CN115674271A - Robot calibration method based on multi-station measurement - Google Patents
Robot calibration method based on multi-station measurement Download PDFInfo
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Abstract
The invention discloses a robot calibration method based on multi-station measurement, which is characterized in that a 3D displacement measuring device is switched to different station calibration devices through a multi-station base, and the robot calibration method comprises a measuring device arranged in a working space of a robot, a 3D measuring ball rod arranged at the tail end of the robot and a data processing device. The device solves the problem that the calibration measuring device is fixed at the tail end of the extension rod to cause the deformation of the extension rod to influence the measuring precision, reduces the deformation of the extension rod as much as possible while expanding the motion range of the mechanical arm, reduces the possibility of motion collision interference, improves the ill-posed property of an equation set in calibration calculation, and further improves the calibration precision of the robot.
Description
Technical Field
The invention relates to a robot calibration method based on multi-station measurement.
Background
Because the mechanical arm can produce certain error in the manufacturing and installing process, the actual kinematics parameter of the mechanical arm has deviation with the designed kinematics parameter, and in some application occasions with higher requirements on the precision of the mechanical arm, the mechanical arm needs to be calibrated to determine the actual kinematics parameter, so that the mechanical arm can be put into application.
Calibration generally requires high-precision measurement through an external and/or self-measuring device, specifically, the mechanical arm is moved to a plurality of different poses, then each joint angle or the tail end of the mechanical arm is measured, and then real kinematic parameters are identified through a complex algorithm.
The conventional external measuring devices for calibrating the mechanical arm, such as a laser tracker and a three-coordinate measuring instrument, are very expensive, are not easy to directly calibrate the mechanical arm on site in a narrow mechanical arm working environment, and cannot meet the requirements of the industrial world on a calibrating device. However, the calibration method for the device or the calibration method for the multi-station base has not been studied in depth.
Disclosure of Invention
The calibration measuring device is fixed on the substrate, and the calibration data is obtained in a mode that the measuring ball is fixed at the tail end of the mechanical arm, so that the problem that the deformation of the extension rod influences the measuring precision due to the fact that the calibration measuring device is fixed at the tail end of the extension rod is solved; and the tail end of the robot is provided with the measuring ball through the extension rod to measure the multi-station pose and the joint angle, so that the deformation of the extension rod is reduced as much as possible while the motion range of the mechanical arm is expanded, and the possibility of motion collision interference is reduced. In addition, how to maximize the calibration effect of the calibration measuring device, such as which attitude joint angles the mechanical arm needs to move to for measurement, the invention also provides a solution, namely based on the observability index of the robot, the optimal attitude joint angle combination is selected through iteration.
In order to achieve the purpose, the invention adopts the technical scheme that:
a robot calibration method based on multi-station measurement comprises the following steps:
s01, fixing a base near the base of the robot, installing the displacement measuring device on one of the stations of the base, connecting a 3D measuring ball rod at the tail end of a mechanical arm, touching a contact of the displacement sensor by adopting a measuring ball on the 3D measuring ball rod in different poses and joint angles, and recording the reading l of the D displacement sensors during each touch by using the data acquisition module i ＝(l i1 ，l i2 ，...，l id ) And corresponding b degree of freedom robot joint angle values theta i ＝(θ i1 ，θ i2 ，...，θ ib ) To obtain m 1 Group data, wherein i =1 1 ；
S02, mounting the displacement measuring devices on the rest (t-1) stations of the base, and repeating the operation to obtain m 2 ，...，m t Group data, wherein,
s03, converting the sphere center coordinates obtained by measuring different stations into the same coordinate system according to the relative position and posture relationship among the different stations, and defining the coordinate system as a measurement coordinate systemI.e. according to the displacement sensor reading l in the m groups of data i ＝(l i1 ，l i2 ，...，l id ) And respectively calculating the sphere center of the measuring sphere in the measuring coordinate system O at the station position E X E Y E Z E Actual three-dimensional coordinates of
Wherein i = 1.. M;
s04, measuring a coordinate system O according to the sphere center of the measuring sphere E X E Y E Z E Establishing an error model according to the relation between the deviation of the actual coordinate and the nominal coordinate and the error of the parameter to be calibrated, and substituting the error model into theta i ＝(θ i1 ，θ i2 ，...，θ ib ) And
and establishing a nonlinear equation set, and identifying the parameters to be calibrated by using a nonlinear optimization algorithm, namely the geometric parameter error of the robot, the coordinates of the measuring sphere center relative to the terminal coordinate system of the robot, and the relative positions of the base coordinate system and the measuring coordinate system of the robot.
Further, the relative pose relationship between different stations on the base is calibrated and measured by a high-precision external measuring device and is used as the inherent information of the base for a long time; the base calibration measurement comprises the following steps:
a. mounting a displacement measuring device on one of the stations of the base, acquiring partial or all geometric characteristics on the displacement measuring device through an external measuring device, and establishing a device coordinate system based on the geometric characteristics;
b. mounting the displacement measuring devices on the rest (t-1) stations of the base, and repeating the operation to obtain t device coordinate systems;
c. and solving the relative pose among different device coordinate systems or between the different device coordinate systems and an additional measurement coordinate system through external measurement software, wherein the representation method of the relative pose is one or a combination of a homogeneous transformation matrix, a 6D parameter and a quaternion.
