A markerless intraoperative real-time registration and tracking method and system for mandibular osteotomy

Abstract

This invention relates to a markerless real-time registration and tracking method and system for mandibular surgery. The method includes the following steps: the patient performs multiple opening and closing movements of the upper and lower jaws while the robotic arm is fixed, and the system synchronously records the changes in the angles of each joint of the robotic arm; based on the forward kinematics of the robotic arm, the continuous motion trajectory of the distal end of the jaw in space is calculated to form an actual jawbone trajectory point cloud; a preoperative image model is formed using the actual jawbone trajectory point cloud, a simulated jawbone trajectory is constructed in the preoperative image model, and the actual trajectory is aligned using the ICP registration algorithm to achieve automatic registration; the system establishes a mapping between angle changes and the spatial posture of the jawbone to achieve dynamic tracking and visual navigation during surgery. This invention solves the problems of large errors, high complexity, many limitations, and low efficiency in preoperative image data registration technology during maxillofacial surgery, avoids the need for preoperative implantation of markers, and achieves high-precision registration, high automation, and strong real-time performance under natural conditions.

Description

Technical Field

[0001] This invention relates to the field of medical image registration and surgical navigation technology, and in particular to a method and device for mandibular bone registration and real-time tracking based on temporomandibular joint movement trajectory without the need for manual markers. It is applicable to scenarios such as maxillofacial surgery, digital implantology, and robot-assisted surgery. Background Technology

[0002] In maxillofacial surgery, to achieve intraoperative navigation and precise manipulation of the mandible, it is usually necessary to register preoperative imaging data (such as CT, cone-beam CT) with the patient's actual anatomical structure. Currently, most methods rely on attaching optical / electromagnetic markers to the bone surface or manually selecting anatomical features during surgery to complete the registration. However, these methods have problems such as complex marker attachment processes, easy detachment or obstruction; limited selection of anatomical points on the bone surface due to the surgical exposure range; and large errors in manual registration, making it difficult to meet the precision requirements of robotic operation.

[0003] Existing relevant technical analysis:

[0004] (1) Patent 1 (CN118840379B) proposes a 2D / 3D detection and segmentation method, device and terminal equipment for orthopedic surgical registration. It uses preoperative CT data to input into a 3D detection network to perform three-dimensional landmark detection and bone tissue segmentation. Its registration technology relies on the detection of three-dimensional landmarks in the image.

[0005] (2) Patent 2 (CN117530708B) provides a surgical registration method and a surgical registration device. The method includes: controlling a radiation device to perform radiation to obtain a CT image sequence containing the surgical site. A metal ball device is placed within the radiation range of the radiation device, and multiple metal balls are arranged in the metal ball device. Point cloud data is generated based on the CT image sequence. However, the surgical registration process depends on the metal ball device within the radiation device range, and the process of attaching marker points is complicated.

[0006] Existing technical problems: The process of attaching markers is complex and they are prone to falling off or being obscured; the selection of anatomical points on the bone surface is limited by the surgical exposure range; and the large error of manual registration makes it difficult to meet the accuracy requirements of robot operation. Summary of the Invention

[0007] To address the issues of large errors, high complexity, numerous limitations, and low efficiency in preoperative image data registration techniques during maxillofacial surgery, a markerless real-time registration and tracking method and system for mandibular surgery is proposed.

[0008] The technical solution of this invention is as follows:

[0009] A markerless mandibular intraoperative real-time registration and tracking method includes the following steps:

[0010] Step 1. Jawbone motion acquisition: With the robotic arm fixed in place, the patient passively or actively performs multiple opening and closing movements of the upper and lower jaws, and the system simultaneously records the changes in the angles of each joint of the robotic arm;

[0011] Step 2. Trajectory Reconstruction: Calculate the continuous motion trajectory of the distal end of the jawbone in space based on the forward kinematics of the robotic arm to form a point cloud of the actual jawbone trajectory;

[0012] Step 3. Markerless registration: A preoperative image model is formed by using the actual jawbone trajectory point cloud. A simulated jawbone trajectory is constructed in the preoperative image model, and the actual trajectory is aligned using the ICP registration algorithm to achieve automatic registration.

