A surgical instrument calibration method and system

Abstract

The application discloses a surgical instrument calibration method and system, comprising the following steps: S1, placing the instrument shaft of a surgical instrument in the calibration space of a calibration device; S2, controlling the surgical instrument to rotate around the instrument shaft, and identifying the trackers on the surgical instrument and the calibration device in real time through a navigation device to obtain the pose transformation relationship between the two; S3, fitting a plane according to the trajectories of the trackers on the surgical instrument at different time points to obtain the corresponding normal vector as the axial direction of the surgical instrument, and performing plane circle fitting on the projection points of the trajectory points on the fitting plane to obtain the corresponding circle center as the axial center of the surgical instrument, and then obtaining the instrument axis of the surgical instrument; and S4, abutting the end of the surgical instrument against any surface of the calibration device, and obtaining the pose transformation relationship between the end of the surgical instrument and the surgical instrument in combination with S2 and S3. The application can complete instrument calibration through a navigation device without needing to measure through a three-coordinate measuring instrument, is simple to operate, and has strong real-time performance.

Description

Technical Field

[0001] This invention relates to the field of medical device technology, and in particular to a method and system for calibrating surgical instruments. Background Technology

[0002] Surgical navigation systems are now widely used in clinical surgery, providing surgeons with visual information about the surgical site and instruments during the procedure, enabling instrument navigation and monitoring. Surgical instruments are the direct tools surgeons use to perform most surgeries, and accurate, real-time tracking and positioning of these instruments is crucial for successful surgical navigation. To achieve accurate instrument tracking during surgery, preoperative calibration of the instruments is necessary, displaying them in real-time on the imaging coordinate system.

[0003] The calibration of surgical instruments usually requires the prior determination of the positional transformation relationship between the end of the surgical instrument and the instrument itself. Traditional instrument calibration methods are measured by coordinate measuring machines, which is very time-consuming and cannot be achieved in real time on the surgical site. Summary of the Invention

[0004] Purpose of the invention: To address the above-mentioned shortcomings, this invention proposes a surgical instrument calibration method and system that eliminates the need for coordinate measuring machines and allows for instrument calibration solely through a navigation device. This method is simple, efficient, and enables real-time calibration during surgery.

[0005] Technical solution:

[0006] A surgical instrument calibration method, comprising:

[0007] S1. Place the instrument axis of the surgical instrument in the calibration space of a calibration device, wherein the calibration space is adapted to the instrument axis of the surgical instrument;

[0008] S2. Control the surgical instruments to rotate around their instrument axis, and use navigation equipment to identify the positions of the tracers set on the surgical instruments and calibration devices in real time to obtain the position and pose transformation relationship between the two.

[0009] S3. Based on the trajectory fitting plane of the tracer on the surgical instrument at different times, the normal vector of the corresponding fitting plane is obtained as the axis of the surgical instrument. The projection points of the trajectory points to the fitting plane are fitted with a plane circle to obtain the corresponding circle center as the axis of the surgical instrument, thereby obtaining the axis of the surgical instrument.

[0010] S4. Place the end of the surgical instrument against any surface of the calibration device, and combine S2 and S3 to obtain the positional transformation relationship of the intersection of the instrument axis of the surgical instrument and the surface with respect to the surgical instrument, thereby obtaining the positional transformation relationship of the end of the surgical instrument with respect to the surgical instrument.

[0011] Specifically, S3 includes:

[0012] S31. The tracer includes a plurality of tracer balls, and a plane is fitted according to the trajectory points of the center of each tracer ball on the surgical instrument at different times.

[0013] S32. Calculate the fitting error of each of the fitting planes, and select the tracer ball with the smallest fitting error as the reference tracer ball;

[0014] S33. Perform circle fitting on the projection points from the trajectory points of the center of the reference tracer sphere to its corresponding fitting plane, take the center of the fitted circle as the axis of the surgical instrument, and take the normal vector of the fitting plane corresponding to the trajectory points of the center of the reference tracer sphere as the axis of the surgical instrument, to obtain the instrument axis of the surgical instrument.

[0015] More specifically, in S33, performing circle fitting on the projection points from the trajectory points of the center of the reference tracer sphere to its corresponding fitting plane, and using the center of the fitted circle as the axis of the surgical instrument, specifically involves:

[0016] (1) Calculate the normal vector of the fitting plane corresponding to the trajectory point of the center of the reference tracer sphere;

[0017] (2) Calculate the projection points of the trajectory points of the reference tracer ball obtained in step (1) onto the corresponding fitting plane;

[0018] (3) Calculate the centroid of each projection point obtained in step (2), and construct a two-dimensional spatial coordinate system on the fitting plane corresponding to the trajectory point of the reference tracer sphere, with the centroid of each projection point as the origin.

[0019] (4) Calculate the coordinates of each projection point in the two-dimensional coordinate system based on the vector between the centroid of each projection point and the projection point itself.

[0020] (5) Perform circle fitting on each projection point in the two-dimensional spatial coordinate system obtained in step (4), and calculate the two-dimensional coordinates of the center of the fitted circle;

[0021] (6) Based on the two-dimensional spatial coordinate system, the normal vector of the fitting plane corresponding to the trajectory point of the center of the reference tracer sphere, and the centroid of each projection point, construct a transformation matrix to transform the two-dimensional coordinates of the center of the fitting circle obtained in step (5) to three-dimensional space, and obtain the three-dimensional coordinates of the center of the fitting circle.

