurement system, such as Figure 3 As shown in the figure, the system consists of a laser tracker, a target ball, a spinal surgery robot, a six-axis force sensor, and a spherical mold. The target ball is fixed at the end of the robot. The laser tracker is a Leica-AT960 laser tracker.

[0117] The flange coordinate system {E}, base coordinate system {B} and tool coordinate system {T} of the spinal surgery robot are established, and the homogeneous transformation matrix is ​​used to represent the transformation relationship between the coordinate systems. The transformation relationship between the flange coordinate system {E} and the base coordinate system {B} of the spinal surgery robot is expressed by the matrix B T E express:

[0118]

[0119] in, B R E Represents the rotation matrix of the robot flange coordinate system {E} relative to the robot base coordinate system {B}, including three direction vectors B n E , B o E and B a E , used to represent the direction cosines of the three unit principal vectors of {E} relative to {B}; B p E It is represented as the position vector of {E} relative to {B};

[0120] matrix B T T It can also be used to represent the transformation relationship between the tool coordinate system {T} of the spine surgery robot and the base coordinate system {B}. E T TTo express the transformation relationship between the tool coordinate system {T} of the spinal surgery robot and the flange coordinate system {E}, the end tool grinding head of the robot is fixed on the end of the robot, so E T T It is fixed and is derived from the structure when the terminal is designed;

[0121] At the same time, the formula is obtained:

[0122] B T E · E T T = B T T ; (2)

[0123] The position of the target ball P in the robot flange coordinate system {E} is obtained by the above method, and the position of the target ball center in the robot base coordinate system {B} is obtained. Then, the coordinates of the target ball center P in the laser tracker coordinate system are directly obtained by the laser tracker. The conversion between the laser tracker and the robot base coordinate system is realized according to the common point conversion.

[0124] S212, calibration of tool coordinate system and acquisition of space transformation matrix;

[0125] The position of the target ball center P in the robot base coordinate system {B} is expressed by formula (3):

[0126]

[0127] in, B T E represents the transformation matrix of the spine surgery robot flange coordinate system {E} in the robot base coordinate system {B}, P E represents the position of the target ball P in the flange coordinate system {E}, and N represents the number of positions. By moving the robot, two different positions m and n are obtained, and their deviation in the robot base coordinate system is:

[0128]

[0129] The deviation of the target sphere center P in the laser tracker coordinate system is:

[0130]

[0131] Although the positions m and n are displayed as different coordinates in the robot base coordinate system and the laser tracker coordinate system, the distance between the positions m and n is the same in the laser tracker and robot base coordinates, namely:

[0132]

[0133] Substituting equations (4) and (5) into the equation, we obtain:

[0134]

[0135] In the above formula, Can be read directly in the robot teaching box, is the result of the laser tracker measurement; according to formula (7), the coordinate P of the target ball center P in the robot flange coordinate system {E} is obtained by the least squares method. E ;

[0136] The position P of the target sphere center P in the flange coordinate system {E} is obtained by the above method. E , then move the robot to more than 4 positions, and record the flange end pendant reading and the position of the target ball center in the laser tracker coordinate system at each position; the position of all target ball centers in the robot base coordinate system can be obtained by formula (3), and the transformation matrix between the robot base coordinate system and the laser tracker coordinate system can be calculated by formula (8): M T B :

[0137] P B =P E B T E =P M M T B ; (8)

[0138] P M is the coordinate of the target sphere center P in the laser tracker coordinate system {M};

[0139] During the experiment, the relative position of the laser tracker and the spinal surgery robot must remain unchanged. In the process of solving the equation, there are three unknowns, but due to the existence of errors, the fewer coordinate points are used, the lower the accuracy of the solution. Therefore, this paper selects 6 points for solution. The coordinates of the points measured by the laser tracker are shown in Table 1.

[0140] Table 1 Coordinates of the calibration points measured by laser tracker

[0141]

[0142] The flange end position data corresponding to the 6 calibration points read by the robot teaching box are shown in Table 2, and then the E T B .

[0143] Table 2 Robot flange end position parameters

[0144]

[0145] By calibrating the tool coordinate system using the method described above, the position of the target ball in the end flange coordinate system (22.451, 47.792, 34.618) can be obtained. Then the coordinates of these six calibration points in the robot base coordinate system are calculated as shown in Table 3.

