Surgical robot error analysis and compensation method

Abstract

The invention relates to the technical field of robots, in particular to a surgical robot error analysis and compensation method. Establishing an error model among hardware systems of the surgical robot according to the hardware systems of the surgical robot; the hardware system comprises a CT, an optical tracking system and a mechanical arm hardware system; establishing an error transfer model of the surgical robot according to the error model among the hardware systems of the surgical robot; and according to the error transfer model, geometric parameters of the robot are calibrated, and non-geometric errors of the robot are compensated. According to the technical scheme provided by the invention, the positioning precision of the surgical robot system is improved by considering the error analysis and compensation of the error transfer coupling relationship among the components of the surgical robot system, so that a reference can be provided for the positioning error analysis and compensation of the surgical robot.

Description

Technical Field

[0001] The present invention relates to the field of robotics technology, and in particular to a surgical robot error analysis and compensation method. Background Art

[0002] Precision and minimally invasive treatment is the main theme of orthopedic surgery in the 21st century and has become the development trend of orthopedic clinical treatment. Due to its precision and minimally invasive characteristics, medical robots can not only improve surgical accuracy and reduce surgical injuries, but also effectively reduce the labor intensity of doctors. However, due to the structural complexity of the surgical robot system and the coupling transmission problem of errors, the traditional surgical robot positioning method still has certain errors.

[0003] The current compensation methods for robot positioning errors, on the one hand, are mainly aimed at industrial robots, and do not take into account components such as the CT reconstruction system used for planning and the optical positioning system used for tracking in the surgical robot system, and are not fully applicable to the application scenarios of surgical robots. On the other hand, the calibration technology mainly based on equipment such as laser trackers and three-dimensional coordinate measuring machines only corrects the geometric errors of the robot, without considering other non-geometric error factors. Summary of the invention

[0004] In order to solve the problems existing in the prior art, the present invention provides a method for error analysis and compensation of a surgical robot, which includes: establishing a surgical robot error model according to the surgical robot hardware system, establishing a surgical robot error transfer model according to the surgical robot error model, and realizing calibration of robot geometric parameters and compensation of non-geometric errors according to the error transfer model; for geometric errors, a kinematic calibration method is adopted to calculate the error between the actual target posture and the expected target posture, and the calibrated kinematic parameter values ​​are obtained after multiple iterations; for non-geometric errors, a neural network is trained by a back propagation algorithm, the expected target posture is input, and the position error and posture error are output, so as to correct the actual target posture; according to the technical solution provided by the present invention, a reference can be provided for surgical robot positioning error analysis and compensation.

[0005] The present invention adopts the following technical solution, a surgical robot error analysis and compensation method, comprising:

[0006] Establishing an error model between various hardware systems of the surgical robot according to the hardware system of the surgical robot; the hardware system includes CT, optical tracking system, and robotic arm hardware system;

[0007] An error transfer model of the surgical robot is established based on the error models between the various hardware systems of the surgical robot;

[0008] The robot's geometric parameters are calibrated and the robot's non-geometric errors are compensated based on the error transfer model.

[0009] Furthermore, the CT reconstruction system is specifically: a reconstruction system and an optical tracking system registration model, and the model is obtained as follows:

[0010] Obtain the coordinate set P of the positioning target in the CT reconstruction coordinate system;

[0011] Obtain the coordinate set Q of the positioning target in the optical tracking system coordinate system;

[0012] The iterative closest point algorithm is used for optimization to obtain the coordinate transformation matrix between the CT reconstruction system and the optical tracking system:

[0013]

[0014] Among them, the coordinate set P and the coordinate set Q are both matrices with n rows and 3 columns, and each row represents the coordinate value of a positioning target in a space; R is a matrix with 3 rows and 3 columns, representing the coordinate rotation transformation relationship between the CT reconstruction system and the optical tracking system; T is a matrix with 3 rows and 1 column, representing the coordinate translation transformation relationship between the CT reconstruction system and the optical tracking system.

