CN115091455A - Industrial robot positioning error compensation method - Google Patents
Industrial robot positioning error compensation method Download PDFInfo
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Abstract
The application discloses an industrial robot positioning error compensation method. The method comprises the steps of constructing a positioning error model considering joint flexibility; inputting the motion data sample of the joint of the industrial robot into a positioning error model considering the flexibility of the joint to obtain positioning error low-fidelity data of the industrial robot; establishing a measurement reference coordinate system matched with the joint coordinate system, and measuring the corresponding positioning error high-fidelity data of the industrial robot under each joint motion data in real time by using a laser tracker; fusing the low-fidelity data and the high-fidelity data to obtain a multi-fidelity positioning error model of the industrial robot; and meanwhile, updating each motion data of the industrial robot through the positioning error data, and driving the industrial robot to perform motion after the positioning error compensation to realize the positioning error compensation.
Description
Technical Field
The invention relates to the technical field of industrial robots, in particular to a method for compensating positioning errors of an industrial robot.
Background
As a representative of intelligent manufacturing equipment, the industrial robot has the characteristics of repeated programming, simplicity in operation, high working efficiency and the like, and is praised as a bright pearl at the top of the manufacturing industry crown by the academic and industrial fields. With the increasingly deep application of industrial robots in the fields of spraying, assembling, welding and the like, the absolute positioning accuracy of the industrial robots also becomes more and more a concern to relevant practitioners. The absolute positioning precision level of the industrial robot directly influences the quality consistency of auxiliary manufactured products of the industrial robot, and the absolute positioning precision level is also a core element of the domestic industrial robot participating in international market competition. Therefore, the method for compensating the positioning error of the industrial robot has important significance for improving the absolute positioning precision level of the industrial robot.
At present, methods for improving the absolute positioning accuracy of an industrial robot mainly comprise an error prevention method and a parameter calibration method. The error prevention method is mainly used for improving the absolute positioning accuracy by improving the machining accuracy of robot parts and the rigidity of the robot, and is generally limited by high cost and the structure of the robot, so that the application is limited. The parameter calibration method can be divided into two compensation modes of off-line compensation and on-line compensation. The off-line compensation method establishes a robot error calibration model by means of the mapping relation between kinematic parameter errors and terminal pose errors, and realizes identification and compensation of kinematic error parameters by measuring terminal positioning error data of the robot. On-line compensation needs to be realized by adding a testing device in a robot working environment to measure the tail end positioning error of the robot in real time, the compensation precision is generally high, but the testing cost is increased due to the addition of the testing device, and the practical application and popularization of the industrial robot are restricted. Therefore, we propose an industrial robot positioning error compensation method to solve the above problems.
Disclosure of Invention
In view of the above-mentioned defects or shortcomings in the prior art, it is desirable to provide a method for compensating the positioning error of an industrial robot, which has high precision, high efficiency and low compensation cost.
In a first aspect, the present application provides a method for compensating a positioning error of an industrial robot, wherein the industrial robot is a multi-degree-of-freedom industrial robot and has a plurality of joints; the positioning error compensation method comprises the following steps:
s1: acquiring joint motion data of the industrial robot; the joint motion data is obtained by the movement of the joint of the industrial robot in a joint coordinate system according to a preset track;
s2: calculating dynamic data according to the joint motion data of the industrial robot;
s3: identifying relevant kinetic parameters, and constructing a rigid body kinetic model by combining kinetic data;
s4: in the rigid body dynamic model, identifying the rigidity of each joint of the industrial robot, and constructing a dynamic model considering the flexibility of the joint;
s5: establishing a mapping relation between the motion parameters of each joint and the tail end positioning error, and establishing a positioning error model considering the flexibility of the joint;
s6: acquiring an industrial robot joint motion data sample; the joint motion data sample is randomly generated by an industrial robot in a joint space angular displacement, angular velocity and angular acceleration constraint interval;
s7: inputting the joint motion data sample of the industrial robot into a positioning error model considering joint flexibility to obtain the low-fidelity data of the positioning error of the industrial robot;
s8: establishing a measurement reference coordinate system matched with the joint coordinate system;
s9: under a measurement reference coordinate system, a laser tracker is used for measuring the corresponding positioning error high-fidelity data of the industrial robot under each joint motion data in real time;
s10: fusing low-fidelity data and high-fidelity data of the positioning error of the industrial robot to obtain a multi-fidelity positioning error model of the industrial robot;
s11: calculating a root mean square error and a correlation coefficient in a multi-fidelity positioning error model of the industrial robot;
s12: judging that the root mean square error is smaller than a root mean square error threshold value and the correlation coefficient is larger than a correlation coefficient threshold value, wherein the multi-fidelity positioning error model of the industrial robot meets the model precision standard; otherwise, executing the steps S6-S9 to obtain a low fidelity data set and a high fidelity data set until the multi-fidelity positioning error model of the industrial robot meets the model precision standard;
s13: and (3) building a digital twin platform, and compensating motion data of each joint of the industrial robot by combining positioning error data of the multi-fidelity positioning error model of the industrial robot with an industrial robot entity.
