CN114918920B - Industrial robot calibration method based on neural network and distance error model - Google Patents
Industrial robot calibration method based on neural network and distance error model Download PDFInfo
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Abstract
The invention belongs to the technical field of industrial robot calibration, and relates to an industrial robot calibration method based on a neural network and a distance error model. Comprising the following steps: s1, establishing a DH kinematic model; s2, establishing a positioning error identification model of coupling connecting rod parameters and joint flexibility; s3, converting the positioning error identification model into a distance error identification model; and S4, recording the joint rotation angle value of each sampling point and the measured value under the coordinates of the laser tracker. S5, identifying error parameters by using a damping iterative least square method; and S6, compensating the residual error based on the neural network, and inputting the residual error into a control system. According to the invention, the conversion error of a coordinate system in the calibration process can be avoided by establishing the model relation between the robot tail end distance error and the robot kinematic parameter error, and the absolute positioning accuracy of the industrial robot is improved by taking the link error and the joint flexibility error into consideration and fitting the residual error through the neural network after the error parameter is identified.
Description
Technical Field
The invention relates to the technical field of industrial robot calibration, in particular to an industrial robot calibration method based on a neural network and a distance error model.
Background
As industrial robots are increasingly used, higher demands are being placed on the accuracy of the industrial robots. The repeated positioning accuracy of the industrial robot is high, but the application of the industrial robot in certain fields is limited by the characteristic of low absolute positioning accuracy. The calibration technology is one of the most effective methods for improving the absolute positioning accuracy of the industrial robot at present. However, in the calibration process of the industrial robot, due to the fact that manufacturing and assembling errors of the robot connecting rod are accumulated, the connecting rod dead weight and inertia exist in the movement process, the deviation and the flexible deformation of each joint of the robot can be accumulated and transmitted to the end effector in a superimposed mode, and therefore the positioning accuracy of the tail end of the robot is reduced, and the positioning error is increased.
The existing calibration method mainly comprises two types: error prevention and error compensation methods. Compared with an error prediction method, the error compensation method is low in cost and obvious in compensation effect, and is an important way for robot positioning compensation. The error compensation method is based on a reasonable error identification model and an advanced measurement means, and identifies the actual parameter error to compensate the error. The conventional error compensation method generally adopts a position error model, and a complex coordinate system is required to be converted to cause precision loss, so that residual errors existing after identification are not analyzed and processed, and the terminal positioning precision of the robot is not improved.
Disclosure of Invention
In order to solve the technical problems in the prior art, the invention designs an industrial robot calibration method based on a neural network and a distance error model aiming at the absolute positioning accuracy of the tail end of the industrial robot.
The method specifically comprises the following steps:
s1, establishing a DH kinematic model according to structural parameters of an industrial robot;
s2, analyzing and considering the influence of the joint flexibility and the reduction ratio of the industrial robot on the terminal pose, and establishing a positioning error identification model of coupling link parameters and the joint flexibility;
s3, converting the positioning error identification model into a distance error identification model according to the relation between the distance error and the positioning error of the robot;
s4, randomly sampling a large amount of samples in a robot working space, and respectively recording the joint rotation angle value of each sampling point and the measured value under the coordinates of a laser tracker;
and S5, combining the data in the robot distance error model step 4 established in the step 3, and identifying error parameters by using a damping iterative least square method (Levenberg-Marquardt method).
And S6, compensating residual errors of parameter identification based on the neural network, and inputting the residual errors into a control system to improve the absolute positioning accuracy of the industrial robot.
Further, the step S1 specifically includes:
establishing a kinematic model based on a D-H model method, wherein the first step is to determine a coordinate system corresponding to each connecting rod of the robot according to the D-H method; second, each rod parameter and motion parameter (joint rotation angle θ) are analyzed and determined i Link offset d i Angle alpha of joint torsion i Length of connecting rod a i ) The method comprises the steps of carrying out a first treatment on the surface of the Thirdly, determining a transformation matrix between adjacent coordinate systems; taking the spatial variation of the link coordinate system between joint i and joint i+1 as an example, it is possible to pass θ i 、d i 、α i 、a i The four kinematic parameters are mathematically described, decomposing the linkage transformation into four sub-transformations:
1) Linkage coordinate system { i } is z-wound i Shaft rotation theta i The angle, the coordinate system { i }', i.e., rot (z i ,θ i )；
2) Coordinate system { i }' along z i Shaft movement d i The coordinate system { i }', i.e., trans (z i ,d i )；
3) Coordinate system { i } "is along x i+1 Shaft movement a i The coordinate system { i }', i.e. Trans (x i+1 ,a i )；
4) Coordinate system { i }' is wrapped around x i+1 Shaft rotation alpha i Angle, a coordinate system { i+1}, i.e. Rot (x i+1 ,θ i )；
According to the sub-transformation, the transformation matrix of the adjacent coordinate system of the connecting rod can be obtained as
The link transformations are multiplied in turn according to the principle of 'left to right', and a transformation matrix is obtained
The transformation matrixes of the connecting rods are multiplied in sequence to obtain a robot positive kinematics model, namely for an n-degree-of-freedom serial robot, the terminal pose transformation matrix is as follows:
in the formula (3), the coordinate system 0 is converted into the coordinate system N in turn according to the principle of matrix continuous multiplication,representing a transformation matrix from the ith coordinate system to the (i+1) th coordinate system, ">Rotation matrix representing coordinate system {0} to { N }, a ∈>The translation matrix representing the coordinate system {0} to { N } is required to be greater than or equal to 1.
