A micro-motion real-time tracking control system for an orthopedic surgery robot

Abstract

The application provides a micro-motion real-time tracking control system for an orthopedic surgery robot, which judges whether the bone tissue produces micro-motion by judging whether the contact force is consistent with the expected contact force, because when the bone tissue produces micro-motion, the bone tissue will give the cutter a reverse force, so that the contact force is inconsistent with the expected contact force; and when the micro-motion is produced, the contact force is close to the expected contact force by solving the optimal control input; that is, the application carries out real-time path planning through the state quantity fed back by the robot and the sensor, and does not need to use a neural network for prediction, so that the micro-motion real-time tracking is not dependent on the length of collected data and is not affected by the individual patient.

Description

Technical Field

[0001] The present invention belongs to the technical field of micro-motion tracking, and in particular relates to a micro-motion real-time tracking control system for an orthopedic surgical robot. Background Art

[0002] Bone tumors are tumors that develop within the bone and accessory tissues of various bones. They most commonly occur in the distal femur, pelvis, cervical spine, thoracic spine, shoulder joint, and other locations, typically presenting as localized swelling or fracture. Surgical resection is one of the most effective treatments for bone tumors. However, during surgery, the patient's breathing and the interaction between surgical instruments and tissue can cause micro-movements in the bone tissue, which can reduce surgical precision and even lead to surgical failure.

[0003] In order to reduce the impact of bone tissue micromotion on surgery, commonly used tissue micromotion tracking methods include:

[0004] Duan et al. used an infrared optical camera to record the patient's bone tissue movement fluctuations over a period of time before surgery. They then used PCA principal component analysis to reduce the collected movement fluctuations to one-dimensional data. The reduced data was used to train an LSTM neural network, with 10-20 consecutive sampling points serving as the network input and 1-4 subsequent points as the output. A sliding window was used to adjust the input points over time, ensuring consistent prediction using limited data. The predicted data was then sent to the robotic arm as target points for micro-motion tracking.

[0005] Qi et al. designed a grinding depth adjustment device consisting of a mounting frame, a bone cutter, a connecting rod, a sliding drive mechanism, and a protective sleeve. The sliding drive mechanism adjusts the position of the protective sleeve, ensuring that after the bone cutter grinding head has ground to a certain depth, the protective sleeve contacts the bone tissue, preventing further grinding. This prevents over-grinding and the high-speed rotation of the grinding head from contacting soft tissue or nerves in the spine, thereby minimizing damage to these soft tissues and nerves. Because the protective sleeve is in contact with the bone tissue, it rises and falls with respiratory movement, enabling micro-motion tracking of the bone cutter grinding head.

[0006] It should be noted that the neural network in solution (1) relies on the collected motion fluctuation data. When the amount of data is small or the individual patient changes, the prediction accuracy will decrease.

[0007] In solution (2), the bone knife grinding head has relatively good micro-motion tracking performance when it contacts the bone tissue vertically. However, in actual surgery, it is almost impossible for the bone knife grinding head to contact the bone tissue vertically, which will cause the axial direction of the protective cover to be inconsistent with the direction of respiratory movement, making it impossible for the protective cover to track the micro-motion of the bone tissue. Summary of the Invention

[0008] To solve the above problems, the present invention provides a real-time tracking and control system for micro-movements of orthopedic surgical robots. It determines whether the bone tissue has micro-movements by checking whether the contact force is consistent with the expected contact force, and adjusts the surgical robot path in real time according to the actual resection force, thereby achieving bone tissue resection at any angle.

[0009] A micro-motion real-time tracking control system for an orthopedic surgical robot, comprising a parameter setting module, a data acquisition module, an optimization solution module, and a control module;

[0010] The parameter setting module is used to set the preset surgical resection path, the initial position of the surgical robot, and the desired contact force between the osteotome located at the end of the surgical robot and the bone tissue to be resected;

[0011] The data acquisition module is used to detect the joint angle, joint speed, and actual contact force of the surgical robot in real time;

[0012] The optimization solution module is used to input the preset surgical resection path, the initial position of the surgical robot, the expected contact force, the joint angles and joint velocities of the surgical robot, and the actual contact force into a joint model composed of a bone tissue resection model and a surgical robot dynamics model, and obtain an optimal control input that minimizes the sum of the contact force error between the expected contact force and the actual contact force and the trajectory tracking error between the preset surgical resection path and the actual surgical resection path;

[0013] The control module is used to generate corresponding control instructions according to the optimal control input to drive the surgical robot to perform specified actions.

