A robot-based lamina cutting trajectory auxiliary planning system

Abstract

The present invention discloses a robot-based lamina cutting trajectory auxiliary planning system, which belongs to the field of artificial intelligence. The system includes a robot subsystem and a trajectory auxiliary planning subsystem, wherein the trajectory auxiliary planning subsystem integrates a trajectory information acquisition module, a trajectory generation module, a trajectory parameter prediction module and a trajectory planning module; the robot subsystem includes a six-degree-of-freedom mechanical arm, an optical positioner, and an optical tracking marker; the trajectory information acquisition module is used to establish a mapping relationship between an optical measurement space and a robot space, and obtain the cutting trajectory information of an artificial lamina in the robot space; the trajectory generation module is used to convert the cutting trajectory information into a motion trajectory of the robot; the trajectory parameter prediction module is used to establish a trajectory parameter prediction model; and the trajectory planning module is used to perform robot trajectory planning based on the predicted trajectory parameters. The present invention improves the robot's cutting skills for the personalized lamina cutting process, and improves the accuracy and efficiency of lamina cutting and forming.

Description

Technical Field

[0001] The invention belongs to the technical field of artificial intelligence, and in particular relates to a robot-based lamina cutting trajectory auxiliary planning system. Background Art

[0002] At present, researchers have developed active, semi-active, passive, collaborative and remote-operated robot systems to perform bone cutting tasks using advanced robotics and image navigation technologies. Robotic navigation technology can further expand vision and operation skills and help reduce bone tissue damage. Traditional orthopedic robots use CT image navigation systems to generate robot cutting trajectories. However, the accuracy of CT image navigation depends on the accuracy of medical image registration and positioning. The cutting displacement and deformation of bones during cutting will reduce the surgical accuracy of the system's planned trajectory. The admittance-controlled robot has the ability to flexibly follow the operator's traction, and the virtual fixture ensures the safety of cutting to a certain extent. However, for high-risk operations, its positioning accuracy still depends on the operator's experience. At present, orthopedic robots cannot dynamically adapt to unstructured working environments with large individual differences. The cutting trajectory is heavily dependent on human design, the bone layer cutting trajectory is too programmed, and the cutting process lacks a cutting skill learning mechanism. Conventional planning methods have obvious limitations in ensuring the cutting accuracy and safety of robot execution. Therefore, it is particularly necessary to improve the robot's processing accuracy and cutting skills for personalized lamina cutting. The method of robot's personalized lamina cutting trajectory for patients under skill learning needs to be further studied. Summary of the invention

[0003] In view of the above problems existing in the prior art, the present invention proposes a robot-based lamina cutting trajectory auxiliary planning system, which has a reasonable design, solves the shortcomings of the prior art and has good effects.

[0004] A robot-based laminectomy trajectory auxiliary planning system comprises a robot subsystem and a trajectory auxiliary planning subsystem, wherein the trajectory auxiliary planning subsystem integrates a trajectory information acquisition module, a trajectory generation module, a trajectory parameter prediction module and a trajectory planning module;

[0005] The robot subsystem includes a robot, an optical locator and an optical tracking marker. The robot is provided with a terminal surgical instrument, which includes a ball milling cutter, a DC brushless motor and a connector. The optical tracking marker is fixed on the connector. The optical locator and the optical tracking marker are used to record the trajectory of the operator operating the terminal surgical instrument to cut the artificial vertebral cutting area.

[0006] The trajectory information acquisition module is used to establish a mapping relationship between the optical measurement space and the robot space, obtain the original point cloud information of the lamina cutting in the optical measurement space, and perform preprocessing, curve fitting and parameterized discrete processing, so as to obtain the cutting trajectory information of the artificial lamina in the robot space;

[0007] The trajectory generation module is used to convert the cutting trajectory information into the motion trajectory of the robot;

[0008] The trajectory parameter prediction module is used to establish a trajectory parameter prediction model using a BP neural network;

[0009] The trajectory planning module is used to perform trajectory planning of the robot based on the predicted trajectory parameters, including obtaining key points of the cutting trajectory and optimizing the turning points of the cutting trajectory.

[0010] Furthermore, in the trajectory information acquisition module, a robot base coordinate system {B}, a robot flange coordinate system {E}, an optical surgical instrument coordinate system {O}, and an optical tracking marker coordinate system {P} are established;

[0011] Solve the pose transformation matrix between the surgical instrument coordinate system {O} and the robot flange coordinate system {E} O T E , specifically including:

[0012] The four-point method is used for position calibration, so that the ball milling cutter touches the fixed reference point N on the calibration block in four different postures to ensure that the position of the calibration block does not change, thereby ensuring that the position of the reference point N on the calibration block remains unchanged;

[0013] The positional relationship between the surgical instrument coordinate system and the robot flange coordinate system is:

[0014]

[0015] in,( E R B )1、( E R B )2、( E R B )3、( E R B )4 are the rotation matrices between the robot flange coordinate system and the robot base coordinate system corresponding to the four different postures, ( E P B )1、( E P B )2、( E P B )3、( E P B)4 are the translation matrices between the robot flange coordinate system and the robot base coordinate system corresponding to the four different postures;

[0016] Four different postures E R B , E P B Substituting into formula (1), we get O P E The value of

[0017] The "Z / X direction method" is used for posture calibration. First, the robot end surgical instrument is controlled to move a certain distance along the determined positive direction of the X axis, and the transformation matrix between the robot flange coordinate system and the robot base coordinate system is recorded ( E T B ) x , where the rotation matrix is ​​recorded as ( E R B ) x , the translation matrix is ​​recorded as ( E P B ) x , and then move a certain distance along the determined positive direction of the Z axis, and record the transformation matrix between the robot flange coordinate system and the robot base coordinate system here ( E T B ) z , where the rotation matrix is ​​recorded as ( E R B ) z , the translation matrix is ​​recorded as ( E P B ) z ;

[0018] By fixing the reference point and the transformation matrix ( E T B ) x The pose point at determines the vector in the positive direction of the X-axis of the surgical instrument coordinate system B v (x) for:

[0019] B v (x) =( E R B ) x O P E -( E R B ) n O P E +( E P B ) x -( E P B) n ; (11)

[0020] in,( E R B ) n is the rotation matrix between the robot flange coordinate system at the fixed reference point and the robot base coordinate system, ( E P B ) n is the translation matrix between the robot flange coordinate system at the fixed reference point and the robot base coordinate system;

[0021] The vector in the positive direction of the Z axis is:

[0022] B v (z) =( E R B ) z O P E -( E R B ) n O P E +( E P B ) z -( E P B ) n ; (12)

[0023] The orthogonality between the X-axis and Z-axis of the surgical instrument coordinate system can be used to obtain the vector in the positive direction of the Y-axis of the surgical instrument coordinate system. B v (y) :

[0024] B v (y) = B v (z) × B v (x) ; (13)

[0025] After obtaining the axial vectors of the three axes, they are normalized to obtain the spatial posture transformation matrix of the surgical instrument relative to the robot flange.