According to the technical scheme provided by the embodiment of the application, the steps S2-S4 comprise the following steps:
establishing a mapping relation between the generalized driving moment of the industrial robot and the generalized force borne by the tail end according to the following formula:
wherein the generalized driving torque Gamma is epsilon R 6×1 (ii) a The end bears generalized force W epsilon R 6×1 ；
A Jacobian matrix corresponding to the industrial robot at the point of application of the external load, an
Calculating the driving moment of the industrial robot relative to the action of the external load according to the following formula:
Γ＝K θ △θ；(1-2)
wherein, K θ Is rigidity of each joint of the industrial robot, and
delta theta is a rotation angle of each joint of the industrial robot relative to an initial position;
in an operation space, establishing a mapping relation between the end pose deformation of the industrial robot and an external load acted by the end pose deformation according to the following formula:
W＝K x △X＝K x J m △θ；(1-3)
wherein, K x Rigidity of an end reference point of an industrial robot, and K x ∈R 6×6 (ii) a Delta X is the deformation of the end pose of the industrial robot, and the Delta X belongs to R 6×1 ；J m A Jacobian matrix at the deformation measuring point of the end pose of the industrial robot, and J m ∈R 6×6 ；
Establishing a mapping relation between a joint stiffness matrix of the industrial robot in a joint space and a stiffness matrix of an end reference point of the industrial robot in an operation space according to the following formula:
wherein, K c For industrial robot joint stiffness compensation matrix, and K c ∈R 6×6 ：
Calculating the rigidity of each joint of the industrial robot according to the following formula:
wherein W is an external load; and delta X is the pose error of the reference point at the tail end of the industrial robot acquired by the laser tracker.
According to the technical scheme provided by the embodiment of the application, in step S5:
the relationship between the motor side torque and the joint side torque is obtained according to the following formula:
wherein, tau m Is the motor side driving torque; tau is joint side driving moment; b is a motor rotor inertia matrix;
is the motor side angular acceleration.
According to the technical scheme provided by the embodiment of the application, in step S5:
the motor side angular acceleration is expressed according to the following formula:
wherein the content of the first and second substances,
is the second derivative of the joint side rotation angle;
is a joint stiffness inverse matrix;
substituting the formula (1-7) into the formula (1-6) to obtain the relation between the motor side torque and the joint side torque:
according to the technical solution provided by the embodiment of the present application, in step S5, positioning error data is calculated from the joint-side torque:
according to the technical scheme provided by the embodiment of the application, in step S6:
randomly generating an industrial robot joint motion data sample by utilizing Latin hypercube sampling:
S lf ＝[x lf (1) ,x lf (2) ,…,x lf (n) ] T 。
a method for compensating positioning errors of an industrial robot according to claim 1, characterized in that in step S7 a low fidelity dataset of positioning errors of an industrial robot is obtained:
using the positioning error data: y is lf (x)＝[y(x lf (1) ),y(x lf (2) ),…,y(x lf (n) )] T And the input joint motion data: s lf ＝[x lf (1) ,x lf (2) ,…,x lf (n) ] T Collectively, a low fidelity dataset is constructed.