[0014] Furthermore, the joint model is:

[0015]

[0016] in, They are the joint angle, joint angular velocity, and joint angular acceleration of the surgical robot, respectively. M is the mass matrix of the surgical robot, u is the control input, C is the Coriolis force matrix, G is the gravity matrix, J is the Jacobian matrix, and F e is the actual contact force between the osteotome and the bone tissue to be removed, and T represents the transposition.

[0017] Furthermore, the method of obtaining the optimal control input through the joint model is as follows:

[0018] The joint model is discretized using the Euler method, and the following discrete state equation is obtained:

[0019] x(k+1)=f(x(k),u(k))

[0020] Among them, x(k+1) represents the actual state at time k+1 x(k) represents the actual state at time k u(k) represents the control input at time k; f(x(k),u(k)) represents the ideal state at time k+1;

[0021] The objective function is constructed based on the discrete state equation as follows:

[0022]

[0023] Wherein, the contact force error at time k is ΔF(k) = F z -R -1 F d , F z is the state at time k Medium F e The component on the z-axis in the direction of the bone knife tip, F d is the expected contact force, ΔF(0) = 0, Q is the weight matrix related to the contact force; the trajectory tracking error at time k is e(k) = K(q(k))-s k , q(k) is the joint angle of the surgical robot at time k, K is the forward kinematics operator of the surgical robot, and K(q(k)) represents the conversion of q(k) to the Cartesian coordinate system, s k is the spatial position of the surgical robot at time k in the surgical resection path, e(0) = 0; W is the weight matrix related to the trajectory tracking error; R is the weight matrix related to the control input; N represents the total number of moments;

[0024] The augmented Lagrangian function is constructed based on the objective function as follows:

[0025]

[0026] Among them, ρ is the penalty function, λ is the weight factor at time k, is the two-norm;

[0027] The augmented Lagrangian function is solved to obtain the optimal control input.

[0028] Furthermore, the solution method of the augmented Lagrangian function is:

[0029] Split the augmented Lagrangian function into three penalty terms of state quantities:

[0030]

[0031] Among them, I(q(k),u(k),ΔF(k)) is the constraint condition, ρ j is the Lagrange multiplier related to the joint angle of the surgical robot, ρ u is the Lagrange multiplier related to the control input, ρ fis the Lagrange multiplier related to the contact force error, v j is the dual variable related to the joint angle of the surgical robot in the constraint condition, v u is the dual variable related to the control input in the constraint condition, v f is the dual variable related to the contact force error in the constraint condition;

[0032] Solve the augmented Lagrangian function of the penalty term split into three state quantities according to the following iterative formula:

[0033] x(k)=L ρ (x,u(k-1),λ(k-1))

[0034] u(k)=L ρ (x(k),u,λ(k-1))

[0035] λ(k)=L ρ (x(k),u(k),λ)

[0036] Each time an iteration is performed, it is determined whether the trajectory tracking error corresponding to the current iteration is less than the set threshold. If it is, the control input corresponding to the current iteration is the optimal control input. If the iteration reaches the maximum upper limit N, and the trajectory tracking errors corresponding to N iterations are not less than the set threshold, the control input corresponding to the minimum value of the trajectory tracking errors corresponding to N iterations is used as the optimal control input.

[0037] Furthermore, the constraints I(q(k),u(k),ΔF(k)) are as follows:

[0038]

[0039] Where ΔF lower and ΔF upper are the lower limit and upper limit of the contact force error, respectively, lower With q upper are the lower limit and upper limit of the joint angle of the surgical robot, u lower with u upper They are the lower and upper limits of the control input respectively.

[0040] Furthermore, the weight matrix R related to the control input is the rotation matrix between the micro-motion direction of the bone tissue and the direction of the end of the osteotome, and the method for obtaining the micro-motion direction of the bone tissue is:

[0041] Before the surgical operation, an optical navigation marker is installed within a set vicinity of the bone tissue, and the optical navigation marker is fixed on the bone tissue;

[0042] By measuring the positions of optical navigation markers at different times, the direction of bone tissue micro-motion is calculated.

