CN115107024A - Industrial robot kinematic parameter identification method based on laser tracker multi-station technology - Google Patents
Industrial robot kinematic parameter identification method based on laser tracker multi-station technology Download PDFInfo
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Abstract
The invention discloses an industrial robot kinematic parameter identification method based on a laser tracker multi-station technology, which comprises the steps of firstly planning a theoretical path in a robot working space, measuring to obtain an actual three-dimensional coordinate of a measuring point corresponding to a planned path under a robot coordinate system based on the laser tracker multi-station technology, and obtaining a robot tail end positioning error based on a laser tracker multi-station measurement model; then, based on the kinematic model of the robot, a positioning error model describing the relationship between the positioning error of the tail end of the industrial robot and the 24 kinematic parameter errors is constructed; and finally, accurately identifying 24 kinematic parameters of the robot by using an LASSO algorithm, and improving the positioning accuracy of the tail end of the robot.
Description
Technical Field
The invention relates to a method for identifying kinematic parameter errors of an industrial robot, in particular to a technical method based on multi-station laser tracker measurement, and belongs to the field of kinematic parameter identification and error compensation of industrial robots.
Background
Along with the application expansion of industrial robot to fields such as precision finishing and precision assembly, also higher and higher to its absolute positioning accuracy's requirement, the current absolute positioning accuracy level of industrial robot has hardly satisfied the requirement, and how to further promote industrial robot's absolute positioning accuracy has become the urgent necessity.
The absolute positioning error of the industrial robot is mainly caused by the kinematic parameter error and accounts for more than 90% of the total error of the tail end of the industrial robot. Kinematic parameter error compensation for industrial robots can generally be divided into four areas: and establishing a kinematic model, establishing a measuring system to obtain a positioning error, and analyzing and compensating the positioning error based on the parameter identification and the positioning error of the kinematic error model of the robot. Before robot kinematic parameter identification, a positioning error of a robot is firstly obtained, and commonly used measuring equipment comprises: the device comprises a ball rod instrument, a theodolite, a three-coordinate measuring machine, a multi-view vision measuring system, a laser tracking measuring system and the like. The comprehensive consideration of measurement accuracy, measurement efficiency, measurement range and portability, the laser tracking measurement technology is undoubtedly the first choice for detecting the positioning error of the tail end of the industrial robot. Because the precision of the laser tracker measurement is limited, and the measurement uncertainty increases with the increase of the measurement range. The laser tracker adopts a standard ball design means, and the deviation of a mechanical rotating shaft of the laser tracker does not obviously influence the measurement precision, so that the measurement precision of the space distance of the laser tracker is greatly improved.
The invention uses the multi-station measuring technology of the laser tracker to measure the positioning error of the industrial robot. After the positioning error of the industrial robot is obtained, an error model is established, and the kinematic parameters of the robot are identified. When the least square method is used for parameter identification, the least square calculation amount is small, the convergence rate is high, but when the complex coefficient matrix is a singular matrix, an error which can affect the calculation result is generated in the numerical calculation process, so that the parameter error identification precision is reduced. Therefore, the invention provides an LASSO algorithm for identifying kinematic parameters of an industrial robot, and the algorithm introduces a regularization item into a loss function, effectively solves the problems of irreversible coefficient matrix and the like in the process of solving an error matrix equation, and can more accurately identify kinematic parameter errors.
Disclosure of Invention
The multi-station measuring technology of the laser tracker in the citation (application number/patent number: CN201610889315.5 'a four-shaft machine tool calibration method based on multi-station measurement of the laser tracker'). The invention aims to provide an industrial robot kinematic parameter identification method based on the laser tracker multi-station technology, which comprises the steps of firstly, measuring by using the laser tracker multi-station technology to obtain three-dimensional coordinates of a measuring point corresponding to a planned path under a robot coordinate system, and obtaining a robot positioning error based on a laser tracker multi-station measurement model; then, based on the kinematic model of the robot, a positioning error model describing the relationship between the positioning error of the tail end of the industrial robot and the 24 kinematic parameter errors is constructed; and finally, accurately identifying 24 kinematic parameters of the robot by using an LASSO algorithm, and improving the positioning precision of the tail end of the industrial robot.
In order to achieve the purpose, the invention adopts the following technical scheme:
an industrial robot kinematic parameter identification method based on a laser tracker multi-station technology comprises the following steps:
the method comprises the following steps: and planning a theoretical path for measuring the absolute positioning error of the industrial robot to obtain a theoretical three-dimensional coordinate of a measuring point corresponding to the planned path in a robot coordinate system.
