Micro-motion real-time tracking control system for orthopedic surgery robot

Abstract

According to the micro-motion real-time tracking control system for the orthopedic surgery robot, whether the bone tissue generates micro-motion or not is judged by judging whether the contact force is consistent with the expected contact force or not, and when the bone tissue generates micro-motion, the bone tissue can give a reverse force to a cutter, so that the contact force is inconsistent with the expected contact force; when micro motion is generated, the contact force is made to be close to the expected contact force by solving the optimal control input; that is to say, real-time path planning is carried out through the state quantity fed back by the robot and the sensor, a neural network does not need to be used for prediction, and therefore micro-motion real-time tracking does not depend 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 refer to tumors that occur in bone tissue and accessory tissues of various types of bones. They often occur in the distal femur, pelvis, cervical spine, thoracic spine, shoulder joint and other parts, and generally manifest as local swelling or fracture. Surgical resection is one of the most effective methods for treating bone tumors. However, during the operation, the patient's breathing and the interaction between the surgical instruments and tissues can cause micro-movement of bone tissue, which can reduce the accuracy of the surgical operation and even cause the operation to fail.

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

[0004] Duan et al. used an infrared optical camera to record the patient's bone tissue movement fluctuation data within a certain period of time before the operation, and used the PCA principal component analysis method to reduce the collected movement fluctuation data into one-dimensional data. The reduced data was used to train the LSTM neural network, where 10-20 consecutive sampling points were used as network input and the output was the subsequent 1-4 points. The sliding window allowed the continuous input points to pass over time, thereby ensuring that predictions could be made with limited data. The predicted data was sent to the robotic arm as the target point to achieve micro-motion tracking.

[0005] Qi et al. designed a grinding depth adjustment device, which includes a mounting frame, a bone knife, a connecting rod, a sliding drive mechanism, and a protective cover. The device can adjust the position of the protective cover through the sliding drive mechanism, so that after the bone knife grinding head grinds a certain depth, the protective cover contacts the bone tissue. At this time, the bone knife grinding head can no longer continue to grind the bone tissue, and there will be no over-grinding. The high-speed rotating grinding head will not contact the soft tissue or nerves in the spine, thereby avoiding damage to the soft tissue and nerves. Since the protective cover of the device is in contact with the bone tissue, the protective cover can also rise and fall with the breathing movement, realizing the micro-motion tracking of the bone knife 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 a 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 respiratory movement direction, 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-motion of an orthopedic surgical robot, which determines whether the bone tissue has micro-motion by checking whether the contact force is consistent with the expected contact force, and adjusts the path of the surgical robot 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 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, 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, are the joint angles, joint angular velocities, and joint angular accelerations 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 by 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 cutter 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 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 transformation of q(k) into 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 trajectory tracking error 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 With ΔF upper are the lower and upper limits of the contact force error, respectively, and q lower With q upper are the lower limit and upper limit of the joint angle of the surgical robot, respectively. 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 a rotation matrix between the micro-motion direction of the bone tissue and the direction of the end of the bone cutter, 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 micro-motion real-time tracking and control system for an orthopedic surgical robot. It determines whether the bone tissue has micro-motion by checking whether the contact force is consistent with the expected contact force. When the bone tissue has micro-motion, the bone tissue will give the tool a reverse force, thereby making the contact force inconsistent with the expected contact force. When micro-motion occurs, the contact force is made 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 quantity fed back by the robot and the sensor, without the need to use a neural network for prediction. Therefore, the real-time tracking of micro-motion 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-motion of an orthopedic surgical robot. The micro-motion 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 path of the surgical robot can be adjusted in real time according to the real resection force, thereby achieving bone tissue resection at any angle. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 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 A flow chart 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 schematic 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 a surgical robot, and a desired contact force between a bone cutter 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 angles of the surgical robot, the joint speeds, and the actual contact force into a joint model consisting 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, 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 a grid, or a network model based on data drive. 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 by 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 the bone tissue at different rotation speeds, powers and different bone tissues when the bone knife is resecting the bone tissue, using parameters such as rotation 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 bone knife operation parameters, 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 the micro-movement of the bone tissue can be calculated. The doctor then adjusts the angle of the bone cutter at the end of the surgical robot and moves it to the appropriate initial position. The direction of the micro-movement of the bone tissue is related to the direction of the end of the bone cutter ( Figure 3 Medium F x ,F y ,F z ) is represented by the rotation matrix R. The operation parameters of the osteotome are set, including speed, power, water flow rate and other parameters. The surgical robot starts to work 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 sensors of the device record the joint angle q and joint angular velocity And through the force sensor ( 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 construct a prediction model. The more accurate the prediction model is, the more accurate the optimal control input is. 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, are the joint angles, joint angular velocities, and joint angular accelerations 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 by 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 bone knife 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 the contact force error is minimized, 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 cutter tip, Fd 为 Expected contact force, ΔF(0) = 0, Q is the weight matrix related to the contact force; the trajectory tracking error at time k 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 transformation of q(k) into 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 the safety of surgery, relevant constraints need to be set:

