CN110125982B - Method for measuring motion trajectory orthogonality of three-degree-of-freedom motion control system of micro-operation robot - Google Patents

Method for measuring motion trajectory orthogonality of three-degree-of-freedom motion control system of micro-operation robot Download PDF

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CN110125982B
CN110125982B CN201910456218.0A CN201910456218A CN110125982B CN 110125982 B CN110125982 B CN 110125982B CN 201910456218 A CN201910456218 A CN 201910456218A CN 110125982 B CN110125982 B CN 110125982B
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orthogonality
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CN110125982A (en
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王跃宗
陈浩
张鑫
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Beijing University of Technology
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Beijing University of Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J19/00—Accessories fitted to manipulators, e.g. for monitoring, for viewing; Safety devices combined with or specially adapted for use in connection with manipulators
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J19/00—Accessories fitted to manipulators, e.g. for monitoring, for viewing; Safety devices combined with or specially adapted for use in connection with manipulators
    • B25J19/0095—Means or methods for testing manipulators
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning

Abstract

The invention relates to a method for measuring the orthogonality of a motion trail of a three-degree-of-freedom motion control system of a micro-operation robot, in particular to a method for evaluating the orthogonality of the motion trail by adopting the motion control system and a method for correcting the non-orthogonality of the motion trail. The method mainly comprises the following steps: constructing a motion track orthogonality measuring system, analyzing the orthogonality of a standard orthogonal reference system, collecting the motion track, linearly fitting the motion track, evaluating the orthogonality of the motion track and correcting the non-orthogonality of the motion track. The invention solves the problem of non-orthogonal motion tracks of the motion control system, realizes accurate positioning under the orthogonal condition, and effectively ensures the positioning accuracy of the micro-operation robot.

Description

Method for measuring motion trajectory orthogonality of three-degree-of-freedom motion control system of micro-operation robot
Technical Field
The invention relates to a method for measuring the orthogonality of a motion trail of a three-degree-of-freedom motion control system of a micro-operation robot, in particular to a method for evaluating the orthogonality of the motion trail of the motion control system and a method for correcting the non-orthogonality of the motion trail, which are used for realizing accurate positioning under the orthogonal condition and effectively ensuring the positioning accuracy of the micro-operation robot.
Background
The micro-operation robot is an operation system for grabbing, transferring and assembling micro objects (such as biological tissues, cells, MEMS microstructures, micro-electro-mechanical systems and the like) with the size ranging from micron to sub-millimeter in the micron or submicron precision range, is used in various fields such as micro-assembly, micro-injection, biological engineering, minimally invasive surgery and the like, and generally comprises a vision system, a micro-operator and a motion control system. A visual system constructed by taking an optical stereo microscope as a main body is combined with micro-operation to form a special micro-operation robot, the robot positions and tracks a micro-operator and an operated object through the visual system of the stereo microscope to obtain the position information of the operated object, and then the micro-operator is driven to move by a motion control system to finish various micro-operation precise operations.
The motion control system is an important component of the micro-operation robot, mainly realizes the motion control and precise positioning of a micro-operator, the performance of the motion control system influences the positioning accuracy of the micro-operation robot, the motion control system generally comprises a plurality of degrees of freedom, and the degrees of freedom mainly comprise a translation degree of freedom and a rotation degree of freedom, and the motion control system with three translation degrees of freedom is a common type. The performance indexes of the motion control system with three translation degrees of freedom mainly comprise three types: assembly orthogonality, positioning accuracy and three-axis motion trajectory orthogonality. The assembly orthogonality can be evaluated by an angle measurement method, the positioning accuracy can be evaluated by a laser interference distance measurement method, and the two indexes are easy to measure; the orthogonality of the three-axis motion tracks is difficult to evaluate, and is often ignored in the existing micro-operation research, but the indexes are important factors influencing the precise positioning of the micro-operation robot. Sun Yanbo et al (2013) propose evaluation indexes and test methods for assembly orthogonality of the motion control system, mainly measure parallelism, perpendicularity and straightness of the assembly of the motion control system. In the actual use process, although the motion control system has good assembly orthogonality, the motion trajectories of the three axes cannot be guaranteed to have good orthogonality, that is, the motion trajectories of the three axes do not necessarily satisfy the absolute orthogonal relationship. If the motion trajectory of the motion control system is not orthogonal, even if the coordinates of the object space points obtained by visual calculation are accurate, the accuracy of object space positioning cannot be guaranteed, so that the actual position variation of the micromanipulator is inconsistent with the calculated position variation, and the deviation of the two positions is influenced by the orthogonality of the motion trajectory of the motion control system. Aiming at the problems, the invention provides a method for measuring the orthogonality of the motion trail of a three-degree-of-freedom motion control system of a micro-operation robot, and the method has special significance for the micro-operation robot, and is represented by the following steps: (1) the established laser displacement positioning system can be used as a standard orthogonal reference system and can provide necessary basic data for the motion trajectory orthogonality measurement of the motion control system; (2) the motion trail orthogonality measuring method provides a basis for the motion trail orthogonality evaluation of the micro-operation robot motion control system; (3) the established non-orthogonality correction method of the motion trail can effectively ensure the positioning accuracy of the micro-operation robot.
