CN117349990B - Method and system for rapidly calibrating robot - Google Patents
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Abstract
The invention discloses a method and a system for rapidly calibrating a robot, which aim to solve the problems of high workload and time cost, complicated flow and lower efficiency of the existing robot calibration method and improve the operation precision of the robot. The invention expands the original robot calibration system model and considers the motion characteristics and structure of the robot more comprehensively. The method adopts a two-step strategy calibration method, and firstly, an improved index optimization algorithm is used as an initial calibration tool to obtain a calibration system parameter estimation value; and secondly, combining with the LM algorithm to perform identification on accuracy so as to obtain a more accurate identification result. According to the invention, the actual motion data of the robot is fully utilized by adopting a two-step strategy, the workload of independently measuring the coordinate system is reduced, and the calibration efficiency and precision are improved. Experiments prove that the calibration method can quickly and effectively improve the calibration precision of the robot and remarkably reduce errors.
Description
Technical Field
The invention belongs to the technical field of robot calibration, and particularly relates to a method and a system for quickly calibrating a robot.
Background
Currently, robots are an important component of the manufacturing industry, and the precision of the operations thereof has been attracting attention. However, the existing methods have at least the following disadvantages:
1. the independent measurement coordinate system is cumbersome: the existing method needs to carry out a plurality of independent experiments and measuring processes, and the calibration workload and time cost are increased.
2. Practical motion data of the robot are not fully utilized: the actual motion mode and constraint conditions of the robot are not considered in the calibration process of the traditional method, so that the calibration process is complicated and the efficiency is low.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a method and a system for quickly calibrating a robot.
In order to achieve the expected effect, the invention adopts the following technical scheme:
the invention discloses a method for rapidly calibrating a robot, which comprises the following steps:
s1, deriving a robot error kinematic model according to a robot kinematic model and a pose differential transformation relation;
s2, expanding the robot error kinematics model to a calibration system model;
s3, inputting the actual position point location coordinates detected by the measuring device and the current joint gesture of the robot into a calibration system model for primary parameter identification, and obtaining the parameter value of a transformation matrix of a measuring part in the calibration system model;
s4, performing sub-step parameter optimization by combining the theoretical parameter value of the robot and the parameter value of the transformation matrix of the measurement part to obtain a first calibration value of the kinematic parameter of the robot;
s5, when the first calibration value is within the error threshold range, taking the first calibration value as a final calibration value, otherwise, respectively correcting the theoretical parameter value of the robot and the parameter value of the transformation matrix of the measurement part through the first calibration value, and re-executing S4.
Further, the step S1 specifically includes:
obtaining a robot kinematics model by using an improved DH parameter method;
performing error deduction through a robot kinematic model and a position differential transformation relation;
according to a differential transformation method, transforming a transformation matrix error generated by an error factor into a robot tail end coordinate system;
and after the second-order differential minor terms are ignored, differential errors of all the connecting rods are transmitted to an end coordinate system, and the accumulated sum of all the connecting rod errors in the end coordinate system is the robot error kinematic model.
Further, the step S2 specifically includes: and combining an error matrix from the measuring device measuring coordinate system to the robot base coordinate system, an error matrix from the robot tail end flange coordinate system to the measuring device measuring coordinate system and the robot error kinematic model to obtain the calibration system model.
Further, the measurement section transforms matrix parameter values including transformation matrix initial parameters from the measurement coordinate system of the measurement device to the robot base coordinate system, transformation matrix initial parameters from the robot end flange coordinate system to the measurement coordinate system of the measurement device.
Further, the step of inputting the actual position point location coordinates detected by the measuring device and the current joint gesture of the robot into the calibration system model for preliminary parameter identification, and the step of obtaining the parameter value of the transformation matrix of the measuring part in the calibration system model specifically comprises the following steps:
inputting the actual position point position coordinates detected by the measuring device and the current joint gesture of the measured robot into a simplified calibration system model, and carrying out parameter identification by adopting an improved index optimization algorithm to obtain the parameters of a transformation matrix of a measurement part in the simplified calibration system model.