Further, the step S2 specifically includes:
when the parameters of each connecting rod of the industrial robot have errors, the actual transformation matrix between the adjacent connecting rods is formed byBecomes as followsWherein the differential error amount can be written as:
the differential error is defined as the opposite joint rotation angle θ in the formula (4) i Link offset d i Angle alpha of joint torsion i Length of connecting rod a i Is calculated by partial derivative operation:wherein Δθ i+1 Is the angle error of the connecting rod, delta d i+1 Is the offset error of the connecting rod, delta a i Is the length error of the connecting rod, delta alpha i A connecting rod torsion angle error; />For transformation of the partial derivative of the matrix with respect to the link angle, < >>Partial derivative of the link bias for the transformation matrix, +.>For transformation of the partial derivative of the matrix with respect to the length of the connecting rod, < >>Is the partial derivative of the transformation matrix with respect to the torsion angle of the connecting rod.
The industrial robot compliance joint is always influenced by the equivalent acting force of dead weight, so that the robot joint generates angle deviation, and the generated compliance error is mutually coupled with the tail end pose error of the robot. The joint compliance deformation can be expressed as:
δθ c ＝C θ T θ (5)
the joint compliance deformation is defined in equation (5) by the joint compliance coefficient multiplied by the joint equivalent torque wherein: delta theta c A joint deflection angle resulting from the flexible deformation of the joint for the rotation angle θ; c (C) θ Is the joint flexibility coefficient; t (T) θ Is the equivalent moment received at the joint.
Equivalent moment T of ith joint of N-degree-of-freedom industrial robot θi The calculation method is as follows:
in the formula (6), the weights of the joint i and all joints after the joint i are considered according to an equivalent torque conversion principle to be equivalent to the joint axis i, so as to obtain an expression (6) of the equivalent torque of the joint axis i, wherein: t (T) θi Representing the equivalent moment of the joint axis i, G i (i=1.2 … N) represents the gravity center and the weight of the arm link i, L i (i=1.2 … N) represents the length of the link i, l i (i=1.2 … N) represents the distance from the center of gravity of the connecting rod i to the axis of the joint axis i, and considering the general case that the center of gravity of the connecting rod may not be on the joint line or axis, the center of gravity of the joint i (i=1.2 … N) is offset by an angle θ around the joint axis Gi (i＝1.2…N)，θ i (i=1.2 … N) is the joint rotation angle of joint i relative to the joint zero position;
taking equation (6) into equation (5) yields the joint flexibility error δθ of the joint axis i under its own weight i The method comprises the following steps:
to facilitate analysis and simplify non-major factors affecting compliance error, assumptions are made about the parameters in equation (7): weight G of mechanical arm i Distance l between center of gravity and rotation axis i Center of gravity offset θ Gi The change is very small when the pose of the robot changes, the pose is defined as a constant, and the influence of the compliance error on the pose is ignored. And taking zero offset at the joint corner into consideration, comprehensively obtaining an error expression:
equation (8) defines a simplified integrated error expression for joint axis i, where: Δθ i Represents θ i Angle error at the position; Δθ 0i Indicating the rotation angle theta i Zero error at the position; definition k 1 And is the constant of the zero offset of the rotation angle, k i 、k i1 、k N 、k N1 Are joint flexibility coefficients C θ Weight G of mechanical arm i Distance l between center of gravity and rotation axis i Center of gravity offset θ Gi The different constant values combined are expressed as follows:
the final positioning error identification model can be obtained by comprehensively considering the connecting rod error and the joint flexibility error:
the positioning error Δp model representation is defined in equation (10) as two matrix multiplications, where: j is an error coefficient matrix, which is the derivative of the end position of the robot with respect to the robot kinematic parameters, and is only related to a nominal kinematic model and nominal geometric parameters; Δx is a parameter matrix to be identified; matrix column number q α 、q a 、q θ 、q d 、q k The number of the kinematic error parameters participating in the operation is respectively represented by a torsion angle error coefficient, a connecting rod length error coefficient, a connecting rod rotation angle error coefficient, a connecting rod offset error coefficient and a flexibility error coefficient; the matrix rows delta alpha, delta a, delta theta, delta d and delta k are error parameters to be specifically identified, and respectively represent a connecting rod torsion angle error, a connecting rod length error, a connecting rod rotation angle error, a connecting rod offset error and a flexibility constant deviation.
Further, the step S3 specifically includes:
in an ideal situation, the distance between two points in the robot coordinate system and the distance between two points corresponding to the measurement coordinate system should be the same, but there is a small error in practice, so that the distance error is expressed as:
Δd(i+1)＝‖d R (i+1)‖-‖d o (i+1)‖ (11)
Δd (i+1) in equation 15 is a defined distance error scalar, d R (i+1) is the distance vector of two adjacent points on the actual track, d o (i+1) is a distance vector corresponding to an adjacent on ideal trajectory;
the vector relation of the distance error can be obtained according to the vector relation:
Δd(i+1)＝d R (i+1)-d o (i+1)
＝dP(i+1)-dP(i) (12)
wherein Δd (i+1) is a defined distance error vector, and dP (i+1) and dP (i) are positioning error vectors of two adjacent endpoints;
and (3) the following steps:
d o (i+1)Δd(i+1)＝‖d o (i+1)‖‖Δd(i+1)‖cosθ (13)
and because cos θ is approximately equal to ±1, and Δd (i+1) is approximately equal to the distance error Δd (i+1) of the robot, the relationship between the distance error of the robot and the positioning error of the robot, namely, the distance error identification model is obtained:
in [ x ] 0 (i)-x 0 (i+1) y 0 (i)-y 0 (i+1) z 0 (i)-z 0 (i+1)]For the coordinate values of two adjacent points in the robot coordinate system, J (i+1) and J (i) are error coefficient matrixes of positioning errors in the step S2, and Deltax is a parameter matrix to be identified.
