CN115502968A - Mechanical arm tail end position error compensation method based on calibration restoration rigid-flexible coupling model - Google Patents
Mechanical arm tail end position error compensation method based on calibration restoration rigid-flexible coupling model Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1679—Programme controls characterised by the tasks executed
- B25J9/1692—Calibration of manipulator
Abstract
The invention provides a mechanical arm tail end position error compensation method based on a calibration restoration rigid-flexible coupling model, which comprises the following steps: step one, establishing a kinematic model based on D-H; step two, carrying out D-H parameter and joint angle error sensitivity analysis; step three, establishing an error model and parameter identification; step four, calibrating the kinematic parameters; and step five, establishing a flexible joint model of the robot. And step six, establishing a robot flexible connecting rod model. And step seven, establishing a robot comprehensive rigid-flexible coupling model. The method simultaneously compensates the structural parameter error and the non-structural parameter error of the robot, has certain universality, solves the problem of error compensation under uncertain information of load and environment in the assembly operation process of the construction robot under a complex working condition, and improves the precision and the efficiency of an error compensation model under the condition of certain cost.
Description
Technical Field
The invention relates to the technical field of robots, in particular to a mechanical arm tail end position error compensation method based on a calibration restoration rigid-flexible coupling model.
Background
With the increasing development of digital processing and intelligent manufacturing, the application range and depth of industrial robots are increasing, and the precision is one of the important indexes for measuring the performance of robots, and is gradually concerned by the industry and experts. Although the repeated positioning accuracy of the industrial robot is high, the absolute positioning accuracy of the industrial robot is generally poor, generally above millimeter level, and the application range of the industrial robot is seriously influenced. The positioning error of the industrial robot mainly comes from a plurality of complex factors such as manufacturing error, assembly error, transmission error of robot parts, deformation caused by stress and temperature change and the like.
The robot structure parameter compensation is completed by kinematics parameter calibration, generally including 4 steps of modeling, measuring, parameter identification and compensation, and the non-structure parameter error is mainly affected by the deformation of rod and joint, temperature and the like. However, at present, university mathematics learners can only correct robot manufacturing and assembling errors by modeling based on robot kinematics, and can not compensate for non-structural parameter errors, and meanwhile, the established error proxy model is only an error proxy model of a local working range of the robot under a specific working condition, and the established error proxy model has no universality for complex and variable robot conditions. Therefore, a method for simultaneously compensating the structural parameter error and the non-structural parameter error of the robot while having certain universality is lacked at home and abroad.
Disclosure of Invention
This section is for the purpose of summarizing some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. In this section, as well as in the abstract and the title of the invention of this application, simplifications or omissions may be made to avoid obscuring the purpose of the section, the abstract and the title, and such simplifications or omissions are not intended to limit the scope of the invention.
Aiming at the defects, the invention provides a mechanical arm tail end position error compensation method based on a calibration restoration rigid-flexible coupling model.
The technical scheme adopted by the invention for solving the technical problems is as follows: a mechanical arm tail end position error compensation method based on a calibration restoration rigid-flexible coupling model comprises the following steps: step one, establishing a kinematic model based on D-H; step two, carrying out D-H parameter and joint angle error sensitivity analysis; step three, establishing an error model and parameter identification; step four, calibrating the kinematic parameters; and step five, establishing a flexible joint model of the robot. And step six, establishing a robot flexible connecting rod model. And step seven, establishing a robot comprehensive rigid-flexible coupling model.
Further, the first step comprises: the invention takes a self-made six-freedom-degree construction robot as a research object, and utilizes a D-H parameter method to establish a corresponding kinematics model, wherein the method comprises the following steps of w Is the world coordinate system, { O } o Using the coordinate system as a base coordinate system, coinciding with the world coordinate system, and establishing a local coordinate system { O } at the end of each connecting rod i } (i =1,2, 7). The center of each joint is taken as the origin O of a coordinate system, the z-axis is along the axis direction of each joint, the x-axis is along the common perpendicular direction of the adjacent joint axes, the front axis points to the rear axis (if the two joint axes are intersected, the x-axis is perpendicular to the plane formed by the two joint axes), and the y-axis is determined by the right-hand rule. For a six-degree-of-freedom tandem robot, each adjacent link matrix
Multiplying to obtain a conversion matrix of the base coordinate system and the tail end coordinate system of the mechanical arm as follows:
further, the second step comprises: the kinematic parameters in the commonly established industrial robot model are all theoretical parameters (alpha) i 、a i 、d i 、θ i ) However, due to the influence of each error source in practice, each parameter has a certain error value, which can be divided into length error δ a i 、δd i And angle error delta alpha i 、δθ i These 4 parametersThe error integration ultimately results in positioning errors of the robot end-effector.