[0013] ICP registration algorithm: Using the actual jawbone motion trajectory point cloud as the source data, and the mandibular motion trajectory constructed by the preoperative image model as the target data, the iterative nearest point algorithm ICP is used to calculate the rigid body transformation matrix, and automatically complete the spatial alignment between the actual position of the jawbone and the preoperative model.

[0014] Step 4. Real-time tracking: After registration, the system establishes a mapping between angle changes and jawbone spatial posture, enabling dynamic tracking and visual navigation during surgery.

[0015] Furthermore, the conditions for fixing the robotic arms in step 1 are as follows: passive arm installation and initial positioning. Before the operation, the two robotic arms are installed and stably connected to the mandible, and the locking device of the robotic arms is loosened to allow their range of motion. The robotic arms contain a multi-link stabilization mechanism, which is fixedly connected to the sensor module through a connecting structure.

[0016] Furthermore, the acquisition of joint angle changes in step 1 and the modeling of forward kinematics in step 2: The system acquires the angle change data of each joint of the robotic arm in real time, and forms a continuous jaw movement trajectory mark through the complete opening and closing motion of the jawbone. Combined with the known structural parameters of the robotic arm, the position and posture of the end effector of the robotic arm configured at each moment are calculated through the forward kinematics model, and then the three-dimensional motion trajectory data of the fixed point of the mandible are deduced.

[0017] Furthermore, the formation of the actual jawbone trajectory point cloud in step 2:

[0018] 3D trajectory construction and noise reduction: A complete 3D motion trajectory point cloud of the mandible is constructed through multiple continuous opening and closing movements; the system performs filtering processing on the original trajectory, including mean filtering, median filtering and curvature smoothing.

[0019] Furthermore, in step 3, the preoperative image model is constructed and the jawbone trajectory is simulated: preoperative enhanced CT data of the patient's maxillofacial region is acquired, three-dimensional reconstruction is performed, and the jawbone model is extracted; based on the geometric rotation center and motion axis of the temporomandibular joint, the jawbone motion trajectory is constructed.

[0020] Furthermore, the real-time tracking in step 4 specifically involves:

[0021] Intraoperative real-time tracking and mapping: After registration, the system establishes a real-time mapping model between the changes in the angles of each joint of the passive robotic arm and the spatial pose of the mandible in the preoperative image coordinate system. During the operation, the position and posture of the mandible can be updated and visualized in real time.

[0022] Furthermore, the ICP registration algorithm in step 3, namely the markerless mandibular trajectory registration method, is described in detail below:

[0023] Step 3.1, Input point cloud definition:

[0024] Let the actual collected mandibular motion trajectory point cloud be the source point set:

[0025] P = {p_i ∈ ³ | i = 1, ..., N}

[0026] Where p_i represents the end-effector pose coordinates of the robotic arm in the i-th frame calculated from the robotic arm's structural parameters and forward kinematics; N is the number of point clouds, representing the number of points in the trajectory point cloud or the number of sampling frames; ³ represents three-dimensional Euclidean space, that is, three-dimensional space in the set of real numbers: used to describe the position coordinates of any point in the space;

[0027] Let the simulated mandibular motion trajectory in the preoperative enhanced CT model of the maxillofacial region be the target point set:

[0028] Q = {q_i ∈ ³ | i = 1, ..., N}

[0029] Where q_i represents the point in the target point cloud that matches p_i, which comes from the preoperative CT simulation trajectory;

[0030] This trajectory can be obtained by modeling rotation around the joint center;

[0031] Step 3.2, Point-to-point matching:

[0032] For each source point p_i ∈ P, find the nearest point q_i ∈ Q in the target point set such that:

[0033] q_i = argmin_q∈Q ||p_i - q||

[0034] Construct a set of paired points (p_i, q_i), with a total of N pairs;

[0035] Step 3.3, Rigid Body Transformation Estimation:

[0036] Define the transformation objective: find the rotation matrix R ∈ SO(3) and the translation vector t ∈ ³, which minimizes the matching error of the transformed source point cloud:

[0037] min_{R,t} Σ ||q_i - (R·p_i + t)||²

[0038] Where R ∈ SO(3) denotes a three-dimensional rotation matrix, and indicates that the rotation matrix R belongs to the three-dimensional special orthogonal group SO(3):

[0039] SO(3) = {R ∈ ^{3×3} | R^T·R = I and det(R) = 1}

[0040] This matrix represents the rotation of a rigid body in three-dimensional space while maintaining the coordinate system without distortion; where T is the transpose symbol, I represents the identity matrix, used to verify the orthogonality of R; Σ represents the summation symbol, indicating that the errors of all matching points are summed.