Further, the step S4 specifically includes:
randomly sampling in a robot working space, recording joint rotation angle values of each sampling point and corresponding coordinate measurement values of a laser tracker, and calculating distance values II d of two adjacent points under the coordinate of the laser tracker based on a distance error identification matrix in the step S3 R II, calculating a coordinate theoretical value P of the sampling point by combining the positive kinematics of the step S1, and calculating a distance value II d of two adjacent points under an ideal track o And II, further calculating a distance error scalar delta d for parameter identification.
Further, the step S5 specifically includes:
combining the distance error identification model of the step S3 and the distance value II d of two adjacent points under the coordinates of the laser tracker of each sampling point of the step S4 R II distance value II d from adjacent two points under ideal track o And II, substituting the damping iteration least square formula (15), solving a total convergence solution, and realizing the identification of error parameters:
Δx t ＝(H t (i+1) T H t (i+1)+μ t I) -1 H t (i+1) T Δd t (i+1) (15)
wherein the subscript t denotes that in the t-th iteration, deltax t Is the error parameter obtained, H t (i+1) is reduced for the expression excluding the identification parameters in step S3, μ t Is the damping coefficient, Δd t (i+1) is a distance error value, Δd t (i+1) a distance value II d equal to the adjacent two points under the theoretical value of the coordinates of the t-th iteration sampling point o II distance value between two adjacent points of the measured value II d R And the difference between.
Further, the step S6 specifically includes:
and (3) fitting the residual errors of parameter identification through a BP neural network, correcting and compensating the original parameters by using the error parameters obtained by the identification in the step (5), performing positive kinematic calculation by using the updated parameters, obtaining a difference value between a coordinate point position and an ideal point position, namely, taking the joint angle value of the industrial robot recorded in the step (4) as an input, taking the residual errors generated by the error identification iteration in the step (5) as an output, constructing the BP neural network, adopting a genetic algorithm to allocate the optimal initial weight and a threshold value to the neural network, and inputting the obtained neural network model into a control system to realize the improvement of the absolute positioning accuracy of the industrial robot.
The invention has the beneficial effects that:
according to the invention, the D-H model is taken as a basis, a distance error model is constructed, the loss of precision caused by complex coordinate conversion in data processing is avoided, meanwhile, the influence of robot geometric parameter errors and joint flexibility errors on the absolute positioning precision of the tail end is considered, finally, the identified residual error is fitted by adopting a BP neural network, the identified geometric parameters and a training network are input into a control system, and the absolute positioning precision of the industrial robot is more effectively improved.
Drawings
FIG. 1 is a schematic diagram of an industrial robot object (model UR16e robot from Shanghai robot trade Co., ltd.) embodying the present invention
FIG. 2 is a schematic diagram of the error compensation effect of the present invention;
FIG. 3 is a schematic flow chart of the control method of the present invention;
FIG. 4 is a graph of the neural network fitting effect of step S6 of the present invention;
Detailed Description
In order to make the objects, technical solutions and technical effects of the present invention more apparent, the technical solutions of the present invention will be described in further detail below with reference to the accompanying drawings and specific implementation steps.
The invention provides an industrial robot calibration method based on a neural network and a distance error model, which can avoid the conversion error of a coordinate system in the calibration process by establishing a model relation between the distance error of the tail end of a robot and the kinematic parameter error of the robot, and can identify the actual kinematic model of the industrial robot by considering the link error and the joint flexibility error, and then can achieve the aim of improving the absolute positioning accuracy of the industrial robot by fitting residual errors through the neural network.
As shown in fig. 3, the method specifically includes the following steps:
s1, establishing a DH kinematic model according to structural parameters of an industrial robot;
s2, analyzing and considering the influence of the joint flexibility of the industrial robot on the terminal pose, and establishing a positioning error identification model of coupling link parameters and the joint flexibility;
s3, converting the positioning error identification model into a distance error identification model according to the relation between the distance error and the positioning error of the robot;
s4, randomly sampling a large amount of samples in a robot working space, and respectively recording the joint rotation angle value of each sampling point and the measured value under the coordinates of a laser tracker;
and S5, combining the data in the robot distance error model step 4 established in the step 3, and identifying error parameters by using a damping iterative least square method (Levenberg-Marquardt method).
And S6, compensating residual errors based on the neural network, and inputting the residual errors into a control system to improve the absolute positioning accuracy of the industrial robot.