D-H parameter error sensitivity analysis is firstly carried out. Presetting a parameter error value; introducing a preset parameter error into a theoretical kinematics model, correcting each kinematics parameter, and taking the kinematics parameter as a new kinematics parameter; sequentially enabling each shaft to rotate through the respective maximum angle range, and drawing the tail end track of the robot by using a robot tool box according to a theoretical kinematics model and a kinematics model introducing a preset error respectively; and (5) subtracting the coordinates of the two tracks to obtain the comprehensive position error values of the x direction, the y direction, the z direction and the tail end.
And secondly, carrying out joint angle error sensitivity analysis. The joint rotation angle error is an important factor affecting the accuracy of the tip position. Under different poses, the influence degree of joint corner errors on the total positioning accuracy is different, so that the joint corner errors of joints i (i =1,2,.., 6) are preset; assuming that the joint 1 has errors, joint rotation angles of other joints are theoretical values, and the robot has no errors of other kinematic parameters; presetting a working space of the joint corner error traversing robot, and solving a positioning error value of each track point
And repeating the steps to finally obtain the positioning error distribution of the end effector when the different joint angles have errors.
Further, the third step comprises: due to the existence of error sources such as manufacturing assembly errors, encoder errors, joint abrasion, flexible deformation of the robot and the like, when two adjacent joints of the mechanical arm are close to be parallel, the kinematic parameters can be changed remarkably as long as small angular deviation occurs between the two joints. In order to solve the singularity problem of the DH parameter method, the M-DH parameter method introduces a rotation term Rot (y) on the basis of DH parameters i ，β i )(β i Indicating a slight angle of rotation between the parallel axes). And establishing a geometric error model of the robot based on an M-DH method. Selecting enough sample points in the working space of the robot for measurement to obtain an actual value of the surgical end position, and solving an optimal value of delta by using an LM method:
Δδ＝(J δ T J δ ) -1 J δ T ΔP
compensating the link parameter error delta obtained by identification into a theoretical model of the robot, identifying the parameters again according to the newly obtained model of the robot, and iterating repeatedly until P x 、P y 、P z Until the value is less than the set threshold value. And at this point, the compensation of the parameter error of the connecting rod is completed.
Further, the fourth step includes: on the basis of the established kinematic model, adopting a Monte Carlo algorithm to solve the working space of the robot, measuring the representative actual position of a sampling point spanning the whole working space by using a laser tracker, and recording a corresponding joint angle; solving the theoretical position of each sampling point by using the established kinematic model; converting a coordinate system aiming at the specific configuration of a self-made six-axis building robot, unifying an actual value measured by a laser tracker and a theoretical value calculated according to an established kinematic model under the same coordinate system, and calculating the position error corresponding to each group of joint angles after difference; substituting each group of joint angles into a formula:
obtaining an error coefficient matrix, and further according to a formula:
Δδ＝(J δ T J δ ) -1 J δ T ΔP
and identifying the error value of the connecting rod parameter, compensating the result into the theoretical model and performing iterative identification to obtain the connecting rod parameter correction value meeting the requirement, thereby providing an accurate model basis for the rigid-flexible coupling model.
Further, the fifth step comprises: the joint flexibility is described as a torsion spring, the proportionality coefficient of the torsion spring is the elastic coefficient of the joint, a rotor of a motor is taken as a whole on a rotating shaft, and a flexible joint model is built according to the proportionality coefficient of the torsion spring:
Δθ＝C θ ·T
wherein Δ θ is a joint deflection angle due to joint flexibilityIn radians; c θ Is the compliance coefficient of the joint i; t is the equivalent moment applied on the axis of the joint i. And establishing a self-weight flexible joint model and an externally-loaded flexible joint model.