Further, 3m is larger than the number of parameters to be calibrated, and d =3.
Further, when the displacement sensor is an incremental displacement sensor, the displacement measuring device is provided with a travel switch or a limiting piece, the measuring head is firstly pushed to the travel switch or the limiting piece before the step S01, the reading of the displacement sensor at the moment is recorded as a zero position when the travel switch is triggered or the displacement sensor is limited by the limiting piece, and then all l i ＝(l i1 ，l i2 ，...，l id ) Are both displacement amounts relative to the null position; or the displacement sensor is an absolute displacement sensor. 5. The calibration method according to claim 1, wherein the origin of the device coordinate system is established at the center of the 3D measuring club when all the displacement sensors are at zero positions.
Further, when the measuring head of the displacement sensor is a flat measuring head, the method for establishing the coordinate system of the device specifically comprises the following steps: the method comprises the steps of respectively measuring and fitting planes A1, B1 and C1 of three flat measuring heads in zero positions through an external measuring device, then respectively measuring and fitting the axes of three displacement sensors, respectively offsetting the planes A1, B1 and C1 along the axes of the three displacement sensors by a certain distance to obtain planes A2, B2 and C2, wherein the distance is equal to the spherical radius of a 3D measuring ball rod, taking the intersection O2 of the planes A2, B2 and C2 as the origin of a device coordinate system, then taking the intersection line of the planes A2 and B2 as the X axis of the device coordinate system, then taking the perpendicular line of the X axis passing through O2 on the plane A2 as the Y axis, then taking O2 as the normal vector of the plane A2 as the Z axis, and adjusting the directions of the axes to enable the planes to accord with the definition of a Cartesian coordinate system.
Further, when the measuring head of the displacement sensor is a flat measuring head and the axes of the three displacement sensors are perpendicular to each other, the XYZ coordinates of the center of sphere relative to the device coordinate system are the displacement amounts of the displacement sensors in the XYZ directions relative to the zero position, respectively.
Further, when the displacement sensor contact is a ball head measuring head, step S03 specifically includes:
a. measuring the coordinates of the center of the ball head measuring head under a measurement coordinate system and the linear equation of the measurement axis of the 3 displacement sensors under the measurement coordinate system by using an external measuring device;
b. from 3 readings of the displacement sensor i ＝(l i1 ，l i2 ，l i3 ) And calculating three-dimensional coordinates of the current 3 displacement sensor contacts in a measurement coordinate system, and respectively recording the three-dimensional coordinates as: p is i1 ＝[x i1 ，y i1 ，z i1 ] T ，P i2 ＝[x i2 ，y i2 ，z i2 ] T ，P i3 ＝[x i3 ，y i3 ，z i3 ] T ；
c. According to the three-dimensional coordinates of the current 3 displacement sensor contacts and the diameter of the calibration ball, the spherical center of the calibration ball can be calculated in a measurement coordinate system O by using a Grobner base method according to a formula (5) E X E Y E Z E Actual coordinates of
Wherein D is the diameter of the measuring ball, and D is the diameter of the ball head measuring head.
Further, the nonlinear optimization algorithm is a Newton iteration method or an LM algorithm.
The invention has the following beneficial effects:
1. the displacement measuring device is arranged on the desktop base plate, and the problem that the tail end of the extension rod is fixed by the calibration measuring device to cause deformation of the extension rod to influence the measuring precision is solved.
2. According to the invention, the tail end of the robot is provided with the measuring ball to measure the multi-station pose and the joint angle, the movement range of the mechanical arm is expanded, the deformation of the extension rod is reduced as much as possible, and the possibility of movement collision interference is reduced.
3. And iteratively screening calibration data through the mechanical arm observability indexes, and selecting an optimal pose joint angle combination to reduce the ill-posed property of a calibration equation set.
Drawings
FIG. 1 is a schematic diagram of a robot calibration system based on multi-station measurement according to the present invention;
FIG. 2 is a schematic view of a 3D measuring ball rod in the multi-station measurement-based robot calibration system in contact with a flat measuring head of a displacement sensor;
fig. 3 is a side view of the base and the substrate of the displacement measuring device in the calibration system of the robot based on multi-station measurement according to the present invention.
Fig. 4 is a schematic view of an angle-adjustable calibration measuring device in the robot calibration system based on multi-station measurement according to the present invention.
In the figure: 2-a substrate; 4-positioning pin; 5-positioning ball; 6-fastening component; 7-base; 8-connecting rod; 9-angle adjusting seat; 10-a measuring head; 11-electric control box; 12-measuring ball; 13-an extension rod; 14-flat probe; 15-calibration points; 16-adapter.