[0022] Furthermore, in step (2), the method for calculating the projection point is as follows:

[0023] P tj .x=P.x+H*Wx

[0024] Ptj .y=P.y+H*Wy

[0025] p tj .z=P.z+H*Wz

[0026] H = -(Wx*P) bj .x+Wy*P bj .y+Wz*P bj .zP.x*Wx-Py*Wy-Pz*Wz) / (Wx*W.x+

[0027] Wy*W.y+Wz*Wz)

[0028] Among them, P tj .x、P tj .y、P tj .z represents the trajectory point P bj The projection point P of the fitting plane corresponding to the trajectory point to the center of the reference tracer sphere tj The three coordinate values ​​of Px, Py, and Pz are the three coordinate values ​​of any point P on the fitting plane corresponding to the trajectory point of the center of the reference tracer sphere; the three coordinate values ​​of Wx, Wy, and Wz are the three coordinate values ​​of the normal vector W of the fitting plane corresponding to the trajectory point of the center of the reference tracer sphere; P bj .x、P bj .y、P bj .z represents the trajectory point P bj The three coordinate values.

[0029] Further, in step (3), the construction of the two-dimensional spatial coordinate system specifically involves: calculating the centroid of each projection point obtained in step (2), taking the centroid of each projection point as the origin, calculating the vector between the first projection point and the origin and normalizing it as the x-axis, taking the cross product of the normal vector of the fitting plane corresponding to the trajectory point of the reference tracer sphere and the vector containing the x-axis as the y-axis, and constructing a two-dimensional spatial coordinate system on the fitting plane corresponding to the trajectory point of the reference tracer sphere.

[0030] Further, in step (4), calculating the coordinates of each projection point in the two-dimensional coordinate system based on the vector between the centroid of each projection point and each projection point is specifically as follows:

[0031] Calculate the centroid P of each projection point ta With each projection point P tj The vector V between j :

[0032] V j =(P tj .xP ta .x, P tj .yPta .y, P tj .zP ta .z)

[0033] Therefore, the coordinates P of each projection point in the two-dimensional coordinate system can be calculated. tj2d (x,y):

[0034] P tj2d x = V j .x*X.x+V j .y*X.y+V j .z*Xz

[0035] P tj2d .y=V j .x*Y.y+V j .y*Y.y+V j .z*Yz

[0036] Among them, P tj2d.x P tj2d.y These are the two coordinate values ​​of the projection point in the two-dimensional coordinate system; V j .x、V j .y、V j .z represents vector V j The three coordinates in three-dimensional space; Xx, Xy, Xz are the three coordinates of the vector of the x-axis in the two-dimensional coordinate system in three-dimensional space; Yx, Yy, Yz are the three coordinates of the vector of the y-axis in the two-dimensional coordinate system in three-dimensional space.

[0037] Further, in step (6), the transformation matrix is ​​constructed based on the two-dimensional spatial coordinate system, the normal vector of the fitting plane corresponding to the trajectory point of the center of the reference tracer sphere, and the centroid of each projection point, specifically as follows:

[0038] The transformation matrix Z is initialized as a 4x4 identity matrix, and its elements are reassigned:

[0039] Z(0,0)=X(0), Z(1,0)=X(1), Z(2,0)=X(2);

[0040] Z(0,1)=Y(0), Z(1,1)=Y(1), Z(2,1)=Y(2);

[0041] Z(0,2)=W(0), Z(1,2)=W(1), Z(2,2)=W(2);

[0042] Z(0,3)=P ta .x,Z(1,3)=P ta .y,Z(2,3)=P ta .z;

[0043] Wherein, X(0), X(1), and X(2) are the components of the x-axis vector of the two-dimensional coordinate system in the x, y, and z directions of the three-dimensional space; Y(0), Y(1), and Y(2) are the components of the y-axis vector of the two-dimensional coordinate system in the x, y, and z directions of the three-dimensional space; W(0), W(1), and W(2) are the components of the normal vector W of the fitting plane corresponding to the trajectory point of the center of the reference tracer sphere in the x, y, and z directions of the three-dimensional space.

[0044] More specifically, S32 involves: calculating the average distance from the trajectory point of each tracer ball's center on the surgical instrument to its corresponding fitting plane as the fitting error, and selecting the tracer ball with the smallest average distance as the reference tracer ball.

[0045] Specifically, in S1, the calibration space is a plurality of calibration holes adapted to the instrument shafts of surgical instruments of different diameters or a V-groove formed on the surface of the calibration device for accommodating the instrument shafts of the surgical instruments.

[0046] Specifically, in S2, the navigation device identifies the surgical instruments and the tracer ball on the calibration device respectively, and constructs the instrument coordinate system and the calibration device coordinate system with the corresponding tracer ball positions respectively. Based on this, the transformation relationship between the instrument coordinate system and the calibration device coordinate system is calculated, that is, the pose transformation relationship between the surgical instruments and the calibration device is obtained.

[0047] A surgical instrument calibration system, comprising:

[0048] A calibration device includes a carrier on which a first tracer is mounted, and a calibration space on the carrier that corresponds to and mates with the instrument axis of a surgical instrument.

[0049] Surgical instruments, equipped with a second tracer;

[0050] A navigation device is used to identify the pose of the first tracer and the second tracer in real time during the process of the surgical instrument being set in the calibration space and rotating about its instrument axis, and when the end of the surgical instrument abuts against any surface of the calibration device.

[0051] The processing device acquires the pose identified by the navigation device, and then obtains the pose transformation relationship between the surgical instrument and the calibration device. It fits a planar circle based on the trajectory of the first tracer and obtains the instrument axis of the surgical instrument based on its normal vector and the center of the circle.