Further, the improved exponential optimization algorithm adopts a least square method to calculate and obtain a preset transformation matrix initial parameter value, a random solution set is generated by taking the value as a center, and a population iteration mode is set as the distance between an average solution and an optimal solution in the current winner solution.
Further, the calibration system model is simplified by taking the minimum average distance between the measurement point of the calibration system model and the theoretical calibration coordinate point as a process target, so that a simplified calibration system model is obtained.
Further, the objective function of the simplified calibration system model is expressed as:
；
in the method, in the process of the invention,coordinate values obtained by measuring the laser tracker; />For the theoretical calibration coordinate value under the condition of the same joint angle of the robot, < >>For the target value, N is a positive integer, and min () is a minimization function.
Further, the step S4 specifically includes: substituting the theoretical parameter value of the robot and the parameter value of the transformation matrix of the measurement part into a calibration system model, and optimizing by adopting an iterative weighting LM algorithm to obtain a first calibration value.
The invention also discloses a system for rapidly calibrating the robot, which comprises:
the input module is used for inputting various data required by the calibration of the robot;
and the calibration module is used for carrying out quick calibration on the robot according to any one of the methods.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a method and a system for rapidly calibrating a robot, which aim to solve the problems of high workload, high time cost, complicated flow and low efficiency of the existing robot calibration method. The invention adopts an improved DH parameter method and differential transformation, and in the modeling stage, the coordinate transformation matrix is jointly measured, a position error model is built, and a calibration system model with redundancy removed is built. The invention expands the robot model and considers the motion characteristics and structure of the robot more comprehensively. The method adopts a two-step strategy calibration method, and firstly, an improved index optimization algorithm is used as an initial calibration tool to obtain an initial calibration system parameter estimation value; and secondly, carrying out precision identification by combining an iteration weighting LM algorithm so as to obtain a more accurate identification result. According to the invention, the actual motion data of the robot is fully utilized by adopting a two-step strategy, the workload of independently measuring the coordinate system is reduced, and the calibration efficiency and precision are improved. Experiments prove that the calibration method can quickly and effectively improve the calibration precision of the robot and remarkably reduce errors. The optimized kinematic calibration scheme has remarkable advantages in improving the positioning accuracy and motion control of the robot, is suitable for various points, and has wide application prospect.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings described below are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic diagram of an improvement effect of an exponential optimization algorithm according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a point location according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a unified point location effect according to an embodiment of the present invention.
Fig. 4 is a flowchart of a method for quickly calibrating a robot according to an embodiment of the present invention.
Fig. 5 is a schematic diagram of an error of a measurement point and an error after calibration according to an embodiment of the present invention.
Fig. 6 is a schematic diagram of a distance error according to an embodiment of the present invention.
Fig. 7 is a schematic diagram of an error in the x-direction according to an embodiment of the present invention.
Fig. 8 is a schematic diagram of an error in the y direction according to an embodiment of the present invention.
Fig. 9 is a schematic diagram of error in the z direction according to an embodiment of the present invention.
FIG. 10 is a schematic diagram of data before and after calibration according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1 to 10, the invention discloses a method for rapidly calibrating a robot, which comprises the following steps:
s1, deriving a robot error kinematic model according to the robot kinematic model and the pose differential transformation relation.
In a preferred embodiment, the S1 specifically includes:
obtaining a robot kinematics model by using an improved DH parameter method;
performing error deduction through a robot kinematic model and a position differential transformation relation;
according to a differential transformation method, transforming a transformation matrix error generated by an error factor into a robot tail end coordinate system;
and after the second-order differential minor terms are ignored, differential errors of all the connecting rods are transmitted to an end coordinate system, and the accumulated sum of all the connecting rod errors in the end coordinate system is the robot error kinematic model.
S2, expanding the robot error kinematics model to a calibration system model; the step eliminates the defect of independently measuring the front and rear coordinates in the traditional method, and the actual motion data is directly substituted into the parameter identification process to improve the calibration accuracy.