Further, the sixth step comprises: as can be known from error sensitivity analysis, the positioning precision of the mechanical arm has very low sensitivity to the deformation of the connecting rod, and the deformation of the connecting rod is very small, so that the flexible deformation of the connecting rod of the mechanical arm is simply modeled and is regarded as a cantilever beam under the comprehensive action of uniformly distributed loads, concentrated loads and concentrated couples, the deformation of the cantilever beam is solved by using a flexible line equation, and the flexible line equation is as follows:
and establishing a self-weight flexible connecting rod model and an externally-loaded flexible connecting rod model based on a deflection equation.
Further, the seventh step includes: the joint and the connecting rod flexibility under the action of the self weight of the mechanical arm and an external load are comprehensively considered, the joint corner error and the connecting rod deflection deformation are converted into the influence on the space positioning precision of the tail end of the mechanical arm, and a model support is provided for robot error compensation, so that the aim of improving the robot operation precision under various working conditions is fulfilled.
The method has the advantages that the tail end position error compensation method of the mechanical arm based on the calibration restoration rigid-flexible coupling model is provided, the structural parameter error and the non-structural parameter error of the robot are compensated simultaneously, meanwhile, the method has certain universality, the problem of error compensation under uncertain information of load and environment in the assembly operation process of the construction robot under a complex working condition is solved, and the precision and the efficiency of an error compensation model are improved under the condition of certain cost.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without inventive exercise.
FIG. 1 is a flow cycle chart of the present invention;
FIG. 2 is a schematic diagram of the structure of the self-made six-degree-of-freedom robot of the invention;
FIG. 3 is a coordinate system of each joint connecting rod of the self-made robot of the invention;
FIG. 4 is a calibration experiment flow of the present invention;
FIG. 5 is a self-weight flexible joint model of the robot arm of the present invention;
FIG. 6 is a model of a flexible joint with an external load applied to a mechanical arm according to the present invention;
FIG. 7 is a schematic view of a cantilever beam deformation according to the present invention;
FIG. 8 is a model of a robot arm deadweight flexible link according to the present invention;
FIG. 9 is a model of a robot arm with an externally loaded flexible link according to the present invention.
Reference numbers in the figures: 1. a connecting rod 1; 2. a joint 1; 3. a connecting rod 2; 4. a joint 2; 5. a connecting rod 3; 6. A joint 3; 7. a connecting rod 4; 8. a joint 4; 9. a connecting rod 5; 10. a joint 5; 11. a connecting rod 6; 12. and a joint 6.
Detailed Description
Referring to fig. 1, a mechanical arm end position error compensation method based on a calibration restoration rigid-flexible coupling model includes the following steps: step one, establishing a kinematic model based on D-H; step two, carrying out D-H parameter and joint angle error sensitivity analysis; step three, establishing an error model and parameter identification; step four, calibrating the kinematic parameters; and step five, establishing a flexible joint model of the robot. And step six, establishing a robot flexible connecting rod model. And step seven, establishing a robot comprehensive rigid-flexible coupling model.
Referring to fig. 1,2 and 3, the first step includes: the invention takes a self-made six-freedom-degree construction robot as a research object, and utilizes a D-H parameter method to establish a corresponding kinematics model, wherein the method comprises the following steps of w Is the world coordinate system, { O o The base coordinate system is coincident with the world coordinate system, and a local seat is established at the tail end of each connecting rodThe system of symbols { O i } (i =1,2, 7). The center of each joint is taken as the origin O of a coordinate system, the z-axis is along the axis direction of each joint, the x-axis is along the common perpendicular direction of the adjacent joint axes, the front axis points to the rear axis (if the two joint axes are intersected, the x-axis is perpendicular to the plane formed by the two joint axes), and the y-axis is determined by the right-hand rule. Using connecting rod torsion angle alpha i-1 Length of connecting rod a i-1 Offset distance d of connecting rod i Angle of rotation of joint theta i Four parameters are used for describing the pose relation between the adjacent connecting rods, wherein alpha is i-1 Is the angle of the axes of adjacent joints to the common vertical line, a i-1 The length of a common perpendicular line between adjacent joint axes, d i Is the distance of adjacent common perpendiculars on the axis of the medial joint, θ i The angle labels i and i-1 represent the joint numbers for the angles of adjacent common perpendicular lines with respect to the axis of the medial joint.