Step two: and constructing a multi-station measuring model of the laser tracker under an industrial robot coordinate system.
Theoretical three-dimensional coordinate P of corresponding measuring point of planned path in robot coordinate system i (x i ,y i ,z i ) I is 1,2,3, …, n, n represents the number of theoretical measurement points and is a positive integer; the laser tracker has a station coordinate of B j (X j ,Y j ,Z j ) Wherein j is 1,2,3, …, m represents the number of the station coordinates and takes a positive integer; laser tracker station B j To the initial measuring point P 1 A distance of d j (ii) a In the measuring process, the relative interference length of the cat eye reflector is measured to be l by the laser tracker ij . Establishing the following relation according to a three-dimensional space two-point distance formula:
the number of equations is m × n, and the number of unknowns is 4m +3 n. In order to solve the equation set, m multiplied by n is more than or equal to 4m +3n, m and n satisfy m is more than or equal to 4, and n is more than or equal to 16.
Step three: and measuring to obtain the actual three-dimensional coordinates of the measuring points corresponding to the planned path in the robot coordinate system based on the multi-station technology of the laser tracker.
Step four: and acquiring the positioning error of the tail end of the robot.
P ai (x ai ,y ai ,z ai ) Actual three-dimensional coordinates, delta P, of corresponding measuring points of a planned path in a robot coordinate system i ＝(Δx i ,Δy i ,Δz i ) T The end of the industrial robot at point i is measured for the positioning error.
Step five: and performing kinematic modeling on the robot by using an improved D-H method, and constructing a homogeneous transformation matrix of a reference coordinate system of adjacent joints.
Step six: and establishing an industrial robot position error model according to the homogeneous transformation matrix.
Step seven: and solving the position error model of the industrial robot by using a LASSO algorithm, and accurately identifying 24 kinematic parameter errors delta X.
Preprocessing of the data is required to solve for the 24-term kinematic parameter errors.
The coefficient matrix J is normalized to mean 0 and unit length. The matrix Δ P consisting of the positioning errors is normalized to mean 0, i.e.
Where u is the number of equations, u is 1,2,3, …,3 n;
n is the number of measuring points;
p is the number of p-th parameter errors, and p is 24.
A set of linear regression coefficients can be obtained
So that
The optimization goal of LASSO is
In the formula, t is a harmonic parameter (greater than or equal to zero), and J is a coefficient matrix.
And solving 24 kinematic parameter errors by using a LASSO algorithm.
In summary, compared with the prior art, the invention has the following advantages and beneficial effects:
(1) the laser tracker needs to establish a conversion matrix between the coordinate system of the laser tracker and the coordinate system of the robot when obtaining the three-dimensional coordinates of the measuring points under the coordinate system of the robot, and the matrix usually has poor precision and can introduce a certain error.
(2) The algorithm commonly used for identifying parameter errors of the industrial robot is a least square method, an over-determined equation set is obtained by measuring the positioning errors of the measuring points under the planned path through a laser tracker, and the least square solution of the parameter errors is solved. The least square method has the advantages of fast convergence, small calculation amount and the like, but when a complex coefficient matrix is a singular matrix and is irreversible or becomes a pathological matrix, the kinematic parameter error solved by the ordinary least square method is wrong, so the method is unstable. The method adopts the LASSO algorithm, introduces the regularization item into the loss function, effectively solves the problems that the coefficient matrix is irreversible and the like in the process of solving the position error model of the industrial robot, can more accurately identify the kinematic parameter error, and effectively improves the absolute positioning error of the industrial robot.
Drawings
FIG. 1 is a schematic diagram of a laser tracker multi-station technology measuring industrial robot positioning error;
FIG. 2 is a schematic diagram of improved D-H kinematics modeling.
Detailed Description
The present invention is described in further detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description text. The specific implementation steps are as follows:
the method comprises the following steps: and planning a theoretical path of the absolute positioning error measurement of the industrial robot.
The motion requirements of the robot during the measurement of the positioning error in the industrial robot performance specification and the test method GB/T12642-2013: when the robot moves between all positions, all joints should move. According to the requirement, a sphere path is planned in a working space of the industrial robot, and 60 spherical points are randomly generated under a robot coordinate system by taking selected points (1600,0 and 900) as sphere center points of the sphere path and setting the radius to be 500 mm. The demonstrator is programmed to control the tail end of the robot to move from the sphere center point to the sphere center point and return to the sphere center point, and the robot sequentially walks through 60 sphere points.
