CN112587237A - Method for reducing operation error of orthopedic operation robot - Google Patents

Method for reducing operation error of orthopedic operation robot Download PDF

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CN112587237A
CN112587237A CN202011461982.6A CN202011461982A CN112587237A CN 112587237 A CN112587237 A CN 112587237A CN 202011461982 A CN202011461982 A CN 202011461982A CN 112587237 A CN112587237 A CN 112587237A
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coordinate system
transformation matrix
error
matrix
transformation
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芦颖僖
侯礼春
朱江水
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Nanjing Linghua Microelectronics Technology Co ltd
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Nanjing Linghua Microelectronics Technology Co ltd
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    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/30Surgical robots
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/10Computer-aided planning, simulation or modelling of surgical operations
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/20Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/70Manipulators specially adapted for use in surgery
    • A61B34/77Manipulators with motion or force scaling
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/11Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13Differential equations
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/16Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/10Computer-aided planning, simulation or modelling of surgical operations
    • A61B2034/108Computer aided selection or customisation of medical implants or cutting guides
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/20Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
    • A61B2034/2046Tracking techniques
    • A61B2034/2055Optical tracking systems
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/20Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
    • A61B2034/2046Tracking techniques
    • A61B2034/2065Tracking using image or pattern recognition
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/20Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
    • A61B2034/2068Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis using pointers, e.g. pointers having reference marks for determining coordinates of body points

Abstract

The invention discloses a method for reducing operation errors of an orthopedic surgery robot, relates to the field of surgery robots, and can compensate system precision by using an error compensation algorithm. The invention comprises the following steps: establishing coordinate systems of the surgical robot system and relations among the coordinate systems; calculating transformation matrixes of the tool coordinate system and the user coordinate system relative to the real coordinate system, calculating relative coordinates given by the navigator through the transformation matrixes, and solving the actual form of the transformation matrixes; the actual form of the transformation matrix is estimated through the first-order fully differential form of the differential motion vector and the error coefficient matrix, the estimation error is obtained by utilizing the relation between the actual form of the transformation matrix and the theoretical form of the transformation matrix, the estimation error is compensated, and the system error is eliminated.