[0026] Furthermore, in the trajectory information acquisition module, a posture transformation matrix between the surgical instrument coordinate system and the optical tracking marker coordinate system is established. P T O , specifically including:

[0027] The end surgical instrument with optical tracking marker is rotated around a fixed point, and the rotation angle is 30-45° with the vertical line of the rotation point surface. Multiple different position point information is collected, and the corresponding rotation matrix R is calculated for each point. mk and the translation matrix T mk The pose matrix composed of k represents the kth position point, and 1≤k≤n;

[0028] Set the offset of the origin O of the surgical instrument coordinate system in the optical tracking marker coordinate system to X = (x, y, z) T , when rotating around a fixed reference point, the pose matrix expression of the optical tracking marker obtained by the optical positioning system is:

[0029] R m1 X+T m1 =R m2 X+T m2 =……R mn X+T mn ; (14)

[0030] The following formula is obtained based on two sets of data collected at different times:

[0031] X k =(R mk -R m(k+1) ) -1 (T m(k+1) -T mk ), k is 1, 2, 3, ..., n-1; (15)

[0032] X k Solve for the average value:

[0033]

[0034] Since the optical positioning system can directly obtain the position information of the optical tracking marker, the values ​​of n-1 surgical instrument offsets X are obtained, and the offset X between the end of the surgical instrument and the optical tracking marker is obtained by calculating the average value;

[0035] The optical locator is used to obtain the position information of the optical tracking marker in real time, thereby obtaining the position matrix of the surgical instrument in the optical measurement coordinate system; the recorded position information is converted to the robot base coordinate system through the conversion relationship between various coordinate systems, so that the robot can obtain the operator's lamina cutting trajectory information;

[0036] Preprocessing includes using voxel rasterization method to simplify the original point cloud data, using statistical filtering method to reduce noise, and removing noise points and outliers in the point cloud data;

[0037] Then, the NURBS curve fitting method is used to fit the curve of the point cloud data. Finally, the curve is discretized through the toolbox in the MATLAB software, and the required robot cutting point cloud coordinate information is obtained.

[0038] Furthermore, in the trajectory generation module, a point cloud set P is randomly selected from the robot cutting point cloud data, and any point p in the set P is ij As the current cutting point, the position vector of this point is p and the normal vector is v n ; Take the direction of the line connecting the current cutting point and the next cutting point as the tangent vector, and use v t Indicates that the tangent vector is the direction of the surgical instrument during the cutting process, that is, the direction in which the ball-end milling cutter moves; given a vector v e , and satisfy the cross product v e =v t ×v n ; Establish cutting processing point p ij is the coordinate origin, v n , v t , v e The cutting point coordinate system {p ij}; The conversion between the cutting point coordinate system and the robot base coordinate system is realized through matrix transformation. for:

[0039]

[0040] After completing the above coordinate system conversion, the point cloud data information is converted into the robot posture, and the robot posture information is obtained as follows:

[0041]

[0042] In the formula, is the cutting point p ij The robot pose matrix, O T E is the transformation matrix between the robot flange coordinate system and the end surgical instrument coordinate system, is the transformation matrix between the surgical instrument coordinate system and the cutting point coordinate system. When the robot cuts the lamina, the surgical instrument coordinate system and the cutting point coordinate system coincide with each other, that is, O T p =I, I is the unit matrix; the robot's posture matrix is:

[0043]

[0044]

[0045] In the formula, Γ -1is the inverse kinematics model of the robot, θ=(θ1θ2...θ6) is the rotation angle of each joint of the robot; the above formula is used to obtain the robot processing posture information corresponding to the cutting trajectory point, and the joint rotation angle of the robot is calculated through inverse kinematics, so that the robot reaches the predetermined cutting trajectory point position in sequence, and each cutting trajectory point is connected in series to generate the trajectory of the robot cutting the lamina.

[0046] Furthermore, in the trajectory parameter prediction module, the trajectory parameter prediction model includes an input layer, a hidden layer and an output layer. The input layer includes two neurons, and the input quantities of the input layer are the width X0 and the depth D0 of the personalized laminectomy area of ​​the given patient; the output layer includes two neurons, which are the lateral cutting trajectory line spacing r i The number h and the longitudinal cutting depth d j The number of layers is c; the hidden layer is a single hidden layer, which contains 9 neurons; tansig is selected as the transfer function between the input layer and the hidden layer, purelin is selected as the transfer function between the hidden layer and the output layer, and the trainlm algorithm is selected as the training function of the neural network; and the learning rate of the neural network is set to 0.01;

[0047] 3D modeling and printing were performed based on the vertebral imaging data information of different patients. The 3D printed vertebral model was used as the experimental object to determine the cutting area. The robot was dragged to perform the cutting experiment. The cutting trajectory information of the artificial vertebral plate in the robot space was obtained through the mapping relationship between the optical measurement space and the robot space. This process was repeated to collect several groups of personalized sample data to form a training set.