Establishing a transformation matrix between adjacent link coordinate systems of a robot
Comprises the following steps:
in the formula:
a homogeneous transformation matrix representing the ith joint coordinate system relative to the ith-1 coordinate system; trans represents the translation term; rot represents a rotation term; s and c in the matrix represent trigonometric functions sin and cos, respectively.
For a six-degree-of-freedom tandem robot, each adjacent link matrix
Multiplying to obtain a conversion matrix of the base coordinate system and the tail end coordinate system of the mechanical arm as follows:
expressed in the form of a uniform matrix, i.e.
In the formula:
is a robot terminal pose matrix; r is a 3 x 3 attitude matrix; p is a 3 x 1 position matrix.
In order to realize motion control of 6 joint angles of the robot, the inverse kinematics of the robot needs to be solved, namely, each joint angle is solved by the terminal pose. Because the inverse kinematics solution has a multi-solution problem, the solution is carried out on the principle that the motion path of the adjacent target point is shortest, namely: let θ is And theta io For the starting and ending joint angles of the ith joint, the optimal inverse solution for the ith joint can be expressed as:
referring to fig. 1, step two includes: first, the error sensitivity analysis of the D-H parameters is performed. Presetting a parameter error value; introducing a preset parameter error into a theoretical kinematics model, correcting each kinematics parameter, and taking the kinematics parameter as a new kinematics parameter; sequentially enabling each shaft to rotate through the respective maximum angle range, and drawing the tail end track of the robot by using a robot tool box according to a theoretical kinematics model and a kinematics model introducing a preset error respectively; and (5) subtracting the coordinates of the two tracks to obtain the comprehensive position error values of the x direction, the y direction, the z direction and the tail end.
And secondly, performing joint angle error sensitivity analysis. Presetting a joint rotation angle error of a joint i (i =1,2.., 6); assuming that the joint 1 has errors, the joint rotation angles of the other joints are theoretical values, and the robot does not storeErrors in other kinematic parameters; presetting a working space of the joint corner error traversing robot, and solving a positioning error value of each track point
And repeating the steps to finally obtain the positioning error distribution of the end effector when the different joint angles have errors.
Referring to fig. 1, step three includes: introducing a rotation term Rot (y) based on a DH parameter by an M-DH parameter method i ，β i )(β i Indicating a slight angle of rotation between the parallel axes). According to the M-DH model, the transformation relationship between adjacent coordinate systems of the robot is rewritten as:
then:
under theoretical kinematic parameters, the end position of the robot can be expressed as:
in the formula: the subscript (1: 3,4) indicates the number of rows and columns from which the pose matrix is extracted; β =0.
Let Delta alpha i-1 、Δa i-1 、Δd i 、Δθ i (i =1,2,.., 6) respectively represents the geometrical parameter errors of the connecting rod, and the theoretical positions of the tail end of the robot are as follows:
the robot tip positioning error is expressed as:
ΔP＝P-P
in fact, a tableWhat parameter error delta alpha i-1 、Δa i-1 、Δd i 、Δθ i 、Δβ i Generally, the mapping relationship between the robot end positioning error and the geometric parameter error is very small, and therefore, the mapping relationship can be described by a differential equation to obtain:
it is represented in matrix form:
ΔP＝J δ Δδ
wherein, J δ The error coefficient matrix is used for storing known quantities, and the specific form is as follows:
delta is a connecting rod parameter error matrix and is used for storing unknown quantity, namely parameters to be identified, and the specific form is as follows:
selecting enough sample points in the working space of the robot for measurement to obtain an actual value of the end position, and solving an optimal value of delta by using an LM method:
Δδ＝(J δ T J δ ) -1 J δ T ΔP
compensating the link parameter error delta obtained by identification into a theoretical model of the robot, identifying the parameters again according to the newly obtained model of the robot, and iterating repeatedly until P x 、P y 、P z Until the value is less than the set threshold value. And at this point, the compensation of the parameter error of the connecting rod is completed.