[0146] Table 3 Coordinates P of the calibration points in the robot base coordinate system B

[0147]

[0148]

[0149] According to the formula P B =P E E T B =P M M T B , the homogeneous transformation matrix of the spine surgery robot base coordinate system relative to the laser tracker coordinate system can be obtained M T B for:

[0150]

[0151] S22, acquiring and preprocessing robot grinding trajectory point cloud data;

[0152] S22 includes the following sub-steps:

[0153] S221, obtaining point cloud data;

[0154] Place the laser tracker in a place with good lighting conditions, and control the point selection through the computer to ensure that the position of the target ball is not blocked during the entire grinding process; the handheld robot end grinds the vertebral plate of the 3D printed spine, and the laser tracker records the point cloud of the path, such as Figure 4 As shown;

[0155] However, when using a laser tracker to measure the doctor's grinding trajectory, it will be affected by various factors, such as the vibration caused by the grinding head grinding the artificial vertebra, the degree of fixation of the target ball, the scanning speed of the laser tracker, the angle between the laser plane and the measurement plane, etc. Due to these influences, the obtained point cloud data will be inaccurate. In addition, due to the limitations of the measurement method, there may be a blind spot in the measurement. Therefore, before the spinal surgery robot obtains the grinding path, it is necessary to perform pre-processing such as filtering on the obtained point cloud to enhance the reliability of the point cloud data.

[0156] S222: Filter the point cloud data to remove outliers in the point cloud data.

[0157] First, the mean filter is used to process the data, such as Figure 5 As shown in the figure, the outliers in the point cloud data are removed by first finding the average distance between each point and its neighboring points. Since the distance is farther from the target, the distance is longer. Then, the data points with long distances are deleted, and the discrete points can be deleted. After deleting the average distance of three times all distance values, the significant outliers can be removed.

[0158] S23, generating a grinding trajectory.

[0159] S231, NURBS curve fitting of point cloud data;

[0160] The fitting formula of NURBS curve is:

[0161] Among them, B i,3 represents the cubic B-spline basis function, W i represents the weight factor, D i represents the control vertex, and u represents the parameter value;

[0162] B i,3 The calculation formula is:

[0163]

[0164] Among them, u i Represents the parameter value of the i-th node;

[0165] The fitting of NURBS curves requires three parameters: control vertices, node vectors, and weight factors. Among these parameters, control vertices have the most significant impact on the quality of the curve, and the shape of the curve will change significantly with the change of the position and number of control vertices.

[0166] Let the weight factor W i =1, the B-spline basis function satisfies:

[0167]

[0168] Transform formula (24) into:

[0169]

[0170] For any discrete point p j , there is a point p(u j ) corresponds to:

[0171]

[0172] Among them, u j represents the corresponding parameter value, and the deviation between the discrete point and the curve is |P(u j )-pj |, optimize it to get the control vertex, so that the total deviation of the fitting curve to all discrete points is minimized, and the functional relationship between the total deviation and the control vertex is:

[0173]

[0174] Where m represents the number of discrete points before NURBS curve fitting;

[0175] From formula (12) to formula (14), the vertex value of any control point is obtained, and the fitting equation is obtained;

[0176] After fitting is completed, the spacing between adjacent points is determined according to the accuracy requirements in actual lamina grinding, and the NURBS curve is discretized into a straight line point cloud to eliminate the slight fluctuations of the original data and obtain a smooth line point cloud, such as Figure 6 As shown;

[0177] S232, estimating a normal vector for the point cloud data;

[0178] Assume that the point cloud set is P = {l 1 ,l 2 ,…,l n}, each line segment point cloud is l i ={p i1 ,p i2 ,…,p in}, p ij is the current calculation point. Search the point cloud set P to find the point that matches p ij On the same line p ij-1 and p ij+1 , and then find the p closest to P on the two adjacent lines i-1j and p i+1j , then we can get {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} as the vertices of the four triangles, by adjusting the order of the triangle vertices, so that they can meet the right-hand rule. Assign the coordinate values ​​of all the vertices of all triangles to a, b, c respectively, where:

[0179] a=(x a ,y a ,z a ) T b=(xb ,y b ,z b ) T , c=(x c ,y c ,z c ) T ;

[0180] The normal vector of a triangle can be calculated using formula (15):

[0181]

[0182] Using equations (15)-(17), we can find the four normal vectors of the four triangles, which are n 1 , n 2 , n 3 , n 4 , take the weighted average of the normal vectors of the four triangles as the common vertex p ij The normal vector n ij =(n x ,n y ,n z ) T , the weight coefficient is determined by the area of ​​each triangle.

[0183] Use the above method to traverse all the points in the point cloud, that is, i = 1, 2, ..., n and j = 1, 2, ..., n, and then get the normal vectors of all the points.