[0052] When the end of the surgical instrument abuts against any surface of the calibration device, the processing device calculates the intersection point of the instrument axis and the surface of the calibration device, and combines the pose transformation relationship between the surgical instrument and the calibration device to obtain the pose transformation relationship of the end of the surgical instrument relative to the surgical instrument.

[0053] Furthermore, a conical hole adapted to the end of the surgical instrument is provided on the calibration device, the end of the surgical instrument is placed in the conical hole and can rotate around its end at any angle;

[0054] The processing device acquires the position of the tracker obtained by the navigation device, performs spherical fitting on the motion trajectory of the tracker at different times, and obtains the position of the end of the surgical instrument as the center of the sphere, thereby obtaining the pose transformation relationship of the end of the surgical instrument relative to the surgical instrument.

[0055] Furthermore, the tracer includes several tracer balls. The processing device fits the spheres according to the trajectory points of the center of each tracer ball on the surgical instrument at different times, calculates the fitting error of each fitted sphere, selects the tracer ball with the smallest fitting error as the reference tracer ball, and uses the center of the sphere fitted by the trajectory point of the center of the reference tracer ball as the position of the end of the surgical instrument.

[0056] Beneficial effects: This invention eliminates the need for coordinate measuring machines (CMMs), enabling instrument calibration solely through a navigation device. It is not only simple to operate but also highly real-time, allowing for calibration during surgery. Furthermore, this invention provides a unique instrument calibration method for surgical instruments with tapered ends, resulting in more accurate calibration results. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the calibration device of the present invention;

[0058] Figure 2 This is a schematic diagram of the structure of a surgical instrument;

[0059] Figure 3 This is a schematic diagram of the tapered hole in the present invention;

[0060] Figure 4 This is a flowchart of the surgical instrument calibration method of the present invention.

[0061] In the figure, 1 is the calibration device, 11 is the carrier, 12 is the first tracer ball, 13 is the calibration hole, 14 is the calibration groove, and 15 is the conical hole;

[0062] 2 is the surgical instrument, 21 is the second tracer ball, and 22 is the instrument axis. Detailed Implementation

[0063] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.

[0064] This invention provides a surgical instrument calibration system, including a calibration device 1, a navigation device, and a processing device, wherein the calibration device 1 can be referenced... Figure 1 It includes a carrier 11, on which at least three non-collinear first tracer balls 12 are carried. These first tracer balls 12 constitute the tracer of the calibration device and can be identified by the navigation device.

[0065] The carrier 11 is also provided with several calibration holes 13 of different diameters. The calibration holes 13 can be used with surgical instruments with cylindrical shafts of different diameters. By designing calibration holes 13 of different diameters, this invention can accommodate surgical instruments of different diameters, which is more conducive to the alignment of the center of the calibration hole 13 and the center of the instrument, thus ensuring calibration accuracy. Specifically, the inner end face of the calibration hole 13 is a plane perpendicular to the axis of the calibration hole 13.

[0066] Reference Figure 2 and Figure 3 At least three non-collinear second tracer balls 21 are also installed on the surgical instrument 2. These second tracer balls 21 constitute the tracer of the surgical instrument 2 and can be identified by the navigation device. The surgical instrument has an instrument shaft 22, which is generally a cylindrical structure. The instrument shaft 21 of the surgical instrument 2 can be inserted into the corresponding calibration hole 13 on the carrier 11.

[0067] Therefore, the navigation device can identify the tracer balls on the surgical instrument 2 and the carrier 11 respectively, and then obtain the poses of the tracers on the surgical instrument 2 and the calibration device respectively. Since the tracer balls on the surgical instrument 2 and the calibration device are rigidly connected, and the instrument shaft 22 passes through the calibration hole 12 on the carrier 11, the pose transformation relationship between the surgical instrument and the calibration device can be obtained by converting the pose transformation relationship between the two tracers. This transformation relationship is denoted as T.

[0068] Specifically, the navigation device identifies the tracer balls on the surgical instrument 2 and the carrier 11 respectively, and constructs the instrument coordinate system and the calibration device coordinate system with the corresponding tracer ball positions. Based on this, the transformation relationship between the instrument coordinate system and the calibration device coordinate system is calculated, which is to obtain the pose transformation relationship T between the surgical instrument and the calibration device.

[0069] More specifically, you can refer to Figure 2 and Figure 3 Surgical instruments can be either sleeve instruments or probe instruments, depending on the actual needs.

[0070] Furthermore, the calibration hole 12 can be set on any surface of the carrier 11, and the first tracer ball 12 can be installed on the top or side surface of the carrier 11 to abut the tip of the surgical instrument 2 against any surface of the carrier 11.