δ i+1 ＝δ i +Δδ
In the formula: delta i And obtaining a connecting rod parameter error matrix for the ith identification.
Referring to fig. 1 and 4, the fourth step includes: adopting a Monte Carlo algorithm to solve the working space of the robot on the basis of the established kinematic model, measuring the actual position of a representative sampling point spanning the whole working space by using a laser tracker, and recording the corresponding joint angle; solving the theoretical position of each sampling point by using the established kinematic model; converting a coordinate system aiming at the specific configuration of a self-made six-axis building robot, unifying an actual value measured by a laser tracker and a theoretical value calculated according to an established kinematic model under the same coordinate system, and calculating the position error corresponding to each group of joint angles after difference; substituting each group of joint angles into a formula:
obtaining an error coefficient matrix, and further according to a formula:
Δδ＝(J δ T J δ ) -1 J δ T ΔP
and identifying the error value of the connecting rod parameter, compensating the result into the theoretical model, and performing iterative identification to obtain the connecting rod parameter correction value meeting the requirement, thereby providing an accurate model basis for the rigid-flexible coupling model.
Referring to fig. 1, 5, and 6, step five includes: the joint flexibility is described as a torsion spring, the proportionality coefficient of the torsion spring is the elastic coefficient of the joint, a rotor of a motor is taken as a whole on a rotating shaft, and a flexible joint model is built according to the torsion spring, wherein the torsion spring comprises the following components:
Δθ＝C θ ·T
in the formula, delta theta is a joint deflection angle caused by joint flexibility and is expressed in radian; c θ The compliance coefficient of the joint i; t is the equivalent moment applied on the axis of the joint i.
According to the error sensitivity analysis and the normal working condition of the self-made six-axis robot, the influence of the flexible deformation of the joints 2, 3 and 5 on the positioning precision of the tail end of the robot is most obvious, so that the flexibility of the joints 3 is only considered, other joints with smaller influence are ideally rigid, and a self-weight flexible joint model and an externally-loaded flexible joint model are established.
Firstly, a self-weight flexible joint model is established. Wherein m is 3 g、m 4 g、m 6 g is link 3, link 4 (link 4 and link 5 are considered as one rod, called link 4,m, depending on the robot arm configuration 4 ＝m 4 +m 5 ) The connecting rod 6 bears the gravity; d c3 、d c4 、d c6 The distance between the gravity center of the corresponding connecting rod and the joint at the front end of the connecting rod; l is a radical of an alcohol 3 、 d 4 、d 5 、d 6 Is the corresponding connecting rod length; theta.theta. 2 、θ 3 、θ 5 Zero joint angle value of the corresponding joint; c 2 、C 3 And C 5 The compliance coefficient of the corresponding joint. Substituting the above parameters into Δ θ = C θ T, obtaining the angles of the joints 2, 3 and 5 rotated under the action of the self weight of the mechanical arm, wherein the angles are respectively as follows:
by Q g5a 、Q g3a 、Q g3b 、Q g3c 、Q g2a 、Q g2b 、Q g2c 、Q g2d 、Q g2e 、Q g2f Respectively represents the joint flexibility C, the connecting rod mass m and the gravity center distance L in the above formula c And d c The length L of the rod and the offset distance d, and the matrix form of the self-weight flexible joint model is obtained as follows:
in the formula,. DELTA.theta. g Is a joint angle error vector, T, generated by the self weight of the mechanical arm gJ Is a matrix of the joint angle of the joint's degree of flexibility of the dead weight, the value of which changes with the pose of the arm, Q g Is a matrix of the self-weight joint flexibility coefficient, and the value of the determined robot is constant.