[0015] Furthermore, the optical tracking system is specifically: an internal imaging model of the optical tracking system, and the model is obtained by:

[0016] According to the optical camera imaging model, the conversion relationship between the camera imaging coordinate system and the world coordinate system is obtained as follows:

[0017]

[0018] where u 1 ,v 1 Indicates the coordinates in the left camera imaging coordinate system, u 2 ,v 2 Indicates the coordinates of the right camera imaging coordinate system, X w ,Y w ,Z w Represents the coordinates of the target point in the world coordinate system, S 1 ,S 2 is the scaling factor, K 1 ,K 2 Represents the left and right camera intrinsic parameter matrices, R, T is used to describe the relative position of the left and right cameras;

[0019] According to the binocular camera reconstruction principle, the conversion relationship between the camera imaging coordinate system and the internal coordinate system of the optical positioning system is obtained:

[0020]

[0021] Where b represents the baseline distance between the two cameras, d represents the binocular disparity between the two cameras, and f represents the focal length of the camera.

[0022] Furthermore, the mechanical arm hardware system is specifically: an optical tracking system and a mechanical arm calibration model, which specifically includes:

[0023] According to the different postures of multiple groups of robot ends, obtain the transformation matrix of multiple groups of robot ends relative to the robot base

[0024] According to the coordinates of multiple sets of robot end positions in camera coordinates, the transformation matrix of multiple sets of robot end calibration targets relative to the camera is obtained.

[0025] Solve the matrix equation according to the Tsai robotic arm hand-eye calibration method:

[0026]

[0027] in, represents the inverse matrix of the transformation matrix of the end of the manipulator relative to the base of the manipulator in posture 2, represents the transformation matrix of the end of the manipulator relative to the base of the manipulator in posture 1; Represents the transformation matrix of the camera to be solved with respect to the base of the robotic arm; represents the transformation matrix of the end of the robotic arm relative to the camera in posture 2, Represents the inverse matrix of the transformation matrix of the end of the robotic arm relative to the camera in posture 1;

[0028] Get the calibration matrix between the optical tracking system and the robotic arm

[0029] Furthermore, the mechanical arm hardware system further includes: a mechanical arm kinematics model, which is obtained by:

[0030] The kinematic model of the robotic arm is established according to the improved DH parameter modeling method, and the relationship between the end position and joint angle of the robotic arm is obtained:

[0031]

[0032]

[0033] Among them, α, d, θ, a are the improved DH parameters of the robot arm, Represents the transformation relationship from the base coordinate system to the terminal coordinate system.

[0034] Furthermore, the error model between the hardware systems of the surgical robot is established, including:

[0035] The error model includes: registration error between the CT reconstruction system and the optical tracking system, imaging error inside the optical tracking system, calibration error between the optical tracking system and the manipulator system, and geometric parameter error inside the manipulator system;

[0036] Wherein, the internal geometric parameter error of the robot arm system in the error model is the geometric error;

[0037] The registration error between the CT reconstruction system and the optical tracking system, the internal imaging error of the optical tracking system, and the calibration error between the optical tracking system and the robotic arm system are non-geometric errors;

[0038] The registration error between the CT reconstruction system and the optical tracking system is expressed as:

[0039]

[0040] where p i represents the coordinates of the i-th marker point in the CT reconstruction coordinate system, q i represents the coordinates of the i-th marker point in the optical tracking system coordinate system, R, T represents the transformation matrix calculated using the closest point iteration method;

[0041] The internal imaging error of the optical tracking system is expressed as:

[0042]

[0043] Where b and d represent the baseline distance and binocular parallax of the two cameras, respectively, and f represents the focal length of the camera;

[0044] The calibration error between the optical tracking system and the robotic arm system is expressed as:

[0045]

[0046] The matrix represents the calibration matrix between the optical tracking system and the robotic arm, x origin and x target Respectively represent the expected coordinates and actual coordinates of the terminal calibration target;

[0047] The internal geometric parameter error of the robotic arm system is expressed as:

[0048]

[0049] in represents the position error due to the improved DH parameter error, Represents the attitude error caused by the error in the improved DH parameters.