In a preferred embodiment, the S2 specifically includes: and combining an error matrix from the measuring device measuring coordinate system to the robot base coordinate system, an error matrix from the robot tail end flange coordinate system to the measuring device measuring coordinate system and the robot error kinematic model to obtain the calibration system model.
Illustratively, the invention constructs a robot kinematic model by adopting an improved DH parameter method, and a transformation matrix between adjacent connecting rods can be expressed as follows:
；
wherein: corner angleIs the angle between two adjacent z-axes, also called the joint torsion angle, expressed as about +.>Is a rotation angle of (a); />Represents the length of each plumb line (also called joint offset),>the angle represents the rotation angle around the z-axis, +.>Indicating rotation about the Z axis, i indicating the coordinate system of the ith joint,/o>Representing the distance between two adjacent common perpendicular lines in the z-axis.
Preferably, the transformation matrix is obtained by successive multiplication of transformation matrices between adjacent links.
Exemplary, at a known pointOn the basis of (a), the transformation matrix from the robot base coordinate system to the robot end coordinate system can be deduced as:
；
in the method, in the process of the invention,is a theoretical rotation matrix (such as a 3x3 gesture matrix), and its internal elements are +.>、/>、/>、、/>、/>、/>、/>、/>All representing the direction of the object in the new coordinate system, respectively>Is a displacement vector (3 x1 position matrix can be adopted), and the internal element is +.>、/>、/>The position of the object in the new coordinate system is described separately.
Further, the end actual pose matrix relative to the robot base coordinate system is:
，
in the method, in the process of the invention,representing the terminal actual pose matrix +.>Representing a theoretical terminal pose matrix +.>Representing the pose error between the two, +.>Is a differential transformation matrix for transforming from a theoretical pose to an actual pose.
Specifically, a position differential transformation kinematic error model is constructed to convert errors generated by the various joints to robot tip errors.
At a known positionOn the basis of (a), it can be deduced that:
；
in the method, in the process of the invention,representing the error of the neighboring joint transformation matrix, also denoted +.>For parameter->，/>，，/>Is the full differentiation of (a), namely:
；
in the method, in the process of the invention,for transforming matrix differential operators, it can be expressed as：
。
Order theThe method can obtain:
；
preferably, considering only the first order model, ignoring the second order derivative minutiae, one can obtain:
；
in the method, in the process of the invention,for transforming matrix->To->Is a continuous multiplication of (1), here->。
The differential errors of the connecting rods are transmitted to the terminal coordinate system and then accumulated, so that the actual errors of the terminal coordinate system, namely the overall pose errors of the robot, can be represented by a robot error kinematic model:
；
in the method, in the process of the invention,、/>the errors of the overall pose of the robot are respectively,/>and->Respectively->Is provided, and a displacement vector. Wherein (1)>Representing a first order differential translational component error of the robot tip;indicating the robot tip attitude error.
Deducing the error amount of a single joint at the end of the robot:
；
in the method, in the process of the invention,for the error coefficient matrix of the joint, +.>I.e. the kinematic error column vector.
Preferably, the reconstructing the robot body error model according to the error amount of the single joint at the tail end of the robot specifically includes:
order theThe method can obtain: />；
Wherein,is->Jacobian matrix of the coordinate system of the joint to the terminal coordinate system,>complete jacobian matrix for robot error model, < >>Is a kinematic error column vector of six joints of the robot.
Further, adding a front-back conversion matrix to obtain a calibration system model:；
the front-back conversion matrix comprises a conversion matrix from a measurement coordinate system to a robot base coordinate system and a conversion matrix from a robot tail end flange coordinate system to measurement points of a measurement device.