According to the technical scheme provided by the embodiment of the application, in step S9, a high fidelity data set is acquired:
using the respective joint motion data: s hf ＝[x hf (1) ,x hf (2) ,…,x hf (n) ] T And positioning error data measured by the laser tracker in real time: y is hf (x)＝[y(x hf (1) ),y(x hf (2) ),…,y(x hf (n) )] T Together, a high fidelity dataset is constructed.
According to the technical scheme provided by the embodiment of the application, in step S10:
the low fidelity function is expressed according to the following equation:
wherein, the first and the second end of the pipe are connected with each other,
is a correlation matrix composed of function values between all sample points, and
i is a unit vector, and
r lf a correlation vector composed of correlation relations between an unknown point and all known sample points;
is a predicted value of the low fidelity function;
the high fidelity function is expressed according to the following formula:
solving the multi-fidelity positioning error model of the industrial robot according to the low-fidelity function and the high-fidelity function:
wherein, beta 0 ＝(F T R -1 F) -1 F T R -1 y s Is a scale factor, which is the degree to which a low fidelity function correlates to a high fidelity function.
According to the technical scheme provided by the embodiment of the application, in step S11:
the root mean square error and the correlation coefficient are calculated respectively according to the following formulas:
wherein, y i Is the true value;
is a model predicted value; n is the number of sample points.
In summary, the present application specifically discloses a specific process of a method for compensating a positioning error of an industrial robot. Compared with the prior art, the method and the device have the advantages that the positioning error caused by joint flexibility is considered, and the dynamic data are calculated according to the joint motion data of the industrial robot by acquiring the joint motion data of the industrial robot; identifying relevant kinetic parameters, and constructing a rigid body kinetic model by combining kinetic data; in the rigid body dynamic model, identifying the rigidity of each joint of the industrial robot, and constructing a dynamic model considering the flexibility of the joint; establishing a mapping relation between the motion parameters of each joint and the tail end positioning error, and establishing a positioning error model considering the flexibility of the joint; further, acquiring an industrial robot joint motion data sample; inputting the joint motion data sample of the industrial robot into a positioning error model considering joint flexibility to obtain the low-fidelity data of the positioning error of the industrial robot; establishing a measurement reference coordinate system matched with the joint coordinate system; under a measurement reference coordinate system, a laser tracker is used for measuring the corresponding positioning error high-fidelity data of the industrial robot under each joint motion data in real time; and fusing low-fidelity data and high-fidelity data of the positioning error of the industrial robot to obtain a multi-fidelity positioning error model of the industrial robot. Judging that the root mean square error is smaller than a root mean square error threshold value and the correlation coefficient is larger than a correlation coefficient threshold value, wherein the multi-fidelity positioning error model of the industrial robot meets the model precision standard; or acquiring a low-fidelity data set and a high-fidelity data set until the multi-fidelity positioning error model of the industrial robot meets the model precision standard; and obtaining a high-precision and high-efficiency industrial robot multi-fidelity positioning error model.
The method comprises the steps of building a digital twin platform, building data interaction between an industrial robot entity and a multi-fidelity positioning error model, updating the multi-fidelity positioning error model through a digital twin technology and high-precision positioning error test data added regularly, improving accuracy of the model, enabling the multi-fidelity positioning error model to meet requirements of the digital twin platform on data accuracy and real-time performance, avoiding the problem of model accuracy degradation, calculating positioning error data through the multi-fidelity positioning error model before controlling the movement of the industrial robot, updating all movement data of the industrial robot, feeding back the updated movement data to a controller of the industrial robot, sending the updated movement data of all joints to a driver by the controller, driving the robot to perform movement after positioning error compensation, and achieving compensation of the positioning error.
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Other features, objects and advantages of the present application will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, made with reference to the accompanying drawings in which:
fig. 1 is a schematic flow chart of a method for compensating positioning errors of an industrial robot.