Description

Method for reducing operation error of orthopedic operation robot
Technical Field
The invention relates to the field of surgical robots, in particular to a method for reducing operation errors of an orthopedic surgical robot.
Background
The operating mode of the orthopaedic surgical robot is similar to that of an industrial robot, and the movement track of the actuator can be planned in a computer programming mode only by fixing and accurately calibrating a surgical target, so that the mechanical arm can automatically execute the planned movement track, and a corresponding surgical task is completed.
The systematic error compensation method for orthopedic robotic surgical cutting is of great significance in practical operation. In the operation process, the factors influencing the operation precision mainly include two factors: mechanical arm motion error and navigator measurement error. Because the system respectively obtains the pose information of the end effector by the servo motor encoder and the navigator, the problem of information fusion is involved, and in order to improve the precision and the reliability of the system, the unified modeling and the automatic compensation of system errors are required. Generally, the robot is used as a serial mechanism, the repetition precision is high, the absolute precision is low, and the robot can be automatically calibrated by using a navigator, so that the robot can obtain high local absolute precision near a surgical target to meet the surgical requirements. The main factors influencing the measurement accuracy of the navigator are the posture of the identification body and the distance between the identification body and the camera, and certain special poses can cause great measurement errors of the navigator. Moreover, the confidence coefficients of the two paths of information are different under different poses and measuring conditions, and the respective error distribution characteristics are different.
Disclosure of Invention
The invention provides a method for reducing operation errors of an orthopedic surgery robot, which can compensate system precision by using an error compensation algorithm.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method of an orthopedic surgical robot to reduce operational errors, comprising:
s1, establishing a tool coordinate system, a user coordinate system and a real coordinate system of the surgical robot system and relations among the coordinate systems;
s2, calculating transformation matrixes of the tool coordinate system and the user coordinate system relative to the real coordinate system respectively, and calculating to obtain relative coordinates given by the navigator through the transformation matrixes;
s3, obtaining the actual form of the transformation matrix by considering error factors;
s4, actual form of real matrix and D (T)N) Collectively representing the theoretical form of the transformation matrix, using ΔtRepresenting a differential transformation with respect to a coordinate system t, in combination with a relation between an actual form of the transformation matrix and a theoretical form of the transformation matrix, resulting in ΔtThe specific expression of (1). T isNFor the theoretical form of the transformation matrix, T is the actual form of the transformation matrix, d (T)N) Is TNThe derivative with respect to time, for calculating the transient value.
S5, converting DeltatMarking as a differential motion vector, estimating the actual form of the transformation matrix through a first-order fully differential form of the differential motion vector and an error coefficient matrix, and solving an estimation error by utilizing the relation between the actual form of the transformation matrix and the theoretical form of the transformation matrix;
and S6, compensating the estimation error and eliminating a system error.
Further, in S1, the relationship among the tool coordinate system, the user coordinate system, and the real coordinate system is:
Figure BDA0002825891580000021
wherein the content of the first and second substances,
Figure BDA0002825891580000022
is a transformation matrix of the surgical robot,
Figure BDA0002825891580000023
is a matrix of the tool coordinate system,
Figure BDA0002825891580000024
relative coordinates collected for the navigator;
Figure BDA0002825891580000025
is a transformation matrix of the base coordinate system 0 with respect to the user coordinate system U, t denotes the user coordinate system, U denotes the tool coordinate system, and 7 denotes that the robot has 7 degrees of freedom.
Further, in S3, the actual form of the transformation matrix is:
Figure BDA0002825891580000031
Figure BDA0002825891580000032
wherein alpha istttIs the coordinate of three dimensions of the tool coordinate system, Δ αt,Δβt,ΔγtIs the derivative, x, of the three dimensional coordinates of the tool coordinate system over timet,yt,ztIs the coordinate for t under the real coordinate system { W }, Δ xt,Δyt,ΔztIs the derivative of the three-dimensional coordinate of the real coordinate system T over time, TRIs a relation matrix of the tool coordinate system to the real coordinate system.
αuuuIs the coordinate of three dimensions of the user coordinate system, Δ αu,Δβu,ΔγuIs the derivative, x, of the three-dimensional coordinate of the user coordinate system over timeu,yu,zuIs the coordinate for u, Δ x, under the real coordinate system { W }u,Δyu,ΔzuIs the derivative of the three-dimensional coordinates of the real coordinate system U over time, URIs a relation matrix from the user coordinate system to the real coordinate system.
Further, in the S4, the expression of the theoretical form of the transformation matrix is,
TR≈TN+d(TN)