In the method, in the process of the invention,representing a transformation matrix from the measurement coordinate system to the robot base coordinate system, the elements contained in the transformation matrix being denoted by the subscript m, ">Can be expressed as:
；
in the method, in the process of the invention,、/>、/>respectively representing displacement components in x, y and z directions of an upward continuous coordinate system; />Representing a rotational component about the x-axis; />Representing a rotational component about the y-axis; />Representing a rotational component about the z-axis;
the transformation matrix from the flange coordinate system to the target sphere coordinate is represented, and the subscript t is used for representing the elements contained in the coordinate system, which can be represented as follows: />；
In the middle of、/>、/>Respectively representing displacement components in the x, y and z directions of the previous continuous coordinate system.
Differential error transformation is performed in the manner of deriving the robot model to obtain differential error components of the transformation matrix from the measurement coordinate system to the robot base coordinate system：
；
Based on the same principle, the differential error component of the transformation matrix from the flange coordinate system to the target spherical coordinate system can be obtained：
。
In summary, the calibration system model can be improved as follows:
；
in the method, in the process of the invention,error vector for the actual measurement point, +.>、/>Respectively represent the corresponding jacobian matrix after adding two transformation matrices,>matrix error column vector representing the transformation of the measurement coordinate system to the robot base coordinate system,/for>Error column vector representing transformation matrix from robot end flange coordinate system to measuring point, < >>Jacobian matrix for complete calibration of the system model, < >>Is all the parameters to be identified.
Due to the parallel joints 2, 3 and 4 of the robot model, the jacobian matrixCorresponds to->、/>、/>The same jacobian component can be given +.>. Thus choose to be +.>、/>Removed from the model. Analysis of the jacobian matrix shows that the measurement coordinate system +.>Parameter of->Coupled with the parameters to be identified of the joint 1, the removal parameter is thus selected +.>、/>、/>、/>、/>. Transformation matrix of joint 6 and flange coordinate system to target sphere coordinate system>Is coupled to the parameters of (2) and therefore will->、/>And (5) removing. Finally, 24 identifiable parameters of the system model are calibrated, and the error model after redundant parameters are removed is as follows:
；
in the method, in the process of the invention,error vector for the actual measurement point, +.>Jacobian matrix for calibrating system model after removing redundancy>The parameters to be identified after redundancy elimination.
S3, inputting the actual position point location coordinates detected by the measuring device and the current joint gesture of the robot into a calibration system model for primary parameter identification, and obtaining the parameter values of a transformation matrix of a measuring part in the calibration system model.
Preferably, the measurement part transformation matrix parameter values include transformation matrix initial parameters from the measurement coordinate system of the measurement device to the robot base coordinate system, and transformation matrix initial parameters from the robot end flange coordinate system to the measurement coordinate system of the measurement device.
On the one hand, the step of inputting the actual position point location coordinates detected by the measuring device and the current joint gesture of the robot into the calibration system model for preliminary parameter identification, and the step of obtaining the parameter value of the transformation matrix of the measuring part in the calibration system model specifically comprises the following steps:
inputting the actual position point position coordinates detected by the measuring device and the current joint gesture of the measured robot into a simplified calibration system model, and carrying out parameter identification by adopting an improved index optimization algorithm to obtain the parameter values of a transformation matrix of a measuring part in the simplified calibration system model;
on the other hand, the improved exponential optimization algorithm adopts a least square method to calculate and obtain the initial parameter value of a preset transformation matrix, a random solution set is generated by taking the value as the center, and meanwhile, the population iteration mode is set as the distance between an average solution and the optimal solution in the current winner solution.
In another aspect, the calibration system model is simplified by taking the minimum average distance between the measurement point of the calibration system model and the theoretical calibration coordinate point as a process target to obtain a simplified calibration system model; the initial parameter identification adopts a simplified calibration system model, so as to improve the initial calibration efficiency.
Illustratively, the objective function of the simplified calibration system model may be expressed as:
；
in the method, in the process of the invention,coordinate values obtained by measuring the laser tracker; />For the theoretical calibration coordinate value under the condition of the same joint angle of the robot, < >>For the target value, N is a positive integer, and min () is a minimization function. The simplified calibration system model is used to achieve a target value +.>Minimizing and thus improving the efficiency of subsequent computations.