Step two: a laser tracker multi-station measurement model of an industrial robot is constructed, and a model schematic diagram is shown in figure 1. The target lens of the laser tracker is fixedly connected to the tail end of the industrial robot. 60 spherical points are planned in the working space of the robot, and the number of the laser tracker stations is determined to be 4 by considering the measurement precision and the time required by the experiment.
Step three: and measuring to obtain the actual three-dimensional coordinates of the measuring points corresponding to the planned path in the robot coordinate system based on the multi-station technology of the laser tracker.
Step four: and acquiring the positioning error of the tail end of the robot.
Step five: and (3) performing kinematic modeling on the robot by using an improved D-H method: r is the number of degrees of freedom of the industrial robot, and r is 1,2,3 …, 6. Determination of Z r The axial direction is along the axial direction of the joint shaft r; origin O r Is the intersection point of the joint axis r +1 and the r axis or the common perpendicular line thereof and the joint axis Z r The intersection point of (a); x r The axes being along a common vertical line a r The axial direction of the axis is directed from the joint axis r to the joint axis r +1, and if the joint axis r intersects with the joint axis r +1, X is defined r The axis is perpendicular to the plane of the two joint axes; y is r Axes are determined according to the right hand rule; when the first joint variable is 0, the coordinate system {0} and the coordinate system {1} are defined to coincide with each other, and the origin thereof is determined for the coordinate system { n }, respectivelyAnd x n The direction of the axis can be arbitrarily selected, but the link parameter is selected to be 0 as much as possible. The parameter meaning of the improved D-H method is that the length a of the connecting rod r : is defined as from Z r Move to Z r+1 Along X r The axis is directed positive, which is substantially the length of the plumb line; angle alpha of connecting rod r : is defined as from Z r Rotate to Z r Angle +1, around X i The positive rotation of the shaft is positive; ③ offset d of connecting rod r : is defined as from X r -1 moves to X r Along Z, a distance of r The axis is pointing positive. Which is essentially the distance between two common perpendicular lines. Angle theta of articulation r Is defined as from X r -1 rotation to X r Angle of (about Z) r The shaft rotates positively to positively. The improved D-H method is characterized in that the origin of the connecting rod coordinate system is established at the head end of the corresponding joint connecting rod, and compared with the standard D-H method, the improved D-H method is clearer in system establishment and easy to understand and observe. A schematic diagram of the improved D-H modeling is shown in fig. 2.
Constructing a homogeneous transformation matrix of an adjacent joint reference coordinate system as follows:
step six: and establishing an industrial robot position error model according to the homogeneous transformation matrix.
The pose of the industrial robot end in the base coordinate system is as follows:
the parameter identification method only needs the position information P (x, y, z) of the measuring point, so that the parameter identification method can obtain the following formula:
for more clearly identifying the kinematic parameters of the robot, the above formula is linearized
P＝F(a 1 ,a 2 ,…,a 6 ,d 1 ,d 2 ,…,d 6 ,α 1 ,α 2 ,…,α 6 ,α 1 ,α 2 ,...,α 6 ,θ 1 ,θ 2 ,...,θ 6 ) (8)
In the above equation, F (-) is a function of the kinematic parameters of the robot.
The terminal positioning error is caused by a small error between the actual kinematic parameters and the kinematic parameters in the robot controller. Thus, the actual position of the industrial robot end effector can be written as follows:
P a ＝F(a 1 +Δa 1 ,...,a 6 +Δa 6 ,d 1 +Δd 1 ,...,d 6 +Δd 6 ,α 1 +Δα 1 ,...,α 6 +Δα 6 ,θ 1 +Δθ 1 ,...,θ 6 +Δθ 6 ) (9)
in the above formula,. DELTA.a r Representing the parameter error of the length of the connecting rod; Δ d r Representing the parameter error of the connecting rod offset distance; delta alpha r Representing the parameter error of the connecting rod rotation angle; delta theta r Representing the initial joint angle parameter error.
The error of the kinematic parameter Δ P is usually small and can therefore be written in the form of a linear equation by linearization:
according to the above formula, the tip positioning error (Δ x) of the robot i ,Δy i ,Δz i ) Can be expressed as:
the above equation is a matrix of coefficients, so the position error model is
Wherein
Is a vector of the positioning error that is,
is a kinematic parameter error vector and is,
is the constructed coefficient matrix, i-60.