Disclosure of Invention
The invention provides a method for measuring the orthogonality of a motion track of a three-degree-of-freedom motion control system of a micro-operation robot, and aims to realize accurate positioning under the orthogonal condition and effectively ensure the positioning accuracy of the micro-operation robot by evaluating the orthogonality of the motion track of the motion control system and correcting the non-orthogonality of the motion track.
The invention relates to a method for measuring the orthogonality of a motion track of a three-degree-of-freedom motion control system of a micro-operation robot, which is based on a laser displacement measurement principle, constructs a motion track orthogonality measurement system, establishes an auxiliary standard orthogonal reference system, establishes a simulation method for carrying out the orthogonality analysis of the standard orthogonal reference system, collects the motion track in the standard orthogonal reference system, carries out straight line fitting on the motion track, then establishes a motion track orthogonality evaluation method, and finally carries out the non-orthogonality correction of the motion track on the non-orthogonal motion track to realize the accurate positioning under the orthogonal condition. The method for measuring the orthogonality of the motion trail of the three-degree-of-freedom motion control system of the micro-operation robot comprises the following steps of:
1) system for constructing motion trajectory orthogonality measurement system
And grating rulers for precisely controlling the motion axes in a closed loop are respectively arranged on the three motion axes of the motion control system. In order to collect the motion trail of the motion axis, a standard gauge block is arranged on the motion control system, three adjacent surfaces of the standard gauge block are used as displacement monitoring surfaces, and the normal lines of the three displacement monitoring surfaces are respectively parallel to the three motion axes. The central axes of the three laser displacement sensors are intersected at one point and are vertical to the corresponding displacement monitoring surface, and the three laser displacement sensors are used for measuring the displacement of the standard gauge block. A laser displacement positioning system established by three laser displacement sensors with orthogonal relation is used as an auxiliary standard orthogonal reference system, and the motion trail of the standard gauge block is described in the standard orthogonal reference system.
2) Orthonormal reference system orthogonality analysis
Under the influence of assembly factors, the central axes of the three laser displacement sensors do not necessarily satisfy an absolute orthogonal relationship, the established non-orthogonal standard orthogonal reference system has influence on the measurement of the orthogonality of the motion track, and a simulation method is established for analyzing the influence of the orthogonality of the standard orthogonal reference system on the measurement of the orthogonality of the motion track on the rotation angle of the standard gauge block and the laser displacement sensors. Simulation results show that: when the rotation angle between the standard gauge block and the laser displacement sensor is within 10 degrees, the influence of the orthogonality of the standard orthogonal reference system on the orthogonality measurement of the motion track can be ignored. Therefore, the rotation angle is adjusted to be within 10 degrees when the standard gauge block and the laser displacement sensor are assembled, and then the process goes to step 3).
3) Collecting motion trail
The standard gauge blocks move at equal intervals in the public effective space of the laser displacement sensor in the direction parallel to the three motion axes respectively to generate discrete track points, the three formed motion tracks represent the real motion tracks of the three motion axes, and the three motion tracks are used as the three coordinate axes of a motion track coordinate system (O-XYZ). The three laser displacement sensors can measure the displacement of the standard gauge block, and the three displacement obtained at a certain time are used as the space coordinate vector of the current discrete track point of the standard gauge block in the standard orthogonal reference system.