[0048] Furthermore, in the trajectory planning module, the cutting trajectory parameters h and c are obtained by prediction, and the average value of the travel distance is calculated. and the average value of single cutting depth The expression is:

[0049]

[0050] The 3D printed personalized vertebra is placed in the optical measurement space, and the optical probe tool is operated to determine the boundary of the cutting area, so as to obtain the key point information in the optical measurement coordinate system; then, according to the mapping relationship between the optical positioning system and the robot, the key point information obtained by the probe tool is converted to the robot space. The four key points are the four vertices of the rectangular cutting area, which are recorded as P1, P2, P3 and P4, with P1 as the starting point and P4 as the end point;

[0051] For the turning point k in the trajectory ij Solve, ij represents the jth inflection point of the i-th layer except P2 and P3, calculate the inflection point coordinate k of the first layer 1j , if k1j Located in vector On, P2 and k 1j The distance between them is r', then k 1j The coordinate values ​​are:

[0052]

[0053] In the formula, express The magnitude of a vector;

[0054] If k 1j Located in vector On, P1 and k 1j The distance between them is r", then k 1j The coordinate values ​​are:

[0055]

[0056] The inflection point coordinates k of the second layer 2j The calculation process is: determine the normal vector of the cutting surface based on the known points, select two non-collinear vectors and Calculate the normal vector and then normalize it. The expression is:

[0057]

[0058]

[0059] in, is the normal vector, is the magnitude of the normal vector, is the unit normal vector;

[0060] The first layer P1, P2, P3, P4 and k ij The coordinate points are offset along the normal vector direction, and the coordinates of each point in the second layer after offset are:

[0061]

[0062] Among them, k 2j is the coordinate of the inflection point of the second layer, is the second layer vertex coordinate;

[0063] Calculate all inflection points k in turn ij and the coordinates of the vertices;

[0064] The robot's cutting trajectory planning is completed based on the solved key position point parameters.

[0065] Furthermore, in the trajectory planning module, the trajectory at the corner is circularized so that the robot generates a smooth cutting trajectory; the specific process of circularization of the corner at P2 is as follows:

[0066] First, the turning angle θ1 of the path and the straight line-arc transition points Pt1 and Pt2 are solved, and the expression is:

[0067]

[0068]

[0069] In the formula, r1 is the transition arc radius, s1 is the arc radius adjustment parameter, and the adjustment parameter s i Used to adjust the radius of the arc trajectory and set different adjustment parameters according to the specific trajectory;

[0070] Solve for transition points Pt1 and Pt2:

[0071]

[0072] Perform spatial linear interpolation on the portion between points P1 and Pt1 to complete the trajectory planning of this segment;

[0073] Center O1 and path segment length l i Solve, l1 is the path length between P1 and Pt1, l2 is the arc length between Pt1 and Pt2, M1 is the midpoint of Pt1 and Pt2, and it is on the angle bisector, so we get:

[0074]

[0075] In ΔP2P t1 In O1, according to the trigonometric function relationship, we get:

[0076]

[0077] Finally, find the segment length l i :

[0078]

[0079] The part between Pt1 and Pt2 is processed by arc transition;

[0080] For Pt2 to k 11 The part between the points is interpolated in space to complete the trajectory planning of this section, and the remaining corners are rounded.

[0081] Beneficial technical effects brought by the present invention:

[0082] The present invention uses an optical positioning system to establish a trajectory space mapping relationship, imitates the operator's manual lamina cutting method, and performs robot lamina cutting trajectory planning by fitting the cutting trajectory point cloud and other processes. Through the mapping relationship between manual cutting and robot cutting, the personalized lamina cutting trajectory is converted into the robot space. On this basis, a BP neural network model is established and combined with the trajectory feature parameters to realize the prediction of the lamina cutting trajectory. The robot completely inherits the doctor's cutting skills, realizes the transformation from "operational robot" to "skilled robot", improves the robot's cutting skills for the personalized lamina cutting process, and improves the accuracy and efficiency of personalized lamina cutting. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 A schematic diagram of a robot-based lamina cutting trajectory auxiliary planning system in the present invention;

[0084] Figure 2 It is a position deviation effect diagram under the spatial mapping relationship in the present invention;

[0085] Figure 3 Schematic diagram of the 6-DOF robot configuration in the present invention;

[0086] Figure 4 This is a comparison diagram of the cutting trajectories of the robot and the doctor in the present invention;

[0087] Figure 5 It is a schematic diagram of a local cutting trajectory in the present invention;

[0088] Figure 6 It is a schematic diagram of the rounding analysis of the cutting trajectory corners in the present invention; DETAILED DESCRIPTION

[0089] The specific implementation of the present invention is further described below in conjunction with specific embodiments:

[0090] A robot-based lamina cutting trajectory auxiliary planning system, such as Figure 1 As shown, it includes a robot subsystem and a trajectory auxiliary planning subsystem, and the trajectory auxiliary planning subsystem integrates a trajectory information acquisition module, a trajectory generation module, a trajectory parameter prediction module and a trajectory planning module;

[0091] The robot subsystem includes a robot, an optical locator and an optical tracking marker. The robot is provided with a terminal surgical instrument, which includes a ball milling cutter, a DC brushless motor and a connector. The optical tracking marker is fixed on the connector. The optical locator and the optical tracking marker are used to record the trajectory of the operator operating the terminal surgical instrument to cut the artificial vertebral cutting area.

[0092] The trajectory information acquisition module is used to establish a mapping relationship between the optical measurement space and the robot space, obtain the original point cloud information of the lamina cutting in the optical measurement space, and perform preprocessing, curve fitting and parameterized discrete processing to obtain the cutting trajectory information of the artificial lamina in the robot space;

[0093] A trajectory generation module is used to convert cutting trajectory information into a motion trajectory of the robot;

[0094] A trajectory parameter prediction module is used to establish a trajectory parameter prediction model using a BP neural network;

[0095] The trajectory planning module is used to plan the robot's trajectory based on the predicted trajectory parameters, including obtaining the key points of the cutting trajectory and optimizing the turning points of the cutting trajectory.

[0096] Specifically, in the robot subsystem, the end surgical instrument also includes a connecting flange; in this embodiment, the orthopedic surgical robot uses a 6-DOF collaborative robot, including a six-axis robotic arm, an overall control box and a teaching pendant; the model of the optical locator is AP-STD-100;

[0097] Specifically, in the trajectory information acquisition module, the robot basic coordinate system {B}, the robot flange coordinate system {E}, the optical surgical instrument coordinate system {O}, and the optical tracking marker coordinate system {P} are established; among them, the robot basic coordinate system {B} is fixedly connected to the robot base and is the reference datum of other user coordinate systems; the robot flange coordinate system {E} is fixedly connected to the flange at the end of the robot and is the reference datum of other tool coordinate systems; the optical positioning tracking marker {P} is fixed on the cutting tool at the end of the robot.