[0184] S233, generating a grinding trajectory;

[0185] The generation of robot grinding trajectory is mainly to determine the tool contact point and tool position point data.

[0186] The method to obtain the tool contact point and tool position data is as follows: Take a point in the point cloud set P as the current tool contact point, its position vector is represented by p, and its normal vector is represented by v n Indicates that the line connecting this point and the next point is the tangent vector v t , let v c =v t ·v n ; Construct the knife contact point as the coordinate origin, v c , v n , v t is the coordinate system of the coordinate axis; the transformation matrix of this coordinate system relative to the robot base coordinate system B p t for:

[0187]

[0188] B p tIndicates the tool position data corresponding to the tool contact point;

[0189] The conversion relationship between coordinate systems is:

[0190]

[0191] I is the identity matrix, It is known from the calibration of the tool coordinate system, so the robot's pose matrix can be expressed as:

[0192]

[0193] After solving the inverse kinematics of the spinal surgery robot, a series of robot joint angles are obtained, so that the robot can reach the desired knife contact point position in sequence, and the knife contact points are connected in series to form a processing trajectory planning. The point cloud data of the robot motion recorded by the laser tracker is compared with the point cloud data of the actual grinding. Figure 7 As shown, it can be seen that the robot has replicated the trajectory of lamina grinding well.

[0194] S3, the spinal surgery robot performs grinding trajectory planning on the vertebral plate of the actual surgical object;

[0195] S3 includes sub-steps:

[0196] S31, registration of the artificial vertebrae and the surgical object in the surgical space;

[0197] The robot has obtained the grinding trajectory of the artificial vertebral space. The robotic lamina grinding surgery needs to transfer the grinding trajectory of the artificial vertebral space to the actual patient space. Therefore, the "artificial vertebra-actual patient" must be aligned to ensure that the position in the artificial vertebral space corresponds to the position in the actual patient's vertebrae.

[0198] S31 includes the following sub-steps:

[0199] S311, establishing a surgical space registration coordinate system;

[0200] Establishing the robot base coordinate system {B} and the laser tracker coordinate system {M}, using the probe on the laser tracker to measure the point set of the artificial vertebrae coordinates {P} and the actual vertebrae coordinates {V};

[0201] S312, corresponding point set registration;

[0202] Select 5 registration points on the artificial vertebra and the actual patient vertebra, and let the coordinates of a set of points under the artificial vertebra be P = {p i}, the point set coordinates corresponding to each of them under the actual patient's vertebrae are V = {v i}, where i = 1, 2, ..., n, and n represents the number of registration points. In order to eliminate random errors as much as possible, 10 sets of data are obtained for each coordinate through the probe, and the average value of these 10 sets of coordinates is taken as the coordinate value of each point, as shown in Table 4.

[0203] Table 4 Registration of artificial vertebrae and actual vertebrae

[0204]

[0205]

[0206] S313, find an optimal matrix V T P , let the transformed coordinate p i closest to coordinate v i .

[0207] Furthermore, the specific process of S313 is as follows:

[0208] The transformation matrix is ​​represented by four rotation parameters V T P The rotation transformation in the translation transformation is represented by three translation parameters. The four rotation parameters and three translation parameters are put into a vector q = [q R ,q T ]middle, V T P =q, where q R Represents the rotation matrix obtained by the quaternion, q T represents the obtained translation vector;

[0209] The mathematical problem becomes the problem of finding the minimum value of the objective function f(q):

[0210] Find the centroid p of point sets P and V 0 and v 0 :

[0211]

[0212] Solve the covariance matrix C of point sets P and V:

[0213]

[0214] Construct a symmetric matrix E from matrix C:

[0215]

[0216] Where tr(C) represents the trace of the covariance matrix C, that is, the sum of the diagonal elements of the matrix C;

[0217] Solve the eigenvalues ​​and eigenvectors of the symmetric matrix E. Using Berthold's theory, if the quaternion Q(q 0 ,q x ,q y ,q z ) is the same as the eigenvector corresponding to the maximum eigenvalue of the symmetric matrix E, the rotation transformation matrix q represented by the quaternion R Make the value of the objective function f(q) minimum;

[0218] Using quaternions to find the rotation matrix q R The solution formula is as follows:

[0219]

[0220] According to the centroid p of point sets P and V 0 and v 0 , can be obtained by q R Calculate the translation vector q T :

[0221] q T =v 0 -q R p 0 ;(twenty one)

[0222] Substituting the five sets of data in Table 4 into formulas (20) and (21), we can obtain the spatial transformation matrix from the artificial vertebra to the actual patient vertebra: V T P :

[0223]

[0224] S32. Through the above matrix transformation relationship, the trajectory of the spine surgery robot grinding the vertebrae of the actual surgical object can be obtained.