4) Fitting of motion trajectory straight line
And (3) performing linear fitting on the motion trail represented by the space coordinate vector of the discrete track point in the standard orthogonal reference system, if the distance from the discrete track point to the fitting straight line is more than 0.02mm, considering the discrete track point as a coarse error, removing the discrete track point from the set, and performing linear fitting again. And finally, obtaining a motion track linear equation and vector parameters, namely linear equations and vector parameters of an X axis, a Y axis and a Z axis of the motion track coordinate system.
5) Motion trajectory orthogonality evaluation
Vector orthogonality calculation is carried out according to the motion track vector parameters to obtain included angles among the motion tracks, namely included angles among X axes, Y axes and Z axes of a motion track coordinate system, the motion track orthogonality is evaluated according to the included angles, and the judgment standard for evaluating the motion track orthogonality is as follows: setting an angle threshold value to be 0.3 degrees, and making difference between the three included angles and 90 degrees respectively, wherein when the difference values between the three included angles are less than or equal to the angle threshold value, an orthogonal condition is met, and the motion tracks are orthogonal; if any difference value between the two is larger than the angle threshold value, the orthogonality condition is not met, the motion tracks are not orthogonal, and the step 6) is carried out to carry out motion track non-orthogonality correction.
6) Correction of motion trajectory non-orthogonality
The method comprises the steps of correcting the non-orthogonality of the motion trail of the non-orthogonal motion trail, setting a virtual orthogonal coordinate system, establishing a mapping relation between the virtual orthogonal coordinate system and the non-orthogonal motion trail coordinate system, knowing a coordinate vector of any point in a space in the virtual orthogonal coordinate system, and obtaining the coordinate vector of the point in the non-orthogonal motion trail coordinate system according to the mapping relation, so that a motion control system can accurately move to the point in the non-orthogonal motion trail coordinate system, the accurate positioning under the orthogonal condition is realized, and the positioning accuracy of the micro-operation robot is effectively ensured.
Drawings
FIG. 1 is a flowchart of a method for measuring the orthogonality of the motion trajectory of a three-degree-of-freedom motion control system of a micro-robot according to the present invention
FIG. 2 is a diagram of a motion trajectory orthogonality measuring system according to the present invention
FIG. 3 is a schematic diagram of the motion trajectory acquisition involved in the present invention
FIG. 4 is a schematic view of the linear fitting of the motion trajectory according to the present invention
FIG. 5 is a schematic diagram of the motion trajectory orthogonality evaluation according to the present invention
FIG. 6 is a schematic diagram of non-orthogonality correction of motion trajectory according to the present invention
Reference is made to the accompanying drawings in which:
s1, constructing a motion track orthogonality measuring system
S2, orthonormal reference system orthogonality analysis
S3, collecting motion trail
S4, fitting motion track straight line
S51, motion track orthogonality evaluation
S52, orthogonal motion track
S6, non-orthogonal motion trail
S71 correction of non-orthogonality of motion trail
S72 coordinate vector in virtual orthogonal coordinate system
S73, coordinate vector in motion track coordinate system
S8, realizing accurate positioning under orthogonal condition
1. Motion control system
2. X-axis of motion
3. Y motion axis
4. Z-axis of motion
5. X-motion axis grating ruler
6. Y-motion axis grating ruler
7. Z-motion axis grating ruler
8. Coordinate system of motion track
9. Standard gauge block
10. X-axis monitoring surface
11. Y-axis monitoring surface
12. Z-axis monitoring surface
13. X-axis laser displacement sensor
14. Y-axis laser displacement sensor
15. Z-axis laser displacement sensor
16. Orthonormal reference frame
17. Computer with a memory card
Included angle between alpha, X and Y axes
Angle between beta, X and Z axes
Included angle between gamma, Y axis and Z axis
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings. Fig. 1 is a flowchart of a method for measuring orthogonality of a motion trajectory of a three-degree-of-freedom motion control system of a micro-robot according to the present invention, where the method includes the following steps:
1. system for constructing motion trajectory orthogonality measurement system