Notably, when using the improved exponential optimization algorithm to perform initial parameter search, the improved exponential optimization algorithm is used for optimizing、/>、/>、/>、/>、/>、/>、/>、/>The nine parameters are used for reducing the complexity of the model, so that the calibration efficiency is improved. Meanwhile, the small-range correction process in the later iteration stage is reduced by improving an index optimization algorithm.
Preferably, the specific steps of the improved exponential optimization algorithm are as follows:
step one: the solution set generation mode in the initialization stage is modified, the difference between certain parameters and other parameters in the actual model is too large, so that the sampling space can be filled more uniformly while the population quantity can be reduced, the convergence speed of an optimization algorithm is improved, and the rough calculation is performed by independently using the least square by reducing the complexity of the modelValues and a random solution set is generated centered on the values.
Step two: using an optimization model that follows an exponential distribution, two branches are generated around the search guided solution, one guiding the winning solution to a more optimal iteration and the other guiding the unfavorable solution to the winning solution direction, specifically as follows:
；
in the method, in the process of the invention,for the next round of solution, < > the>An ith solution for a t-th iteration of the memoryless matrix;vector mean of the current optimal solution, +.>Is winning solution; />The value controls the distance between the winner and the variance,to expand the search space of the guide solution, +.>Representing the share of the current optimal solution in the next generation solution set, and iterating the next generation solution set by the combined action of the three solutions>Standard deviation representing an exponential distribution variable;
step three: modifying the iteration mode of the exploration stage, selecting a reduced exploration range for reducing the time required by iteration, and carrying outThe distance between the average solution and the optimal guiding solution of the current winner set is defined, so that the speed of guiding to the optimal solution is increased. The method comprises the following steps:
；
；
wherein,the average value of the current winning set vector is represented by t, which is a positive integer; />In order to adapt the parameters of the device,the value of the product fluctuates and decreases along with the iteration period;
；
representing the distance of the mean from both random (denoted 1, 2) in the winning solution set;
the vector may be expressed as: />。
In a preferred embodiment, to fit the objective function and real-time operation requirements, the following improvements are made to the exponential optimization algorithm:
(1) Modifying the solution set generation mode of the initialization stage: because the difference between some parameters and other parameters in the actual model is too large, in order to reduce the population quantity and fill the sampling space more uniformly, the convergence speed of the optimization algorithm is improved, and the rough calculation is performed by adopting least squareValues and a random solution set is generated centered around this value.
(2) The fully random iterative approach in the original exploration phase is improved to reduce the time required for the iteration: on the one hand by setting the original as the distance of the random value from the mean value in the winning solution setInstead, the distance between the average solution and the optimal guide solution of the current winner set is used, and the aim of reducing the time required by iteration is achieved by selectively reducing the exploration range; on the other hand do not change->The randomness in the iterative process of the original algorithm is reserved, and the possibility of the next generation solution set is reserved.
。
(3) The improved exponential optimization algorithm also introduces a cosine function to improve the self-adaptive parameters, and the improvement result is that:
，
wherein,for the number of iterations->To identify the total period. />
The method changes the mode of random decline of the original adaptive parameters, expands the searching range of the early stage, further can quickly search the optimal solution in an iterative way, and reduces the correction process of the small range of the later stage of the iteration.
And (3) carrying out overall identification on 24 parameters of the calibration system model by using an iterative weighting LM algorithm, and improving the robustness and the precision of a calibration result through residual weighting so as to meet the application requirements of the efficient robot in the manufacturing industry.
S4, performing sub-step parameter optimization by combining the theoretical parameter value of the robot and the parameter value of the transformation matrix of the measurement part to obtain a first calibration value of the kinematic parameter of the robot;
in one embodiment, the step S4 specifically includes: substituting the theoretical parameter value of the robot and the parameter value of the transformation matrix of the measurement part into a calibration system model, and optimizing by adopting an iterative weighting LM algorithm to obtain a first calibration value.