[0098] Solve the pose transformation matrix between the surgical instrument coordinate system {O} and the robot flange coordinate system {E} O T E , specifically including:

[0099] The four-point method is used for position calibration, so that the ball milling cutter touches the fixed reference point N on the calibration block in four different postures. When the posture of the surgical instrument changes, the position of the calibration block is ensured not to change, thereby ensuring that the position of the reference point N on the calibration block remains unchanged;

[0100] When position calibration is performed through four posture transformations, the transformation relationship between the surgical instrument at the four reference points and the robot base coordinate system is:

[0101] ( O T B ) i =( E T B ) i · O TE ; (1)

[0102] From the above formula, we can get:

[0103]

[0104] In the formula, R represents the rotation matrix between the coordinate systems, and P represents the translation matrix between the coordinate systems;

[0105] Decomposing the last column of formula (2), we can get:

[0106] ( O P B ) i =( E R B ) i O P E +( E P B ) i ; (3)

[0107] Since the reference point N of the calibration block does not change, the spatial position under the four different postures remains unchanged, which means that the position vector of the origin of the surgical instrument coordinate system and the origin of the robot base coordinate system will not change. O P B To determine the constant value, combined with formula (3), the following relationship can be obtained:

[0108]

[0109] Arrange formula (4) to obtain its matrix form:

[0110]

[0111] Among them, the relative position of the robot flange and the surgical instrument O P E Determined during structural installation, obtained through robot kinematics E R B , E P B The coefficient matrix of the equation in the analysis formula (5) is a non-invertible matrix, and its form can be seen as A× O P E =b, it is necessary to pass the generalized inverse matrix A + Convert the above formula into the form of formula (6):

[0112] O P E =A + b; (6)

[0113] Since the rank of the coefficient matrix is ​​smaller than the rank of the augmented matrix, equation (5) is an inconsistent system of equations. O P E -b|| derive A + Satisfies the following relationship:

[0114] A + =(A T A) -1 ·A T ; (7)

[0115] Combining equations (6) and (7), the positional relationship between the surgical instrument coordinate system and the robot flange coordinate system is:

[0116]

[0117] in,( E R B )1、( E R B )2、( E R B )3、( E R B )4 are the rotation matrices between the robot flange coordinate system and the robot base coordinate system corresponding to the four different postures, ( E P B )1、( E P B )2、( E P B )3、( E P B )4 are the translation matrices between the robot flange coordinate system and the robot base coordinate system corresponding to the four different postures;

[0118] Four different postures E R B , E P B Substituting into formula (8), we get O P E The value of

[0119] The "Z / X direction method" is used for posture calibration. First, the robot end surgical instrument is controlled to move a certain distance along the determined positive direction of the X axis, and the transformation matrix between the robot flange coordinate system and the robot base coordinate system is recorded ( E T B ) x , where the rotation matrix is ​​recorded as ( E R B ) x , the translation matrix is ​​recorded as ( E PB ) x , and then move a certain distance along the determined positive direction of the Z axis, and record the transformation matrix between the robot flange coordinate system and the robot base coordinate system here ( E T B ) z , where the rotation matrix is ​​recorded as ( E R B ) z , the translation matrix is ​​recorded as ( E P B ) z ;

[0120] From formula (3), we get the equation:

[0121] ( O P B ) n =( E R B ) n O P E +( E P B ) n ; (9)

[0122] ( O P B ) x =( E R B ) x O P E +( E P B ) x ; (10)

[0123] By fixing the reference point and the transformation matrix ( E T B ) x The pose point at determines the vector in the positive direction of the X-axis of the surgical instrument coordinate system B v (x) for:

[0124] B v (x) =( O P B ) x -( O P B ) n =( E R B ) x O P E -( E R B )n O P E +( E P B ) x -( E P B ) n ; (11)

[0125] in,( E R B ) n is the rotation matrix between the robot flange coordinate system at the fixed reference point and the robot base coordinate system, ( E P B ) n is the translation matrix between the robot flange coordinate system at the fixed reference point and the robot base coordinate system;

[0126] The vector in the positive direction of the Z axis is:

[0127] B v (z) =( O P B ) z -( O P B ) n =( E R B ) z O P E -( E R B ) n O P E +( E P B ) z -( E P B ) n ; (12)

[0128] The orthogonality between the X-axis and Z-axis of the surgical instrument coordinate system can be used to obtain the vector in the positive direction of the Y-axis of the surgical instrument coordinate system. B v (y) :

[0129] B v (y) = B v (z) × B v (x) ; (13)

[0130] After obtaining the axial vectors of the three axes, they are normalized to obtain the spatial posture transformation matrix of the surgical instrument relative to the robot flange.

[0131] Specifically, in the trajectory information acquisition module, a posture transformation matrix between the surgical instrument coordinate system and the optical tracking marker coordinate system is established. P T O , specifically including:

[0132] The origin of the surgical instrument coordinate system is set at the tip of the spherical milling cutter, and the origin of the optical tracking marker coordinate system is located at the center of the marker; the end surgical instrument with the optical tracking marker is rotated around a fixed point, and the rotation angle is 30 to 45 degrees from the vertical line of the rotation point surface, and multiple different position point information is collected, and the corresponding rotation matrix R of each point is calculated. mk and the translation matrix T mk The pose matrix composed of k represents the kth position point, and 1≤k≤n;

[0133] Set the offset of the origin O of the surgical instrument coordinate system in the optical tracking marker coordinate system to X = (x, y, z) T , when rotating around a fixed reference point, the pose matrix expression of the optical tracking marker obtained by the optical positioning system is:

[0134] R m1 X+T m1 =R m2 X+T m2 =……R mn X+T mn ; (14)

[0135] The following formula is obtained based on two sets of data collected at different times:

[0136] X k =(R mk -R m(k+1) ) -1 (T m(k+1) -T mk ), k is 1, 2, 3, ..., n-1; (15)

[0137] X k Solve for the average value:

[0138]