Step seven: and solving the position error model of the industrial robot by using a LASSO algorithm, and accurately identifying 24 kinematic parameter errors as shown in the table 1.
TABLE 1 kinematic parameter error identification
Claims (10)
1. An industrial robot kinematics parameter identification method based on a laser tracker multi-station technology is characterized by comprising the following steps: planning a theoretical path in a robot working space; constructing a multi-station measuring model of a laser tracker of an industrial robot; measuring to obtain three-dimensional coordinates of a measuring point corresponding to a planned path under a robot coordinate system based on a multi-station technology of a laser tracker; acquiring a robot tail end positioning error based on a laser tracker multi-station measurement model; performing kinematic modeling on the robot by using an improved D-H method, and constructing a homogeneous transformation matrix of a reference coordinate system of adjacent joints; establishing an industrial robot position error model according to the homogeneous transformation matrix, and expressing the relation between the industrial robot end positioning error and the 24 kinematic parameter errors; and solving an equation set by using a LASSO algorithm to accurately identify the 24-item kinematic parameter error delta X.
2. The method for identifying the kinematic parameters of the industrial robot based on the multi-station technology of the laser tracker as claimed in claim 1, wherein a sphere motion path is planned in the working space of the industrial robot, and 60 spherical points are randomly generated.
3. The method for identifying the kinematic parameters of the industrial robot based on the multi-station technology of the laser tracker in claim 1 is characterized in that a laser tracker multi-station measurement model of the industrial robot is constructed to measure the positioning error of the industrial robot.
4. The method for identifying the kinematic parameters of the industrial robot based on the multi-station technology of the laser tracker as claimed in claim 1, wherein the measurement model of the laser tracker is determined to be four-station by considering the measurement accuracy and the time required for the experiment.
5. The method for identifying the kinematic parameters of the industrial robot based on the multi-station technology of the laser tracker as claimed in claim 1, wherein the actual three-dimensional coordinates of the corresponding measuring points of the planned path in the robot coordinate system are measured based on the multi-station technology of the laser tracker.
6. The method for identifying the kinematic parameters of the industrial robot based on the multi-station technology of the laser tracker as claimed in claim 1, wherein the end positioning error of the industrial robot is obtained based on a measurement model of the multi-station technology of the laser tracker.
7. The method for identifying the kinematic parameters of the industrial robot based on the multi-station technology of the laser tracker as claimed in claim 1, characterized in that the robot is kinematically modeled by an improved D-H method: r is the number of degrees of freedom of the industrial robot, and r is 1,2,3 …, 6; determination of Z r The axial direction is along the axial direction of the joint shaft r; origin O r Is the intersection point of the joint axis r +1 and the r axis or the common perpendicular line thereof and the joint axis Z r Point of intersection of；X r The axes being along a common vertical line a r The axial direction of the axis is directed from the joint axis r to the joint axis r +1, and if the joint axis r intersects with the joint axis r +1, X is defined r The axis is perpendicular to the plane of the two joint axes; y is r Axes are determined according to the right hand rule; when the first joint variable is 0, the coordinate system {0} and the coordinate system {1} are defined to coincide with each other, and the origin and x of the coordinate system { n } are determined to coincide with each other n The direction of the shaft is selected randomly, and the parameters of the connecting rod are 0 when the shaft is selected; the parameter meaning of the improved D-H method is that the length a of the connecting rod r : is defined as from Z r Move to Z r+1 Along X r The axis is directed positive, which is substantially the length of the plumb line; angle alpha of link rod r : is defined as from Z r Rotate to Z r Angle +1, around X i The positive rotation of the shaft is positive; ③ offset d of connecting rod r : is defined as from X r -1 to X r Along Z, of r The axial orientation is positive; which is essentially the distance between two common perpendicular lines; angle theta of articulation r Is defined as from X r -1 rotation to X r Angle of (d), around Z r The shaft rotates positively to positively.
8. The method for identifying the kinematic parameters of the industrial robot based on the multi-station technology of the laser tracker as claimed in claim 1, characterized in that a homogeneous transformation matrix of the reference coordinate systems of adjacent joints is constructed based on a kinematic model of the robot established by an improved D-H method.
9. The method for identifying kinematic parameters of an industrial robot based on the multi-station technology of the laser tracker as claimed in claim 1, wherein the model of the position error of the industrial robot is established based on a homogeneous transformation matrix.
10. The method as claimed in claim 1, wherein the LASSO algorithm is used to solve the system of equations to accurately identify the kinematic parameter error Δ X of 24 items.
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