TNfor transforming the theoretical form of the matrix, TRFor the actual form of the transformation matrix, d (T)N) Is TNThe derivative with respect to time, for calculating the transient value.
Figure BDA0002825891580000033
Wherein, α, β, γ are three dimensional axes of the tool coordinate system, and x, y, z are three dimensional axes of the real coordinate system.
The invention has the beneficial effects that:
according to the invention, by establishing error models of the navigation system and the surgical auxiliary robot system and feeding back the calculated errors to control, more accurate position coordinates are obtained, so that the control precision of the end pose of the robot actuator is improved more ideally.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic diagram of an effective measurement range of a navigator;
FIG. 2 is a schematic diagram of an error analysis;
fig. 3 shows the actual measurement results before and after compensation.
Detailed Description
In order that those skilled in the art will better understand the technical solutions of the present invention, the present invention will be further described in detail with reference to the following detailed description.
The execution precision of the surgical robot system is mainly determined by the positioning precision of the robot body and the detection precision of the optical navigator system, and the remote control operator and the force feedback equipment at the operation end in the force feedback system do not influence the execution precision of the robot, so that the invention only discusses the related precision of the first two subsystems.
In this embodiment, the accuracies of the navigation system and the robot system are respectively:
1. the observation and measurement instrument which is more key in the optical navigation system is an optical three-dimensional tracking system of PST company, and the position measurement error is about: 0.25mm, the measurement range is shown in FIG. 1.
2. The repeated positioning precision of the mechanical arm in the robot body is about: 0.15 mm.
According to the requirements set by the target, on the planned movement track of the scalpel, the movement precision of an actuator, namely the tail end of a cutter, needs to reach within 0.5 mm.
The embodiment provides a method for reducing operation errors of an orthopedic surgery robot, which specifically comprises the following steps:
the surgical robot system coordinate system is established as shown in fig. 2, which identifies all major coordinate systems and general orientations during the system set-up. The relationship between the transformation matrices is:
Figure BDA0002825891580000051
wherein the mechanical arm has 7 degrees of freedom, namely 7-axis mechanical arm, T is a transformation matrix T, U is a transformation matrix U,
Figure BDA0002825891580000052
is a transformation matrix of the surgical robot,
Figure BDA0002825891580000053
the main influencing factors are the geometric errors of the parameters of each connecting rod, and in addition, the influences of thermal deformation and force deformation and the like.
Figure BDA0002825891580000054
The tool coordinate system matrix is a constant value without changing the surgical tool.
Figure BDA0002825891580000055
The matrix transformation relation is directly given by a navigator, and measurement errors exist.
Setting corresponding transformation matrix of tool coordinate system and user coordinate system relative to real coordinate system W
Figure BDA0002825891580000056
And
Figure BDA0002825891580000057
then
Figure BDA0002825891580000058
The measurement error of the initial calibration can be not considered as a known item for estimating other matrixes. If each error model and parameter need to be accurately calculated, certain error analysis and compensation are needed to be carried out on the matrix.
Figure BDA0002825891580000059
Refers to the transformation matrix of the base coordinate system 0 relative to the user coordinate system U, which is a constant in the case of fixed user coordinates. When in actual operation, in order to reduce the error,
Figure BDA00028258915800000510
generally, the calibration method is real-time change or needs frequent calibration, is very intuitive and directly passes through an equation
Figure BDA00028258915800000511
Once for T
Figure BDA00028258915800000512
And (4) finishing. In addition, if the target osteotomy surface of the patient frequently moves in the actual surgical process, which may cause the change of the target coordinate system relative to the robot coordinate system, a real-time automatic calibration method needs to be designed to ensure the correct mapping of the planned trajectory in the robot coordinate system.
Under the existing surgical robot system, mainly throughThe optical navigator acquires the current initial pose of the end point of the mechanical arm actuator relative to a user coordinate system
Figure BDA00028258915800000513
And the role of the upper computer is used as the planning pose of the target point as the target pose
Figure BDA00028258915800000514
And then the angle is sent to a control system (a lower computer) of the mechanical arm, the joint angle of the target position is reversely solved by a program of the lower computer, and then the mechanical arm is driven to start to move to the target point. As shown in fig. 2, we define point 1 as the initial pose of the actuator, i.e., the scalpel, point 3 as the target point pose, and point 2 as the pose actually reached by the robotic arm after executing instructions from the upper computer.