[0071] In this invention, after the instrument axis 21 of the surgical instrument 2 passes through the corresponding calibration hole 13 on the carrier 11, the surgical instrument 2 is controlled to rotate around its instrument axis 21. The navigation device identifies the surgical instrument 2 and the tracer balls on the calibration device 1 in real time. The processing device obtains the pose transformation relationship T between the surgical instrument 2 and the calibration device 1 at different times. Based on this, the trajectory points of the centers of each second tracer ball 21 on the surgical instrument 2 at different times are fitted with planes. The trajectory point of the center of the second tracer ball 21 with the smallest average distance from its center trajectory point to its corresponding fitting plane and its fitting plane are selected. The orientation of the axial direction of the instrument axis 22 relative to the surgical instrument 2 is obtained based on the normal vector of this fitting plane. Then, a two-dimensional spatial coordinate system plane circle fitting is performed on the projection point of the selected second tracer ball 21's center trajectory point to the fitting plane to obtain the position of the center of the plane circle relative to the surgical instrument 2. This position is used as the axis of the instrument axis 21, thereby obtaining the pose of the axis of the instrument axis 22 relative to the surgical instrument 2. Based on the aforementioned pose transformation relationship T between the surgical instrument 2 and the calibration device 1, the pose of the axis of the instrument shaft 22 relative to the calibration device 1 is obtained. This can be achieved by using a navigation device to identify the tracer balls on the surgical instrument 2 and the calibration device 1 in real time, thus obtaining the pose transformation relationship of the instrument shaft 22 relative to the calibration device 1. Then, the end of the surgical instrument 2 is placed against any surface of the carrier 11. The navigation device is used to identify the tracer balls on the surgical instrument 2 and the calibration device 1 in real time, obtaining the pose transformation relationship between the surgical instrument 2 and the calibration device, as well as the pose transformation relationship of the instrument shaft relative to the calibration device 1. Combined with the known pose transformation relationship of the upper plane of the carrier 11 against which the end of the surgical instrument 2 is placed, relative to the calibration device, the intersection point between the instrument shaft and the upper plane of the carrier 11 against which its end is placed is calculated. This yields the pose transformation relationship of the end of the surgical instrument 2 relative to the calibration device. Furthermore, the pose transformation relationship of the end of the surgical instrument 2 relative to the surgical instrument 2 itself can be calculated by combining the pose transformation relationship between the surgical instrument 2 and the calibration device 1.

[0072] This invention also provides a calibration method for instruments with a thin cylindrical shaft. When the diameters of all calibration holes 13 in the calibration device 1 differ significantly from the shaft diameter of the surgical instrument 1 to be calibrated, and they are incompatible, the surgical instrument is a thin cylindrical surgical instrument. The calibration holes 13 corresponding to the shaft of this type of surgical instrument require high precision and are prone to errors during processing. Therefore, this invention provides a V-groove on the carrier 11 of the calibration device to accommodate the instrument shaft. The shaft of the thin cylindrical instrument is positioned within the V-groove and rotates. The navigation device acquires real-time data on the surgical instrument and the tracer ball on the calibration device, thereby obtaining the positional transformation relationship between the surgical instrument and the calibration device at different times. The subsequent steps are the same as described above, thus obtaining the instrument axis of this type of surgical instrument. The end-effector calibration of this type of surgical instrument is also the same as described above, ultimately completing the instrument calibration of this type of surgical instrument.

[0073] Furthermore, in this invention, the aforementioned instrument calibration method is generally designed for cases where the end face of the surgical instrument is flat. Of course, instrument calibration can also be achieved when the end of the surgical instrument has a conical structure. However, in order to further improve the instrument calibration of such surgical instruments, this invention also provides instrument calibration for surgical instruments with conical ends. In this case, the carrier 11 of the calibration device can be provided with a conical hole. The end of the surgical instrument is placed in the conical hole, and its end vertex coincides with the vertex of the conical hole. The surgical instrument is controlled to rotate around its end vertex at any angle. The motion trajectory of the tracer ball on the surgical instrument 2 is obtained in real time through the navigation device. When calibrating the end of such surgical instruments, the motion trajectory of each second tracer ball can be regarded as a sphere rotating around a certain point. Then, the sphere fitting method is used to calculate and select the center of the sphere corresponding to one of the second tracer balls, which is the end vertex of the surgical instrument. Then, the position and pose transformation relationship of the end of the surgical instrument 2 relative to the surgical instrument 2 itself can be calculated based on the tracer ball on the surgical instrument 2 obtained by the navigation device.

[0074] This invention also provides a surgical instrument calibration method, which can be referred to Figure 4 The steps include:

[0075] S1. Place the instrument shaft of the surgical instrument in the calibration hole 13 of the calibration device; In this invention, the instrument shaft of the surgical instrument is adapted to the calibration hole, thereby making the surgical instrument and the calibration hole coaxial and their centers aligned.

[0076] S2. Control the surgical instrument to rotate around its instrument axis, and obtain the tracer ball on the surgical instrument and calibration device in real time through the navigation device, so as to obtain the positional change relationship T between the surgical instrument and calibration device at different times.

[0077] Specifically, it includes:

[0078] The surgical instrument is controlled to rotate around its axis, and the positions of the tracer ball on the surgical instrument and calibration device 1 are identified in real time at different moments via a navigation device. Based on this, the transformation relationship T between the instrument coordinate system and the calibration device coordinate system at different moments is calculated. j , which corresponds to the pose transformation relationship T between the surgical instruments and the calibration device at different times;

[0079] By identifying the positions of the tracer balls on the surgical instruments and calibration device 1 at different times using the navigation equipment, corresponding instrument coordinate systems and calibration device coordinate systems can be constructed. From this, the transformation relationship T between the instrument coordinate system and the calibration device coordinate system at different times can be calculated. j .