Detailed Description
The present invention is explained in further detail below with reference to the drawings and the detailed description, but it should be understood that the scope of the present invention is not limited by the detailed description.
Fig. 1 shows a robot calibration device based on multi-station measurement according to the present invention, which includes four main parts, namely a substrate 2, a displacement measuring device, a 3D measuring ball rod, and a mechanical arm (not shown in this embodiment). The substrate 2 is provided with five mounting positions for mounting a displacement measuring device for calibration data acquisition; the displacement measuring device comprises a base, a connecting rod 8, an angle adjusting seat 9, a measuring head 10, an electric cabinet 11, a flat measuring head 14 and an adapter 16, wherein the measuring head 10 comprises at least three displacement sensors which are orthogonally arranged, the displacement sensors are contact type displacement sensors, the head measuring head of each contact type displacement sensor is a flat measuring head or a ball head measuring head, or the displacement sensors are laser type non-contact type displacement sensors; the 3D measuring ball rod is positioned on the displacement measuring device and detects the position error amount of the calibration object during the point-winding movement through the measuring head 10, in the embodiment, the 3D measuring ball rod comprises a top measuring ball 12 and an extension rod 13, the head measuring head of the contact type displacement sensor is a flat measuring head 14, and the measuring ball 12 and the flat measuring head 14 are always tangent to each other, so that the 3D displacement of the ball center is measured; the measuring ball 12 is connected to a robot arm (not shown in this embodiment) via an extension rod 13.
As shown in fig. 2, the included angles between the axes of two of the three orthogonally arranged displacement sensors and the horizontal plane are the same, the included angles between the plane formed by the two axes and the horizontal plane are marked as measurement angles, and the measurement angles can be adjusted by replacing different angle adjusting seats 9, wherein the angle adjusting seats 9 are multiple; or the bottom of the angle adjusting seat 9 is provided with an angle adjusting locking mechanism which can adjust the measuring angle and lock and fix.
As shown in fig. 3, a set of first positioning elements is disposed on the base 7, and a positioning manner of a positioning surface is formed by three sets of positioning points; the first positioning element is a positioning pin or a positioning ball, or a double positioning pin or a double positioning ball which are arranged in a triangular manner; the double locating pins are two locating pins which are arranged in parallel, the cylindrical surfaces or the conical surfaces of the locating pins protrude out of the bottom surface of the base 7, and the axes of the double locating pins face to the center of the triangular arrangement; the double positioning balls are two positioning balls arranged at a distance, the spherical surfaces of the two positioning balls protrude out of the bottom surface of the base 7, and the perpendicular bisector of the connecting line of the spherical centers of the two positioning balls faces to the center of the triangular arrangement.
A plurality of mounting positions are arranged on the substrate 2, each mounting position is correspondingly provided with a group of second positioning elements, and each group of second positioning elements corresponds to one group of first positioning elements; the second positioning element is a positioning pin or a positioning ball, or a double positioning pin or a double positioning ball which are arranged in a triangular mode; the double positioning pins are two positioning pins which are arranged in parallel, the cylindrical surfaces or the conical surfaces of the positioning pins protrude out of the upper surface of the substrate 2, and the axes of the double positioning pins face to the centers of the triangular arrangement; the double positioning balls are two positioning balls arranged at a distance, the spherical surfaces of the two positioning balls protrude out of the upper surface of the substrate 2, and the perpendicular bisector of the connecting line of the spherical centers of the two positioning balls faces to the center of the triangular arrangement.
In this embodiment, the first positioning element on the base 7 is the positioning pin 4 arranged in a triangular manner, the second positioning element on the substrate 2 is the double positioning balls 5 arranged in a triangular manner, that is, a positioning hole capable of clamping the positioning pin 4 is formed between the two positioning balls 5, each group of positioning balls 5 is embedded on the substrate 2, the three groups of positioning pins 4 are in a triangular structure, and each group of positioning pins 4 can be embedded in the corresponding positioning hole and forms a positioning point with each positioning ball 5 in a tangent manner.
As shown in fig. 4, in order to obtain a better and more convenient measuring angle, the displacement measuring device of the present embodiment may adopt another alternative, where a plurality of angle adjusting bases 9 are provided, and the measuring angle can be adjusted by replacing different angle adjusting bases 9; or the bottom of the angle adjusting seat 9 is provided with an angle adjusting locking mechanism which can adjust the measuring angle and lock and fix. The adapter 16 is adopted in this embodiment, connects through adapter 16 and can change different angle modulation seat 9 and adjust the measuring angle, and the angle of three mutually perpendicular plane on the angle modulation seat 9 and horizontal plane is adjustable like this, and the arm drives and is markd measuring device removal in-process like this to detect by more favorable angle of motion, establish the basis for accurate measurement.
The data processing device comprises a data acquisition module and a calibration module, wherein the data acquisition module is used for acquiring the readings of 3 displacement sensors, the calibration module calculates the geometric parameter error of the robot according to the sensor readings and the joint angle of the robot, and the joint angle of the robot can be directly obtained through a robot controller.