Fig. 2 is a schematic diagram of the joint of the industrial robot moving in a joint coordinate system according to a preset track.
Detailed Description
The present application will be described in further detail with reference to the drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not to be construed as limiting the invention. It should be noted that, for convenience of description, only the portions related to the present invention are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
Example 1
Please refer to fig. 1, which is a schematic flow chart of a first embodiment of a positioning error compensation method for an industrial robot, which is a multi-degree-of-freedom industrial robot and has several joints; the positioning error compensation method comprises the following steps:
s1: acquiring joint motion data of the industrial robot; the joint motion data is obtained by the movement of the joint of the industrial robot in a joint coordinate system according to a preset track;
s2: calculating dynamic data according to the joint motion data of the industrial robot;
s3: identifying relevant kinetic parameters, and constructing a rigid body kinetic model by combining kinetic data;
s4: in the rigid body dynamic model, identifying the rigidity of each joint of the industrial robot, and constructing a dynamic model considering the flexibility of the joint;
s5: establishing a mapping relation between the motion parameters of each joint and the tail end positioning error, and constructing a positioning error model considering the flexibility of the joint;
s6: acquiring an industrial robot joint motion data sample; the joint motion data sample is randomly generated by an industrial robot in a joint space angular displacement, angular velocity and angular acceleration constraint interval;
s7: inputting the joint motion data sample of the industrial robot into a positioning error model considering joint flexibility to obtain the low-fidelity data of the positioning error of the industrial robot;
s8: establishing a measurement reference coordinate system matched with the joint coordinate system;
s9: under the measurement reference coordinate system, a laser tracker is used for measuring the corresponding positioning error high-fidelity data of the industrial robot under each joint motion data in real time;
s10: fusing low-fidelity data and high-fidelity data of the positioning error of the industrial robot to obtain a multi-fidelity positioning error model of the industrial robot;
s11: calculating a root mean square error and a correlation coefficient in a multi-fidelity positioning error model of the industrial robot;
s12: judging that the root mean square error is smaller than a root mean square error threshold value and the correlation coefficient is larger than a correlation coefficient threshold value, wherein the multi-fidelity positioning error model of the industrial robot meets the model precision standard; otherwise, executing the steps S6-S9 to obtain a low fidelity data set and a high fidelity data set until the multi-fidelity positioning error model of the industrial robot meets the model precision standard;
s13: and (3) building a digital twin platform, and compensating motion data of each joint of the industrial robot by combining positioning error data of the multi-fidelity positioning error model of the industrial robot with an industrial robot entity.
In the present embodiment, S1: acquiring joint motion data of an industrial robot; the joint motion data is obtained by the movement of the joint of the industrial robot in a joint coordinate system according to a preset track;
specifically, taking an industrial robot with six degrees of freedom as an example, in a joint coordinate system, taking the circle center of a sixth joint end plane as a reference point, setting an ideal track of the end reference point as a triangle a-B-C, as shown in fig. 2, inputting a track of the end reference point in an application program of inverse kinematics in matlab2018.B, and outputting joint rotation angles, joint angular velocities and angular accelerations corresponding to each joint.
S2: calculating dynamic data according to the motion data of the joints of the industrial robot;
specifically, the Newton-Euler recursion algorithm is used for calculating the generalized interaction force F of each connecting rod, the joint driving moment tau and the second derivative thereof
S3: and identifying relevant kinetic parameters, and combining the kinetic data to construct a rigid body kinetic model.
S4: in the rigid body dynamic model, identifying the rigidity of each joint of the industrial robot, and constructing a dynamic model considering the flexibility of the joint;
wherein, according to the elastic joint model theory, a joint side corner theta and a motor side corner theta are established m Relationship (c), joint side driving torque (tau) and motor side driving torque (tau) m The relationship (c) in (c).
Specifically, 100Kg of external load is applied to the tail end of the industrial robot, the pose error delta X of a tail end reference point of the robot under the track of A → B → C is measured and solved through a laser tracker, and the stiffness of each joint is identified by using an error vector of the loaded tail end pose.