[0041] Step 3.4: Solve using the SVD method as follows:

[0042] Step 3.4.1. Calculate the center of the point set:

[0043] p = (1 / N) Σ p_i,q = (1 / N) Σ q_i

[0044] Step 3.4.2. Construct the covariance matrix:

[0045] H = Σ (p_i - p (q_i - q) )^T

[0046] Step 3.4.3. Perform singular value decomposition (SVD) on the covariance matrix H:

[0047] H = U·Σ·V^T

[0048] In this step, Σ represents the diagonal matrix in Singular Value Decomposition (SVD); U and V are orthogonal matrices, and Σ is a non-negative real diagonal matrix whose diagonal elements are singular values, representing the principal scale directions of H.

[0049] Step 3.4.4. Calculate the optimal rotation and translation:

[0050] R = V·U^T,t = q - R·p

[0051] Step 3.5, Transformation and Iteration:

[0052] The optimal rotation and translation transformation (R, t) is applied to the source point cloud to update the point positions, and point pair matching and rigid body estimation are repeated until convergence, i.e., the error change < ε.

[0053] p_i^{(k+1)} = R^{(k)}·p_i^{(k)} + t^{(k)}

[0054] ε represents the convergence threshold, which is the error convergence threshold during the registration algorithm iteration; the algorithm is considered to have converged when the position change between two consecutive iterations is less than ε; k represents the step number of the current iteration, the kth iteration;

[0055] Step 3.6, Output Results:

[0056] The final output rigid body transformation matrix T ∈ SE(3):

[0057]

[0058] SE(3) is a three-dimensional Euclidean space transformation group, representing a set of rigid body transformations consisting of a rotation matrix R and a three-dimensional translation vector t. This transformation is used to map the preoperative CBCT model to the actual surgical coordinate system, enabling real-time monitoring and navigation of the mandibular posture during surgery.

[0059] A markerless mandibular surgery real-time registration and tracking system is provided to implement the markerless mandibular surgery real-time registration and tracking method as described above. The system includes a robotic arm module, a sensor module, a computing unit module, and a three-dimensional image processing module, wherein:

[0060] Robotic arm module: The end of the robotic arm is connected to the mandible, and high-precision angle encoders are embedded in multiple joints;

[0061] Sensor module: Receives angle data collected by the angle encoder of the robotic arm's multi-joint and outputs it to the computing unit module;

[0062] The calculation unit module receives angle data and performs spatial matching using forward kinematics and the ICP algorithm.

[0063] 3D image processing module: Acquires point cloud of the three-dimensional motion trajectory of the patient's mandible and provides a preoperative CBCT / CT reconstruction model and ICP reference coordinate system.

[0064] An electronic device includes a processor and a memory; the processor executes steps of the markerless mandibular surgery real-time registration and tracking method by calling programs or instructions stored in the memory.

[0065] A computer-readable storage medium storing a program or instructions that causes a computer to perform the steps of the described markerless mandibular intraoperative real-time registration and tracking method.

[0066] The beneficial effects of this invention are as follows:

[0067] 1. Avoid preoperative implantation of markers, reducing trauma and infection risks. This method eliminates the need for preoperative implantation of any metal markers or screws, avoiding additional trauma, infection risks, and marker loosening, significantly improving patient comfort and the safety of intraoperative procedures.

[0068] 2. Achieve high-precision registration under natural conditions. The pose trajectory formed by the natural opening and closing of the jawbone is used as the registration feature, which has high individual stability and repeatability. Rigid body registration of the trajectory is performed by the Iterative Closest Point (ICP) algorithm, which can achieve millimeter-level intraoperative registration accuracy, which is superior to traditional registration methods based on static surface points.

[0069] 3. The registration and tracking process is highly automated, improving surgical efficiency. The entire registration process only requires the patient to open and close their mouth three times. The system can complete data acquisition, trajectory extraction, and automatic registration in real time, eliminating tedious steps such as manual point selection and optical instrument adjustment, and greatly improving the efficiency of surgical preparation.