[0139] Since the optical positioning system can directly obtain the position information of the optical tracking marker, the values ​​of n-1 surgical instrument offsets X can be obtained, and the offset X between the end of the surgical instrument and the optical tracking marker can be obtained by calculating the average value;

[0140] According to the robot configuration design parameters, the transformation relationship between the robot base coordinate system and the robot flange coordinate system is obtained through the robot forward and inverse kinematics, and the transformation matrix between the two coordinate systems can also be obtained. E T B Specifically, the link coordinate system is first established, the DH method is used to represent the relationship between the links, and the relative relationship between the robot flange coordinate system and the robot base coordinate system is represented by the operational relationship between the homogeneous transformation matrices; the pose transformation matrix between the optical tracking marker coordinate system and the optical measurement coordinate system M T P It can be obtained in real time through the calibration relationship between the two;

[0141] The optical positioning system is used to obtain the position and posture information of the optical tracking marker in real time, thereby obtaining the position and posture matrix of the surgical instrument in the optical measurement coordinate system; the recorded position and posture information is converted to the robot base coordinate system through the conversion relationship between various coordinate systems, so that the robot can obtain the operator's lamina cutting trajectory information;

[0142] Preprocessing includes using voxel rasterization method to simplify the original point cloud data, using statistical filtering method to reduce noise, and removing noise points and outliers in the point cloud data;

[0143] Then, the NURBS curve fitting method is used to fit the curve of the point cloud data. Finally, the curve is discretized through the toolbox in the MATLAB software, and the required robot cutting point cloud coordinate information is obtained.

[0144] In order to verify the accuracy of the optical measurement space mapping relationship established by the present invention and the accuracy of the robot's calibration points in the optical positioning system, a spatial mapping relationship accuracy verification experiment was designed. An optical probe tool was used to collect 10 groups of verification points under the optical positioning system, and the coordinate information of the verification points was recorded as the target position for the movement of the robot's end device. According to the optical measurement space mapping conversion relationship, the target position information in the robot space was calculated, and the robot was controlled to move to the target position according to the calculation results. The actual position of the robot's movement was recorded by an optical tracking marker and compared with the target position to verify the accuracy of the mapping relationship.

[0145] The measurement results are shown in Table 1. The error between the target position and the actual position is calculated using the Euclidean distance algorithm, and the average position deviation is calculated to be 0.558 mm. This mapping relationship basically meets the accuracy requirements of surgical positioning. The source of the error is that the spatial mapping relationship is calculated by multiple conversion processes, resulting in cumulative errors.

[0146] Table 1 Verification results of spatial mapping relationship accuracy

[0147]

[0148] According to the position deviation information in Table 1, the position deviation change diagrams of 10 sets of data are obtained, as shown in Figure 2 As shown. It can be seen from the figure that the position deviation change is relatively stable as a whole, but there are still small fluctuations. The main reason is that the positioning accuracy of the robot and the optical positioning system in different postures may fluctuate, and the target information collected in the optical positioning system using the optical probe tool is randomly selected, which will lead to unstable position errors. The spatial mapping relationship established by the present invention can meet the requirements of clinical lamina decompression surgery for orthopedic robot calibration accuracy and calibration efficiency, has good application value, and is prepared for the subsequent research on robot personalized lamina layered cutting trajectory planning.

[0149] Specifically, in the trajectory generation module, a point cloud set P is randomly selected from the robot cutting point cloud data, and any point p in the set P is ij As the current cutting point, the position vector of this point is p and the normal vector is v n ; Take the direction of the line connecting the current cutting point and the next cutting point as the tangent vector, and use v t Indicates that the tangent vector is the direction of the surgical instrument during the cutting process, that is, the direction in which the ball-end milling cutter moves; given a vector v e , and satisfy the cross product v e =v t ×v n ; Establish cutting processing point p ij is the coordinate origin, v n , v t , v e The cutting point coordinate system {p ij}; The conversion between the cutting point coordinate system and the robot base coordinate system is realized through matrix transformation. for:

[0150]

[0151] After completing the above coordinate system conversion, the point cloud data information is converted into the robot posture, and the robot posture information is obtained as follows:

[0152]

[0153] In the formula, is the cutting point p ij The robot pose matrix, O T E is the transformation matrix between the robot flange coordinate system and the end surgical instrument coordinate system, O T E It is known from the calibration of the tool coordinate system that is the transformation matrix between the surgical instrument coordinate system and the cutting point coordinate system. When the robot cuts the lamina, the surgical instrument coordinate system and the cutting point coordinate system coincide with each other, that is, O T p =I, I is the unit matrix; the robot's posture matrix is:

[0154]

[0155]

[0156] In the formula, Γ -1 is the inverse kinematics model of the robot, Θ = (θ1θ2 ... θ6) is the rotation angle of each joint of the robot; according to the configuration of the orthopedic robot, the DH coordinate system and DH parameter table are established to complete the solution of forward kinematics, and the analytical method is used to complete the solution of inverse kinematics. Inverse kinematics is to input the robot posture information to solve the joint angles of the six joints. The six joints include the base, shoulder, elbow, wrist 1, wrist 2, and wrist 3. Figure 3 As shown;

[0157] The robot processing posture information corresponding to the cutting trajectory point is obtained, and the robot's joint rotation angle is calculated through inverse kinematics, so that the robot can reach the predetermined cutting trajectory point position in sequence, and each cutting trajectory point is connected in series to generate the robot's cutting trajectory of the lamina.

[0158] Figure 4 This is a comparison between the robot's lamina cutting simulation trajectory and the doctor's cutting trajectory. It can be seen that the robot has reproduced the doctor's lamina cutting trajectory well. The error between the two is caused by factors such as the robot's calibration accuracy, point cloud preprocessing, and fitting. It can be further clearly seen that the robot's cutting simulation trajectory is smoother, indicating that while learning the doctor's trajectory, the robot also optimizes the accuracy of lamina cutting processing, thereby improving the safety of the operation. Through the robot lamina cutting trajectory planning method proposed in this chapter, the robot has better learned the doctor's cutting skills, and the rationality and effectiveness of the proposed solution have been verified through simulation.