[0043] Beneficial effects:

[0044] 1. The present invention provides a real-time tracking and control system for micro-movements of an orthopedic surgical robot. The system determines whether the bone tissue has micro-movements by checking whether the contact force is consistent with the expected contact force. When micro-movements occur in the bone tissue, the bone tissue will apply a reverse force to the tool, causing the contact force to be inconsistent with the expected contact force. When micro-movements occur, the contact force is brought close to the expected contact force by solving the optimal control input. In other words, the present invention performs real-time path planning through the state quantities fed back by the robot and the sensor, without the need for prediction using a neural network. Therefore, real-time tracking of micro-movements does not depend on the length of the collected data and is not affected by the individual patient.

[0045] 2. The present invention provides a micro-motion real-time tracking control system for an orthopedic surgical robot. Various constraints can be set according to the safety requirements of the operation to ensure the safety of the operation. When solving the optimal control input, the objective function is converted into an augmented Lagrangian function so that the constraints are integrated into the function, and the optimal control input is solved through an iterative calculation method.

[0046] 3. The present invention provides a real-time tracking and control system for micro-movements of orthopedic surgical robots. The micro-movement direction of bone tissue and the end position of the bone knife can be converted through rotation matrix transformation, thereby ensuring that the real resection force can be calculated when the bone knife contacts the tissue in any direction, and the surgical robot path can be adjusted in real time according to the real resection force, thereby realizing bone tissue resection at any angle. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a principle block diagram of a micro-motion real-time tracking control system for an orthopedic surgical robot provided by the present invention;

[0048] Figure 2 Flowchart of the derivation process of the joint model and the method for obtaining the optimal control input provided by the present invention;

[0049] Figure 3 This is a working diagram of a surgical robot for bone tumor resection provided by the present invention. DETAILED DESCRIPTION

[0050] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0051] like Figure 1 As shown, a micro-motion real-time tracking control system for an orthopedic surgical robot includes a parameter setting module 100, a data acquisition module 200, an optimization solution module 300, and a control module 400;

[0052] The parameter setting module 100 is used to set a preset surgical resection path, an initial position of the surgical robot, and a desired contact force between the osteotome located at the end of the surgical robot and the bone tissue to be resected.

[0053] The data acquisition module 200 is used to detect the joint angle, joint speed, and actual contact force of the surgical robot in real time.

[0054] The optimization solution module 300 is used to input the preset surgical resection path, the initial position of the surgical robot, the expected contact force, the joint angle of the surgical robot, the joint speed, and the actual contact force into a joint model composed of a bone tissue resection model and a surgical robot dynamics model, to obtain the optimal control input that minimizes the sum of the contact force error between the expected contact force and the actual contact force and the trajectory tracking error between the preset surgical resection path and the actual surgical resection path.

[0055] The control module 400 is used to generate corresponding control instructions according to the optimal control input to drive the surgical robot to perform specified actions.

[0056] like Figure 2 As shown in the figure, the derivation process of the joint model and the method of obtaining the optimal control input are introduced in detail below.

[0057] S1: Construct a bone tissue resection model, set the surgical robot resection path and expected contact force. First, construct a bone tissue resection model with a bone knife. The resection model can be a physical model based on mechanics, a simulation model based on mesh, or a data-driven network model. The output of the resection model F e is the interaction force between the osteotome and the bone tissue, which has three directions. Set the resection path of the surgical robot, and the resection path uses S = [s1, s2, s3, ..., s t ] indicates that s t represents the spatial position of the surgical robot at time t. Set the expected contact force, which is expressed as F d express.

[0058] It should be noted that the resection model is a mathematical formula for calculating the contact force between the bone knife and bone tissue at different speeds, powers, and bone tissues when the bone knife is resecting. The contact force is calculated using parameters such as speed, power, and bone tissue hardness.

[0059] S2: Adjust the angle and initial position of the bone knife at the end of the surgical robot, set the operating parameters of the bone knife, and the surgical robot starts to perform. Before the operation, the doctor installs an optical navigation marker near the bone tissue ( Figure 3205 in the figure), by recording the two displacement points of the marker, the direction of bone tissue micro-movement can be calculated. The doctor then adjusts the angle of the end bone knife of the surgical robot and moves it to the appropriate initial position. The direction of bone tissue micro-movement is related to the direction of the end bone knife ( Figure 3 Medium F x ,F y ,F z The transformation between the two is represented by the rotation matrix R. The osteotome's operating parameters are set, including speed, power, water flow rate, and other parameters. The surgical robot begins to operate according to the set resection path.