And secondly, establishing an externally-loaded flexible joint model. Considering only the flexible deformation of the joint caused by end loadsThe mechanical arm attribute parameters and the end load mass m l Substitution formula Δ θ = C θ T can be:
in the formula,. DELTA.theta. l5 、Δθ l3 And Δ θ l2 Respectively, the angles through which joints 5, 3 and 2 are turned by the end load of the robot arm.
By Q l5a 、Q l3a 、Q l3b 、Q l2a 、Q l2b And Q l2c Respectively, joint stiffness C and load mass m in the formula (19) l The length L of the rod and the offset distance d, and the matrix form of the external load flexible joint model is obtained as follows:
in the formula,. DELTA.theta. l Representing the joint angle error vector, T, due to the end load of the arm lJ For externally loaded joint compliance joint angle matrices whose values change with changes in the pose of the arm, Q l The joint flexibility coefficient matrix is an externally-added load, and if the load borne by the robot is not changed, the value of the joint flexibility coefficient matrix is constant.
Referring to fig. 1, 7, 8, and 9, step six includes: according to the error sensitivity analysis, the positioning precision of the mechanical arm has low sensitivity to the deformation of the connecting rod, and the deformation of the connecting rod is extremely small, so that the flexible deformation of the connecting rod of the mechanical arm is simply modeled and is regarded as a cantilever beam under the comprehensive action of uniformly distributed loads, concentrated loads and concentrated couples, the deformation of the cantilever beam is solved by using a deflection line equation, and the deflection equation is as follows:
in the robot configuration of the invention, only the rod lengths of the connecting rods 3 and 4 are longer, and the flexible deformation of other connecting rods is negligible due to the smaller rod lengths, so that only the deflection of the connecting rods 3 and 4 is analyzed. And establishing a self-weight flexible connecting rod model and an externally-loaded flexible connecting rod model based on a deflection equation.
Firstly, a self-weight flexible connecting rod model is established. Let E i And I i Is the elastic modulus and moment of inertia of the connecting rods 3,4
The deflection of the connecting rods 3 and 4 caused by the self weight of the mechanical arm is obtained. The deflection is decomposed for the convenience of subsequent compensation, and the tail end horizontal offset w of the two connecting rods under the action of the dead weight of the mechanical arm is obtained gv4 、w gl4 And end vertical offset w gv3 、w gv3 Written as:
by K g4a 、K g4b 、K g4c 、K g4d 、K g3a 、K g3b 、K g3c 、K g3d Respectively represents the elastic modulus E, the inertia moment I, the connecting rod mass m and the gravity center distance L in the formula c And d c The length L of the rod and the offset distance d, and the matrix form of the self-weight flexible connecting rod model is obtained as follows:
in the formula, w g Is a deflection vector of a connecting rod, T, generated by the self weight of the mechanical arm gL Is a matrix of the angle of the own weight link's flexible joint whose value changes with the pose of the arm, K g Is a self-weight link compliance coefficient matrix, the value of which is constant for a determined robot.
And secondly, establishing an externally-loaded flexible connecting rod model. Considering the flexible deformation of the connecting rod caused by the end load, and enabling the attribute parameters of the mechanical arm and the end load mass m l Substituted type
The deflection of the connecting rods 3,4 due to the applied load is obtained. The deflection is decomposed for the convenience of subsequent compensation to obtain the tail end horizontal offset w of the two connecting rods under the action of an external load ll4 、w ll3 And end vertical offset w lv4 、 w lv3 Written as:
by K l4a 、K l4b 、K l4c 、K l3a 、K l3b 、K l3c Respectively represent the applied load mass m in the above formula l Elastic modulus E, moment of inertia I, rod length L and offset distance d, and obtaining a matrix form of the external load flexible connecting rod model as follows:
in the formula, w l Represents the link deflection vector, T, due to the end load of the arm lL For an externally loaded link compliance joint angle matrix whose values change with changes in the pose of the arm, K l The matrix is a flexibility coefficient matrix of the externally-added load connecting rod, and if the load borne by the robot is a certain load, the value of the matrix is constant.
Referring to fig. 1, step seven includes: the total joint angle error under the combined action of the self weight of the mechanical arm and an external load is as follows:
the offset of the end position under the influence of the joint flexibility is:
wherein P is a theoretical position vector, P J Under the influence of joint flexibilityA position vector.