[0159] Specifically, in the trajectory parameter prediction module, the trajectory parameter prediction model includes an input layer, a hidden layer and an output layer. The input layer contains two neurons, and the input quantities of the input layer are the width X0 and depth D0 of the personalized laminectomy area of ​​the given patient; the output layer contains two neurons, which are the horizontal cutting trajectory line spacing r i The number h and the longitudinal cutting depth d j The number of layers c;

[0160] The hidden layer is a single hidden layer. The optimal hidden layer node of the neural network is determined through empirical formulas and multiple debugging during the experiment. The mean square error changes significantly with the change of the number of hidden layer nodes. When the number of hidden layer nodes is 9, the mean square error reaches the minimum value, so the optimal number of hidden layer nodes is determined to be 9.

[0161] Select tansig as the transfer function between the input layer and the hidden layer, purelin as the transfer function between the hidden layer and the output layer, and trainlm algorithm as the training function of the neural network; and set the learning rate of the neural network to 0.01;

[0162] According to the vertebral imaging data information of different patients provided by the cooperative hospital, 3D modeling and printing preparation were performed, the cutting area was determined using the 3D printed vertebral model as the experimental object, and the robot was dragged to perform the cutting experiment. Through the mapping relationship between the optical measurement space and the robot space, the cutting trajectory information of the artificial vertebral plate in the robot space was obtained; the process was repeated to collect several groups of personalized sample data to form a training set. In this embodiment, a total of 118 groups of personalized sample data were collected, including 68 males and 50 females, aged between 42 and 73 years old, with an average age of (57.6±14.9) years old, and a disease course of 10-31 months, with an average of (17.5±6.3) months.

[0163] The training set randomly selects two-thirds of the data from all the data as the training set of the neural network, and one-third of the data as the training test set of the neural network. Through the training of sample data, the neural network can accurately predict the mapping relationship between the patient's cutting area parameters and h and c.

[0164] In the trajectory planning module, the cutting trajectory parameters h and c are obtained by prediction, and the average travel distance is calculated. and the average value of single cutting depth The expression is:

[0165]

[0166] In order to determine the coordinate information of the key points on the lamina cutting trajectory, the 3D printed personalized vertebra is placed in the optical measurement space, and the optical probe tool is operated to determine the boundary of the cutting area, so as to obtain the key point information in the optical measurement coordinate system; then, according to the mapping relationship between the optical positioning system and the robot, the key point information obtained by the probe tool is converted to the robot space. The four key points are the four vertices of the rectangular cutting area, which are recorded as P1, P2, P3 and P4. P1 is set as the starting point and P4 is set as the end point. Figure 5 As shown;

[0167] For the turning point k in the trajectory ijSolve, ij represents the jth inflection point of the i-th layer except P2 and P3. The number of inflection points depends on the prediction results of the neural network in the previous section. Calculate the inflection point coordinates k of the first layer 1j , if k 1j Located in vector On, P2 and k 1j The distance between them is r', then k 1j The coordinate values ​​are:

[0168]

[0169] In the formula, express The magnitude of a vector;

[0170] If k 1j Located in vector On, P1 and k 1j The distance between them is r", then k 1j The coordinate values ​​are:

[0171]

[0172] For example, solving for k 11 Coordinate values: Let the coordinates of P1, P2, P3, and P4 be (x1, y1, z1), (x2, y2, z2), (x3, y3, z3), and (x4, y4, z4), respectively. 11 for The first inflection point on the vector, P2 and k 11 The distance between the two is Solving for k 11 Coordinate values:

[0173]

[0174] Solving for the inflection point k 12 Coordinate values:

[0175]

[0176] Other inflection points k 1j The coordinate value of is the same as the above solution method. Then the single cutting depth The size of is used as the offset of the next layer of lamina cutting, that is, the offset is perpendicular to the cutting surface and downward. The coordinate information of each point after offset is obtained by the following method.

[0177] The inflection point coordinates k of the second layer 2j The calculation process is: determine the normal vector of the cutting surface based on the known points, select two non-collinear vectors and Calculate the normal vector and then normalize it. The expression is:

[0178]

[0179]

[0180] in, is the normal vector, is the magnitude of the normal vector, is the unit normal vector;

[0181] Since the direction of the normal vector is perpendicular to the cutting surface, the first layer P1, P2, P3, P4 and k ij The coordinate points are offset along the normal vector direction, and the coordinates of each point in the second layer after offset are:

[0182]

[0183] Among them, k 2j is the coordinate of the inflection point of the second layer, The second layer vertex coordinates

[0184] Calculate all inflection points k in turn ij and the coordinates of the vertices;

[0185] The robot's cutting trajectory planning is completed based on the solved key position point parameters.

[0186] In the trajectory planning module, the trajectory at the corner is circularized so that the robot can generate a smooth cutting trajectory. The specific process of circularization of the corner at P2 is as follows:

[0187] From P1, P2 and k 11 The schematic diagram of the adjacent trajectory inflection points is as follows: Figure 6 As shown, the purpose is to change the straight line trajectory at the inflection point into a circular arc transition trajectory. i 、r j are the center and radius of the transition arc, Pt i is the straight line-arc transition point, M i is the midpoint of the transition point, l i ,θ i , η are the segment path length, path turning angle and the bisector of the turning angle respectively.

[0188] First, the turning angle θ1 of the path and the straight line-arc transition points Pt1 and Pt2 are solved, and the expression is:

[0189]

[0190]

[0191] In the formula, r1 is the transition arc radius, s1 is the arc radius adjustment parameter, and the adjustment parameter s i It is used to adjust the radius of the arc trajectory and set different adjustment parameters according to the specific trajectory, so as to improve the cutting efficiency and reduce the impact of frequent starting and stopping on the robot.

[0192] Solve for transition points Pt1 and Pt2:

[0193]

[0194] Perform spatial linear interpolation on the portion between points P1 and Pt1 to complete the trajectory planning of this segment;

[0195] Center O1 and path segment length l i Solve, l1 is the path length between P1 and Pt1, l2 is the arc length between Pt1 and Pt2, M1 is the midpoint of Pt1 and Pt2, and it is on the angle bisector η, so we get:

[0196]

[0197] In ΔP2P t1 In O1, according to the trigonometric function relationship, we get:

[0198]

[0199] Finally, find the segment length l i :

[0200]

[0201] The part between Pt1 and Pt2 is processed by arc transition;

[0202] For Pt2 to k 11 The part between the points is interpolated in space to complete the trajectory planning of this section, and the remaining corners are rounded.