[0225] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for planning the trajectory of vertebral plate grinding by a spinal surgery robot, characterized in that: The following steps are involved: S1. 3D reconstruction and preparation of artificial vertebrae, specifically including sub-steps: S11. 3D reconstruction of the vertebrae in the surgical area using MC and MS algorithms; S12. Processing and analysis of the vertebrae surface model based on Geomagic; S13. 3D printing preparation of artificial vertebrae; S2, obtaining the grinding trajectory of the artificial vertebral plate by the doctor controlling the spinal surgery robot, specifically including sub-steps: S21, establishing a trajectory space mapping relationship; S22, obtaining and preprocessing the robot grinding trajectory point cloud data; S23, generating a grinding trajectory; S3, the spinal surgery robot performs grinding trajectory planning on the vertebral plate of the actual surgical object, specifically including sub-steps: S31, registration of the artificial vertebrae in the surgical space with the surgical object; S32, obtaining the grinding trajectory of the spinal surgery robot on the vertebral plate of the surgical object; A robot lamina grinding trajectory measurement system was established, which consisted of a laser tracker, a target ball, and a spinal surgery robot. The target ball was fixed at the end of the robot. The S22 comprises the following sub-steps: S221, obtaining point cloud data; Place the laser tracker in a place with good lighting conditions, and use the computer to control the point selection to ensure that the position of the target ball is not blocked during the entire grinding process; the end of the handheld robot grinds the vertebral lamina of the 3D printed spine, and the laser tracker records the point cloud of the path; S222, filtering the point cloud data to remove outliers in the point cloud data; The S31 includes the following sub-steps: S311, establishing a surgical space registration coordinate system; Establishing the robot base coordinate system {B} and the laser tracker coordinate system {M}, using the probe on the laser tracker to measure the point set of the artificial vertebrae coordinates {P} and the actual vertebrae coordinates {V}; S312, corresponding point set registration; At least four registration points are selected on the artificial vertebra and the actual patient vertebra, and the coordinates of a set of points under the artificial vertebra are set to P = {p i }, the point set coordinates corresponding to each of them under the actual patient's vertebrae are V = {v i }, where i = 1, 2, ..., n, n represents the number of registration points; S313, find an optimal matrix V T P , let the transformed coordinate p i closest to coordinate v i ; The specific process of S313 is as follows: The transformation matrix is ​​represented by four rotation parameters V T P The rotation transformation in the translation transformation is represented by three translation parameters. The four rotation parameters and three translation parameters are put into a vector q = [q R ,q T ]middle, V T P =q, where q R Represents the rotation matrix obtained by the quaternion, q T represents the obtained translation vector; Transform the mathematical problem into a problem of minimizing the objective function f(q): Solve the centroid p0 and v0 of point sets P and V: Solve the covariance matrix C of point sets P and V: Construct a symmetric matrix E from matrix C: Where tr(C) represents the trace of the covariance matrix C, that is, the sum of the diagonal elements of the matrix C; Solve the eigenvalues ​​and eigenvectors of the symmetric matrix E. If the quaternion Q(q0,q x ,q y ,q z ) is the same as the eigenvector corresponding to the maximum eigenvalue of the symmetric matrix E, the rotation transformation matrix q represented by the quaternion R Minimize the value of the objective function f(q); Using quaternions to find the rotation matrix q R The solution formula is as follows: According to the centroids p0 and v0 of point sets P and V, q R Calculate the translation vector q T : q T =v0-q R p0;(19) Get the spatial transformation matrix from the artificial vertebra to the actual patient vertebra V T P .