The measuring device is used for calibrating the three-dimensional coordinates of the sphere center of the measuring ball 12 under a measuring coordinate system and establishing a measuring coordinate system O for the measuring device E X E Y E Z E As shown in FIG. 1, the upper plane of the substrate 2 is used as a reference plane X E O E Y E Using the lower left corner of the substrate 2 as the origin O E The long side of the substrate 2 is X E A shaft. And the measuring device is calibrated by using a three-coordinate machine before being used for calibrating the robot after being processed. The calibration content comprises the following steps: the initial coordinates of the center of the flat measuring head 14 corresponding to the 3 displacement sensors in the measuring coordinate system and the linear equation of the 3 displacement sensors in the measuring coordinate systemAnd 3 plane equations of the flat measuring head corresponding to the displacement sensors in the measuring coordinate system.
As shown in fig. 1, the calibration device is calibrated by using a three-coordinate machine before being used for calibrating the robot after being processed. The calibration content comprises the following steps: the diameter of the ball 12 is measured.
The invention provides a kinematics calibration method based on the robot, which comprises the following steps:
1) As shown in fig. 1, a substrate is fixed near the base of the robot and is kept still relative to the robot all the time, the displacement measuring device is arranged on one of the stations of the substrate on a material object device platform, a calibration device (3D measuring ball rod) is arranged on the tail end of the robot, and the measuring device is placed in the working space of the robot;
2) Initializing a robot control system and initializing a data processing device;
3) M obtained by screening through a calibration pose joint angle selection method by adopting a measuring ball on a calibration device 1 The flat panel measuring head is touched at the optimal group pose and joint angle, and the data acquisition module is used for recording the reading l of the d displacement sensors during each touch i ＝(l i1 ，l i2 ，...，l id ) And a corresponding b-degree-of-freedom robot joint angle value theta i ＝(θ i1 ，θ i2 ，...，θ ib ) To obtain m 1 Group data.
Wherein, i =1 1 。
4) Mounting the displacement measuring devices on the rest (t-1) stations of the substrate, and repeating the operation to obtain m 2 ，...，m t Group data, wherein,
5) The relative pose relationship between different stations is measured by a high-precision measuring device, and the actual three-dimensional coordinate of the sphere center of the measuring sphere under a measuring coordinate system is calculated by measuring data.
When the displacement sensor contact is a flat probe, 5) specifically,
5-1) clamping a displacement measuring device on a station 1 of a substrate, pressing three flat measuring heads of the displacement sensor to zero positions, and measuring a plane equation S of three flat measuring head planes in a world coordinate system under the world coordinate system through an external measuring device (such as a three-coordinate machine, a measuring arm, a laser tracker and the like) 11 ，S 12 ，S 13 (the lower flat probe plane is S 11 The balance being S 12 、S 13 ) Is marked as A 1i x+B 1i y+C 1i z+D 1i =0, (i =1,2,3), the flat panel stylus plane equation is
And the linear equation l of the axes of the three displacement sensors in the world coordinate system 11 、l 12 、l 13 (the lower displacement sensor axis is l 11 The balance being l 12 、l 13 ) The linear direction vector is noted
The direction is a direction away from the displacement sensor. Similarly, repeating the operation on the rest (t-1) stations to obtain a plane equation S of the flat panel measuring head 21 ，S 22 ，S 23 ，...，S n1 ，S n2 ，S n3 Equation of the axis of the displacement sensor 21 ，l 22 ，l 23 ，...，l n1 ，l n2 ，l n3 。
5-2) establishing a coordinate system of the station 1 in the following way, S 11 ，S 12 ，S 13 The intersection O is the origin of the coordinate system and is S 11 The plane is an xOy plane, S 11 And S 12 ，S 13 The intersection line is an x axis and a y axis, the z axis is perpendicular to the xOy plane, and the positive directions of the x axis, the y axis and the z axis are directions far away from the displacement sensor. Similarly, the above operation is repeated for the remaining (t-1) stations to obtain a station 2 coordinate system, …, and a station t coordinate system.