[0203] The working process of the whole system is as follows: first, the trajectory parameters are predicted by the trajectory parameter prediction model, and trajectory planning is performed; then the operator cuts on the artificial vertebra according to the planned trajectory to obtain the cutting trajectory, and finally the robot learns the trajectory.

[0204] 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 robot-based lamina cutting trajectory auxiliary planning system, characterized in that: It includes a robot subsystem and a trajectory auxiliary planning subsystem, wherein the trajectory auxiliary planning subsystem integrates a trajectory information acquisition module, a trajectory generation module, a trajectory parameter prediction module and a trajectory planning module; The robot subsystem includes a robot, an optical locator and an optical tracking marker. The robot is provided with a terminal surgical instrument, which includes a ball milling cutter, a DC brushless motor and a connector. The optical tracking marker is fixed on the connector. The optical locator and the optical tracking marker are used to record the trajectory of the operator operating the terminal surgical instrument to cut the artificial vertebral cutting area. The trajectory information acquisition module is used to establish a mapping relationship between the optical measurement space and the robot space, obtain the original point cloud information of the lamina cutting in the optical measurement space, and perform preprocessing, curve fitting and parameterized discrete processing, so as to obtain the cutting trajectory information of the artificial lamina in the robot space; The trajectory generation module is used to convert the cutting trajectory information into the motion trajectory of the robot; The trajectory parameter prediction module is used to establish a trajectory parameter prediction model using a BP neural network; The trajectory planning module is used to perform trajectory planning of the robot based on the predicted trajectory parameters, including obtaining key points of the cutting trajectory and optimizing the turning points of the cutting trajectory; In the trajectory information acquisition module, a robot base coordinate system {B}, a robot flange coordinate system {E}, an optical surgical instrument coordinate system {O}, and an optical tracking marker coordinate system {P} are established; Solve the pose transformation matrix between the surgical instrument coordinate system {O} and the robot flange coordinate system {E} O T E , specifically including: The four-point method is used for position calibration, so that the ball milling cutter touches the fixed reference point N on the calibration block in four different postures to ensure that the position of the calibration block does not change, thereby ensuring that the position of the reference point N on the calibration block remains unchanged; The positional relationship between the surgical instrument coordinate system and the robot flange coordinate system is: in,( E R B )1、( E R B )2、( E R B )3、( E R B )4 are the rotation matrices between the robot flange coordinate system and the robot base coordinate system corresponding to the four different postures, ( E P B )1、( E P B )2、( E P B )3、( E P B )4 are the translation matrices between the robot flange coordinate system and the robot base coordinate system corresponding to the four different postures; Four different postures E R B , E P B Substituting into formula (8), we get O P E The value of Select the "Z / X direction method" for posture calibration. First, control the robot end surgical instrument to move a certain distance along the determined positive direction of the X axis, and record the transformation matrix between the robot flange coordinate system and the robot base coordinate system ( E T B ) x , where the rotation matrix is ​​recorded as ( E R B ) x , the translation matrix is ​​recorded as ( E P B ) x , and then move a certain distance along the determined positive direction of the Z axis, and record the transformation matrix between the robot flange coordinate system and the robot base coordinate system here ( E T B ) z , where the rotation matrix is ​​recorded as ( E R B ) z , the translation matrix is ​​recorded as ( E P B ) z ; By fixing the reference point and the transformation matrix ( E T B ) x The pose point at determines the vector in the positive direction of the X-axis of the surgical instrument coordinate system B v (x) for: B v (x) =( E R B ) x O P E -( E R B ) n O P E +( E P B ) x -( E P B ) n ;(11) in,( E R B ) n is the rotation matrix between the robot flange coordinate system at the fixed reference point and the robot base coordinate system, ( E P B ) n is the translation matrix between the robot flange coordinate system at the fixed reference point and the robot base coordinate system; The vector in the positive direction of the Z axis is: B v (z) =( E R B ) z O P E -( E R B ) n O P E +( E P B ) z -( E P B ) n ;(12) The orthogonality between the X-axis and Z-axis of the surgical instrument coordinate system can be used to obtain the vector in the positive direction of the Y-axis of the surgical instrument coordinate system. B v (y) : B v (y) = B v (z) × B v (x) ;(13) After obtaining the axial vectors of the three axes, normalize them to obtain the spatial position transformation matrix of the surgical instrument relative to the robot flange; In the trajectory information acquisition module, a posture transformation matrix between the surgical instrument coordinate system and the optical tracking marker coordinate system is established. P T O , specifically including: The end surgical instrument with optical tracking marker is rotated around a fixed point, and the rotation angle is 30-45° with the vertical line of the surface of the rotation point. The information of multiple different position points is collected, and the corresponding rotation matrix R of each point is calculated. mk and the translation matrix T mk The pose matrix composed of k represents the kth position point, and 1≤k≤n; Set the offset of the origin O of the surgical instrument coordinate system in the optical tracking marker coordinate system to X = (x, y, z) T , when rotating around a fixed reference point, the pose matrix expression of the optical tracking marker obtained by the optical positioning system is: R m1 X+T m1 =R m2 X+T m2 =……R mn X+T mn ; (14) The following formula is obtained based on two sets of data collected at different times: X k =(R mk -R m(k+1) ) -1 (T m(k+1) -T mk ), k is 1, 2, 3, ..., n-1; (15) X k Solve for the average value: Since the optical positioning system can directly obtain the position information of the optical tracking marker, the values ​​of n-1 surgical instrument offsets X are obtained, and the offset X between the end of the surgical instrument and the optical tracking marker is obtained by calculating the average value; The optical locator is used to obtain the position information of the optical tracking marker in real time, thereby obtaining the position matrix of the surgical instrument in the optical measurement coordinate system; the recorded position information is converted to the robot base coordinate system through the conversion relationship between various coordinate systems, so that the robot can obtain the operator's lamina cutting trajectory information; Preprocessing includes using voxel rasterization method to simplify the original point cloud data, using statistical filtering method to reduce noise, and removing noise points and outliers in the point cloud data; Then, the NURBS curve fitting method is used to fit the curve of the point cloud data. Finally, the curve is discretized through the toolbox in the MATLAB software, and the required robot cutting point cloud coordinate information is obtained.