Fig. 2 shows a motion trajectory orthogonality measuring system, three degrees of freedom of motion of a motion control system 1 respectively correspond to an X motion axis 2, a Y motion axis 3 and a Z motion axis 4, an X motion axis grating scale 5, a Y motion axis grating scale 6 and a Z motion axis grating scale 7 are respectively mounted on the three motion axes, the resolution is 0.1 micrometer, and the three axes are used for closed-loop precise control of the motion axes. In order to collect the motion trail of the motion axis, a standard gauge block 9 is arranged on the motion control system 1, and an X-axis monitoring surface 10, a Y-axis monitoring surface 11 and a Z-axis monitoring surface 12 adjacent to the standard gauge block are used as displacement monitoring surfaces which have good flatness and orthogonal relation, and the normal lines of the three displacement monitoring surfaces are respectively parallel to the three motion axes. The displacement of three displacement monitoring surfaces is respectively monitored by using an X-axis laser displacement sensor 13, a Y-axis laser displacement sensor 14 and a Z-axis laser displacement sensor 15, the central axes of the three displacement monitoring surfaces are intersected at one point and are perpendicular to the corresponding displacement monitoring surfaces, a laser displacement positioning system established by the three laser displacement sensors with an orthogonal relation is used as an auxiliary standard orthogonal reference system 16, and the motion track of the standard gauge block 9 is described in the standard orthogonal reference system 16.
2. Orthonormal reference system orthogonality analysis
Under the influence of assembly factors, the central axes of the three laser displacement sensors do not necessarily satisfy an absolute orthogonal relationship, the established non-orthogonal standard orthogonal reference system has influence on the measurement of the orthogonality of the motion track, and a simulation method is established for analyzing the influence of the orthogonality of the standard orthogonal reference system on the measurement of the orthogonality of the motion track on the rotation angle of the standard gauge block and the laser displacement sensors.
The simulation method specifically comprises the following steps: three motion tracks l of preset standard gauge blocku1、lv1、lw1The unit vector and the discrete track point, and the included angle between the motion tracks forms an angle vector Λt. The rotation angles of the standard gauge block around the U axis, the V axis and the W axis and the initial coordinate vectors of 8 vertexes are preset, and the coordinate vectors of 8 vertexes after the standard gauge block rotates are calculated. Central axis l of laser displacement sensorA、lB、lCRespectively at a certain point M on the axisA、MB、MCAs a reference point, rotating at a small angle, presetting unit vectors and points M corresponding to three axesA、MB、MCThe coordinate vector of (2).
The standard gauge blocks respectively follow three motion tracks l at the postures of preset rotation anglesu1、lv1、lw1Moving to the position of the preset discrete track point,/, in sequenceA、lB、lCThe intersection points with the corresponding displacement monitoring surface are respectively NA、NB、NCCalculating the currentThe space coordinate vector of the position intersection point is the measured value of the discrete track point, and a corresponding straight line l is obtained through straight line fittingu2、lv2、lw2Then vector orthogonality calculation is carried out to obtain lu2、lv2、lw2Angle vector Λ, Λ formed by the included anglestThe simulation result shows that when the rotation angle of the standard gauge block and the laser displacement sensor is within 10 degrees, the maximum difference value of the preset value and the measured value is 0.0967 degrees, and the influence of the orthogonality of the standard orthogonal reference system on the orthogonality measurement of the motion track can be ignored, so that the rotation angle is adjusted to be within 10 degrees when the standard gauge block and the laser displacement sensor are assembled, and then the step 3 is carried out.
3. Collecting motion trail
Fig. 3 is a schematic diagram of the collected motion trajectory, and the computer 17 controls the motion control system 1 to make the standard gauge blocks 9 move at equal intervals in the direction parallel to the three motion axes to generate discrete trajectory points, so that the three formed motion trajectories represent the real motion trajectories of the three motion axes, and the three motion trajectories are used as the X-axis, the Y-axis and the Z-axis of the motion trajectory coordinate system 8. The three laser displacement sensors can measure the displacement of the standard gauge block 9, and the three displacement obtained at a certain time are used as the space coordinate vector of the current discrete track point of the standard gauge block 9 in the standard orthogonal reference system 16. Discrete track points of the standard gauge block 9 on the X axis correspond to a space coordinate vector { S } in the standard orthogonal reference system 16AN}，{SANThe three components of the standard gauge block 9 are respectively corresponding to the displacement of the three laser displacement sensors at each discrete track point. Similarly, discrete track points of the standard gauge block 9 on the Y axis and the Z axis correspond to a space coordinate vector { S } in the orthonormal reference system 16BMAnd { S }CK}. The samples constructed by the three space coordinate vectors are used as basic data for motion trajectory orthogonality evaluation and are stored in the computer 17.