5-3) clamping the displacement measuring device on the station 1 of the substrate, and passing through an external measuring device (such as a three-coordinate machine, a measuring arm, a laser tracker and the like)) Measuring the coordinates of n points on three flat measuring head planes under a station 2 coordinate system and a station 1 coordinate system, wherein the point set under the station 2 coordinate system is M = { P = 11 ，...，P 1n ，P 21 ，...P 2n ，P 31 ，...，P 3n }, the point set under the coordinate system of the station 1 is N = { p' 11 ，...，P′ 1n ，P′ 21 ，...，P′ 2n ，P′ 31 ，...，P′ 3n And (5) iteratively selecting coordinate values (x) of four groups of points in the set M 1 ，y 1 ，z 1 )，(x 2 ，y 2 ，z 2 )，(x 3 ，y 3 ，z 3 )，(x 4 ，y 4 ，z 4 ) Make the matrix
The condition number of (2) is minimal. The coordinate values of the four groups of points in the set N are (x' 1 ，y′ 1 ，z′ 1 )，(x′ 2 ，y′ 2 ，z′ 2 )，(x′ 3 ，y′ 3 ，z′ 3 )，(x′ 4 ，y′ 4 ，z′ 4 ) Corresponding matrix
The rotation matrix from the station 2 coordinate system to the station 1 coordinate system can be obtained by equation (1),
similarly, repeating the operation on the rest (t-2) stations to obtain a rotation matrix from the station 3 coordinate system to the station 1 coordinate system
…, rotation matrix from workstation t coordinate system to workstation 1 coordinate system
In addition, the main points of the invention areThrough the operation, the rotation matrix from the measurement coordinate system to the station 1 coordinate system can be obtained through calculation
5-4) by rotating matrix
And converting all linear equations and plane equations into a station 1 coordinate system.
5-5) controlling the mechanical arm to enable the tail end measuring ball to touch the flat measuring head on the station 1 at different poses and joint angles, and recording the reading l of 3 displacement sensors during each touch by using the data acquisition module i ＝(l i1 ，l i2 ，l i3 ) Then the moving distance of the 3 flat measuring heads in the normal direction of the measuring head plane is,
d can be calculated according to the formula (3) i1j And the plane equation of the 3 flat probes in touch is A 1j x+B 1j y+C 1j z+D i1j ＝0，
Wherein i represents the ith touch and j represents the jth flat probe.
Similarly, repeating the operation on the rest (t-1) stations to obtain a plane equation A of the 3 flat probes in touch kj x+B kj y+C kj z+D ikj And =0, wherein i represents the ith touch, j represents the jth flat probe, and k represents the kth station.
5-6) according to the plane equation of the current 3 displacement sensors corresponding to the flat measuring head in the measuring coordinate system and the diameter of the measuring ball, the center of the measuring ball in the measuring coordinate system O can be calculated through the formula (4) and the coordinate system transformation E X E Y E Z E Actual coordinates of
Wherein D is the diameter of the measuring ball, i represents the ith touch, and k represents the kth station.
When the displacement sensor contact is a ball head measuring head, 5) specifically comprises:
5-1) calibrating the relative pose among stations on the substrate by using an external measuring device (such as a three-coordinate system, a measuring arm, a laser tracker and the like), calibrating the coordinates of the center of the ball head measuring head under a measuring coordinate system by using the zero position of the 3 displacement sensors, and calibrating the linear equation of the measuring axis of the 3 displacement sensors under the measuring coordinate system;
5-2) reading l from 3 displacement sensors i ＝(l i1 ，l i2 ，l i3 ) And calculating three-dimensional coordinates of the current 3 displacement sensor contacts in a measurement coordinate system, and respectively recording the three-dimensional coordinates as: p i1 ＝[x i1 ，y i1 ，z i1 ] T ，P i2 ＝[x i2 ，y i2 ，z i2 ] T ，P i3 ＝[x i3 ，y i3 ，z i3 ] T ；
5-3) calculating the sphere center of the calibration ball in the measurement coordinate system O by using a Grobner basis method according to the current three-dimensional coordinates of the contact of the 3 displacement sensors and the diameter of the calibration ball by using a formula (5) E X E Y E Z E Actual coordinates of
Wherein D is the diameter of the measuring ball, and D is the diameter of the ball head measuring head.
6) According to the sphere center of the measuring sphere in a measuring coordinate system O E X E Y E Z E Establishing an error model according to the relation between the deviation of the actual coordinate and the nominal coordinate and the error of the parameter to be calibrated, and substituting the error model into theta i ＝(θ i1 ，θ i2 ，...，θ ib ) And
and establishing a nonlinear equation set containing 3m equations, and identifying the parameters to be calibrated by utilizing a nonlinear optimization algorithm. In particular to a method for preparing a high-performance nano-silver alloy,
6-1) adopting a DH model to establish a kinematic model of the robot, wherein the robot with 6 degrees of freedom consists of 6 joints and 7 connecting rods (numbered from 0 to 6), the connecting rod 0 is a base of the robot, and the connecting rod 6 is fixedly connected with the tail end of the robot. Let us note that the link coordinate system is {0}, {1}, {6}, and the transformation matrix of the link coordinate system { j-1} and the link coordinate system { j } is
The transformation matrix from the base coordinate system {0} to the end coordinate system {6}
As indicated by the general representation of the,
6-2) establishing a lower conversion matrix of the terminal coordinate system by using a differential perturbation method
Differential error of
The mapping relation with the geometric parameter error of the robot,
wherein the content of the first and second substances,
dx, dy and dz are the micro-changes of the coordinates of the tail end of the robot, and deltax, deltay and deltaz are the micro-changes of the posture of the tail end of the robot; and delta x is a vector formed by errors of geometric parameters of the robot, and J is a parameter identification Jacobian matrix.