[0050] Furthermore, an error transmission model of the surgical robot is established, including:

[0051] According to the error model, the transformation relationship from the expected target point to the actual target point of the surgical robot is obtained:

[0052]

[0053] According to the transformation relationship from the expected target point to the actual target point, the expression of the total error is obtained:

[0054]

[0055] Where x is the desired target point, is the coordinate transformation matrix between the CT reconstruction system and the optical tracking system, is the coordinate transformation matrix between the optical tracking system and the robot, the functions IK() and FK() are the inverse kinematics and forward kinematics of the robot, respectively, x' is the actual target point, E() represents the non-geometric error, S * Indicates the expected target point.

[0056] Furthermore, the geometric parameters of the robot are calibrated according to the error transfer model, including:

[0057] Select m groups of joint angles and obtain the desired target posture according to the kinematics of the robot arm;

[0058] The actual target position of the robot arm is obtained by measuring the m groups of joint angles using a measuring device;

[0059] Through the error between the expected target posture and the actual target posture, the improved DH parameter error is obtained according to the internal error model of the manipulator system;

[0060] According to the DH parameter error, the robot arm is corrected to improve the DH parameter value;

[0061] The modified improved DH parameter values ​​are used as parameters for the kinematics and inverse kinematics calculations of the robot arm, and the iterations are repeated until the error converges to the set range to obtain the kinematic parameter calibration values.

[0062] Furthermore, the non-geometric errors of the robot are compensated, including:

[0063] Compensate for the robot's non-geometric errors by training a neural network;

[0064] The neural network includes an input layer, a hidden layer and an output layer;

[0065] The input layer contains 6 neurons, and the input is the desired target pose x, y, z, α, β, γ;

[0066] The hidden layer contains n neurons and is fully connected to the input layer;

[0067] The output layer contains 6 neurons, representing the position error and attitude error respectively, Δx, Δy, Δz, Δα, Δβ, Δγ are fully connected with the hidden layer;

[0068] The output of each neuron is calculated as

[0069]

[0070] in represents the output of neuron j in layer k, function f a represents the Noisy ReLU activation function, defined as

[0071] f a (x)=max(0,x+Y),y~N(0,σ(x))

[0072] represents the weight of the connection between neuron j in the kth layer and neuron i in the k-1th layer, represents the output of neuron i in the k-1th layer, represents the bias value of neuron j in the kth layer;

[0073] The neural network is trained by back propagation algorithm, and the non-geometric error compensation value of the robot's target position is obtained using the trained neural network.

[0074] The beneficial effects of the present invention are as follows: the present invention establishes a surgical robot error model based on the surgical robot hardware system, establishes a surgical robot error transfer model based on the surgical robot error model, and realizes the calibration of the robot's geometric parameters and compensation of non-geometric errors based on the error transfer model. Under the condition of comprehensively considering the geometric and non-geometric errors in the surgical robot hardware system, different methods can be used to compensate for the two types of errors, thereby effectively improving the positioning accuracy of the surgical robot system. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0076] Figure 1 A schematic flow chart of a surgical robot error analysis and compensation method according to an embodiment of the present invention;

[0077] Figure 2 A schematic diagram of a process of compensating non-geometric errors by using a neural network and compensating non-geometric errors by using geometric parameter calibration according to an embodiment of the present invention;

[0078] Figure 3 The figure is a schematic diagram of comparing positioning errors before and after error compensation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0079] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0080] A schematic flow chart of a surgical robot error analysis and compensation method according to an embodiment of the present invention is shown in FIG. Figure 1 As shown, including:

[0081] 101. Establish a surgical robot error model based on the surgical robot hardware system;

[0082] In the embodiment of the present invention, the surgical robot hardware system includes three parts: a CT reconstruction system, an optical tracking system, and a mechanical arm hardware system; the surgical robot error transfer model includes the registration error between the CT reconstruction system and the optical tracking system, the internal imaging error of the optical tracking system, the calibration error between the optical tracking system and the mechanical arm system, and the internal geometric parameter error of the mechanical arm system;

[0083] Among them, the internal geometric parameter error of the robotic arm system in the error model belongs to geometric error, and the alignment error between the CT reconstruction system and the optical tracking system, the internal imaging error of the optical tracking system, and the calibration error between the optical tracking system and the robotic arm system belong to non-geometric error; the present invention compensates for the geometric error by geometric parameter calibration, and compensates for the non-geometric error by training a neural network.