4. Fitting of motion trajectory straight line
FIG. 4 is a schematic diagram of linear fitting of motion trajectory, for a space coordinate vector { S } of a discrete trajectory point in a standard orthogonal reference systemAN}、{SBMAnd { S }CKAnd (4) performing linear fitting on the motion tracks represented by the points, if the distance between the discrete track points and the fitted straight line is more than 0.02mm, regarding the discrete track points as coarse errors, removing the discrete track points from the set, and performing linear fitting again. And finally, obtaining a motion track linear equation and vector parameters, namely linear equations and vector parameters of an X axis, a Y axis and a Z axis of the motion track coordinate system. In an orthonormal reference frame, a vector of spatial coordinates SAN}、{SBMAnd { S }CKThe corresponding motion track straight line fitting general formula is as follows:
Figure BDA0002076672100000081
SLFM represents a motion trajectory straight line fitting method with input quantity of { S }AN}、{SBMAnd { S }CKThe output quantity is a motion track vector parameter P obtained by fittinga、PbAnd Pc。
5. Motion trajectory orthogonality evaluation
FIG. 5 is a schematic diagram of motion trajectory orthogonality evaluation, where the included angles between the X-axis and the Y-axis, the X-axis and the Z-axis, and the Y-axis and the Z-axis are represented by α, β, and γ, respectivelya、nbAnd ncThen, vector orthogonality calculation is carried out to obtain α, β and gamma values, wherein the vector orthogonality calculation formula is as follows:
Figure BDA0002076672100000082
estimating the orthogonality of the motion trail according to the sizes of alpha, beta and gamma, wherein the judgment standard for estimating the orthogonality of the motion trail is as follows:
Figure BDA0002076672100000083
in the formula TabcFor the angle threshold, 0.3 degrees is taken. When the three conditions in the formula are all satisfied, the orthogonal condition is satisfied, and the motion track is orthogonal S52; if any condition in the formula is not satisfied, the orthogonal condition is not satisfied, the motion trajectory is non-orthogonal S6, and the process proceeds to step 6 to correct the non-orthogonality of the motion trajectory.
6. Correction of motion trajectory non-orthogonality
The motion trail non-orthogonality correction is carried out on non-orthogonal motion trail S71, FIG. 6 is a schematic diagram of the motion trail non-orthogonality correction, a virtual orthogonal coordinate system (O-XGH) is arranged, the motion trail coordinate system and the virtual orthogonal coordinate system have a common coordinate origin O and a common coordinate axis X, coordinate planes XOY and XOG of the two coordinate systems coincide, a mapping relation between the two coordinate systems is established, and a coordinate vector r of any point P in a virtual orthogonal coordinate system in a known space is known, wherein ∠ XOY ═ α, ∠ XOZ ═ β, and ∠ YOZ ═ gamma of the two coordinate systemsp,gh＝(xp,gh,yp,gh,zp,gh)TCalculating the coordinate vector r of the point P in the motion trail coordinate systemp,yz＝(xp,yz,yp,yz,zp,yz)T。
The parallel line of the H axis of the passing point P intersects with the XOG plane at the projection point P1The passing point P is taken as a parallel line of the Z axis and intersects with the plane XOY at the projection point P11. From point P11A vertical line is drawn to the G axis, and the vertical foot is a point P13Line segment P11P13Intersects the Y axis at a point P12Point P13And P12Are respectively a point P11Projected points on the G-axis and Y-axis. Making a line segment OP by the passing point P11Parallel lines intersecting the Z axis at the projection point P7。
The unit vector of the Y axis in the virtual orthogonal coordinate system is ny,gh＝(cosα,sinα,0)TThe unit vector of the Z axis in the virtual orthogonal coordinate system is nz,gh＝(cosβ,cosβz,gh,cosγz,gh)TCos β can be obtained from the vector dot product formula and the unit vector normalization conditionz,ghAnd cos gammaz,gh. At right triangle P11PP1In is zp,yz＝zp,gh/cosγz,ghAnd z is knownp7,yz＝zp,yzThen can be according to rp7,gh＝zp7,yz·nz,ghFind rp7,gh，rp7,ghIs a point P7Coordinate vectors in a virtual orthogonal coordinate system. Point P11The coordinate vector in the virtual orthogonal coordinate system is rp11,ghThe coordinate vector in the motion trajectory coordinate system is rp11,yzAt right triangle P12OP13The following equation can be obtained from the geometric relationship:
Figure BDA0002076672100000091