[0070] 4. High real-time performance and dynamic updates. This system combines sensor data streams with efficient registration algorithms to achieve real-time tracking of jawbone movement and continuous updates of model posture during surgery. It has dynamic navigation capabilities and is suitable for reconstruction or occlusal guidance surgeries that require adjustment of mandibular position. Detailed Implementation

[0071] The present invention will now be described in detail with reference to specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0072] A markerless mandibular intraoperative real-time registration and tracking system includes:

[0073] 1. Robotic arm module: The end of the robotic arm is connected to the mandible, and high-precision angle encoders are embedded in multiple joints.

[0074] 2. Sensor module: Receives angle data collected by the angle encoder of the multi-joint robotic arm and outputs it to the computing unit module.

[0075] 3. Calculation Unit Module: Receives angle data and performs spatial matching using forward kinematics and the ICP algorithm.

[0076] 4. Three-dimensional image processing module: Acquires point cloud of the three-dimensional motion trajectory of the patient's mandible and provides a preoperative CBCT / CT reconstruction model and ICP reference coordinate system.

[0077] Core workflow of a markerless mandibular intraoperative real-time registration and tracking method:

[0078] Step 1. Jawbone motion acquisition: With the robotic arm fixed in place, the patient passively or actively performs multiple opening and closing movements of the upper and lower jaws, and the system simultaneously records the changes in the angles of each joint of the robotic arm;

[0079] Step 2. Trajectory Reconstruction: Calculate the continuous motion trajectory of the distal end of the jawbone in space based on the forward kinematics of the robotic arm to form a point cloud of the actual jawbone trajectory;

[0080] Step 3. Markerless registration: A preoperative image model is formed by using the actual jawbone trajectory point cloud. A simulated jawbone trajectory is constructed in the preoperative image model, and the actual trajectory is aligned using the ICP registration algorithm to achieve automatic registration.

[0081] Step 4. Real-time tracking: After registration, the system establishes a mapping between angle changes and jawbone spatial posture, enabling dynamic tracking and visual navigation during surgery.

[0082] The key steps and core modules are explained in detail below:

[0083] 1. Conditions for fixing the robotic arm in step 1 - passive arm installation and initial positioning:

[0084] Before the operation, two robotic arms will be installed and stably connected to the mandible. The locking devices of the robotic arms will be released to allow for their movement. The robotic arms contain a multi-link stabilization mechanism, which is fixedly connected to the sensor module through a connecting structure to ensure that the end of the robotic arm can move stably with the mandible during the opening and closing of the mandible without intruding into or damaging soft tissue.

[0085] 2. Data acquisition of joint angle changes in step 1 and modeling of forward kinematics in step 2:

[0086] The system collects the angle change data of each joint of the robotic arm in real time, and forms a continuous jaw movement trajectory mark through the complete opening and closing movement of the jawbone. Combined with the known structural parameters of the robotic arm, the system calculates the position and posture of the end effector of the robotic arm at each moment through a forward kinematics model, and then calculates the three-dimensional motion trajectory data of the fixed point of the mandible.

[0087] 3. Formation of the actual jawbone trajectory point cloud in step 2: 3D trajectory construction and noise reduction:

[0088] By repeatedly opening and closing the jaw, a complete three-dimensional motion trajectory point cloud of the mandible is constructed. To enhance registration accuracy, the system performs filtering processing on the original trajectory, including mean filtering, median filtering, and curvature smoothing, to eliminate high-frequency noise and jitter.

[0089] 4. Construction of the preoperative image model and simulation of the jawbone trajectory in step 3:

[0090] Preoperatively, enhanced CT data of the patient's maxillofacial region were acquired, and three-dimensional reconstruction was performed to extract the jawbone model. Based on the geometric rotation center and motion axis of the temporomandibular joint, an idealized mandibular motion trajectory was constructed for subsequent registration reference.

[0091] 5. ICP registration algorithm in step 3:

[0092] Using the actual jawbone motion trajectory point cloud as source data and the mandibular motion trajectory constructed from the preoperative image model as target data, the Iterative Closest Point (ICP) algorithm is used to calculate the rigid body transformation matrix, automatically aligning the actual jawbone position with the preoperative model in space. The ICP process can integrate weighted error assessment and multiple initial value sampling to enhance robustness.