[0060] It should be noted that bone micromotion refers to the up-and-down movement of the bone caused by inhalation and exhalation. The expected contact force is the contact force set by the doctor, or it can be the pressure between the osteotome and the bone tissue in the initial position.

[0061] S3: Acquire the real-time data of joint angle, joint angular velocity, contact force and control input during the surgical robot resection process when the tissue is slightly moved. Figure 3 201) The joint sensor records the joint angle q, joint angular velocity and through force sensors ( Figure 3 202) records the contact force F, and these three parameters are used as state feedback quantities. express.

[0062] S4: Based on the error between the contact force and the expected contact force, construct an objective function with the minimum error value, and solve the optimized optimal control input. When constructing the objective function, it is necessary to first build a prediction model. The more accurate the prediction model is, the more accurate the optimal control input will be. The bone tissue resection model provided by the present invention The joint model with the surgical robot dynamics model is as follows:

[0063]

[0064] in, They are the joint angle, joint angular velocity, and joint angular acceleration of the surgical robot, respectively. M is the mass matrix of the surgical robot, u is the control input, C is the Coriolis force matrix, G is the gravity matrix, J is the Jacobian matrix, and F e is the actual contact force between the osteotome and the bone tissue to be removed, and T represents the transposition.

[0065] The overall joint model combining the resection model and the surgical robot dynamics model is discretized using the Euler method as follows:

[0066] x(k+1)=f(x(k),u(k))

[0067] Among them, x(k+1) represents the actual state at time k+1 x(k) represents the actual state at time k u(k) represents the control input at time k; f(x(k),u(k)) represents the ideal state at time k+1;

[0068] Since tissue micro-movement will cause the contact force between the osteotome and the tissue to change, it is only necessary to ensure that the contact force error ΔF=F at any time z -R -1 F d At the same time, when ensuring the minimum contact force error, it is also necessary to ensure that the trajectory tracking error e=K(q(k))-s k Minimum, where K is the forward kinematics operator of the surgical robot. Therefore, the following objective function is constructed:

[0069]

[0070] Wherein, the contact force error at time k is ΔF(k) = F z -R -1 F d , F z is the state at time k Medium F e The component on the z-axis in the direction of the bone knife tip, Fd 为 The expected contact force, ΔF(0) = 0, Q is the weight matrix related to the contact force; the trajectory tracking error at time k is e(k) = K(q(k))-s k , q(k) is the joint angle of the surgical robot at time k, K is the forward kinematics operator of the surgical robot, and K(q(k)) represents the conversion of q(k) to the Cartesian coordinate system, s k is the spatial position of the surgical robot at time k in the surgical resection path, e(0) = 0; W is the weight matrix related to the trajectory tracking error; R is the weight matrix related to the control input; N represents the total number of moments; it can be seen that the objective function is a function composed of three quantities: contact force error, trajectory tracking error and control input.

[0071] At the same time, the initial conditions are given:

[0072]

[0073] In order to ensure surgical safety, relevant constraints need to be set:

[0074]

[0075] Where ΔF lower and ΔF upper are the lower limit and upper limit of the contact force error, respectively, lower With qupper are the lower limit and upper limit of the joint angle of the surgical robot, u lower with u upper They are the lower and upper limits of the control input respectively.

[0076] Assume that the objective function J is at the optimal point f * (x(k),u(k)) to obtain the optimal solution J * , so the following Lagrangian function can be constructed:

[0077]

[0078] Therefore, in any region:

[0079]

[0080] We can further know that:

[0081] J * ≥L *

[0082] Therefore, solving the optimal value of the objective function becomes a matter of solving the optimal value of the Lagrangian function. Common methods for solving such problems include the dual ascent method or the dual decomposition method, but these two methods impose strict restrictions on the objective function. Orthopedic surgical robots involve three states during tracking and numerous constraints, making them difficult to solve.