[0084] Specifically, the registration model of the CT reconstruction system and the optical tracking system includes:

[0085] According to the results given by the CT reconstruction system, a coordinate set P of the positioning target in the CT reconstruction coordinate system is obtained;

[0086] According to the results given by the optical tracking system, the coordinate set Q of the positioning target in the optical tracking system coordinate system is obtained;

[0087] Solve the optimization problem using the iterative closest point algorithm: Obtain the coordinate transformation matrix between the CT reconstruction system and the optical tracking system:

[0088]

[0089] The coordinate set P and the coordinate set Q are both matrices with n rows and 3 columns, and each row represents the coordinate value of a positioning target in a space; R is a matrix with 3 rows and 3 columns, representing the coordinate rotation transformation relationship between the CT reconstruction system and the optical tracking system; T is a matrix with 3 rows and 1 column, representing the coordinate translation transformation relationship between the CT reconstruction system and the optical tracking system.

[0090] Establishing the internal imaging model of the optical tracking system specifically includes:

[0091] According to the optical camera imaging model, the conversion relationship between the camera imaging coordinate system and the world coordinate system is obtained:

[0092]

[0093] where u 1 ,v 1 Indicates the coordinates of the left camera imaging coordinate system, u 2 ,v 2 Indicates the coordinates of the right camera imaging coordinate system, X w ,Y w ,Z w Represents the coordinates of the target point in the world coordinate system, S 1 ,S 2 is the scaling factor, K 1 ,K 2 Represents the left and right camera intrinsic parameter matrices, R, T is used to describe the relative position of the left and right cameras;

[0094] According to the binocular camera reconstruction principle, the conversion relationship between the camera imaging coordinate system and the internal coordinate system of the optical positioning system is obtained:

[0095]

[0096] Where b and d represent the baseline distance and binocular disparity of the two cameras, respectively, and f represents the focal length of the camera.

[0097] Establishing the optical tracking system and robotic arm calibration model specifically includes:

[0098] According to the different postures of multiple groups of robot ends, obtain the transformation matrix of multiple groups of robot ends relative to the robot base

[0099] According to the coordinates of multiple sets of robot end positions in camera coordinates, the transformation matrix of multiple sets of robot end calibration targets relative to the camera is obtained.

[0100] Solve the matrix equation according to Tsai robot hand-eye calibration method Get the calibration matrix between the optical tracking system and the robotic arm in, represents the inverse matrix of the transformation matrix of the end of the manipulator relative to the base of the manipulator in posture 2, represents the transformation matrix of the end of the manipulator relative to the base of the manipulator in posture 1; Represents the transformation matrix of the camera to be solved with respect to the robotic arm; represents the transformation matrix of the end of the robotic arm relative to the camera in posture 2, Represents the inverse matrix of the transformation matrix of the end of the robot arm relative to the camera in posture 1.

[0101] Establishing the kinematic model of the robotic arm specifically includes:

[0102] The kinematic model of the robotic arm is established according to the improved DH parameter modeling method, and the relationship between the end position and joint angle of the robotic arm is obtained:

[0103]

[0104]

[0105] Among them, α, d, θ, a are the improved DH parameters of the robot arm, Represents the transformation relationship from the base coordinate system to the terminal coordinate system.