Further, a conversion matrix is obtained from equation (8) by differential conversion
Error matrix of
Thus, the actual transformation matrix from the robot base coordinate system to the end coordinate system
In order to realize the purpose,
6-3) recording a homogeneous transformation matrix of a robot measurement spherical coordinate system and a terminal coordinate system as
The homogeneous transformation matrix of the robot base coordinate system and the measuring coordinate system is
The actual coordinate of the sphere center of the measuring sphere in the measuring sphere coordinate system is known as P 7 Then, according to the coordinate transformation, the nominal coordinate P of the sphere center of the measuring sphere under the measuring coordinate system can be obtained from the formula (10) E ，
6-4) the actual coordinate of the sphere center of the known measuring sphere in the measuring coordinate system is P r Establishing actual coordinates P in the measurement coordinate system according to equation (11) r With a nominal coordinate P E The deviation of (a) and the error of the parameter to be calibrated,
wherein, the robot body geometric parameter error delta x, the robot and the external device conversion matrix
And
is a parameter to be calibrated. Order to
Substituting the parameters into the formula, separating the parameters with known quantity and to be calibrated, merging and simplifying, expressing the error model in a matrix form, wherein the expression is shown as a formula (12),
wherein X = [ m ] 11 ，m 12 ，...，m 34 ，n 11 ，n 12 ，...，n 34 ，Δx] T As vectors of parameters to be calibrated, A 1 、A 2 、A 3 Error coefficient vectors of the error model in x, y and z directions, respectively, b 1 、b 2 、b 3 The constant matrices of the error model in the X, y, and z directions are respectively, and equation (12) is abbreviated as f (X) =0.
When the measuring ball contacts the displacement measuring device from m different poses, m groups of multi-element nonlinear equations are obtained,
the above equation is a complex nonlinear equation system containing a plurality of parameters to be calibrated, and direct solution is difficult. It is converted into an optimization problem: finding an optimal set of parameter values within a given constraint range
So that the following formula is minimized,
in the formula I 3×3 Is a 3 x 3 identity matrix of the cell,
and
are respectively as
And
the rotation matrix of (2) is required to satisfy orthogonality constraints.
In addition to the optimization method of equation (14), redundant parameters of the parameters to be calibrated may be removed first, and then the remaining parameters to be calibrated and errors may be added
An error model similar to the formula (7) is established, and a nonlinear optimization algorithm is adopted to carry out optimization solution on the parameters, so that constraint conditions are avoided being considered in the optimization process.
The formula is optimized by adopting a nonlinear optimization algorithm, and the parameter X to be calibrated is obtained through identification, namely the parameter X comprises a robot bodyError delta x of what parameter, measurement spherical coordinate system and homogeneous transformation matrix of robot terminal coordinate system
Homogeneous transformation matrix of robot base coordinate system and measuring coordinate system
In addition, the pose joint angles adopted in the calibration method can be screened by adopting a calibration pose joint angle selection method, and the method comprises the following steps:
1) In an off-line simulation environment, clamping a displacement measuring device at one station of a substrate, keeping the point constraint of the center of a measuring ball, uniformly distributing attitude angles of a 3D measuring ball rod in a measuring space of the displacement measuring device, enabling the measuring ball at the tail end of an extension rod of a mechanical arm to touch a flat measuring head on the displacement measuring device in different uniformly distributed attitudes, then performing kinematic inverse solution, and screening by taking simulation collision detection, kinematic solvability and mechanical arm configuration as indexes to obtain a reasonable pose and a reasonable joint angle value of a robot,
1-1) under the simulation environment, a displacement measuring device is installed at one of the stations of the substrate, the intersection point of the axes of three orthogonally placed displacement sensors is used as a calibration point of the station, three flat measuring heads are used as reference surfaces, a spherical space with the calibration point as the center of a sphere is divided into eight equal parts, an outward one-eighth open area is used as a measuring space, the measuring space is used as an one-eighth spherical surface, and coordinates (latitude alpha range: 0 to 90 °, longitude β range: 0 to 90 degrees), the connecting line direction of the intersection point of each warp and weft and the sphere center is the z-axis direction of the spherical coordinate system measured at the tail end of the mechanical arm in the pose to be measured, the direction of the x-axis is the rotation angle gamma of the original x-axis around the z-axis under the current pose, and the angle gamma is obtained from-180 to 180 degrees according to a division value d γ And traversing. The selection range of alpha, beta and gamma and the method are specifically that the value range of alpha is 0-90 DEG and the division value d α Traversing;
to ensureThe included angle formed by adjacent poses is approximately the same, the higher the latitude is, the larger the division value of the longitude should be, preferably, under the latitude of alpha (alpha is more than 0), every d α Corresponding longitude is
Thus:
beta is in division value of 0-90 DEG
Traversing;
gamma is in-180 deg. and divided by d γ And traversing.