[0083] In order to reduce the restriction of the objective function and bring the constraint conditions into the objective function, the original Lagrangian function is augmented to obtain the augmented Lagrangian function:

[0084]

[0085] Where ρ is the penalty function. We further simplify λ[f(x(k),u(k))-x(k+1)] to the constraint condition I=(q,u,ΔF), and split it into three state penalty terms:

[0086]

[0087] Among them, I(q(k),u(k),ΔF(k)) is the constraint condition, ρ j is the Lagrange multiplier related to the joint angle of the surgical robot, ρ u is the Lagrange multiplier related to the control input, ρ f is the Lagrange multiplier related to the contact force error, v j is the dual variable related to the joint angle of the surgical robot in the constraint condition, v uis the dual variable related to the control input in the constraint condition, v f is the dual variable related to the contact force error in the constraint condition;

[0088] By converting the objective function into an augmented Lagrangian function, its constraints are integrated into the function, making the original objective function free of constraints. The augmented Lagrangian function is solved through cyclic update iteration. The cyclic iteration sequence is as follows:

[0089] Step 1: x(k) = L ρ (x,u(k-1),λ(k-1))

[0090] Step 2: u(k) = L ρ (x(k),u,λ(k-1))

[0091] Step 3: λ(k) = L ρ (x(k),u(k),λ)

[0092] Each loop requires three iterations. The first iteration requires two variables to be fixed. In step 1, u and λ are input at time k-1, and x(k) is calculated at time k. In step 2, λ is input at time k-1 and x at time k, and u(k) is calculated at time k. In step 3, x and u at time k are input at time k, and λ(k) is calculated at time k. This continues in this manner, with each iteration fixing the two variables from the previous time and solving for one variable at the current time.

[0093] These three steps are iterated continuously. Each time an iteration is performed, it is determined whether the trajectory tracking error corresponding to the current iteration is less than the set threshold. If it is, the control input corresponding to the current iteration is the optimal control input. If the iteration reaches the maximum upper limit N, and the trajectory tracking errors corresponding to N iterations are not less than the set threshold, the control input corresponding to the minimum trajectory tracking error corresponding to N iterations is used as the optimal control input.

[0094] It should be noted that, in addition to the above methods for solving the objective function with constraints, differential dynamic programming algorithms, alternating multiplier algorithms, etc. can also be used for solving the problem.

[0095] S5: Send control inputs to the robot control to track bone micromotion. The control inputs obtained in S4 are passed to the surgical robot's control box. The surgical robot then moves according to the given control inputs, tracking bone micromotion while minimizing path tracking errors.

[0096] It should be noted that the control input is usually a torque, which is used to control the movement of the robotic arm. The relative position between the bone cutter and the robotic arm remains unchanged, and what changes is the movement of the robotic arm with the bone cutter installed at the end.

[0097] Furthermore, if Figure 3 As shown, it is a working diagram of a surgical robot for bone tumor resection, wherein 201 is the surgical robot body, 202 is a force sensor, 203 is a bone knife, 204 is a bone tumor, 205 is an optical navigation marker, and 206 is a preoperatively planned surgical resection path.

[0098] The present invention also provides a real-time micro-motion tracking device for an orthopedic surgical robot, such as Figure 3 As shown, the device includes a parameter setting module 100 , a data acquisition module 200 , an optimization solution module 300 , and a control module 400 .

[0099] The parameter setting module 100 is used to set the surgical resection path (206), set the expected contact force, set the robot initial position, set the bone knife speed, power, and water flow speed.

[0100] The data acquisition module 200 is used to receive the real-time joint angles, joint velocities, contact forces, and control inputs of the surgical robot and record these data.

[0101] The optimization solution module 300 is used to construct the system dynamics, the optimal objective function, the constraints, and solve for the optimal control input, ultimately obtaining the optimal control input. Furthermore, when the system dynamics are inaccurate, the optimization solution module can be used to iterate optimization using received historical data. Furthermore, if there are no constraints during the surgical resection, a simpler and faster solution method can be employed, such as quadratic programming, to solve for the optimal control input. Furthermore, if the solution process continues to iterate and reaches the maximum number of iterations, the optimal result from this iteration can be selected as the control input.

[0102] The control module 400 is used to respond to the received optimal control instruction and determine the robot's operating task.

[0103] In summary, the present invention provides a real-time tracking control system for micro-motions of an orthopedic surgical robot. This system determines whether tissue micro-motions are occurring by measuring whether the contact force is consistent with the desired contact force. This is because when bone tissue micro-motions occur, it exerts a counterforce on the tool, causing the contact force to deviate from the desired contact force. When micro-motions occur, the system optimizes the control input to bring the contact force close to the desired contact force.