point P11R is a projection point of the XOY plane of the point P in the coordinate system of the motion trail and can be established by the formulap,ghAnd rp,yzThe mapping relationship between:
Figure BDA0002076672100000101
according to the mapping relation, the coordinate vector r of the point P in the virtual orthogonal coordinate system can be obtainedp,ghS72 calculating the coordinate vector r corresponding to the coordinate system of the motion trailp,yzS73, the motion control system according to rp,yzThe robot can accurately move to the point P, the accurate positioning S8 under the orthogonal condition is realized, and the positioning accuracy of the micro-operation robot is effectively ensured.
It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention, which is intended to be covered by the present invention insofar as they come within the scope of the appended claims and their equivalents.

Claims (1)

1. The method for measuring the orthogonality of the motion trail of the three-degree-of-freedom motion control system of the micro-operation robot is characterized by comprising the following steps of: based on the laser displacement measurement principle, a motion track orthogonality measurement system is constructed, an auxiliary standard orthogonal reference system is established, a simulation method is established for carrying out standard orthogonal reference system orthogonality analysis, motion tracks are collected in the standard orthogonal reference system, straight line fitting is carried out on the motion tracks, then a motion track orthogonality evaluation method is established, finally motion track non-orthogonality correction is carried out on the non-orthogonal motion tracks, and accurate positioning under the orthogonal condition is achieved, and the method specifically comprises the following steps:
1) system for constructing motion trajectory orthogonality measurement system
Grating rulers for precisely controlling the motion axes in a closed loop are respectively arranged on the three motion axes of the motion control system; in order to collect the motion trail of the motion axis, a standard gauge block is arranged on the motion control system, three adjacent surfaces of the standard gauge block are used as displacement monitoring surfaces, and the normal lines of the three displacement monitoring surfaces are respectively parallel to the three motion axes; the central axes of the three laser displacement sensors are intersected at one point and are vertical to the corresponding displacement monitoring surface, and the three laser displacement sensors are used for measuring the displacement of the standard gauge block; a laser displacement positioning system established by three laser displacement sensors with an orthogonal relation is used as an auxiliary standard orthogonal reference system, and the motion trail of a standard gauge block is described in the standard orthogonal reference system;
2) orthonormal reference system orthogonality analysis
Under the influence of assembly factors, the central axes of the three laser displacement sensors do not necessarily satisfy an absolute orthogonal relationship, the established non-orthogonal standard orthogonal reference system has influence on the measurement of the orthogonality of the motion track, and a simulation method is established for analyzing the influence of the orthogonality of the standard orthogonal reference system on the measurement of the orthogonality of the motion track on how the rotation angle of the standard gauge block and the laser displacement sensors influences the measurement of the orthogonality of the motion track;
three motion tracks and discrete track points of a preset standard gauge block, and included angles among the motion tracks form an angle vector ΛtThe method comprises the steps of presetting a rotation angle between a standard gauge block and a laser displacement sensor, moving the standard gauge block along a preset motion track at the posture of the preset rotation angle, calculating a space coordinate vector of an intersection point of a central axis of the laser displacement sensor and a displacement monitoring surface, namely a measurement value of a discrete track point, and obtaining an angle vector Λ formed by an included angle between three straight lines through straight line fitting and vector orthogonality calculation, ΛtFor the preset values, Λ are measured values, the difference representing the addition of the standard quantityThe change of the motion track orthogonality measuring result after the rotation angle of the block and the laser displacement sensor is used for analyzing the influence of the orthogonality of the standard orthogonal reference system on the motion track orthogonality measurement; simulation results show that: when the rotation angle of the standard gauge block and the laser displacement sensor is within 10 degrees, the maximum difference value between the preset value and the measured value is 0.0967 degrees, and the influence of the orthogonality of the standard orthogonal reference system on the orthogonality measurement of the motion trail is ignored; therefore, when the standard gauge block and the laser displacement sensor are assembled, the rotation angle is adjusted to be within 10 degrees, and then the step 3) is carried out;