[0093] 6. Real-time tracking in step 4 - intraoperative real-time tracking mapping:

[0094] After registration, the system establishes a real-time mapping model between the changes in the angles of each joint of the passive robotic arm and the spatial pose of the mandible in the preoperative image coordinate system. During the operation, the position and posture of the mandible can be updated and visualized in real time, providing continuous and accurate anatomical references for surgical navigation, cutting trajectory planning, or reconstruction positioning.

[0095] The ICP registration algorithm in step 3, namely the markerless mandibular trajectory registration method, is described in detail below:

[0096] Step 3.1, Input point cloud definition:

[0097] Let the actual collected mandibular motion trajectory point cloud be the source point set:

[0098] P = {p_i ∈ ³ | i = 1, ..., N}

[0099] Where p_i represents the end-effector pose coordinates of the robotic arm in the i-th frame, calculated from the robotic arm's structural parameters and forward kinematics. N is the number of points in the point cloud, representing the number of points or sampling frames in the trajectory point cloud, and is usually a positive integer. ³ represents three-dimensional Euclidean space, that is, three-dimensional space within the set of real numbers: ³ = {(x, y, z) | x, y, z ∈ } is used to describe the position coordinates of any point in space.

[0100] Let the simulated mandibular motion trajectory in the preoperative enhanced CT model of the maxillofacial region be the target point set:

[0101] Q = {q_i ∈ ³ | i = 1, ..., N}

[0102] Where q_i represents the point in the target point cloud that matches p_i, which comes from the preoperative CT simulation trajectory.

[0103] This trajectory can be obtained by modeling rotation at the joint center.

[0104] Step 3.2, Point-to-point matching:

[0105] For each source point p_i ∈ P, find the nearest point q_i ∈ Q in the target point set such that:

[0106] q_i = argmin_q∈Q ||p_i - q||

[0107] Construct a set of N pairs of paired points (p_i, q_i).

[0108] Step 3.3, Rigid Body Transformation Estimation:

[0109] Define the transformation objective: find the rotation matrix R ∈ SO(3) and the translation vector t ∈ ³, which minimizes the matching error of the transformed source point cloud:

[0110] min_{R,t} Σ ||q_i - (R·p_i + t)||²

[0111] Where R ∈ SO(3) denotes a three-dimensional rotation matrix, and indicates that the rotation matrix R belongs to the three-dimensional special orthogonal group SO(3):

[0112] SO(3) = {R ∈ ^{3×3} | R^T·R = I and det(R) = 1}

[0113] This matrix represents the rigid body rotation in three-dimensional space, preserving the coordinate system without distortion; where T is the transpose symbol, I represents the identity matrix, used to verify the orthogonality of R. Σ represents the summation symbol, indicating the summation of errors over all matching points:

[0114] Σ_{i=1}^{N} ||q_i - (R·p_i + t)||²

[0115] Step 3.4: Solve using the SVD method as follows:

[0116] Step 3.4.1. Calculate the center of the point set:

[0117] p = (1 / N) Σ p_i,q = (1 / N) Σ q_i

[0118] Step 3.4.2. Construct the covariance matrix:

[0119] H = Σ (p_i - p (q_i - q) )^T

[0120] Step 3.4.3. Perform singular value decomposition (SVD) on H:

[0121] H = U·Σ·V^T

[0122] In this step, Σ denotes the diagonal matrix in the singular value decomposition (SVD). Let the SVD decomposition of the covariance matrix H be: H = U·Σ·V^T, where: U and V are orthogonal matrices, and Σ is a non-negative real diagonal matrix whose diagonal elements are singular values, representing the principal scale directions of H.

[0123] Step 3.4.4. Calculate the optimal rotation and translation:

[0124] R = V·U^T,t = q - R·p

[0125] Step 3.5, Transformation and Iteration:

[0126] Apply the optimal rotation and translation transformation (R, t) to the source point cloud, update the point positions, and repeat point pair matching and rigid body estimation until convergence (error change < ε):

[0127] p_i^{(k+1)} = R^{(k)}·p_i^{(k)} + t^{(k)}

[0128] ε represents the convergence threshold, which is the error convergence threshold during the registration algorithm iteration. The algorithm is considered to have converged when the positional change between two consecutive iterations is less than ε. k represents the step number of the current iteration, the k-th iteration.