The pose deviation between the point 2 and the point 3 is the motion error of the surgical robot system, and under the current experimental condition, the pose deviation is the position error of the actual motion termination point and the planning end point. Factors causing inconsistency between the actual pose and the planned pose of the target point are many, such as measurement errors of a navigator, insufficient absolute positioning accuracy of a mechanical arm, errors of various structural parameters of the mechanical arm, low calibration accuracy of tool coordinates, thermal deformation and influence of force deformation. In addition, the accumulated error of the system is obvious, and the larger the distance between the position of the initial point and the position of the planning end point is, the larger the finally generated error is linearly increased.
Measurement errors prevailing in the system, i.e. relative coordinates given by the navigator
Figure BDA0002825891580000066
This is actually produced:
1) the navigator observes the small reflective ball fixedly connected with the actuator and positioned by the actuator and determines corresponding coordinate values.
2) Determining a transformation matrix of the corresponding tool coordinate system and the user coordinate system with respect to the actual coordinate system W (or the camera coordinate system C), respectively
Figure BDA0002825891580000061
And
Figure BDA0002825891580000062
3) the P coordinate can be obtained:
Figure BDA0002825891580000063
the position quantity and the attitude quantity of the coordinates of u and t (the superscript and the subscript u represent a user coordinate system, and t represents a tool coordinate system) are observed by the optical three-dimensional tracking system, if the previous thought still follows, that is, all the quantities (including the position quantity and the attitude variable) are obtained by measuring the cartesian coordinate values of the light-reflecting ball by the optical three-dimensional tracking system, all the variables have errors, and the system error mainly comes from the measurement error of the optical three-dimensional tracking system.
Transformation matrices of the tool coordinate system and the user coordinate system with respect to the real coordinate system { W }, respectively
Figure BDA0002825891580000064
And
Figure BDA0002825891580000065
can be expressed as:
Figure BDA0002825891580000071
Figure BDA0002825891580000072
αtttis a coordinate of three dimensions, x, of the tool coordinate systemt,yt,ztFor the coordinates of t in the real coordinate system,
Figure BDA0002825891580000073
is a transformation matrix. Alpha, beta, gammaIs the three dimensional axes of the tool coordinate system, x, y, z are the three dimensional axes of the real coordinate system, and c and s represent cos and sin, respectively.
αuuuIs the coordinate of three dimensions, x, of the user's coordinate systemu,yu,zuThe coordinates for u under the real coordinate system W,
Figure BDA0002825891580000074
is its transformation matrix.
Considering the error factor, the actual form of the transformation matrix should be:
Figure BDA0002825891580000075
Figure BDA0002825891580000076
wherein Δ αt,Δβt,ΔγtIs the derivative of the three dimensional coordinates of the tool coordinate system over time, Δ xt,Δyt,ΔztIs the derivative of the three-dimensional coordinate of the real coordinate system T over time, TRIs a relation matrix of the tool coordinate system to the real coordinate system.
Relation matrix delta alphau,Δβu,ΔγuIs the derivative of the three-dimensional coordinate of the user coordinate system over time, Deltaxu,Δyu,ΔzuIs the derivative of the three-dimensional coordinates of the real coordinate system U over time, URIs a relation matrix from the user coordinate system to the real coordinate system.
Let T be used for theoretical form and actual form of transformation matrixNAnd TRDenotes then TNAnd TRThe relationship of (1) is:
TR≈TN+d(TN) (4)
wherein:
Figure BDA0002825891580000081
d(TN) Is TNThe derivative with respect to time, for calculating the transient value.
By DeltatRepresenting a differential transformation with respect to the coordinate system t, there are:
TR-TN=TNΔt (5)
by combining the above equations, one can obtain:
Δt=(TN)-1d(TN) (6)
the simplified result of the calculation is given by:
Figure BDA0002825891580000082
where the pattern of dx, dy, dz is complex, so it is listed separately:
dx=Δxcosαcosβ+Δysinαcosβ-Δzsinβ
dy=Δx(cosαsinβsinγ-sinαcosγ)+Δy(sinαsinβsinγ+cosαcosγ)+Δzcosβsinγ
dz=Δx(cosαsinβcosγ+sinαsinγ)+Δy(sinαsinβcosγ-cosαsinγ)+Δzcosαcosγ
Δtcan be regarded as being formed by differential motion vectors eiIs composed of eiIs defined as: the first 3 elements are position errors, the last 3 elements are attitude errors, namely:
Figure BDA0002825891580000091
in the formula, the physical meaning of δ is to calculate partial derivative, and G is an error coefficient matrix. The above process is to estimate the actual form of the transformation matrix by first-order full differentiation, where eiSo that the sum Δ XiThe inconsistency is due to eiIs TNFor Δ XiAfter each element takes a first order full differentialThe result of the calculation. The matrix t can be obtained by substituting the formula (8) into the formula (4)wActual form T of TROf the first order differential, G.DELTA.XiI.e. to estimate the error, G.DELTA.X is measured by softwareiThe compensation of the estimation error can eliminate the system error and improve the operation precision.
As shown in fig. 3, the maximum error of angular displacement tracking of the robot before compensation is 0.164rad, and the maximum error of angular displacement tracking of the compensation rear angle is 0.085 rad. In conclusion, the embodiment enables the motion track error of the surgical robot to be smaller, and the error change amplitude after compensation is obviously lower than that before compensation.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (4)