The method of the present invention will be further described with reference to a model UR16e robot, which is proposed by the company of the trade of pride robots (Shanghai), as shown in fig. 1, wherein the step S1 specifically includes:
establishing a kinematic model based on a D-H model method, wherein the first step is to determine a coordinate system corresponding to each connecting rod of the robot according to the D-H method; second, each rod parameter and motion parameter (joint rotation angle θ) are analyzed and determined i Link offset d i Angle alpha of joint torsion i Length of connecting rod a i ) The method comprises the steps of carrying out a first treatment on the surface of the Thirdly, determining a transformation matrix between adjacent coordinate systems; taking the spatial variation of the link coordinate system between joint i and joint i+1 as an example, it is possible to pass θ i 、d i 、α i 、a i These four kinematic parameters are enteredThe mathematical description, the linkage transformation is decomposed into four sub-transformations:
1) Linkage coordinate system { i } is z-wound i Shaft rotation theta i The angle, the coordinate system { i }', i.e., rot (z i ,θ i )；
2) Coordinate system { i }' along z i Shaft movement d i The coordinate system { i }', i.e., trans (z i ,d i )；
3) Coordinate system { i } "is along x i+1 Shaft movement a i The coordinate system { i }', i.e. Trans (x i+1 ,a i )；
4) Coordinate system { i }' is wrapped around x i+1 Shaft rotation alpha i Angle, a coordinate system { i+1}, i.e. Rot (x i+1 ,θ i )；；
According to the sub-transformation, the transformation matrix of the adjacent coordinate system of the connecting rod can be obtained as
The link transformations are multiplied in turn according to the principle of 'left to right', and a transformation matrix is obtained
The transformation matrixes of the connecting rods are multiplied in sequence to obtain a robot positive kinematics model, namely for an n-degree-of-freedom serial robot, the terminal pose transformation matrix is as follows:
in the formula (3), the coordinate system 0 is converted into the coordinate system N in turn according to the principle of matrix continuous multiplication,representing a transformation matrix from the ith coordinate system to the (i+1) th coordinate system, ">Rotation matrix representing coordinate system {0} to { N }, a ∈>The translation matrix representing the coordinate system {0} to { N } is required to be greater than or equal to 1.
Further, the step S2 specifically includes:
when the parameters of each connecting rod of the industrial robot have errors, the actual transformation matrix between the adjacent connecting rods is formed byBecomes as followsWherein the differential error amount can be written as:
the differential error is defined as the opposite joint rotation angle θ in the formula (4) i Link offset d i Angle alpha of joint torsion i Length of connecting rod a i Is calculated by partial derivative operation:wherein Δθ i+1 Is the angle error of the connecting rod, delta d i+1 Is the offset error of the connecting rod, delta a i Is the length error of the connecting rod, delta alpha i A connecting rod torsion angle error; />For transformation of the partial derivative of the matrix with respect to the link angle, < >>Partial derivative of the link bias for the transformation matrix, +.>For transformation of the partial derivative of the matrix with respect to the length of the connecting rod, < >>Is the partial derivative of the transformation matrix with respect to the torsion angle of the connecting rod.
The industrial robot compliance joint is always influenced by the equivalent acting force of dead weight, so that the robot joint generates angle deviation, and the generated compliance error is mutually coupled with the tail end pose error of the robot. The joint compliance deformation can be expressed as:
δθ c ＝C θ T θ (5)
the joint compliance deformation is defined in equation (5) by the joint compliance coefficient multiplied by the joint equivalent torque wherein: delta theta c A joint deflection angle resulting from the flexible deformation of the joint for the rotation angle θ; c (C) θ Is the joint flexibility coefficient; t (T) θ Is the equivalent moment received at the joint.
After the industrial robot is fixedly installed, the axial direction of the joint shaft 1 is in the same direction as gravity and is not influenced by dead weight equivalent moment, and the joint shafts 4, 5 and 6 are little influenced by dead weight and little influence on the terminal pose after deviation is generated, so that only joint compliance errors generated by the dead weight influence of the joint shafts 2 and 3 are considered. The moments received by the joint shaft 2 and the joint shaft 3 are respectively:
T θ2 ＝G 3 l 3 cos(θ 2 +θ 3 +θ G3 )+G 2 L 2 cosθ 2 +G 2 l 2 (θ 2 -θ G2 ) (6)
T θ3 ＝G 3 l 3 cos(θ 2 +θ 3 +θ G3 ) (7)
in the formulas (6) and (7), the gravity of the joint 2 and the joint 3 is considered according to the equivalent torque conversion principle to be respectively equivalent to the joint shaft 2 and the joint shaft 3, so that the expression of the equivalent moment of the joint shaft is obtained, wherein: t (T) θ2 、T θ3 The moment of the joint axis 2 and the joint axis 3 are indicated,G 2 and G 3 Represents the gravity center and the weight of the mechanical arm connecting rod 2 and the connecting rod 3, L 2 Indicating the length of the connecting rod 2, l 2 Represents the distance l between the center of gravity of the connecting rod 2 and the axis of the joint shaft 2 3 Representing the distance between the gravity center of the connecting rod 3 and the axis of the joint shaft 3, the gravity center of the connecting rod may not be on the joint connecting line or the axis, and the gravity center position is offset by an angle theta around the joint axis G2 And theta G3 ，θ 2 And theta 3 Is the joint rotation angle relative to the joint zero position. The joint flexibility error of the joint shaft 2 and the joint shaft 3 under the equivalent moment can be obtained by the method (5):
δθ c2 ＝C θ2 (G 3 l 3 cos(θ 2 +θ 3 +θ G3 )+G 3 L 2 cosθ 2 +G 2 l 2 (θ 2 -θ G2 )) (8)
δθ c3 ＝C θ3 (G 3 l 3 cos(θ 2 +θ 3 +θ G3 )) (9)
to facilitate analysis and simplify non-major factors affecting compliance errors, assume the following equations (8) and (9): weight G of mechanical arm i Distance l between center of gravity and rotation axis i Center of gravity offset θ Gi The robot pose has small variation, is defined as constant, and the influence of the compliance error on the robot pose is ignored. Taking into account the zero offset error expression at the joint rotation angle:
Δθ 2 ＝k 21 +k 22 cosθ 2 +k 23 sinθ 2 +k 24 cos(θ 2 +θ 3 )+k 25 sin(θ 2 +θ 3 ) (10)
Δθ 3 ＝k 31 +k 32 cos(θ 2 +θ 3 )+k 33 sin(θ 2 +θ 3 ) (11)
formulas (10) and (11) define simplified integrated error expressions at joint axis 2 and joint axis 3, respectively, which are θ 2 Angle error at the position; Δθ 3 Represents θ 3 Angle error at the position; Δθ 02 Indicating the rotation angle theta 2 Where (a)Zero error; angle of rotation theta 3 Zero error at the position; definition k 21 And k 31 Is a constant zero deviation of the rotation angle, k 22 、k 23 、k 24 、k 25 Weight G of k mechanical arm i Distance l between center of gravity and rotation axis i Center of gravity offset θ Gi Combined into different constant values.