[0129] Step 3.6, Output Results:

[0130] The final output rigid body transformation matrix T ∈ SE(3):

[0131]

[0132] SE(3) is the three-dimensional Euclidean space transformation group, representing the set of rigid body transformations consisting of rotation matrix R and three-dimensional translation vector t.

[0133] This transformation is used to map the preoperative CBCT model to the actual surgical coordinate system, enabling real-time monitoring and navigation of the mandibular surgical posture.

[0134] The above-described embodiments are merely one implementation of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention should be determined by the appended claims.

Claims

1. A markerless mandibular intraoperative real-time registration and tracking system, characterized in that, It includes a robotic arm module, a sensor module, a computing unit module, and a 3D image processing module, among which: Robotic arm module: The end of the robotic arm is connected to the mandible, and high-precision angle encoders are embedded in multiple joints; Sensor module: Receives angle data collected by the angle encoder of the robotic arm's multi-joint and outputs it to the computing unit module; The calculation unit module receives angle data and performs spatial matching using forward kinematics and the ICP algorithm. 3D image processing module: Acquires point cloud of the three-dimensional motion trajectory of the patient's mandible and provides preoperative CBCT / CT reconstruction model and ICP reference coordinate system; This can be achieved through the following steps: Step 1. Jawbone motion acquisition: With the robotic arm fixed in place, the patient passively or actively performs multiple opening and closing movements of the upper and lower jaws, and the system simultaneously records the changes in the angles of each joint of the robotic arm; Step 2. Trajectory Reconstruction: Calculate the continuous motion trajectory of the distal end of the jawbone in space based on the forward kinematics of the robotic arm to form a point cloud of the actual jawbone trajectory; Step 3. Markerless registration: A preoperative image model is formed by using the actual jawbone trajectory point cloud. A simulated jawbone trajectory is constructed in the preoperative image model, and the actual trajectory is aligned using the ICP registration algorithm to achieve automatic registration. ICP registration algorithm: Using the actual jawbone motion trajectory point cloud as the source data, and the mandibular motion trajectory constructed by the preoperative image model as the target data, the iterative nearest point algorithm ICP is used to calculate the rigid body transformation matrix, and automatically complete the spatial alignment between the actual position of the jawbone and the preoperative model. Step 4. Real-time tracking: After registration, the system establishes a mapping between angle changes and jawbone spatial posture, enabling dynamic tracking and visual navigation during surgery.

2. The markerless mandibular intraoperative real-time registration and tracking system according to claim 1, characterized in that, The conditions for fixing the robotic arms in step 1 are as follows: passive arm installation and initial positioning. Before the operation, the two robotic arms are installed and stably connected to the mandible. The locking device of the robotic arms is then loosened to allow for their movement. The robotic arms contain a multi-link stabilization mechanism, which is fixedly connected to the sensor module through a connecting structure.

3. The markerless mandibular intraoperative real-time registration and tracking system according to claim 1, characterized in that, The acquisition of joint angle changes in step 1 and the modeling of forward kinematics in step 2: The system acquires the angle change data of each joint of the robotic arm in real time, and forms a continuous jaw movement trajectory mark through the complete opening and closing motion of the jawbone. Combined with the known structural parameters of the robotic arm, the position and posture of the end effector of the robotic arm configured at each moment are calculated through the forward kinematics model, and then the three-dimensional motion trajectory data of the fixed point of the mandible are deduced.

4. The markerless mandibular intraoperative real-time registration and tracking system according to claim 1, characterized in that, Formation of the actual jawbone trajectory point cloud in step 2: 3D trajectory construction and noise reduction: A complete 3D motion trajectory point cloud of the mandible is constructed through multiple continuous opening and closing movements; the system performs filtering processing on the original trajectory, including mean filtering, median filtering and curvature smoothing.

5. The markerless mandibular intraoperative real-time registration and tracking system according to claim 1, characterized in that, Step 3: Construction of preoperative image model and simulation of jaw trajectory: Acquire enhanced CT data of the patient's maxillofacial region before surgery, perform three-dimensional reconstruction, and extract the jaw model; construct the jaw movement trajectory based on the geometric rotation center and motion axis of the temporomandibular joint.