Specifically, in order to minimize the linearization error of the whole calibration system model, after the initial parameters of the calibration coordinate system are obtained, the parameters of the calibration system model are accurately identified by using an iterative weighted LM algorithm, and at this time, the objective equation is as follows:
wherein,indicate->Actual measurement and theoretical space coordinate error during iteration; />Is->Iterating the jacobian matrix; />Representing the kth time parameter;
the parameter error obtained by adopting the iteration weighting LM algorithm to carry out the kth iteration is as follows:
；
in the method, in the process of the invention,
as a matrix of weight factors,
for a preset constant->；
I is an identity matrix.
In another embodimentIn an embodiment, the weight factor matrix is:；
wherein,
the distance difference value vector is identified for the corresponding coordinate point;
expressed as: />
Is->Standard deviation of (2).
It is noted that after the initial parameter estimation value is obtained, in order to improve the robustness and the precision of the calibration result, the residual error of each group of measurement positions and theoretical position distances is weighted, different weights are given to different data points through residual error weighting, and more attention of the algorithm is focused on the data points with larger errors. The invention uses the reciprocal of the sum of the effective residuals to represent the weight factor, and uses the standard deviation of the residuals to select the basis of the weight in consideration of the fact that the whole residual in the model is small but still has fluctuation. The residual fluctuation is measured through standard deviation, so that the influence of abnormal values can be greatly reduced.
S5, when the first calibration value is within the error threshold range, taking the first calibration value as a final calibration value, otherwise, respectively correcting the theoretical parameter value of the robot and the parameter value of the transformation matrix of the measurement part through the first calibration value, and re-executing S4.
Specifically, a preliminary calibration value is obtained after the preliminary identification is completed, and parameters in the model are corrected by using the calibration value, so that a more accurate model is obtainedThe accurate calibration system model can further enable the position error of the tail end to be smaller. Repeating the above steps until the condition is satisfiedAnd when the whole calibration process is finished. Wherein (1)>Is->Measuring and theoretical space coordinate errors during iteration; />Measuring and theoretical space coordinate errors for the k+1th iteration; />And when the algorithm iteration is a preset value, the algorithm iteration is ended after the descending space of the current algorithm iteration and the next algorithm iteration is small.
After the measuring points are compensated, the displayed error curve is wholly reduced, the fluctuation is stable, and the error fluctuation amplitude is reduced; the greater the error, the more pronounced the effect of the compensation. And the degree of dispersion in the x, y and z directions is well reduced, and especially the fluctuation of errors in the y axis direction and the z axis direction is obviously reduced. Experimental data shows that after the simulation compensation of the model parameters of the robot is performed, the average value of the position errors of the robot is reduced by 80.28%, and the root mean square error is reduced by 71.61%. According to the subsequent verification data, the average value and the root mean square error of the robot position error are respectively reduced by 57.13 percent and 52.44 percent, which proves the effectiveness of the calibration identification result of the robot. The calibration effect of the invention has good robustness in combination with experimental data, and the invention has good generalization capability, is suitable for common point positions, and has wide application prospect.
The invention also discloses a system for rapidly calibrating the robot, which comprises:
the input module is used for inputting various data required by the calibration of the robot;
and the calibration module is used for carrying out quick calibration on the robot according to any one of the methods.
The system embodiments and the foregoing method embodiments may be implemented in a one-to-one correspondence, and are not described herein.
The invention can rapidly, effectively and accurately calibrate the kinematic parameters of the robot so as to remarkably improve the positioning precision and the motion control performance of the robot. The invention is mainly used for rapidly calibrating the kinematic parameters of the robot so as to improve the positioning precision and the motion control capability of the robot. The invention has wide application prospect in the fields of robot manufacturing and automation.