Establishing a mapping relation between the generalized driving torque of the industrial robot and the generalized force borne by the tail end according to the following formula:
wherein the generalized driving torque T ∈ R 6×1 (ii) a The end bears generalized force W epsilon R 6×1 ；
A Jacobian matrix corresponding to the industrial robot at the point of application of the external load, an
Calculating the driving moment of the industrial robot relative to the action of the external load according to the following formula:
Γ＝K θ △θ；(1-2)
wherein, K θ Rigidity of each joint of the industrial robot, and
delta theta is a rotation angle of each joint of the industrial robot relative to an initial position;
in an operation space, establishing a mapping relation between the end pose deformation of the industrial robot and an external load acted by the end pose deformation according to the following formula:
W＝K x △X＝K x J m △θ；(1-3)
wherein, K x Rigidity of the end reference point of the industrial robot, and K x ∈R 6×6 (ii) a Delta X is the deformation of the end pose of the industrial robot, and the Delta X belongs to R 6×1 ；J m A Jacobian matrix at the deformation measuring point of the end pose of the industrial robot, and J m ∈R 6×6 ；
Establishing a mapping relation between a joint stiffness matrix of the industrial robot in a joint space and a stiffness matrix of an end reference point of the industrial robot in an operation space according to the following formula:
wherein, K c For industrial robot joint stiffness compensation matrix, and K c ∈R 6×6 ：
Calculating the rigidity of each joint of the industrial robot according to the following formula:
wherein W is an external load; and the delta X is the pose error of the reference point of the tail end of the industrial robot acquired by the laser tracker.
S5: establishing a mapping relation between the motion parameters of each joint and the tail end positioning error, and establishing a positioning error model considering the flexibility of the joint;
specifically, the relationship between the motor-side torque and the joint-side torque is obtained according to the following formula:
wherein, tau m The motor side driving torque; tau is joint side driving moment; b is a motor rotor inertia matrix;
is the motor side angular acceleration.
Alternatively, the motor-side angular acceleration is expressed according to the following equation:
wherein the content of the first and second substances,
is the second derivative of the joint side rotation angle;
is a joint stiffness inverse matrix;
substituting the formula (1-7) into the formula (1-6) to obtain the relation between the motor side torque and the joint side torque:
further, in step S5, the positioning error data of the positioning error model in consideration of the joint flexibility is calculated from the joint-side torque:
namely: the method comprises the steps of taking motion data of each joint in an industrial robot controller as input of a positioning error model considering joint flexibility, utilizing a laser tracker to measure actual positioning errors of the tail end of the industrial robot in real time for updating unknown parameters of the positioning error model considering the joint flexibility, inputting the motion data of each joint after the parameters are updated, and calculating the tail end positioning errors as output.
S6: acquiring an industrial robot joint motion data sample; the joint motion data sample is randomly generated by an industrial robot in a joint space angular displacement, angular velocity and angular acceleration constraint interval;
specifically, a Latin hypercube sampling is utilized to randomly generate an industrial robot joint motion data sample:
S lf ＝[x lf (1) ,x lf (2) ,…,x lf (n) ] T 。
s7: inputting the joint motion data sample of the industrial robot into a positioning error model considering joint flexibility to obtain the low-fidelity data of the positioning error of the industrial robot;
further, using the positioning error data: y is lf (x)＝[y(x lf (1) ),y(x lf (2) ),…,y(x lf (n) )] T And the input joint motion data: s. the lf ＝[x lf (1) ,x lf (2) ,…,x lf (n) ] T Collectively constructing a low fidelity dataset。
S8: establishing a measurement reference coordinate system matched with the joint coordinate system;
specifically, as shown in fig. 2, first, a joint of the industrial robot generally rotating around the base is defined as a joint 1, which is located at a position where the base is in contact with the industrial robot; controlling the joint 1 to do uniaxial motion, measuring the track of a terminal reference point in the motion process by using a laser tracker, and fitting the measured track to obtain a rotation axis of the joint 1, wherein the rotation axis is the Z direction of a measurement reference coordinate system; the joint 2 is defined to be located at a position which is a point above the joint 1, then the joint 1 is adjusted to a zero position, the movement of the joint 2 is controlled in the same way, a corresponding rotation axis is obtained, the rotation axis is the Y direction of the measurement reference coordinate system, and the two axes are vertically arranged. And finally, establishing a measurement reference coordinate system matched with the coordinate system of the robot by the laser tracker according to the constructed joint axis 1 and the constructed joint axis 2.