[0106] In the embodiment of the present invention, based on the above-constructed system models, an error model between the systems is further established, specifically:

[0107] The registration error between the CT reconstruction system and the optical tracking system: The registration error between the CT reconstruction system and the optical tracking system is obtained according to the registration model of the CT reconstruction system and the optical tracking system:

[0108]

[0109] where p i represents the coordinates of the i-th marker point in the CT reconstruction coordinate system, q i represents the coordinates of the i-th marker point in the optical tracking system coordinate system, and R, T represents the transformation matrix calculated using the nearest point iteration method.

[0110] Internal imaging error of the optical tracking system: The internal imaging error of the optical tracking system is obtained according to the internal imaging model of the optical tracking system:

[0111]

[0112] Where b and d represent the baseline distance and binocular parallax of the two cameras, respectively, and f represents the focal length of the camera.

[0113] Calibration error of optical tracking system and robotic arm system: According to the calibration model of optical tracking system and robotic arm, the calibration error of optical tracking system and robotic arm system is obtained:

[0114]

[0115] The matrix represents the calibration matrix between the optical tracking system and the robotic arm, x origin and x target They represent the expected coordinates and actual coordinates of the terminal calibration target respectively.

[0116] Internal error of the robot system: According to the robot kinematic model, the internal error of the robot system is obtained:

[0117]

[0118] in represents the position error due to the improved DH parameter error, Represents the attitude error caused by the error in the improved DH parameters.

[0119] 102. Establish an error transfer model of the surgical robot based on the error models between the hardware systems of the surgical robot;

[0120] The embodiment of the present invention further obtains the conversion relationship from the expected target point to the actual target point of the surgical robot based on the above error model:

[0121]

[0122] because As well as the inaccuracy of DH parameters, there is an error between the expected target point x and the actual target point x'. According to the conversion relationship from the expected target point to the actual target point, the expression of the total error is obtained:

[0123]

[0124] Where x is the desired target point, is the coordinate transformation matrix between the CT reconstruction system and the optical tracking system, is the coordinate transformation matrix between the optical tracking system and the robot, the functions IK() and FK() are the inverse kinematics and forward kinematics of the robot, respectively, x' is the actual target point, E() represents the non-geometric error, s * Indicates the expected target point.

[0125] 103. According to the error transfer model, the robot geometric parameters are calibrated and the non-geometric errors are compensated;

[0126] like Figure 2 As shown, the embodiment of the present invention adopts a geometric parameter calibration method to compensate for the geometric error, specifically:

[0127] Select m groups of joint angles and obtain the desired target posture according to the kinematics of the robot arm;

[0128] Using laser trackers and other measuring equipment, the actual target position of the robot arm is obtained based on the m groups of joint angles;

[0129] Through the error between the expected target posture and the actual target posture, the improved DH parameter error is obtained according to the internal error model of the manipulator system;

[0130] Through the DH parameter error, the robot arm is corrected to improve the DH parameter value;

[0131] The modified improved DH parameter values ​​are used as parameters for calculating the kinematics and inverse kinematics of the robot arm, and the above process is repeated until the error converges to the set range to obtain the kinematic parameter calibration value.

[0132] Further, the embodiment of the present invention compensates for the non-geometric error by training a neural network, the neural network comprising an input layer, a hidden layer and an output layer, wherein the input layer comprises 6 neurons, and the input is the desired target posture x, y, z, α, β, γ; the hidden layer comprises n neurons, which are fully connected to the input layer; the output layer comprises 6 neurons, which represent the position error and the posture error respectively, and Δx, Δy, Δz, Δα, Δβ, Δγ are fully connected to the hidden layer;

[0133] The output calculation method of each neuron is:

[0134]

[0135] in represents the output of neuron j in layer k, function f a represents the Noisy ReLU activation function, defined as

[0136] f a (x)=max(0,x+Y),y~N(0,σ(x))

[0137] represents the weight of the connection between neuron j in the kth layer and neuron i in the k-1th layer, represents the output of neuron i in the k-1th layer, represents the bias value of neuron j in the kth layer;

[0138] The neural network is trained by the back propagation algorithm, and the non-geometric error compensation value of the robot's target position is obtained using the trained neural network.