[0080] S3, Instrument axis calibration;

[0081] S31. Based on the transformation relationship T between the instrument coordinate system and the calibration device coordinate system obtained in S2 j The positions P of the centers of the second tracer balls on the surgical instrument at different times in the coordinate system of the calibration device were calculated. ij ;

[0082] Specifically:

[0083] P ij =T j* P i

[0084] Where i is the index of the second tracer ball on the surgical instrument, i = 1, 2, ..., m, and m is the number of second tracer balls on the surgical instrument; j is the index of the time, j = 1, 2, ..., n, and n is the last time the surgical instrument rotates around its instrument axis; P i Let P be the coordinates of the center of the i-th second tracer sphere on the surgical instrument in the instrument coordinate system. ij Let be the coordinates of the center of the i-th second tracer ball in the calibration device coordinate system at time j;

[0085] S32. The positions of the centers of the second tracer balls on the surgical instrument at different times, obtained in S31, in the coordinate system of the calibration device. Plane fitting is performed to obtain the fitting plane corresponding to each second tracer ball, and the motion trajectory of the center of one of the second tracer balls and its corresponding fitting plane are selected.

[0086] The trajectory of the center of the second tracer ball, obtained by identifying the rotation of the surgical instrument around its axis, can be considered as a planar circle formed by the rotation around the surgical instrument's axis. Therefore, the positions of the centers of the second tracer balls on the surgical instrument at different times, obtained in S31, in the coordinate system of the calibration device can be determined. Plane fitting is performed to obtain the fitting plane corresponding to each second tracer sphere. In this invention, the least squares method is used for plane fitting, and the equation of the fitting plane corresponding to each second tracer sphere is: Ax+By+Cz+D=0.

[0087] The average distance between the trajectory points of the center of each second tracer ball at different times and their corresponding fitting planes is calculated as the first fitting error. The second tracer ball with the smallest first fitting error is selected as the benchmark. The trajectory points of the center of the second tracer ball at different times are denoted as the discrete point set G, and the fitting plane corresponding to the trajectory points in the discrete point set G is denoted as the plane E.

[0088] The average distance between the trajectory points of the center of each second tracer sphere at different times and their corresponding fitting plane is calculated using the following formula:

[0089]

[0090] Among them, P ij .x、P ij .y、P ij .z represent the three coordinate values ​​of the center of the i-th second tracer ball at time j in the coordinate system of the calibration device;

[0091] S33. Based on S32, the motion trajectory of the center of the second tracer ball as the reference and its corresponding fitting plane are obtained, namely the trajectory points in the discrete point set G and the plane E. The normal vector of the plane E is the direction vector of the instrument axis. The projection points of each trajectory point in the discrete point set G onto the plane E are fitted with a plane circle in the two-dimensional spatial coordinate system. The center of the plane circle is the axis of the instrument axis. Then, based on the transformation relationship between the instrument coordinate system and the calibration device coordinate system obtained in real time, the calibration of the instrument axis in the instrument coordinate system can be completed.

[0092] Specifically as follows:

[0093] (1) Based on S32, obtain the discrete point set G and plane E, calculate the normal vector W of plane E, and let any point on plane E be P(x,y,z);

[0094] (2) Calculate the trajectory points P in the discrete point set G according to step (1). bj The projection point P onto plane E tj ;

[0095] The calculation method for the projection point is as follows:

[0096] P tj .x=P.x+H*Wx

[0097] P tj .y=P.y+H*Wy

[0098] p tj .z=P.z+H*Wz

[0099] H = -(Wx*P) bj .x+Wy*P bj .y+Wz*P bj .zP.x*Wx-Py*Wy-Pz*Wz) / (Wx*W.x+

[0100] Wy*W.y+Wz*Wz)

[0101] Among them, P tj .x、P tj .y、P tj .z represents the trajectory point P in the discrete point set G. bj The projection point P onto plane E tj The coordinates of point P are given by Px, Py, and Pz respectively; the coordinates of point P on plane E are given by Px, Wy, and Wz respectively; the coordinates of the normal vector W on plane E are given by Px, Wy, and Wz respectively. bj .x、P bj .y、P bj .z represents the trajectory point P in the discrete point set G. bj The three coordinate values;

[0102] (3) Calculate the centroid P of each projection point obtained in step (2). ta Based on this, a two-dimensional spatial coordinate system is constructed in plane E;

[0103] Among them, the centroid P of each projection point ta It is obtained by calculating the average value of the coordinates of each projection point;

[0104] Then, construct the following two-dimensional spatial coordinate system on plane E:

[0105] With the centroid P of each projection point ta As the origin, select the first projection point P. t0 Calculate the origin and the projection point P. t0 The vectors between them are normalized and used as the x-axis of the two-dimensional coordinate system;

[0106] Then the vector along the x-axis can be expressed as: X = (P t0 .xP ta .x, P t0 .yP ta .y, P t0 .zP ta .z);

[0107] The normal vector of plane E is W, so the y-axis can be obtained. The vector of the y-axis can be expressed as: Y = X × W;

[0108] (4) Calculate the coordinates of each projection point in the two-dimensional coordinate system;

[0109] Calculate the centroid P of each projection point ta With each projection point P tj The vector V between j :

[0110] V j =(P tj .xP ta .x, P tj .yP ta .y, P tj .zP ta .z)

[0111] Therefore, the coordinates P of each projection point in the two-dimensional coordinate system can be calculated. tj2d (x,y):

[0112] P tj2d x = V j .x*X.x+V j .y*X.y+V j .z*Xz

[0113] P tj2d .y=V j .x*Y.y+V j .y*Y.y+V j .z*Yz

[0114] Among them, P tj2d.x P tj2d.y These are the two coordinate values ​​of the projection point in the two-dimensional coordinate system; V j .x、V j .y、V j .z represents vector V j The three coordinate values ​​of the calibration device coordinate system; Xx, Xy, and Xz are the three coordinate values ​​of the vectors along the x-axis in the calibration device coordinate system; Yx, Yy, and Yz are the three coordinate values ​​of the vectors along the y-axis in the calibration device coordinate system.