S9: under a measurement reference coordinate system, a laser tracker is used for measuring the corresponding positioning error high-fidelity data of the industrial robot under each joint motion data in real time;
further, using the respective joint motion data: s hf ＝[x hf (1) ,x hf (2) ,…,x hf (n) ] T And positioning error data measured by the laser tracker in real time: y is hf (x)＝[y(x hf (1) ),y(x hf (2) ),…,y(x hf (n) )] T Together, a high fidelity dataset is constructed.
S10: fusing low-fidelity data and high-fidelity data of the positioning error of the industrial robot to obtain a multi-fidelity positioning error model of the industrial robot;
for example, a Kriging model is used for fusing low-fidelity error data and high-fidelity error data, the model in the whole domain is trained through the high-fidelity positioning error data and the low-fidelity positioning error data, unknown parameters are solved, and the multi-fidelity positioning error model of the industrial robot is established.
Specifically, the low fidelity function is expressed according to the following equation:
wherein the content of the first and second substances,
is a correlation matrix composed of function values between all sample points, and
i is a unit vector, an
r lf A correlation vector consisting of correlation relations between the unknown point and all known sample points;
is a predicted value of the low fidelity function;
the high fidelity function is expressed according to the following formula:
solving the multi-fidelity positioning error model of the industrial robot according to the low-fidelity function and the high-fidelity function:
wherein, beta 0 ＝(F T R -1 F) -1 F T R -1 y s Is a scale factor, which is the degree to which a low fidelity function correlates to a high fidelity function.
S11: calculating a root mean square error and a correlation coefficient in a multi-fidelity positioning error model of the industrial robot;
verifying the accuracy of the established industrial robot multi-fidelity positioning error model by using the root mean square error and the correlation coefficient:
specifically, the root mean square error and the correlation coefficient are calculated respectively according to the following formulas:
wherein, y i Is the true value;
is a model predicted value; n is the number of sample points.
S12: judging that the root mean square error is smaller than a root mean square error threshold value and the correlation coefficient is larger than a correlation coefficient threshold value, wherein the multi-fidelity positioning error model of the industrial robot meets the model precision standard; otherwise, executing steps S6-S9, and acquiring the low-fidelity data set and the high-fidelity data set until the multi-fidelity positioning error model of the industrial robot meets the model precision standard.
The smaller the root mean square error value is, the closer the correlation coefficient is to 1, and the higher the accuracy of the multi-fidelity positioning error model of the industrial robot is; in addition, the correlation coefficient ranges from 0 to 1.
S13: and (3) building a digital twin platform, and compensating motion data of each joint of the industrial robot by combining positioning error data of the multi-fidelity positioning error model of the industrial robot with an industrial robot entity.
The essence of the digital twin platform is that the multi-fidelity positioning error model is used as a virtual model, and the industrial robot entity positioning error is used as an entity model, so that data interaction between the multi-fidelity positioning error model and the industrial robot entity positioning error is realized.
The specific compensation process comprises the following steps:
before controlling the motion of the industrial robot, a motion instruction is sent to the multi-fidelity positioning error model through the upper computer, the multi-fidelity positioning error model calculates positioning error data according to the motion instruction sent by the upper computer, then the motion data of each joint is updated and fed back to a controller of the industrial robot, the controller sends the updated motion data of each joint to a driver, the robot is driven to move after positioning error compensation, and the compensation of the positioning error is realized.