[0104] Of course, the present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may of course make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A micro-motion real-time tracking control system for an orthopedic surgical robot, characterized in that: Including parameter setting module, data acquisition module, optimization solution module, and control module; The parameter setting module is used to set the preset surgical resection path, the initial position of the surgical robot, and the desired contact force between the osteotome located at the end of the surgical robot and the bone tissue to be resected; The data acquisition module is used to detect the joint angle, joint speed, and actual contact force of the surgical robot in real time; The optimization solution module is used to input the preset surgical resection path, the initial position of the surgical robot, the expected contact force, the joint angles and joint velocities of the surgical robot, and the actual contact force into a joint model composed of a bone tissue resection model and a surgical robot dynamics model, and obtain an optimal control input that minimizes the sum of the contact force error between the expected contact force and the actual contact force and the trajectory tracking error between the preset surgical resection path and the actual surgical resection path; The control module is used to generate corresponding control instructions according to the optimal control input to drive the surgical robot to perform specified actions; The joint model is: in, They are the joint angle, joint angular velocity, and joint angular acceleration of the surgical robot, is the mass matrix of the surgical robot, is the control input, is the Coriolis force matrix, is the gravity matrix, is the Jacobian matrix, is the actual contact force between the osteotome and the bone tissue to be removed, and T represents the transposition; The method to obtain the optimal control input through the joint model is as follows: The joint model is discretized using the Euler method, and the following discrete state equation is obtained: in, express The actual state at the moment ; express The actual state at the moment ; express Control input at each moment; express The ideal state of the moment; The objective function is constructed based on the discrete state equation as follows: in, Contact force error at the moment , for State of the moment middle The component on the z-axis in the direction of the bone knife tip, is the expected contact force, , is the weight matrix related to the contact force; Trajectory tracking error at time , for The joint angles of the surgical robot at the moment, is the forward kinematics operator of the surgical robot, and Indicates that Converted to Cartesian coordinate system, In the surgical resection path The spatial position of the surgical robot at the moment, ; is the weight matrix related to the trajectory tracking error; is the weight matrix related to the control input; N represents the total number of moments; The augmented Lagrangian function is constructed based on the objective function as follows: in, is the penalty function, for The weight factor at the moment, is the two-norm; The augmented Lagrangian function is solved to obtain the optimal control input.

2. A micro-motion real-time tracking control system for an orthopedic surgical robot according to claim 1, characterized in that: The solution method of the augmented Lagrangian function is: Split the augmented Lagrangian function into three penalty terms of state quantities: in, is the constraint condition, is the Lagrange multiplier related to the joint angle of the surgical robot, is the Lagrange multiplier related to the control input, is the Lagrange multiplier related to the contact force error, is the dual variable related to the joint angle of the surgical robot in the constraint condition, is the dual variable related to the control input in the constraint condition, is the dual variable related to the contact force error in the constraint condition; Solve the augmented Lagrangian function of the penalty term split into three state quantities according to the following iterative formula: Each time an iteration is performed, it is determined whether the trajectory tracking error corresponding to the current iteration is less than the set threshold. If it is, the control input corresponding to the current iteration is the optimal control input. If the iteration reaches the maximum upper limit N, and the trajectory tracking errors corresponding to N iterations are not less than the set threshold, the control input corresponding to the minimum value of the trajectory tracking errors corresponding to N iterations is used as the optimal control input.

3. A micro-motion real-time tracking control system for an orthopedic surgical robot according to claim 2, characterized in that: Constraints The details are as follows: in, and are the lower limit and upper limit of the contact force error, and are the lower and upper limits of the joint angles of the surgical robot, and They are the lower and upper limits of the control input respectively.

4. The micro-motion real-time tracking control system for an orthopedic surgical robot according to claim 1, characterized in that: The weight matrix associated with the control input is the rotation matrix between the micro-motion direction of the bone tissue and the end direction of the osteotome, and the micro-motion direction of the bone tissue is obtained as follows: Before the surgical operation, an optical navigation marker is installed within a set vicinity of the bone tissue, and the optical navigation marker is fixed on the bone tissue; By measuring the positions of optical navigation markers at different times, the direction of bone tissue micro-motion is calculated.

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