[0115] (5) Perform planar circle fitting on each projection point in the two-dimensional spatial coordinate system obtained in step (4), and calculate the center coordinates P of the fitted two-dimensional planar circle. tc2d ;

[0116] In a two-dimensional coordinate system, the least squares method is used to fit a plane circle to each projection point. The fitted plane circle is denoted as the fitted circle F, and the coordinates P of the center of the fitted circle F are calculated.tc2d .

[0117] (6) Transform the center coordinates of the fitted circle F in the two-dimensional spatial coordinate system obtained in step (5) to the calibration device coordinate system to obtain the center coordinates of the fitted circle F in three-dimensional space.

[0118] (61) From step (5), we know that the center coordinates P of the fitted circle F are... tc2d The matrix is ​​represented as Z1(P) tc2d .x,P tc2d .y,0,1);

[0119] (62) Based on the two-dimensional spatial coordinate system, the normal vector W of plane E, and the centroid P of each projection point ta Construct a transformation matrix Z, initialized as a 4x4 identity matrix, and reassign values ​​to its elements:

[0120] Z(0,0)=X(0), Z(1,0)=X(1), Z(2,0)=X(2);

[0121] Z(0,1)=Y(0), Z(1,1)=Y(1), Z(2,1)=Y(2);

[0122] Z(0,2)=W(0), Z(1,2)=W(1), Z(2,2)=W(2);

[0123] Z(0,3)=P ta .x,Z(1,3)=P ta .y,Z(2,3)=P ta .z;

[0124] Where X(0), X(1), and X(2) are the components of the vector of the x-axis of the two-dimensional spatial coordinate system in the x, y, and z directions of the calibration device coordinate system, respectively; Y(0), Y(1), and Y(2) are the components of the vector of the y-axis of the two-dimensional spatial coordinate system in the x, y, and z directions of the calibration device coordinate system, respectively; W(0), W(1), and W(2) are the components of the normal vector W of the plane containing the spatial circle in the x, y, and z directions of the calibration device coordinate system, respectively.

[0125] (63) The center coordinates of the fitted circle F in the calibration device coordinate system can be calculated according to steps (61) and (62);

[0126] The matrix representation Z2(P) of the center coordinates of the fitted circle F in the calibration device coordinate system is obtained by calculating steps (61) and (62). tc3d .x,P tc3d .y,P tc3d .z,1), Z2=Z*Z1;

[0127] Therefore, the coordinates P of the center of the fitted circle F in the coordinate system of the calibration device can be obtained. tc3d That is, the coordinates of the center of the fitted circle F in three-dimensional space are obtained;

[0128] (7) Obtain the direction vector of the instrument axis according to the normal vector W of the plane E obtained in step (1), obtain the axis center of the instrument axis according to the center coordinates of the fitted circle F in three-dimensional space obtained in step (6), and then complete the calibration of the instrument axis in the calibration device coordinate system. Then, according to the transformation relationship between the instrument coordinate system and the calibration device coordinate system obtained in real time, complete the calibration of the instrument axis in the instrument coordinate system.

[0129] S4. End-effector calibration;

[0130] S33 has completed the calibration of the instrument axis in the instrument coordinate system, and the linear equation corresponding to the instrument axis can be obtained. By placing the end of the surgical instrument against any surface of the carrier, the pose of that surface of the carrier in the calibration device coordinate system can be determined. Based on the intersection point between the calculated linear line corresponding to the instrument axis and the plane against which the end of the surgical instrument is abutted, the position of the end of the surgical instrument in the calibration device coordinate system can be calculated. Then, through coordinate system transformation, the position of the end of the surgical instrument in the instrument coordinate system can be obtained, that is, the pose transformation relationship of the end of the surgical instrument relative to the surgical instrument itself can be obtained.

[0131] Furthermore, the present invention also provides a calibration method for instruments with a thin cylindrical shaft. The calibration holes corresponding to the shaft of such surgical instruments require high precision and are subject to errors during processing. Therefore, the present invention provides a V-groove on the carrier 1 of the calibration device to accommodate the instrument shaft. The instrument shaft of the thin cylindrical instrument is set in the V-groove and rotates. The navigation device acquires the position and pose transformation relationship between the surgical instrument and the calibration device in real time, thereby obtaining the position and pose transformation relationship between the surgical instrument and the calibration device at different times. The subsequent steps are the same as those described in S3 and S4 above.

[0132] Similarly, the calibration of the end of this type of surgical instrument is the same as described above.

[0133] The present invention also provides a calibration method for surgical instruments with tapered ends, the calibration of such surgical instruments includes the following steps:

[0134] The motion trajectory of the second tracer ball is treated as a sphere rotating around a certain point. Spherical fitting is performed on the motion trajectory of each second tracer ball, and the center of the fitted ball corresponding to one of the second tracer balls is selected as the position of the end of the surgical instrument in the instrument coordinate system. Thus, the pose transformation relationship of the end of the surgical instrument relative to the surgical instrument itself is obtained.

[0135] The center of the fitted sphere corresponding to one of the second tracer spheres is obtained as follows:

[0136] The average distance between the trajectory point of each second tracer ball's center at different times and its corresponding fitted ball is calculated as the second fitting error. The center of the fitted ball corresponding to the second tracer ball with the smallest second fitting error is selected as the position of the surgical instrument's end in the instrument coordinate system.