3) collecting motion trail
The standard gauge blocks move at equal intervals in the public effective space of the laser displacement sensor in the direction parallel to the three motion axes respectively to generate discrete track points, the three formed motion tracks represent the real motion tracks of the three motion axes, and the three motion tracks are used as three coordinate axes of a motion track coordinate system O-XYZ; measuring the displacement of the standard gauge block by the three laser displacement sensors, and taking the three displacement obtained at a certain moment as the space coordinate vector of the current discrete track point of the standard gauge block in the standard orthogonal reference system;
4) fitting of motion trajectory straight line
Performing linear fitting on the motion trail represented by the space coordinate vector of the discrete track point in the standard orthogonal reference system, if the distance from the discrete track point to the fitting straight line is more than 0.02mm, considering the discrete track point as a coarse error, removing the discrete track point from the set, and performing linear fitting again; finally, a motion trail linear equation and vector parameters are obtained, namely linear equations and vector parameters of an X axis, a Y axis and a Z axis of a motion trail coordinate system;
5) motion trajectory orthogonality evaluation
Vector orthogonality calculation is carried out according to the motion track vector parameters to obtain included angles among the motion tracks, namely included angles among X axes, Y axes and Z axes of a motion track coordinate system, the motion track orthogonality is evaluated according to the included angles, and the judgment standard for evaluating the motion track orthogonality is as follows: setting an angle threshold value to be 0.3 degrees, and making difference between the three included angles and 90 degrees respectively, wherein when the difference values between the three included angles are less than or equal to the angle threshold value, an orthogonal condition is met, and the motion tracks are orthogonal; if any difference value between the two is larger than the angle threshold value, the orthogonality condition is not met, the motion trail is not orthogonal, and the step 6) is carried out to carry out the non-orthogonal correction of the motion trail;
6) correction of motion trajectory non-orthogonality
Correcting the non-orthogonality of the motion trail of the non-orthogonal motion trail; setting a virtual orthogonal coordinate system O-XGH, wherein the motion trail coordinate system and the virtual orthogonal coordinate system have a common coordinate origin O and a common coordinate axis X, the coordinate planes XOY and XOG of the two coordinate systems are overlapped, the angle XOY is alpha, the angle XOZ is beta, and the angle YOZ is gamma, and establishing a mapping relation between the virtual orthogonal coordinate system and the motion trail coordinate system:
Figure FDA0002500461540000031
in the formula, rp,yz＝(xp,yz,yp,yz,zp,yz)T，xp,yzIs the coordinate of point P on the X-axis of the O-XYZ coordinate system, yp,yzIs the coordinate of point P on the Y-axis of O-XYZ coordinate system, zp,yzThe coordinate of the point P on the Z axis of the O-XYZ coordinate system; r isp,gh＝(xp,gh,yp,gh,zp,gh)T，xp,ghIs the coordinate of point P on the X-axis of the O-XGH coordinate system, yp,ghIs the coordinate of point P on the G axis of the O-XGH coordinate system, zp,ghThe coordinate of the point P on the H axis of the O-XGH coordinate system; n isz,gh＝(cosβ,cosβz,gh,cosγz,gh)TIs a unit vector of Z axis in O-XGH coordinate system, cos βz,ghCosine value of ∠ ZOG, cos gammaz,ghA cosine value of ∠ ZOH;
according to the mapping relation, the coordinate vector r of the point P in the virtual orthogonal coordinate systemp,ghCalculating the coordinate vector r corresponding to the coordinate system of the motion trailp,yzThe motion control system is based on rp,yzMoving exactly to point P.
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