[0139] like Figure 3As shown, a schematic diagram comparing the position and posture errors before and after error compensation by the method of the present invention is given. The positioning error is reduced from 2.33 mm before compensation to 0.73 mm, a reduction of 67.2%. It can be seen that the error analysis and compensation method provided by the embodiment of the present invention can significantly improve the positioning accuracy of the surgical robot, thereby providing a reference for the positioning error analysis and compensation of the surgical robot.

[0140] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A surgical robot error analysis and compensation method, It is characterized in that include: Establishing an error model between various hardware systems of the surgical robot according to the hardware system of the surgical robot; the hardware system includes CT, optical tracking system, and robotic arm hardware system; An error transfer model of the surgical robot is established based on the error models between the various hardware systems of the surgical robot; The robot's geometric parameters are calibrated and the robot's non-geometric errors are compensated based on the error transfer model.

2. A surgical robot error analysis and compensation method according to claim 1, Features: The CT reconstruction system is specifically: a registration model of the reconstruction system and the optical tracking system, and the model is obtained as follows: Obtain the coordinate set P of the positioning target in the CT reconstruction coordinate system; Obtain the coordinate set Q of the positioning target in the optical tracking system coordinate system; The iterative closest point algorithm is used for optimization to obtain the coordinate transformation matrix between the CT reconstruction system and the optical tracking system: Among them, the coordinate set P and the coordinate set Q are both matrices with n rows and 3 columns, and each row represents the coordinate value of a positioning target in a space; R is a matrix with 3 rows and 3 columns, representing the coordinate rotation transformation relationship between the CT reconstruction system and the optical tracking system; T is a matrix with 3 rows and 1 column, representing the coordinate translation transformation relationship between the CT reconstruction system and the optical tracking system.

3. A surgical robot error analysis and compensation method according to claim 1, Features: The optical tracking system is specifically: an internal imaging model of the optical tracking system, and the model is obtained in the following manner: According to the optical camera imaging model, the conversion relationship between the camera imaging coordinate system and the world coordinate system is obtained as follows: where u 1 ,v 1 Indicates the coordinates in the left camera imaging coordinate system, u 2 ,v 2 Indicates the coordinates of the right camera imaging coordinate system, X w ,Y w ,Z w Represents the coordinates of the target point in the world coordinate system, S 1 ,S 2 is the scaling factor, K 1 ,K 2 Represents the left and right camera intrinsic parameter matrices, R, T is used to describe the relative position of the left and right cameras; According to the binocular camera reconstruction principle, the conversion relationship between the camera imaging coordinate system and the internal coordinate system of the optical positioning system is obtained: Where b represents the baseline distance between the two cameras, d represents the binocular disparity between the two cameras, and f represents the focal length of the camera.

4. A surgical robot error analysis and compensation method according to claim 1, Features: The mechanical arm hardware system specifically includes: an optical tracking system and a mechanical arm calibration model, which specifically includes: According to the different postures of multiple groups of robot ends, obtain the transformation matrix of multiple groups of robot ends relative to the robot base According to the coordinates of multiple sets of robot end positions in camera coordinates, the transformation matrix of multiple sets of robot end calibration targets relative to the camera is obtained. Solve the matrix equation according to the Tsai robotic arm hand-eye calibration method: in, represents the inverse matrix of the transformation matrix of the end of the manipulator relative to the base of the manipulator in posture 2, represents the transformation matrix of the end of the manipulator relative to the base of the manipulator in posture 1; Represents the transformation matrix of the camera to be solved with respect to the base of the robotic arm; represents the transformation matrix of the end of the robotic arm relative to the camera in posture 2, Represents the inverse matrix of the transformation matrix of the end of the robotic arm relative to the camera in posture 1; Get the calibration matrix between the optical tracking system and the robotic arm 5. A surgical robot error analysis and compensation method according to claim 1, Features: The mechanical arm hardware system further includes: a mechanical arm kinematics model, which is obtained by: The kinematic model of the robotic arm is established according to the improved DH parameter modeling method, and the relationship between the end position and joint angle of the robotic arm is obtained: Among them, α, d, θ, a are the improved DH parameters of the robot arm, Represents the transformation relationship from the base coordinate system to the terminal coordinate system.