[0137] This invention designs a calibration device that carries a tracer ball for tracking. The calibration device is equipped with calibration holes and / or V-grooves adapted to surgical instruments of different diameters. By controlling the rotation of the surgical instrument placed within the calibration hole or V-groove around its axis, and using a navigation device to acquire real-time data on the surgical instrument and the tracer ball on the calibration device, the axis center and axial direction of the instrument are obtained by fitting the trajectory of the tracer ball, thus determining the instrument axis. Then, by having the end of the surgical instrument abut against any surface of the calibration device, the positional transformation relationship of the end of the surgical instrument relative to the instrument itself is obtained through the intersection of the instrument axis and the surface, completing the instrument calibration. This invention eliminates the need for a coordinate measuring machine; instrument calibration can be completed solely through a navigation device. It is not only simple to operate but also highly real-time, allowing for real-time calibration during surgery.

[0138] In addition, the present invention provides a special instrument calibration method for surgical instruments with a tapered end, which results in more accurate calibration results.

[0139] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations (such as quantity, shape, position, etc.) can be made to the technical solution of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A method for calibrating surgical instruments, characterized in that, include: S1. Place the instrument axis of the surgical instrument in the calibration space of a calibration device, wherein the calibration space is adapted to the instrument axis of the surgical instrument; S2. Control the surgical instruments to rotate around their instrument axis, and use navigation equipment to identify the positions of the tracers set on the surgical instruments and calibration devices in real time to obtain the position and pose transformation relationship between the two. S3. Based on the trajectory fitting plane of the tracer on the surgical instrument at different times, the normal vector of the corresponding fitting plane is obtained as the axis of the surgical instrument. The center of the corresponding circle is obtained by fitting the projection points of the trajectory points to the fitting plane as the axis of the surgical instrument, and thus the axis of the surgical instrument is obtained. include: S31. The tracer includes a plurality of tracer balls, and a plane is fitted according to the trajectory points of the center of each tracer ball on the surgical instrument at different times. S32. Calculate the fitting error of each of the fitting planes, and select the tracer ball with the smallest fitting error as the reference tracer ball; S33. Perform circle fitting on the projection points from the trajectory points of the center of the reference tracer sphere to its corresponding fitting plane, take the center of the circle fitting as the axis of the surgical instrument, and take the normal vector of the fitting plane corresponding to the trajectory points of the center of the reference tracer sphere as the axis of the surgical instrument to obtain the instrument axis of the surgical instrument. In step S33, the trajectory point of the center of the reference tracer sphere to the projection point of its corresponding fitting plane is subjected to circular fitting, and the center of the fitted circle is used as the axis of the surgical instrument. (1) Calculate the normal vector of the fitting plane corresponding to the trajectory point of the center of the reference tracer sphere; (2) Calculate the projection points of the trajectory points of the reference tracer ball obtained in step (1) onto the corresponding fitting plane; (3) Calculate the centroid of each projection point obtained in step (2), and construct a two-dimensional spatial coordinate system on the fitting plane corresponding to the trajectory point of the reference tracer sphere, with the centroid of each projection point as the origin; (4) Calculate the coordinates of each projection point in the two-dimensional coordinate system based on the vector between the centroid of each projection point and the projection point itself; (5) Perform circle fitting on each projection point in the two-dimensional spatial coordinate system obtained in step (4), and calculate the two-dimensional coordinates of the center of the fitted circle; (6) Based on the two-dimensional spatial coordinate system, the normal vector of the fitting plane corresponding to the trajectory point of the center of the reference tracer sphere, and the centroid of each projection point, construct a transformation matrix to transform the two-dimensional coordinates of the center of the fitting circle obtained in step (5) to three-dimensional space, and obtain the three-dimensional coordinates of the center of the fitting circle. S4. Place the end of the surgical instrument against any surface of the calibration device, and combine S2 and S3 to obtain the positional transformation relationship of the intersection of the instrument axis of the surgical instrument and the surface with respect to the surgical instrument, thereby obtaining the positional transformation relationship of the end of the surgical instrument with respect to the surgical instrument.

2. The surgical instrument calibration method according to claim 1, characterized in that, In step S3, the method for calculating the projection point is as follows: ； ； ； ； Among them, P tj .x、P tj .y、P tj .z represents the trajectory point P bj The projection point P of the fitting plane corresponding to the trajectory point to the center of the reference tracer sphere tj The three coordinate values ​​of Px, Py, and Pz are the three coordinate values ​​of any point P on the fitting plane corresponding to the trajectory point of the center of the reference tracer sphere; the three coordinate values ​​of Wx, Wy, and Wz are the three coordinate values ​​of the normal vector W of the fitting plane corresponding to the trajectory point of the center of the reference tracer sphere; P bj .x、P bj .y、P bj .z represents the trajectory point P bj The three coordinate values.

3. The surgical instrument calibration method according to claim 1, characterized in that, In step S3, the construction of the two-dimensional spatial coordinate system is specifically as follows: taking the centroid of each projection point as the origin, calculating the vector between the first projection point and the origin and normalizing it as the x-axis, and taking the cross product of the normal vector of the fitting plane corresponding to the trajectory point of the reference tracer sphere and the vector containing the x-axis as the y-axis, and constructing a two-dimensional spatial coordinate system on the fitting plane corresponding to the trajectory point of the reference tracer sphere.