The total connecting rod deflection error of the mechanical arm under the combined action of self weight and external load is as follows:
the offset of the tail end position under the influence of the flexibility of the connecting rod is the opposite number of the deflection error of the total connecting rod:
therefore, considering the flexibility of the joint and the connecting rod, the actual positions of the tail end of the mechanical arm under the action of self weight and external load are as follows:
P real ＝P+ΔP J +ΔP L
the above description is only exemplary of the invention and should not be taken as limiting the scope of the invention, so that the invention is intended to cover all modifications and equivalents of the embodiments described herein. In addition, the technical characteristics can be freely combined with each other, the technical characteristics can be freely combined with the technical scheme, and the technical scheme can be freely combined with the technical scheme.
Claims (9)
1. A mechanical arm tail end position error compensation method based on a calibration restoration rigid-flexible coupling model is characterized by comprising the following steps: the method comprises the following steps: step one, establishing a kinematic model based on D-H; step two, analyzing the sensitivity of the D-H parameters and the joint angle errors; step three, establishing an error model and parameter identification; step four, calibrating the kinematic parameters; and step five, establishing a flexible joint model of the robot. And step six, establishing a robot flexible connecting rod model. And step seven, establishing a robot comprehensive rigid-flexible coupling model.
2. The mechanical arm tail end position based on calibration and restoration rigid-flexible coupling model according to claim 1The error compensation method is characterized in that: the first step comprises the following steps: the invention takes a self-made six-freedom-degree construction robot as a research object, establishes a corresponding kinematic model by using a D-H parameter method, and for a six-freedom-degree series robot, each adjacent connecting rod matrix
And multiplying to obtain a conversion matrix of the base coordinate system and the tail end coordinate system of the mechanical arm.
3. The mechanical arm tail end position error compensation method based on calibration and repair of the rigid-flexible coupling model according to claim 1, characterized by comprising the following steps: in the second step, D-H parameter error sensitivity analysis is carried out firstly, and a parameter error value is preset; introducing a preset parameter error into a theoretical kinematics model, correcting each kinematics parameter, and taking the kinematics parameter as a new kinematics parameter; sequentially enabling each shaft to rotate through the respective maximum angle range, and drawing the tail end track of the robot by using a robot tool box according to a theoretical kinematics model and a kinematics model introducing a preset error respectively; and (4) performing difference on the coordinates of the two tracks to obtain the error values of the comprehensive positions of the X, Y and Z directions and the tail end.
4. The mechanical arm tail end position error compensation method based on the calibration and repair rigid-flexible coupling model according to claim 3, characterized in that: secondly, joint angle error sensitivity analysis is carried out, joint corner errors have different influence degrees on the total positioning accuracy under different poses, so that joint corner errors of joints i (i =1,2, … and 6) are preset, the joint corners of other joints are theoretical values on the assumption that the joint 1 has errors, other kinematic parameter errors do not exist in the robot, the preset joint corner errors traverse the working space of the robot, and the positioning error value of each track point is solved
And repeating the steps to finally obtain the positioning error distribution of the end effector when the different joint angles have errors.
5. The mechanical arm tail end position error compensation method based on the calibration and repair rigid-flexible coupling model according to claim 1, characterized in that: in the third step: due to the existence of error sources such as manufacturing assembly errors, encoder errors, joint abrasion, flexible deformation of a robot and the like, when two adjacent joints of a mechanical arm are close to be parallel, the kinematic parameters can be obviously changed as long as small angular deviation occurs between the two adjacent joints, and in order to solve the singularity problem of a DH parameter method, a rotation term Rot (y) is introduced on the basis of a DH parameter by an M-DH parameter method i ，β i )(β i Representing a tiny corner between parallel axes), establishing a geometric error model of the robot based on an M-DH method, selecting enough sample points in a working space of the robot to measure to obtain an actual value of a tail end position, and solving an optimal value of delta by using an LM method:
Δδ＝(J δ T J δ ) -1 J δ T ΔP
compensating the link parameter error delta obtained by identification into a theoretical model of the robot, identifying the parameters again according to the newly obtained model of the robot, and iterating repeatedly until P x 、P y 、P z Until the value is less than the set threshold value. And at this point, the compensation of the parameter error of the connecting rod is completed.