The final positioning error identification model can be obtained by comprehensively considering the connecting rod error and the joint flexibility error:
the positioning error Δp model representation is defined in equation (12) as two matrix multiplications, where: j is a matrix of type 3 x 32, which is a matrix of error coefficients, is the derivative of the robot tip position with respect to the robot kinematics, and is related only to the nominal kinematics model and the nominal geometry. Matrix column number q α 、q a 、q θ 、q d 、q k The number of the kinematic error parameters involved in the operation is the torsion angle error coefficient, the connecting rod length error coefficient, the connecting rod rotation angle error coefficient, the connecting rod offset error coefficient and the flexibility error coefficient. J and Δx are specifically expanded as:
the specific expressions of the error coefficient matrix and the identification matrix are shown in the formulas (13) and (14), wherein:for the torsion angle error coefficient of 6 joints, < >>Length error coefficient of connecting rod of 6 joints, < >>For the joint rotation angle error coefficient of 6 joints, < >>Error coefficient for the link bias of 6 joints, < >>Is 6 compliance error coefficients. Δα 1 ,…,Δα 6 For 6 torsion angle parameters to be identified Δa 1 ,…,Δa 6 For the length parameters of 6 connecting rod rods to be identified, delta theta 1 ,…,Δθ 6 For 6 joint rotation angle parameters to be identified, Δd 1 ,…,Δd 6 For the 6 link bias parameters to be identified, Δk 1 ,…,Δk 6 Is 6 parameters of compliance constant to be identified.
Further, the step S3 specifically includes
In an ideal state, the distance between two points in the robot coordinate system and the distance between two points corresponding to the measurement coordinate system should be the same, but there is a small error in practice, so the distance error can be expressed as:
Δd(i+1)＝‖d R (i+1)‖-‖d o (i+1)‖ (15)
where Δd (i+1) is a defined distance error scalar, d R (i+1) is the distance vector of two adjacent points on the actual track, d o (i+1) is a distance vector adjacent on the corresponding ideal trajectory.
The vector relation of the distance error can be obtained according to the vector relation:
Δd(i+1)＝d R (i+1)-d o (i+1)＝dP(i+1)-dP(i)
(16)
where Δd (i+1) is a defined distance error vector, and dP (i+1) and dP (i) are positioning error vectors of two adjacent endpoints.
And (3) the following steps:
d o (i+1)Δd(i+1)＝‖d o (i+1)‖‖Δd(i+1)‖cosθ
(17)
further, because cos θ is approximately equal to ±1, and Δd (i+1) is approximately equal to the distance error Δd (i+1) of the robot, the relationship between the distance error of the robot and the positioning error of the robot can be obtained:
in [ x ] 0 (i)-x 0 (i+1) y 0 (i)-y 0 (i+1) z 0 (i)-z 0 (i+1)]For the coordinate values of two adjacent points in the robot coordinate system, J (i+1) and J (i) are error coefficient matrices of the positioning errors in step S2, and Δx is a parameter to be identified.
Further, the step S4 specifically includes:
randomly sampling in a robot working space, recording joint angles of each sampling point and corresponding coordinate measurement values of a laser tracker, and calculating distance values II d of two adjacent points under the coordinate of the laser tracker based on a distance error identification matrix in the step S3 R II, calculating the distance value II d of two adjacent points under the ideal track according to the theoretical value P of the coordinate of the sampling point calculated by the positive kinematics of the step S1 o And II, further calculating a distance error scalar delta d for parameter identification.
Further, the step S5 specifically includes:
combining the distance error model of the step S3 and the distance value II d of two adjacent points under the coordinates of the laser tracker of each sampling point of the step S4 R II distance value II d from adjacent two points under ideal track o And II, substituting the damping iterative least square method into the formula (1), and solving the convergence solution of the total office to realize the identification of error parameters.