6. A surgical robot error analysis and compensation method according to claim 1, Features: Establish the error model between the hardware systems of the surgical robot, including: The error model includes: registration error between the CT reconstruction system and the optical tracking system, imaging error inside the optical tracking system, calibration error between the optical tracking system and the manipulator system, and geometric parameter error inside the manipulator system; Wherein, the internal geometric parameter error of the robot arm system in the error model is the geometric error; The registration error between the CT reconstruction system and the optical tracking system, the internal imaging error of the optical tracking system, and the calibration error between the optical tracking system and the robotic arm system are non-geometric errors; The registration error between the CT reconstruction system and the optical tracking system is expressed as: where p i represents the coordinates of the i-th marker point in the CT reconstruction coordinate system, q i represents the coordinates of the i-th marker point in the optical tracking system coordinate system, R, T represents the transformation matrix calculated using the closest point iteration method; The internal imaging error of the optical tracking system is expressed as: Where b and d represent the baseline distance and binocular parallax of the two cameras, respectively, and f represents the focal length of the camera; The calibration error between the optical tracking system and the robotic arm system is expressed as: The matrix represents the calibration matrix between the optical tracking system and the robotic arm, x origin and x target Respectively represent the expected coordinates and actual coordinates of the terminal calibration target; The internal geometric parameter error of the robotic arm system is expressed as: in represents the position error due to the improved DH parameter error, Represents the attitude error caused by the error in the improved DH parameters.

7. A surgical robot error analysis and compensation method according to claim 1, Features: Establish an error propagation model for surgical robots, including: According to the error model, the transformation relationship from the expected target point to the actual target point of the surgical robot is obtained: According to the transformation relationship from the expected target point to the actual target point, the expression of the total error is obtained: Where x is the desired target point, is the coordinate transformation matrix between the CT reconstruction system and the optical tracking system, is the coordinate transformation matrix between the optical tracking system and the robot, the functions IK() and FK() are the inverse kinematics and forward kinematics of the robot, respectively, x' is the actual target point, E() represents the non-geometric error, s * Indicates the expected target point.

8. A surgical robot error analysis and compensation method according to claim 1, Features: The robot's geometric parameters are calibrated according to the error transfer model, including: Select m groups of joint angles and obtain the desired target posture according to the kinematics of the robot arm; The actual target position of the robot arm is obtained by measuring the m groups of joint angles using a measuring device; Through the error between the expected target posture and the actual target posture, the improved DH parameter error is obtained according to the internal error model of the manipulator system; According to the DH parameter error, the robot arm is corrected to improve the DH parameter value; The modified improved DH parameter values ​​are used as parameters for the kinematics and inverse kinematics calculations of the robot arm, and the iterations are repeated until the error converges to the set range to obtain the kinematic parameter calibration values.

9. A surgical robot error analysis and compensation method according to claim 1, Features: Compensation for non-geometric errors of the robot, including: Compensate for the robot's non-geometric errors by training a neural network; The neural network includes an input layer, a hidden layer and an output layer; The input layer contains 6 neurons, and the input is the desired target pose x, y, z, α, β, γ; The hidden layer contains n neurons and is fully connected to the input layer; The output layer contains 6 neurons, representing the position error and attitude error respectively, Δx, Δy, Δz, Δα, Δβ, Δγ are fully connected with the hidden layer; The output of each neuron is calculated as in represents the output of neuron j in layer k, function f a represents the Noisy ReLU activation function, defined as f a (x)=max(0,x+Y),y~N(0,σ(x)) represents the weight of the connection between neuron j in the kth layer and neuron i in the k-1th layer, represents the output of neuron i in the k-1th layer, represents the bias value of neuron j in the kth layer; The neural network is trained by back propagation algorithm, and the non-geometric error compensation value of the robot's target position is obtained using the trained neural network.

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