The method comprises the steps that a laser tracker is used for measuring multiple groups of actual positioning error data of the industrial robot again regularly, on one hand, the laser tracker is used for updating joint stiffness data and then updating a positioning error model considering joint flexibility, and more accurate low-fidelity data are obtained; on one hand, the method is used for updating high fidelity data, and both the high fidelity data and the high fidelity data are used for updating a multi-fidelity positioning error model, so that the accuracy of the model is improved. Compared with the prior art, the method does not need to adopt a laser tracker to obtain the tail end positioning error data of the robot in real time, ensures the updating of the model, avoids the problem of model precision degradation, and combines a digital twin technology and a multi-fidelity positioning error model to provide an effective solution for solving the problems of low off-line compensation precision and high on-line compensation cost.
The above description is only a preferred embodiment of the application and is illustrative of the principles of the technology employed. It will be appreciated by a person skilled in the art that the scope of the invention as referred to in the present application is not limited to the embodiments with a specific combination of the above-mentioned features, but also covers other embodiments with any combination of the above-mentioned features or their equivalents without departing from the inventive concept. For example, the above features may be replaced with (but not limited to) features having similar functions disclosed in the present application.
Claims (10)
1. A method for compensating positioning error of an industrial robot is provided, wherein the industrial robot is a multi-degree-of-freedom industrial robot and is provided with a plurality of joints; the method for compensating the positioning error is characterized by comprising the following steps of:
s1: acquiring joint motion data of the industrial robot; the joint motion data is obtained by the movement of the joint of the industrial robot in a joint coordinate system according to a preset track;
s2: calculating dynamic data according to the joint motion data of the industrial robot;
s3: identifying relevant kinetic parameters, and constructing a rigid body kinetic model by combining kinetic data;
s4: in the rigid body dynamic model, identifying the rigidity of each joint of the industrial robot, and constructing a dynamic model considering the flexibility of the joint;
s5: establishing a mapping relation between the motion parameters of each joint and the tail end positioning error, and establishing a positioning error model considering the flexibility of the joint;
s6: acquiring an industrial robot joint motion data sample; the joint motion data sample is randomly generated by an industrial robot in a joint space angular displacement, angular velocity and angular acceleration constraint interval;
s7: inputting the joint motion data sample of the industrial robot into a positioning error model considering joint flexibility to obtain the low-fidelity data of the positioning error of the industrial robot;
s8: establishing a measurement reference coordinate system matched with the joint coordinate system;
s9: under a measurement reference coordinate system, a laser tracker is used for measuring the corresponding positioning error high-fidelity data of the industrial robot under each joint motion data in real time;
s10: fusing low-fidelity data and high-fidelity data of the positioning error of the industrial robot to obtain a multi-fidelity positioning error model of the industrial robot;
s11: calculating a root mean square error and a correlation coefficient in a multi-fidelity positioning error model of the industrial robot;
s12: judging that the root mean square error is smaller than a root mean square error threshold value and the correlation coefficient is larger than a correlation coefficient threshold value, wherein the multi-fidelity positioning error model of the industrial robot meets the model precision standard; otherwise, executing steps S6-S9 to obtain a low fidelity data set and a high fidelity data set until the multi-fidelity positioning error model of the industrial robot meets the model precision standard;
s13: and (3) building a digital twin platform, and compensating motion data of each joint of the industrial robot by combining positioning error data of the multi-fidelity positioning error model of the industrial robot with an industrial robot entity.