[0074]

[0075] Where, ΔF lower With ΔF upper are the lower and upper limits of the contact force error, respectively, and q lower With qupper are the lower limit and upper limit of the joint angle of the surgical robot, respectively. 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] Further information:

[0081] J * ≥L *

[0082] Therefore, solving the optimal value of the objective function becomes solving the optimal value problem of the Lagrangian function. Common methods for solving such problems can be the dual ascent method or the dual decomposition method, but these two methods have strict restrictions on the objective function. There are three states involved in the tracking of orthopedic surgical robots and there are many constraints, so it is 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, and λ[f(x(k),u(k))-x(k+1)] is further simplified to the constraint condition I=(q,u,ΔF), and split into three state quantity 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] After the objective function is converted into an augmented Lagrangian function, its constraints are integrated into the function, so that the original objective function has no constraints. The augmented Lagrangian function is solved by loop update iteration. The loop 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] Three iterations are performed in each loop, and the first iteration requires two variables to be fixed. In step 1, input u and λ at time k-1, and then calculate x(k) at time k; in step 2, input λ at time k-1 and x at time k, and then calculate u(k) at time k; in step 3, input x at time k and u at time k, and then calculate λ(k) at time k. In this way, in each loop, the two variables at the previous moment are fixed, and then one variable at the current moment is solved.

[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 method for solving the objective function with constraints, it can also be solved by differential dynamic programming algorithm, alternating multiplier algorithm, etc.

[0095] S5: Send control input to the robot control to achieve bone tissue micro-motion tracking. The control input obtained based on S4 is transmitted to the control box of the surgical robot. The surgical robot will move according to the given control input, while tracking the micro-motion of the tissue and achieving the minimum path tracking error.

[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 surgical resection path planned before surgery.

[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 cutter speed, power, and water flow rate.

[0100] The data acquisition module 200 is used to receive the real-time joint angle, joint speed, contact force and control input of the surgical robot and record these data.

[0101] The optimization solution module 300 is used to construct system dynamics, optimal objective function, constraints, and solve the optimal control input, and obtain the result with the most control input. In addition, the optimization solution module can also be used to perform optimization iterations through the received historical data when the system dynamics are inaccurate. At the same time, if there are no constraints during the surgical resection process, a simpler and faster solution method can be used, such as using quadratic programming to solve the optimal control input. In addition, if the solution process is iterated and reaches the maximum number of iterations, the optimal result in the iterative process 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 operation task.

[0103] In summary, the present invention provides a micro-motion real-time tracking control system for an orthopedic surgical robot, which determines whether the tissue has micro-motion by checking whether the contact force is consistent with the expected contact force, because when the bone tissue has micro-motion, the bone tissue will give the tool a reverse force, so that the contact force is inconsistent with the expected contact force. When micro-motion occurs, the contact force is made close to the expected contact force by solving the optimal control input.

[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 certainly 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: It includes 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 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, 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.

2. A micro-motion real-time tracking control system for an orthopedic surgical robot as claimed in claim 1, characterized in that: The joint model is: in, are the joint angles, joint angular velocities, and joint angular accelerations 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.

3. A micro-motion real-time tracking control system for an orthopedic surgical robot as claimed in claim 2, characterized in that: The method to obtain the optimal control input through the joint model is as follows: The joint model is discretized by the Euler method, and the following discrete state equation is obtained: x(k+1)=f(x(k),u(k)) 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; The objective function is constructed based on the discrete state equation as follows: 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 cutter 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 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 transformation of q(k) into 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; The augmented Lagrangian function is constructed based on the objective function as follows: Among them, ρ is the penalty function, λ is the weight factor at time k, is the two-norm; The augmented Lagrangian function is solved to obtain the optimal control input.

4. A micro-motion real-time tracking control system for an orthopedic surgical robot as claimed in claim 3, characterized in that: The solution method of the augmented Lagrangian function is: Split the augmented Lagrangian function into three penalty terms of state quantities: 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 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; Solve the augmented Lagrangian function of the penalty term split into three state quantities according to the following iterative formula: x(k)=L ρ (x,u(k-1),λ(k-1)) u(k)=L ρ (x(k),u,λ(k-1)) λ(k)=Lρ(x(k),u(k),λ) 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.

5. A micro-motion real-time tracking control system for an orthopedic surgical robot as claimed in claim 4, characterized in that: The constraints I(q(k), u(k), ΔF(k)) are as follows: Where, ΔF lower With ΔF upper are the lower and upper limits of the contact force error, respectively, and q lower With q upper are the lower limit and upper limit of the joint angle of the surgical robot, respectively. lower with u upper They are the lower and upper limits of the control input respectively.

6. A micro-motion real-time tracking control system for an orthopedic surgical robot as claimed in claim 3, characterized in that: 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 bone cutter, and the method for obtaining the micro-motion direction of the bone tissue is: 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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