Δx t ＝(H t (i+1) T H t (i+1)+μ t I) -1 H t (i+1) T Δd t (i+1) (19)
Wherein the subscript t denotes that in the t-th iteration, deltax t Is obtained byError parameter, H t (i+1) is reduced for the expression excluding the identification parameters in step S3, μ t Is the damping coefficient, Δd t (i+1) is a distance error value, Δd t (i+1) a distance value II d equal to the adjacent two points under the theoretical value of the coordinates of the t-th iteration sampling point o II distance value between two adjacent points of the measured value II d R And the difference between.
Further, the step S6 specifically includes:
and (3) fitting the residual errors of parameter identification through a BP neural network, correcting and compensating the original parameters by using the error parameters obtained by the identification in the step (5), performing positive kinematic calculation by using the updated parameters, obtaining a difference value between a coordinate point position and an ideal point position, namely, taking the joint angle value of the industrial robot recorded in the step (4) as an input, taking the residual errors generated by the error identification iteration in the step (5) as an output, constructing the BP neural network, adopting a genetic algorithm to allocate the optimal initial weight and threshold value to the neural network, ensuring the accuracy of prediction, and finally inputting the obtained neural network model into a control system to realize the improvement of the absolute positioning accuracy of the industrial robot.
As shown in fig. 2 and 4, the distance error model is constructed based on the D-H model, so that the loss of precision caused by complex coordinate conversion in data processing is avoided, meanwhile, the influence of robot geometric parameter errors, joint flexibility errors and gear transmission errors on the absolute positioning precision of the tail end is considered, finally, the recognized residual error is fitted by adopting a BP neural network, the recognized geometric parameters and a training network are input into a control system, and the absolute positioning precision of the industrial robot is more effectively improved.
Claims (4)
1. An industrial robot calibration method based on a neural network and a distance error model is characterized in that: according to the method, a model relation between the tail end distance error of the robot and the kinematic parameter error of the robot is established, the conversion error of a coordinate system in the calibration process is avoided, the actual kinematic model of the industrial robot is identified by considering the connecting rod error and the joint flexibility error, and the absolute positioning accuracy of the industrial robot is improved by fitting residual errors through a neural network;
the method specifically comprises the following steps:
s1, establishing a D-H kinematic model according to structural parameters of an industrial robot;
s2, analyzing and considering the influence of the joint flexibility of the industrial robot on the terminal pose, and establishing a positioning error identification model of coupling link parameters and the joint flexibility;
s3, converting the positioning error identification model into a distance error identification model according to the relation between the distance error and the positioning error of the robot;
s4, randomly sampling in a robot working space, and respectively recording the joint rotation angle value of each sampling point and the corresponding coordinate measurement value of the laser tracker;
s5, combining the robot distance error identification model established in the step 3, the joint rotation angle value obtained in the step 4 and the corresponding laser tracker coordinate measurement value, and identifying error parameters by using a damping iterative least square method;
s6, compensating residual errors of parameter identification based on a neural network, and inputting the residual errors into a control system to improve absolute positioning accuracy of the industrial robot;
the step S1 specifically includes:
s11, determining a coordinate system corresponding to each connecting rod of the robot according to a D-H method;
s12, analyzing and determining parameters of each rod piece and motion parameters including joint rotation angle theta i Link offset d i Angle alpha of joint torsion i Length of connecting rod a i ；
S13, determining a transformation matrix between adjacent coordinate systems; the spatial variation of the link coordinate system between joint i and joint i+1 is through θ i 、d i 、α i 、a i The four kinematic parameters are mathematically described, decomposing the linkage transformation into four sub-transformations:
1) Linkage coordinate system { i } is z-wound i Shaft rotation theta i The angle, the coordinate system { i }', i.e., rot (z i ，θ i )；
2) Coordinate system { i }' along z i Axial movementDynamic d i The coordinate system { i }', i.e., trans (z i ，d i )；
3) Coordinate system { i } "is along x i+1 Shaft movement a i The coordinate system { i }', i.e. Trans (x i+1 ，a i )；
4) Coordinate system { i }' is wrapped around x i+1 Shaft rotation alpha i Angle, a coordinate system { i+1}, i.e. Rot (x i+1 ，θ i )；
According to the four sub-transformations, the link adjacent coordinate system transformation matrix is obtained as follows:
the link transformations are multiplied in turn according to the principle of 'left to right', and a transformation matrix is obtained
The transformation matrixes of the connecting rods are multiplied in sequence to obtain a robot positive kinematics model, namely for the N-degree-of-freedom serial robot, the terminal pose transformation matrix is as follows:
in the formula (3), the coordinate system 0 is converted into the coordinate system N in turn according to the principle of matrix continuous multiplication,representing a transformation matrix from the ith coordinate system to the (i+1) th coordinate system, ">Rotation matrix representing coordinate system {0} to { N }, a ∈>A translation matrix from the coordinate system {0} to { N } is represented, and the value of N is more than or equal to 1;
the step S2 specifically includes:
when the parameters of each connecting rod of the industrial robot have errors, the actual transformation matrix between the adjacent connecting rods is formed byBecomes as followsWherein the differential error amount->The writing is as follows:
the differential error is defined as the opposite joint rotation angle θ in the formula (4) i Link offset d i Angle alpha of joint torsion i Length of connecting rod a i Is calculated by partial derivative operation:wherein Δθ i+1 Is the angle error of the connecting rod, delta d i+1 Is the offset error of the connecting rod, delta a i Is the length error of the connecting rod, delta alpha i A connecting rod torsion angle error; />For transformation of the partial derivative of the matrix with respect to the link angle, < >>Partial derivatives of link bias for transformation matrices，/>For transformation of the partial derivative of the matrix with respect to the length of the connecting rod, < >>The partial derivative of the transformation matrix to the torsion angle of the connecting rod;
the industrial robot compliance joint is always influenced by the equivalent acting force of dead weight, so that the robot joint generates angle deviation, the generated compliance error is mutually coupled with the tail end pose error of the robot, and the joint compliance deformation is expressed as:
δθ c ＝C θ T θ (5)
the joint compliance deformation is defined in equation (5) by the joint compliance coefficient multiplied by the joint equivalent torque, wherein: delta theta c A joint deflection angle resulting from the flexible deformation of the joint for the rotation angle θ; c (C) θ The joint flexibility coefficient is a constant; t (T) θ Equivalent moment received by the joint;
equivalent moment T of ith joint of N-degree-of-freedom industrial robot θi The calculation method is as follows:
in the formula (6), the weights of the joint i and all joints after the joint i are considered according to an equivalent torque conversion principle to be equivalent to the joint axis i, so as to obtain an expression (6) of the equivalent torque of the joint axis i, wherein: t (T) θi Representing the equivalent moment of the joint axis i, G i (i=1.2 … N) represents the gravity center and the weight of the arm link i, L i (i=1.2 … N) represents the length of the link i, l i (i=1.2 … N) represents the distance from the center of gravity of the link i to the axis of the joint axis i, and considering the general case that the center of gravity of the link may not be on the joint line or axis, the center of gravity position of the joint i (i=1.2 … N) is offset by the center of gravity shift θ around the joint axis by the rotation angle Gi (i＝1.2…N)，θ i (i＝1.2 … N) is the joint rotation angle of the joint i relative to the joint zero position;
taking equation (6) into equation (5) yields the joint flexibility error δθ of the joint axis i under its own weight i The method comprises the following steps:
to facilitate analysis and simplify non-major factors affecting compliance error, assumptions are made about the parameters in equation (7): weight G of mechanical arm i Distance l between center of gravity and rotation axis i Center of gravity offset θ Gi When the pose of the robot changes, the change is extremely small, the pose is defined as a constant, the influence of the compliance error on the pose is ignored, zero offset at the joint corner is considered, and an error expression is comprehensively obtained:
equation (8) defines a simplified integrated error expression for joint axis i, where: Δθ i Represents θ i Angle error at the position; Δθ 0i Indicating the rotation angle theta i Zero error at the position; definition k 1 Is a constant zero deviation of the rotation angle, k i 、k i1 、k N 、k N1 Are joint flexibility coefficients C θ Weight G of mechanical arm i Distance l between center of gravity and rotation axis i Center of gravity offset θ Gi The different constant values combined are expressed as follows:
comprehensively considering the connecting rod error and the joint flexibility error to obtain a final positioning error identification model:
the positioning error recognition model Δp is defined in equation (10) as two matrix multiplications, where: j is an error coefficient matrix, which is the derivative of the end position of the robot with respect to the robot kinematic parameters, and is only related to a nominal kinematic model and nominal geometric parameters; Δx is a parameter matrix to be identified; matrix column number q α 、q a 、q θ 、q d 、q k The number of the kinematic error parameters participating in the operation is respectively represented by a torsion angle error coefficient, a connecting rod length error coefficient, a connecting rod rotation angle error coefficient, a connecting rod offset error coefficient and a flexibility error coefficient; the matrix line numbers delta alpha, delta a, delta theta, delta d and delta k are error parameters to be specifically identified, and respectively represent a connecting rod torsion angle error, a connecting rod length error, a connecting rod rotation angle error, a connecting rod offset error and a flexibility constant deviation;
the step S3 specifically includes:
in an ideal situation, the distance between two points in the robot coordinate system and the distance between two points corresponding to the measurement coordinate system should be the same, but there is a small error in practice, so that the distance error is expressed as:
Δd(i+1)＝||d R (i+1)||-||d o (i+1)|| (11)
Δd (i+1) in equation 15 is a defined distance error scalar, d R (i+1) is the distance vector of two adjacent points on the actual track, d o (i+1) is a distance vector corresponding to an adjacent on ideal trajectory;
the vector relation of the distance error can be obtained according to the vector relation:
Δd(i+1)＝d R (i+1)-d o (i+1)
＝dP(i+1)-dP(i) (12)
wherein Δd (i+1) is a defined distance error vector, and dP (i+1) and dP (i) are positioning error vectors of two adjacent endpoints;
and (3) the following steps:
d o (i+1)Δd(i+1)＝||d o (i+1)||||Δd(i+1)||cosθ (13)
and because cos θ is approximately equal to ±1, and Δd (i+1) is approximately equal to the distance error Δd (i+1) of the robot, the relationship between the distance error of the robot and the positioning error of the robot, namely, the distance error identification model is obtained:
in [ x ] 0 (i)-x 0 (i+1) y 0 (i)-y 0 (i+1) z 0 (i)-z 0 (i+1)]For the coordinate values of two adjacent points in the robot coordinate system, J (i+1) and J (i) are error coefficient matrixes of positioning errors in the step S2, and Deltax is a parameter matrix to be identified.