4. The surgical instrument calibration method according to claim 1, characterized in that, In step S3, the coordinates of each projection point in the two-dimensional coordinate system are calculated based on the vector between the centroid of each projection point and the projection point itself. Specifically: Calculate the centroid P of each projection point ta With each projection point P tj The vector V between j : V j =(P tj .x-P ta .x,P tj .y-P ta .y,P tj .z-P ta .z); Therefore, the coordinates P of each projection point in the two-dimensional coordinate system can be calculated. tj2d (x,y): ； ； Among them, P tj2d.x P tj2d.y These are the two coordinate values ​​of the projection point in the two-dimensional coordinate system; V j .x、V j .y、V j .z represents vector V j The three coordinates in three-dimensional space; Xx, Xy, Xz are the three coordinates of the vector of the x-axis in the two-dimensional coordinate system in three-dimensional space; Yx, Yy, Yz are the three coordinates of the vector of the y-axis in the two-dimensional coordinate system in three-dimensional space.

5. The surgical instrument calibration method according to claim 1, characterized in that, In step S3, a transformation matrix is ​​constructed based on the two-dimensional spatial coordinate system, the normal vector of the fitting plane corresponding to the trajectory point of the reference tracer sphere, and the centroid of each projection point. Specifically: The transformation matrix Z is initialized as a 4x4 identity matrix, and its elements are reassigned: Z(0,0)=X(0), Z(1,0)=X(1), Z(2,0)=X(2); Z(0,1)=Y(0), Z(1,1)=Y(1), Z(2,1)=Y(2); Z(0,2)=W(0), Z(1,2)=W(1), Z(2,2)=W(2); Z(0,3)=P ta .x,Z(1,3)=P ta .y,Z(2,3)=P ta .z; Wherein, X(0), X(1), and X(2) are the components of the x-axis vector of the two-dimensional coordinate system in the x, y, and z directions of the three-dimensional space; Y(0), Y(1), and Y(2) are the components of the y-axis vector of the two-dimensional coordinate system in the x, y, and z directions of the three-dimensional space; W(0), W(1), and W(2) are the components of the normal vector W of the fitting plane corresponding to the trajectory point of the center of the reference tracer sphere in the x, y, and z directions of the three-dimensional space.

6. The surgical instrument calibration method according to claim 1, characterized in that, In step S3, the tracer ball with the smallest fitting error is selected as the reference tracer ball. Specifically, the average distance from the trajectory point of each tracer ball's center on the surgical instrument to its corresponding fitting plane is calculated as the fitting error, and the tracer ball with the smallest average distance is selected as the reference tracer ball.

7. The surgical instrument calibration method according to claim 1, characterized in that, In S1, the calibration space is a plurality of calibration holes adapted to the instrument shafts of surgical instruments of different diameters or a V-groove formed on the surface of the calibration device for accommodating the instrument shafts of the surgical instruments.

8. The surgical instrument calibration method according to claim 1, characterized in that, In step S2, the navigation device identifies the surgical instruments and the tracer balls on the calibration device respectively, and constructs the instrument coordinate system and the calibration device coordinate system with the corresponding tracer ball positions. Based on this, the transformation relationship between the instrument coordinate system and the calibration device coordinate system is calculated, that is, the pose transformation relationship between the surgical instruments and the calibration device is obtained.

9. A surgical instrument calibration system, characterized in that, include: A calibration device includes a carrier on which a first tracer is mounted, and a calibration space on the carrier that corresponds to and mates with the instrument axis of a surgical instrument. Surgical instruments, equipped with a second tracer; A navigation device is used to identify the pose of the first tracer and the second tracer in real time during the process of the surgical instrument being set in the calibration space and rotating about its instrument axis, and when the end of the surgical instrument abuts against any surface of the calibration device. The processing device acquires the pose identified by the navigation device, and then obtains the pose transformation relationship between the surgical instrument and the calibration device. Based on the trajectory of the center of each tracer ball of the first tracer at different times, it fits a plane, calculates the fitting error of each fitting plane, selects the tracer ball with the smallest fitting error as the reference tracer ball, calculates the normal vector of the fitting plane corresponding to the trajectory point of the center of the reference tracer ball, calculates the projection point from the trajectory point of the center of the reference tracer ball to its corresponding fitting plane, and constructs a two-dimensional coordinate system on the corresponding fitting plane using the centroid of each projection point as the origin. In a 3D coordinate system, the coordinates of each projection point in the 2D coordinate system are calculated based on the vector between the centroid of each projection point and the projection point itself. A planar circle is fitted to each projection point, and the 2D coordinates of the center of the fitted circle are calculated. A transformation matrix is ​​constructed by combining the normal vector of the fitting plane corresponding to the trajectory point of the reference tracer sphere and the centroid of each projection point. The 2D coordinates of the center of the fitted circle are transformed to 3D space, and the 3D coordinates of the center of the fitted circle are used as the axis of the surgical instrument. The normal vector of the fitting plane corresponding to the trajectory point of the reference tracer sphere is used as the axis of the surgical instrument, thereby obtaining the instrument axis of the surgical instrument. When the end of the surgical instrument abuts against any surface of the calibration device, the processing device calculates the intersection point of the instrument axis and the surface of the calibration device, and combines the pose transformation relationship between the surgical instrument and the calibration device to obtain the pose transformation relationship of the end of the surgical instrument relative to the surgical instrument.

10. The surgical instrument calibration system according to claim 9, characterized in that, The calibration device also has a tapered hole adapted to the end of the surgical instrument. The end of the surgical instrument is placed in the tapered hole and can rotate around its end at any angle. The processing device acquires the position of the tracker obtained by the navigation device, performs spherical fitting on the motion trajectory of the tracker at different times, and obtains the position of the end of the surgical instrument as the center of the sphere, thereby obtaining the pose transformation relationship of the end of the surgical instrument relative to the surgical instrument.

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