The rotation matrix of the measuring spherical coordinate system relative to the base coordinate system can be obtained according to alpha, beta, gamma, theta and the robot kinematics model
Or, coordinate points on the spherical surface are not defined by longitude and latitude, but are directly and uniformly distributed on the spherical surface, and the direction of a connecting line between the uniformly distributed points and the spherical center is defined as the direction of the z axis of the spherical coordinate system measured by the tail end of the mechanical arm.
1-2) calculating a kinematic inverse solution for each pose to obtain a corresponding joint angle, and then screening the corresponding joint angles as follows: (1) if the pose has no inverse solution or only has the elbow downward configuration, rejecting the pose; (2) respectively calculating corresponding Jacobian matrix condition numbers for the joint angles corresponding to the pose, and removing the condition numbers which are larger than a threshold value k limit The joint angle of (a); (3) if the mechanical arm moves to a certain joint angle corresponding to the pose and then can generate self collision or collision with the outside (through collision detection and judgment in simulation, the self collision means that the mechanical arm collides with each joint connecting rod, and the collision with the outside means that the mechanical arm collides with a desktop, a substrate and a measuring device), the joint angle is removed; (4) if the mechanical arm linearly interpolates and moves a certain joint angle corresponding to the pose from the initial pose and can generate dynamic collision (including self collision and collision with the outside) when moving back and forth, the joint angle is removed. After the screening, theThe feasible pose and the corresponding feasible joint angle and configuration are recorded as a reasonable pose T i Reasonable joint angle value theta of robot i And configuration, and repeating the above operations for all poses to obtain n 1 Group data. Wherein i =1 1 。
2) Mounting the displacement measuring device on the rest (t-1) stations of the substrate, and repeating the process 1) to obtain n 2 ，...，n t Group data.
3) Iteratively selecting m groups of optimal pose joint angle combinations based on observability indexes, specifically,
3-1) from
Uniformly selecting m groups of data from the group joint angle data, and calculating the observability evaluation index OI value of the m groups of data by the following method:
j is a matrix obtained by vertically stacking Jacobian matrixes of m groups of joint angle data, the dimensionality is 3m multiplied by q, m is the number of data groups, and the number of kinematic parameters to be calibrated is 30 and q.
OI 3 ＝σ q (15-3)
Wherein σ i (i＝1，2，…，q，σ q ≤…≤σ 1 ) Is the singular value of the stacked Jacobian matrix J, q is the singular value numberQuantity, m is the number of data sets. The observability index has various evaluation modes, and the larger the OI value is, the better the flexibility of the mechanical arm under the group of joint angles is.
3-2) in the rest
And traversing and screening a group of data in the group of data, so that the (m + 1) group of data OI value after the group of data is added into the originally selected m groups of data is the maximum.
3-3) traversing and screening one group of data in the (m + 1) groups of data, so that the reduction amplitude of the OI value of the m groups of data after the group of data is deleted is minimum.
3-4) continuously and circularly traversing until the deleted group of data is just the added group of data, thereby obtaining m groups of data with the maximum OI value, and obtaining higher calibration parameter accuracy through the m groups of data. Wherein, the optimal pose joint angle combination on each station has m i The number of the groups is set to be,
the invention has the innovation points that a set of robot calibration method is developed based on multi-station measurement design, the precision of the calibration result is improved, the displacement measurement device is arranged on a desktop substrate, and the problem that the measurement precision is influenced by the deformation of an extension rod caused by the fact that the calibration measurement device is fixed at the tail end of the extension rod is solved; the tail end of the robot is provided with the measuring ball through the extension rod to measure the multi-station pose and the joint angle, so that the movement range of the mechanical arm is expanded, the deformation of the extension rod is reduced as much as possible, and the possibility of collision interference of movement is reduced; and iteratively screening calibration data through the mechanical arm observability indexes, and selecting an optimal pose joint angle combination to reduce the ill-posed property of a calibration equation set.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (9)
1. A robot calibration method based on multi-station measurement is characterized by comprising the following steps:
s01, fixing a base near the base of the robot, installing the displacement measuring device on one of the stations of the base, connecting a 3D measuring ball rod at the tail end of a mechanical arm, touching a contact of the displacement sensor by adopting a measuring ball on the 3D measuring ball rod in different poses and joint angles, and recording the reading l of the D displacement sensors during each touch by using the data acquisition module i ＝(l i1 ，l i2 ，...，l id ) And corresponding b degree of freedom robot joint angle values theta i ＝(θ i1 ，θ i2 ，...，θ ib ) To obtain m 1 Group data, wherein i =1 1 ；
S02, mounting the displacement measuring devices on the rest (t-1) stations of the base, and repeating the operation to obtain m 2 ，...，m t Group data, wherein,
s03, converting the sphere center coordinates measured by different stations into the same coordinate system according to the relative position and posture relation among the different stations, and defining the coordinate system as a measurement coordinate system, namely according to the reading l of the displacement sensor in the m groups of data i ＝(l i1 ，l i2 ，...，l id ) And respectively calculating the sphere center of the measuring sphere in the measuring coordinate system O at the station position E X E Y E Z E Actual three-dimensional coordinates of
Wherein i = 1.. M;
s04, according to the center of the measuring ball, measuringVolume coordinate system O E X E Y E Z E Establishing an error model according to the relation between the deviation of the actual coordinate and the nominal coordinate and the error of the parameter to be calibrated, and substituting the error model into theta i ＝(θ i1 ，θ i2 ，...，θ ib ) And
and establishing a nonlinear equation set, and identifying the parameters to be calibrated by using a nonlinear optimization algorithm, namely the geometric parameter error of the robot, the coordinates of the measuring sphere center relative to the terminal coordinate system of the robot, and the relative positions of the base coordinate system and the measuring coordinate system of the robot.