2. The industrial robot calibration method based on the neural network and the distance error model according to claim 1, wherein the step S4 specifically includes:
randomly sampling in a robot working space, recording joint rotation angle values of each sampling point and corresponding coordinate measurement values of a laser tracker, and calculating distance values of two adjacent points in the coordinate of the laser tracker based on a distance error identification matrix in the step S3 R Calculating a coordinate theoretical value P of the sampling point by combining the positive kinematics of the step S1, and calculating a distance value d of two adjacent points under an ideal track o And (3) further calculating a distance error scalar delta d for parameter identification.
3. The industrial robot calibration method based on the neural network and the distance error model as set forth in claim 1, wherein the step S5 specifically includes:
combining the distance error identification model of the step S3 and the distance value d of two adjacent points under the coordinates of the laser tracker of each sampling point of the step S4 R Distance value d between two adjacent points under ideal track o Substituting the I into a damping iteration least square formula (15), solving the convergence solution of the total office, and realizing the identification of error parameters:
Δx t ＝(H t (i+1) T H t (i+1)+μ t I) -1 H t (i+1) T Δd t (i+1) (15)
wherein the subscript t denotes that in the t-th iteration, deltax t Is the error parameter obtained, H t (i+1) is reduced for the expression excluding the identification parameters in step S3, μ t Is the damping coefficient, Δd t (i+1) is a distance error value, Δd t (i+1) is equal to the distance value of two adjacent points under the theoretical value of coordinates of the t-th iteration sampling point in value o Distance value d between two adjacent points of the measured value R Difference between the I.
4. The industrial robot calibration method based on the neural network and the distance error model of claim 1, wherein the step S6 specifically includes:
and (3) fitting the residual errors of parameter identification through a BP neural network, correcting and compensating the original parameters by using the error parameters obtained by the identification in the step (5), performing positive kinematic calculation by using the updated parameters, obtaining a difference value between a coordinate point position and an ideal point position, namely, taking the joint angle value of the industrial robot recorded in the step (4) as an input, taking the residual errors generated by the error identification iteration in the step (5) as an output, constructing the BP neural network, adopting a genetic algorithm to allocate the optimal initial weight and a threshold value to the neural network, and inputting the obtained neural network model into a control system to realize the improvement of the absolute positioning accuracy of the industrial robot.
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Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20090060752A (en) * | 2007-12-10 | 2009-06-15 | 현대중공업 주식회사 | Robot calibration method with joint stiffness parameters for the enhanced positioning accuracy |
| CN103231375A (en) * | 2013-04-28 | 2013-08-07 | 苏州大学 | Industrial robot calibration method based on distance error models |
| CN108406768A (en) * | 2018-03-09 | 2018-08-17 | 汇川技术（东莞）有限公司 | A kind of robot calibration method and system based on dead weight and load deformation compensation |
| CN110053051A (en) * | 2019-04-30 | 2019-07-26 | 杭州亿恒科技有限公司 | Industrial serial manipulator joint stiffness parameter identification method |
| CN111360836A (en) * | 2020-04-02 | 2020-07-03 | 易思维（杭州）科技有限公司 | Robot calibration method for optimizing identification parameters |
| CN112873199A (en) * | 2021-01-08 | 2021-06-01 | 西北工业大学 | Robot absolute positioning precision calibration method based on kinematics and spatial interpolation |
| CN113927599A (en) * | 2021-11-05 | 2022-01-14 | 上海新时达电气股份有限公司 | Absolute precision compensation method, system, device and computer readable storage medium |
-
2022
- 2022-06-01 CN CN202210621677.1A patent/CN114918920B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20090060752A (en) * | 2007-12-10 | 2009-06-15 | 현대중공업 주식회사 | Robot calibration method with joint stiffness parameters for the enhanced positioning accuracy |
| CN103231375A (en) * | 2013-04-28 | 2013-08-07 | 苏州大学 | Industrial robot calibration method based on distance error models |
| CN108406768A (en) * | 2018-03-09 | 2018-08-17 | 汇川技术（东莞）有限公司 | A kind of robot calibration method and system based on dead weight and load deformation compensation |
| CN110053051A (en) * | 2019-04-30 | 2019-07-26 | 杭州亿恒科技有限公司 | Industrial serial manipulator joint stiffness parameter identification method |
| CN111360836A (en) * | 2020-04-02 | 2020-07-03 | 易思维（杭州）科技有限公司 | Robot calibration method for optimizing identification parameters |
| CN112873199A (en) * | 2021-01-08 | 2021-06-01 | 西北工业大学 | Robot absolute positioning precision calibration method based on kinematics and spatial interpolation |
| CN113927599A (en) * | 2021-11-05 | 2022-01-14 | 上海新时达电气股份有限公司 | Absolute precision compensation method, system, device and computer readable storage medium |
Non-Patent Citations (4)
| Title |
|---|
| 丁燕 ; 刘鑫 ; 黄炜亮 ; .排爆机器人机械臂定位精度误差自动补偿方法研究.计算机测量与控制.2019,(第12期),全文. * |
| 李林.基于视觉测量的六自由度串联机器人标定方法研究.《中国优秀硕士学位论文全文数据库 信息科技辑》.2021,第31-42页. * |
| 王一 ; 刘常杰 ; 任永杰 ; 叶声华 ; .工业坐标测量机器人定位误差补偿技术.机械工程学报.2011,(第15期),全文. * |
| 考虑关节柔性误差的机器人参数辨识方法研究;齐飞;平雪良;刘洁;蒋毅;;机械科学与技术(第04期);全文 * |
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