2. A method for compensating positioning error of an industrial robot according to claim 1, characterized in that in steps S2-S4, the following steps are included:
establishing a mapping relation between the generalized driving moment of the industrial robot and the generalized force borne by the tail end according to the following formula:
wherein the generalized driving torque Gamma is epsilon R 6×1 (ii) a The end bears generalized force W epsilon R 6×1 ；
A Jacobian matrix corresponding to the industrial robot at the point of application of the external load, an
Calculating the driving moment of the industrial robot relative to the action of the external load according to the following formula:
Γ＝K θ △θ；(1-2)
wherein, K θ Is rigidity of each joint of the industrial robot, and
delta theta is a rotation angle of each joint of the industrial robot relative to an initial position;
in an operation space, establishing a mapping relation between the end pose deformation of the industrial robot and an external load acted by the end pose deformation according to the following formula:
W＝K x △X＝K x J m △θ；(1-3)
wherein, K x For industrial machinesStiffness of the human distal reference point, and K x ∈R 6×6 (ii) a Delta X is the deformation of the end pose of the industrial robot, and the Delta X belongs to R 6×1 ；J m A Jacobian matrix at the deformation measuring point of the end pose of the industrial robot, and J m ∈R 6×6 ；
Establishing a mapping relation between a joint stiffness matrix of the industrial robot in a joint space and a stiffness matrix of an end reference point of the industrial robot in an operation space according to the following formula:
wherein, K c For industrial robot joint stiffness compensation matrix, and K c ∈R 6×6 ：
Calculating the rigidity of each joint of the industrial robot according to the following formula:
wherein W is an external load; and the delta X is the pose error of the reference point of the tail end of the industrial robot acquired by the laser tracker.
3. A method for compensating positioning error of an industrial robot according to claim 1, characterized in that in step S5:
the relationship between the motor side torque and the joint side torque is obtained according to the following formula:
wherein, tau m The motor side driving torque; tau is articular sideA driving torque; b is a motor rotor inertia matrix;
is the motor side angular acceleration.
4. A method for compensating positioning error of an industrial robot according to claim 3, characterized in that in step S5:
the motor side angular acceleration is expressed according to the following formula:
wherein the content of the first and second substances,
is the second derivative of the joint side rotation angle;
is a joint stiffness inverse matrix;
substituting the formula (1-7) into the formula (1-6) to obtain the relation between the motor side torque and the joint side torque:
5. the positioning error compensation method of an industrial robot according to claim 1, characterized in that in step S5, positioning error data is calculated from the joint-side torque:
6. a method for compensating positioning error of an industrial robot according to claim 1, characterized in that in step S6:
randomly generating an industrial robot joint motion data sample by utilizing Latin hypercube sampling:
S lf ＝[x lf (1) ,x lf (2) ,…,x lf (n) ] T 。
7. a method for compensating positioning errors of an industrial robot according to claim 1, characterized in that in step S7 a low fidelity dataset of positioning errors of an industrial robot is obtained:
using the positioning error data: y is lf (x)＝[y(x lf (1) ),y(x lf (2) ),…,y(x lf (n) )] T And the input joint motion data: s lf ＝[x lf (1) ,x lf (2) ,…,x lf (n) ] T Together, a low fidelity dataset is constructed.
8. A method for compensating positioning errors of an industrial robot according to claim 1, characterized in that in step S9 a high fidelity dataset is acquired:
using the respective joint motion data: s hf ＝[x hf (1) ,x hf (2) ,…,x hf (n) ] T And positioning error data measured by the laser tracker in real time: y is hf (x)＝[y(x hf (1) ),y(x hf (2) ),…,y(x hf (n) )] T Together, a high fidelity dataset is constructed.
9. A method for compensating positioning error of an industrial robot according to claim 1, characterized in that in step S10:
the low fidelity function is expressed according to the following equation:
wherein, the first and the second end of the pipe are connected with each other,
is a correlation matrix composed of function values between all sample points, and
i is a unit vector, and
r lf a correlation vector composed of correlation relations between an unknown point and all known sample points;
is a predicted value of the low fidelity function;
the high fidelity function is expressed according to the following formula:
solving a multi-fidelity positioning error model of the industrial robot according to the low-fidelity function and the high-fidelity function:
wherein, beta 0 ＝(F T R -1 F) -1 F T R -1 y s Is a scale factor, which is the degree to which a low fidelity function correlates to a high fidelity function.
10. A method for compensating positioning error of an industrial robot according to claim 1, characterized in that in step S11:
the root mean square error and the correlation coefficient are calculated respectively according to the following formulas:
wherein, y i Is the true value;
is a model predicted value; n is the number of sample points.
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