1. A method of reducing operational errors in an orthopedic surgical robot, comprising:
s1, establishing a tool coordinate system, a user coordinate system and a real coordinate system of the surgical robot system and relations among the coordinate systems;
s2, calculating transformation matrixes of the tool coordinate system and the user coordinate system relative to the real coordinate system respectively, and calculating to obtain relative coordinates given by the navigator through the transformation matrixes;
s3, obtaining the actual form of the transformation matrix by considering error factors;
s4, actual form of transformation matrix and d (T)N) Collectively representing the theoretical form of the transformation matrix, using ΔtRepresenting a differential transformation with respect to a coordinate system t, in combination with a relation between an actual form of the transformation matrix and a theoretical form of the transformation matrix, resulting in ΔtWherein T isNFor the theoretical form of the transformation matrix, T is the actual form of the transformation matrix, d (T)N) Is TNTo timeA derivative of (a);
s5, converting DeltatMarking as a differential motion vector, estimating the actual form of the transformation matrix through a first-order fully differential form of the differential motion vector and an error coefficient matrix, and solving an estimation error by utilizing the relation between the actual form of the transformation matrix and the theoretical form of the transformation matrix;
and S6, compensating the estimation error and eliminating a system error.
2. The method for reducing the operation error of the orthopaedic surgical robot of claim 1, wherein in the S1, the relation among the tool coordinate system, the user coordinate system and the real coordinate system is:
Figure FDA0002825891570000011
wherein the content of the first and second substances,
Figure FDA0002825891570000012
is a transformation matrix of the surgical robot,
Figure FDA0002825891570000013
is a matrix of the tool coordinate system,
Figure FDA0002825891570000014
relative coordinates collected for the navigator;
Figure FDA0002825891570000015
is a transformation matrix of the base coordinate system 0 with respect to the user coordinate system U, t denotes the user coordinate system, U denotes the tool coordinate system, and 7 denotes that the robot has 7 degrees of freedom.
3. The method for reducing the operation error of the orthopaedic surgical robot of claim 1, wherein in the S3, the transformation matrix is in the actual form:
Figure FDA0002825891570000021
Figure FDA0002825891570000022
wherein alpha istttIs the coordinate of three dimensions of the tool coordinate system, Δ αt,Δβt,ΔγtIs the derivative, x, of the three dimensional coordinates of the tool coordinate system over timet,yt,ztIs the coordinate for t under the real coordinate system { W }, Δ xt,Δyt,ΔztIs the derivative of the three-dimensional coordinate of the real coordinate system T over time, TRIs a relation matrix from a tool coordinate system to a real coordinate system; alpha is alphauuuIs the coordinate of three dimensions of the user coordinate system, Δ αu,Δβu,ΔγuIs the derivative, x, of the three-dimensional coordinate of the user coordinate system over timeu,yu,zuIs the coordinate for u, Δ x, under the real coordinate system { W }u,Δyu,ΔzuIs the derivative of the three-dimensional coordinates of the real coordinate system U over time, URIs a relation matrix from the user coordinate system to the real coordinate system.
4. The method for reducing the operation error of the orthopaedic surgical robot of claim 1, wherein in the S4, the expression of the theoretical form of the transformation matrix is,
TR≈TN+d(TN)
TNfor transforming the theoretical form of the matrix, TRFor the actual form of the transformation matrix, d (T)N) Is TNA derivative with respect to time; .
Figure FDA0002825891570000023
Wherein, α, β, γ are three dimensional axes of the tool coordinate system, and x, y, z are three dimensional axes of the real coordinate system.
CN202011461982.6A 2020-12-09 2020-12-09 Method for reducing operation error of orthopedic operation robot Pending CN112587237A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114098960A (en) * 2021-11-29 2022-03-01 杭州柳叶刀机器人有限公司 Automatic positioning method and device for medical instrument, mechanical arm and readable storage medium
CN114469354A (en) * 2022-04-13 2022-05-13 深圳市爱博医疗机器人有限公司 Slave end initialization method and readable storage medium for interventional operation robot

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114098960A (en) * 2021-11-29 2022-03-01 杭州柳叶刀机器人有限公司 Automatic positioning method and device for medical instrument, mechanical arm and readable storage medium
CN114469354A (en) * 2022-04-13 2022-05-13 深圳市爱博医疗机器人有限公司 Slave end initialization method and readable storage medium for interventional operation robot

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Application publication date: 20210402