6. The mechanical arm tail end position error compensation method based on the calibration and repair rigid-flexible coupling model according to claim 1, characterized in that: in the fourth step, the working space of the robot is solved by adopting a Monte Carlo algorithm on the basis of the established kinematic model, the representative actual position of the sampling point crossing the whole working space is measured by using a laser tracker, and the corresponding joint angle is recorded; solving the theoretical position of each sampling point by using the established kinematic model; and (3) converting a coordinate system aiming at the specific configuration of the self-made six-axis building robot, unifying an actual value measured by the laser tracker and a theoretical value calculated according to the established kinematic model under the same coordinate system, and calculating the position error corresponding to each group of joint angles after difference. Further according to the formula:
Δδ＝(J δ T J δ ) -1 J δ T ΔP
and identifying the error value of the connecting rod parameter, compensating the result into the theoretical model, and performing iterative identification to obtain the connecting rod parameter correction value meeting the requirement, thereby providing an accurate model basis for the rigid-flexible coupling model.
7. The mechanical arm tail end position error compensation method based on the calibration and repair rigid-flexible coupling model according to claim 1, characterized in that: in the fifth step: the joint flexibility is described as a torsion spring, the proportionality coefficient of the torsion spring is the elastic coefficient of the joint, a rotor of a motor is taken as a whole on a rotating shaft, and a flexible joint model is built according to the torsion spring, wherein the torsion spring comprises the following components:
Δθ＝C θ ·T
in the formula, delta theta is a joint deflection angle caused by joint flexibility and is expressed in radian; c θ Is the compliance coefficient of the joint i; and T is an equivalent moment applied to the axis of the joint i, and a self-weight flexible joint model and an externally-loaded flexible joint model are established.
8. The mechanical arm tail end position error compensation method based on the calibration and repair rigid-flexible coupling model according to claim 1, characterized in that: in the sixth step: as can be known from error sensitivity analysis, the positioning precision of the mechanical arm has very low sensitivity to the deformation of the connecting rod, and the deformation of the connecting rod is very small, so that the flexible deformation of the connecting rod of the mechanical arm is simply modeled and is regarded as a cantilever beam under the comprehensive action of uniformly distributed loads, concentrated loads and concentrated couples, the deformation of the cantilever beam is solved by using a flexible line equation, and the flexible line equation is as follows:
and establishing a self-weight flexible connecting rod model and an externally-loaded flexible connecting rod model based on a deflection equation.
9. The mechanical arm tail end position error compensation method based on the calibration and repair rigid-flexible coupling model according to claim 1, characterized in that: step seven: the joint and the connecting rod flexibility under the action of the self weight of the mechanical arm and an external load are comprehensively considered, the joint corner error and the connecting rod deflection deformation are converted into the influence on the space positioning precision of the tail end of the mechanical arm, model support is provided for robot error compensation, and the aim of improving the robot operation precision under various working conditions is fulfilled.
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| CN116673966A (en) * | 2023-08-02 | 2023-09-01 | 北京迁移科技有限公司 | Joint angle generation method for robot and robot system |
| CN117415857A (en) * | 2023-12-18 | 2024-01-19 | 浙江大学 | Multifunctional leg-foot type robot test platform with position compensation mechanism |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116673966A (en) * | 2023-08-02 | 2023-09-01 | 北京迁移科技有限公司 | Joint angle generation method for robot and robot system |
| CN116673966B (en) * | 2023-08-02 | 2023-10-03 | 北京迁移科技有限公司 | Joint angle generation method for robot and robot system |
| CN117415857A (en) * | 2023-12-18 | 2024-01-19 | 浙江大学 | Multifunctional leg-foot type robot test platform with position compensation mechanism |
| CN117415857B (en) * | 2023-12-18 | 2024-03-22 | 浙江大学 | Multifunctional leg-foot type robot test platform with position compensation mechanism |
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