6. The markerless mandibular intraoperative real-time registration and tracking system according to claim 1, characterized in that, The real-time tracking in step 4 specifically refers to: Intraoperative real-time tracking and mapping: After registration, the system establishes a real-time mapping model between the changes in the angles of each joint of the passive robotic arm and the spatial pose of the mandible in the preoperative image coordinate system. During the operation, the position and posture of the mandible can be updated and visualized in real time.

7. The markerless mandibular intraoperative real-time registration and tracking system according to claim 1, characterized in that, The ICP registration algorithm in step 3, namely the markerless mandibular trajectory registration method, is described in detail below: Step 3.1, Input point cloud definition: Let the actual collected mandibular motion trajectory point cloud be the source point set: P = {p_i ∈ ³ | i = 1, ..., N} Where p_i represents the end-effector pose coordinates of the robotic arm in the i-th frame calculated from the robotic arm's structural parameters and forward kinematics; N is the number of point clouds, representing the number of points in the trajectory point cloud or the number of sampling frames; ³ represents three-dimensional Euclidean space, that is, three-dimensional space in the set of real numbers: used to describe the position coordinates of any point in the space; Let the simulated mandibular motion trajectory in the preoperative enhanced CT model of the maxillofacial region be the target point set: Q = {q_i ∈ ³ | i = 1, ..., N} Where q_i represents the point in the target point cloud that matches p_i, which comes from the preoperative CT simulation trajectory; This trajectory can be obtained by modeling rotation around the joint center; Step 3.2, Point-to-point matching: For each source point p_i ∈ P, find the nearest point q_i ∈ Q in the target point set such that: q_i = argmin_q∈Q ||p_i - q|| Construct a set of paired points (p_i, q_i), with a total of N pairs; Step 3.3, Rigid Body Transformation Estimation: Define the transformation objective: find the rotation matrix R ∈ SO(3) and the translation vector t ∈ ³, which minimizes the matching error of the transformed source point cloud: min_{R,t} Σ ||q_i - (R·p_i + t)||² Where R ∈ SO(3) denotes a three-dimensional rotation matrix, and indicates that the rotation matrix R belongs to the three-dimensional special orthogonal group SO(3): SO(3)=\{R\in ^{3\times3}\mid R^T\cdot R = I\text{ and}\det(R)=1\} This matrix represents the rotation of a rigid body in three-dimensional space while maintaining the coordinate system without distortion; where T is the transpose symbol, I represents the identity matrix, used to verify the orthogonality of R; Σ represents the summation symbol, indicating that the errors of all matching points are accumulated and summed. Step 3.4: Solve using the SVD method as follows: Step 3.4.

1. Calculate the center of the point set: p = (1 / N) Σ p_i,q = (1 / N) Σ q_i Step 3.4.

2. Construct the covariance matrix: H = Σ (p_i - p )(q_i - q )^T Step 3.4.

3. Perform singular value decomposition (SVD) on the covariance matrix H: H = U·Σ·V^T In this step, Σ represents the diagonal matrix in Singular Value Decomposition (SVD); U and V are orthogonal matrices, and Σ is a non-negative real diagonal matrix whose diagonal elements are singular values, representing the principal scale direction of H. Step 3.4.

4. Calculate the optimal rotation and translation: R = V·U^T,t = q - R·p Step 3.5, Transformation and Iteration: The optimal rotation and translation transformation (R, t) is applied to the source point cloud to update the point positions, and point pair matching and rigid body estimation are repeated until convergence, i.e., the error change < ε. p_i^{(k+1)} = R^{(k)}·p_i^{(k)} + t^{(k)} ε represents the convergence threshold, which is the error convergence threshold during the registration algorithm iteration. The algorithm is considered to have converged when the positional change between two consecutive iterations is less than ε. k represents the step number of the current iteration, the kth iteration. Step 3.6, Output Results: The final output rigid body transformation matrix T ∈ SE(3): SE(3) is a three-dimensional Euclidean space transformation group, representing a set of rigid body transformations consisting of a rotation matrix R and a three-dimensional translation vector t. This transformation is used to map the preoperative CBCT model to the actual surgical coordinate system, enabling real-time monitoring and navigation of the mandibular posture during surgery.

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