2. A robot-based lamina cutting trajectory auxiliary planning system according to claim 1, characterized in that: In the trajectory generation module, any point cloud set P is randomly selected from the robot cutting point cloud data, and any point p in the set P is ij As the current cutting point, the position vector of this point is p and the normal vector is v n ; Take the direction of the line connecting the current cutting point and the next cutting point as the tangent vector, and use v t Indicates that the tangent vector is the direction of the surgical instrument during the cutting process, that is, the direction in which the ball-end milling cutter moves; given a vector v e , and satisfy the cross product v e =v t ×v n ; Establish cutting processing point p ij is the coordinate origin, v n , v t , v e The cutting point coordinate system {p ij }; The conversion between the cutting point coordinate system and the robot base coordinate system is realized through matrix transformation. for: After completing the above coordinate system conversion, the point cloud data information is converted into the robot posture, and the robot posture information is obtained as follows: In the formula, is the cutting point p ij The robot pose matrix, O T E is the transformation matrix between the robot flange coordinate system and the end surgical instrument coordinate system, is the transformation matrix between the surgical instrument coordinate system and the cutting point coordinate system. When the robot cuts the lamina, the surgical instrument coordinate system and the cutting point coordinate system coincide with each other, that is, O T p =I, I is the unit matrix; the robot's posture matrix is: In the formula, Γ -1 is the inverse kinematics model of the robot, θ=(θ1θ2...θ6) is the rotation angle of each joint of the robot; the above formula is used to obtain the robot processing posture information corresponding to the cutting trajectory point, and the joint rotation angle of the robot is calculated through inverse kinematics, so that the robot reaches the predetermined cutting trajectory point position in sequence, and each cutting trajectory point is connected in series to generate the trajectory of the robot cutting the lamina.

3. The robot-based laminectomy trajectory auxiliary planning system according to claim 1, characterized in that: In the trajectory parameter prediction module, the trajectory parameter prediction model includes an input layer, a hidden layer and an output layer. The input layer contains two neurons, and the input quantities of the input layer are the width X0 and the depth D0 of the personalized laminectomy area of ​​the given patient; the output layer contains two neurons, which are the horizontal cutting trajectory line spacing r i The number h and the longitudinal cutting depth d j The number of layers is c; the hidden layer is a single hidden layer, which contains 9 neurons; tansig is selected as the transfer function between the input layer and the hidden layer, purelin is selected as the transfer function between the hidden layer and the output layer, and the trainlm algorithm is selected as the training function of the neural network; and the learning rate of the neural network is set to 0.01; 3D modeling and printing were performed based on the vertebral imaging data information of different patients. The 3D printed vertebral model was used as the experimental object to determine the cutting area. The robot was dragged to perform the cutting experiment. The cutting trajectory information of the artificial vertebral plate in the robot space was obtained through the mapping relationship between the optical measurement space and the robot space. This process was repeated to collect several groups of personalized sample data to form a training set.

4. The robot-based laminectomy trajectory auxiliary planning system according to claim 1, characterized in that: In the trajectory planning module, the cutting trajectory parameters h and c are obtained by prediction, and the average value of the travel distance is calculated. and the average value of single cutting depth The expression is: The 3D printed personalized vertebra is placed in the optical measurement space, and the optical probe tool is operated to determine the boundary of the cutting area, so as to obtain the key point information in the optical measurement coordinate system; then, according to the mapping relationship between the optical positioning system and the robot, the key point information obtained by the probe tool is converted to the robot space. The four key points are the four vertices of the rectangular cutting area, which are recorded as P1, P2, P3 and P4, with P1 as the starting point and P4 as the end point; For the turning point k in the trajectory ij Solve, ij represents the jth inflection point of the i-th layer except P2 and P3, calculate the inflection point coordinate k of the first layer 1j , if k 1j Located on vector P2P3, P2 and k 1j The distance between them is r', then k 1j The coordinate values ​​are: In the formula, express The magnitude of a vector; If k 1j Located in vector On, P1 and k 1j The distance between them is r", then k 1j The coordinate values ​​are: The inflection point coordinates k of the second layer 2j The calculation process is: determine the normal vector of the cutting surface based on the known points, select two non-collinear vectors and Calculate the normal vector and then normalize it. The expression is: in, is the normal vector, is the magnitude of the normal vector, is the unit normal vector; The first layer P1, P2, P3, P4 and k ij The coordinate points are offset along the normal vector direction, and the coordinates of each point in the second layer after offset are: Among them, k 2j is the coordinate of the inflection point of the second layer, P m 2 is the second layer vertex coordinate; Calculate all inflection points k in turn ij and the coordinates of the vertices; The robot's cutting trajectory planning is completed based on the solved key position point parameters.

5. The robot-based laminectomy trajectory auxiliary planning system according to claim 1, characterized in that: In the trajectory planning module, the trajectory at the corner is circularized so that the robot generates a smooth cutting trajectory; the specific process of circularization of the corner at P2 is as follows: First, the turning angle θ1 of the path and the straight line-arc transition points Pt1 and Pt2 are solved, and the expression is: In the formula, r1 is the transition arc radius, s1 is the arc radius adjustment parameter, and the adjustment parameter s i Used to adjust the radius of the arc trajectory and set different adjustment parameters according to the specific trajectory; Solve for transition points Pt1 and Pt2: Perform spatial linear interpolation on the portion between points P1 and Pt1 to complete the trajectory planning of this segment; Center O1 and path segment length l i Solve, l1 is the path length between P1 and Pt1, l2 is the arc length between Pt1 and Pt2, M1 is the midpoint of Pt1 and Pt2, and it is on the angle bisector, so we get: In ΔP2P t1 In O1, according to the trigonometric function relationship, we get: Finally, find the segment length l i : The part between Pt1 and Pt2 is processed by arc transition; For Pt2 to k 11 The part between the points is interpolated in space to complete the trajectory planning of this section, and the remaining corners are rounded.

Images