2. The calibration method according to claim 1, wherein the relative pose relationship between different stations on the base is calibrated and measured by a high-precision external measuring device and is used as the intrinsic information of the base for a long time; the base calibration measurement comprises the following steps:
a. mounting a displacement measuring device on one of the stations of the base, acquiring partial or all geometric characteristics on the displacement measuring device through an external measuring device, and establishing a device coordinate system based on the geometric characteristics;
b. mounting the displacement measuring devices on the rest (t-1) stations of the base, and repeating the operation to obtain t device coordinate systems;
c. and solving the relative pose among different device coordinate systems or between the different device coordinate systems and an additional measurement coordinate system through external measurement software, wherein the representation method of the relative pose is one or a combination of a homogeneous transformation matrix, a 6D parameter and a quaternion.
3. The calibration method according to claim 1, wherein 3m is greater than the number of parameters to be calibrated, and d =3.
4. The calibration method according to claim 1, wherein when the displacement sensor is increasedWhen the displacement sensor is a volume displacement sensor, the displacement measuring device is provided with a travel switch or a limiting part, a measuring head is firstly pushed to the travel switch or the limiting part before the step S01, the reading of the displacement sensor at the moment is recorded as a zero position when the travel switch is triggered or the displacement sensor is limited by the limiting part, and then all l recorded readings are recorded i ＝(l i1 ，l i2 ，...，l id ) Are both displacement amounts relative to the null position; or the displacement sensor is an absolute displacement sensor.
5. The calibration method according to claim 1, wherein the origin of the device coordinate system is established at the center of the 3D measuring club when all the displacement sensors are at zero positions.
6. The calibration method according to claim 1, wherein when the measurement head of the displacement sensor is a flat-panel measurement head, the establishment method of the device coordinate system specifically comprises:
the method comprises the steps of respectively measuring and fitting planes A1, B1 and C1 of three flat measuring heads in zero positions through an external measuring device, then respectively measuring and fitting the axes of three displacement sensors, respectively offsetting the planes A1, B1 and C1 along the axes of the three displacement sensors by a certain distance to obtain planes A2, B2 and C2, wherein the distance is equal to the spherical radius of a 3D measuring ball rod, taking the intersection O2 of the planes A2, B2 and C2 as the origin of a device coordinate system, then taking the intersection line of the planes A2 and B2 as the X axis of the device coordinate system, then taking the perpendicular line of the X axis passing through O2 on the plane A2 as the Y axis, then taking O2 as the normal vector of the plane A2 as the Z axis, and adjusting the directions of the axes to enable the planes to accord with the definition of a Cartesian coordinate system.
7. The calibration method according to claim 1, wherein when the measurement head of the displacement sensor is a flat probe and the axes of the three displacement sensors are perpendicular to each other, the XYZ coordinates of the center of sphere with respect to the apparatus coordinate system are the displacement amounts of the displacement sensors in the XYZ directions with respect to the zero position, respectively.
8. The calibration method according to claim 1, wherein when the displacement sensor contact is a ball head probe, step S03 specifically comprises:
a. measuring the coordinates of the center of the ball head measuring head under a measurement coordinate system and the linear equation of the measurement axis of the 3 displacement sensors under the measurement coordinate system by using an external measuring device;
b. according to the reading l of 3 displacement sensors i ＝(l i1 ，l i2 ，l i3 ) And calculating three-dimensional coordinates of the current 3 displacement sensor contacts in a measurement coordinate system, and respectively recording the three-dimensional coordinates as: p i1 ＝[x i1 ，y i1 ，z i1 ] T ，P i2 ＝[x i2 ，y i2 ，z i2 ] T ，P i3 ＝[x i3 ，y i3 ，z i3 ] T ；
c. According to the three-dimensional coordinates of the current 3 displacement sensor contacts and the diameter of the calibration ball, the spherical center of the calibration ball in the measurement coordinate system can be calculated by using a Grobner base method according to a formula (5) E X E Y E Z E Actual coordinates of
Wherein D is the diameter of the measuring ball, and D is the diameter of the ball head measuring head.
9. The calibration method according to claim 6, wherein the nonlinear optimization algorithm is Newton's iteration method or LM algorithm.
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