2. A method for planning vertebral plate grinding trajectory of a spinal surgery robot according to claim 1, characterized in that: The S21 comprises the following sub-steps: S211. Establish a robot lamina grinding trajectory measurement system, which consists of a laser tracker, a target ball and a spinal surgery robot, and the target ball is fixed at the end of the robot; Establish the flange coordinate system {E}, base coordinate system {B} and tool coordinate system {T} of the spinal surgery robot. The transformation relationship between the flange coordinate system {E} and the base coordinate system {B} is expressed by the matrix B T E express: in, B R E Represents the rotation matrix of the robot flange coordinate system {E} relative to the robot base coordinate system {B}, including three direction vectors B n E , B o E and B a E , used to represent the direction cosines of the three unit principal vectors of {E} relative to {B}; B p E It is represented as the position vector of {E} relative to {B}; matrix B T T It can also be used to represent the transformation relationship between the tool coordinate system {T} of the spine surgery robot and the base coordinate system {B}. E T T To express the transformation relationship between the tool coordinate system {T} of the spinal surgery robot and the flange coordinate system {E}, the end tool grinding head of the robot is fixed on the end of the robot, so E T T It is fixed and is derived from the structure when the terminal is designed; At the same time, the formula is obtained: B T E · E T T = B T T ;(2) The position of the target ball center P in the robot flange coordinate system {E} is obtained by the above method, and the position of the target ball center in the robot base coordinate system {B} is obtained. Then, the coordinates of the target ball center P in the laser tracker coordinate system {M} are directly obtained by the laser tracker. The conversion between the laser tracker coordinate system and the robot base coordinate system is realized according to the common point conversion. S212, calibration of tool coordinate system and acquisition of space transformation matrix; The position of the target ball center P in the robot base coordinate system {B} is expressed by formula (3): in, B T E represents the transformation matrix of the spine surgery robot flange coordinate system {E} in the robot base coordinate system {B}, P E represents the position of the target ball P in the flange coordinate system {E}, and N represents the number of positions; two different positions m and n are obtained by moving the robot, and their deviation in the robot base coordinate system is: The deviation of the target sphere center P in the laser tracker coordinate system {M} is: The distance between positions m and n is the same in the laser tracker and robot base coordinates, namely: Substituting equations (4) and (5) into the equation, we obtain: In the above formula, Can be read directly in the robot teaching box, is the result of the laser tracker measurement; according to formula (7), the coordinate P of the target ball center P in the robot flange coordinate system {E} is obtained by the least squares method. E ; The position P of the target sphere center P in the flange coordinate system {E} is obtained by formula (7): E Then move the robot to more than 4 positions, and record the flange end pendant reading and the position of the target ball center in the laser tracker coordinate system {M} at each position; the positions of all target ball centers in the robot base coordinate system can be obtained by formula (3), and the transformation matrix between the robot base coordinate system and the laser tracker coordinate system {M} can be obtained by formula (8): M T B : P B =P E B T E =P M M T B (8)。 3. The method for planning the vertebral plate grinding trajectory of a spinal surgery robot according to claim 1, characterized in that: The S23 comprises the following sub-steps: S231, NURBS curve fitting of point cloud data; The fitting formula of NURBS curve is: Among them, B i,3 represents the cubic B-spline basis function, W i represents the weight factor, D i represents the control vertex, and u represents the parameter value; B i,3 The calculation formula is: Among them, u i Represents the parameter value of the i-th node; Let the weight factor W i =1, the B-spline basis function satisfies: Transform formula (9) into: For any discrete point pj, there is a point p(u j ) corresponds to: Among them, u j represents the corresponding parameter value, and the deviation between the discrete point and the curve is |P(u j )-p j |, optimize it to get the control vertex, so that the total deviation of the fitting curve to all discrete points is minimized, and the functional relationship between the total deviation and the control vertex is: Where m represents the number of discrete points before NURBS curve fitting; From formula (12) to formula (14), the vertex value of any control point is obtained, and the fitting equation is obtained; After fitting is completed, the spacing between adjacent points is determined according to the accuracy requirements in actual lamina grinding, and the NURBS curve is discretized into a straight line point cloud to eliminate the slight fluctuations of the original data and obtain a smooth line point cloud; S232, estimating a normal vector for the point cloud data; S233, generating a grinding trajectory; The robot grinding trajectory is generated to determine the tool contact point and tool position data. The method to obtain the tool contact point and tool position data is as follows: take a point in the point cloud set P as the current tool contact point, its position vector is represented by p, and its normal vector is represented by v n Indicates that the line connecting this point and the next point is the tangent vector v t , let v c =v t ·v n ; Construct the knife contact point as the coordinate origin, v c , v n , v t is the coordinate system of the coordinate axis; the transformation matrix of this coordinate system relative to the robot base coordinate system B p t for: B p t Indicates the tool position data corresponding to the tool contact point; The conversion relationship between coordinate systems is: I is the identity matrix, It is known from the calibration of the tool coordinate system, so the robot's pose matrix is ​​expressed as: After solving the inverse kinematics of the spinal surgery robot, a series of robot joint angles are obtained, and the knife contact points are connected in series to form the grinding trajectory planning.

Images