Based on the same thought, the invention also discloses electronic equipment, which can comprise: the device comprises a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory are in communication with each other through the communication bus. The processor may call logic instructions in the memory to perform a method for fast calibration of a robot, comprising:
s1, deriving a robot error kinematic model according to a robot kinematic model and a pose differential transformation relation;
s2, expanding the robot error kinematics model to a calibration system model;
s3, inputting the actual position point location coordinates detected by the measuring device and the current joint gesture of the robot into a calibration system model for primary parameter identification, and obtaining the parameter value of a transformation matrix of a measuring part in the calibration system model;
s4, performing sub-step parameter optimization by combining the theoretical parameter value of the robot and the parameter value of the transformation matrix of the measurement part to obtain a first calibration value of the kinematic parameter of the robot;
s5, when the first calibration value is within the error threshold range, taking the first calibration value as a final calibration value, otherwise, respectively correcting the theoretical parameter value of the robot and the parameter value of the transformation matrix of the measurement part through the first calibration value, and re-executing S4.
Further, the logic instructions in the memory described above may be implemented in the form of software functional units and stored in a computer-readable storage medium when sold or used as a stand-alone product. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
In another aspect, embodiments of the present invention further provide a computer program product, including a computer program stored on a non-transitory computer readable storage medium, the computer program including program instructions which, when executed by a computer, enable the computer to perform a method for quickly calibrating a robot provided by the above method embodiments, including:
s1, deriving a robot error kinematic model according to a robot kinematic model and a pose differential transformation relation;
s2, expanding the robot error kinematics model to a calibration system model;
s3, inputting the actual position point location coordinates detected by the measuring device and the current joint gesture of the robot into a calibration system model for primary parameter identification, and obtaining the parameter value of a transformation matrix of a measuring part in the calibration system model;
s4, performing sub-step parameter optimization by combining the theoretical parameter value of the robot and the parameter value of the transformation matrix of the measurement part to obtain a first calibration value of the kinematic parameter of the robot;
s5, when the first calibration value is within the error threshold range, taking the first calibration value as a final calibration value, otherwise, respectively correcting the theoretical parameter value of the robot and the parameter value of the transformation matrix of the measurement part through the first calibration value, and re-executing S4.
In still another aspect, an embodiment of the present invention further provides a non-transitory computer readable storage medium having stored thereon a computer program, which when executed by a processor, is implemented to perform a method for quickly calibrating a robot provided in the foregoing embodiments, including:
s1, deriving a robot error kinematic model according to a robot kinematic model and a pose differential transformation relation;
s2, expanding the robot error kinematics model to a calibration system model;
s3, inputting the actual position point location coordinates detected by the measuring device and the current joint gesture of the robot into a calibration system model for primary parameter identification, and obtaining the parameter value of a transformation matrix of a measuring part in the calibration system model;
s4, performing sub-step parameter optimization by combining the theoretical parameter value of the robot and the parameter value of the transformation matrix of the measurement part to obtain a first calibration value of the kinematic parameter of the robot;
s5, when the first calibration value is within the error threshold range, taking the first calibration value as a final calibration value, otherwise, respectively correcting the theoretical parameter value of the robot and the parameter value of the transformation matrix of the measurement part through the first calibration value, and re-executing S4.
It should be understood that, although the steps in the flowcharts of the figures are shown in order as indicated by the arrows, these steps are not necessarily performed in order as indicated by the arrows. The steps are not strictly limited in order and may be performed in other orders, unless explicitly stated herein. Moreover, at least some of the steps in the flowcharts of the figures may include a plurality of sub-steps or stages that are not necessarily performed at the same time, but may be performed at different times, the order of their execution not necessarily being sequential, but may be performed in turn or alternately with other steps or at least a portion of the other steps or stages.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
Claims (6)
1. A method for quickly calibrating a robot, comprising:
s1, deriving a robot error kinematic model according to a robot kinematic model and a pose differential transformation relation;
the S1 specifically comprises the following steps:
obtaining a robot kinematics model by using an improved DH parameter method;
performing error deduction through a robot kinematic model and a position differential transformation relation;
according to a differential transformation method, transforming a transformation matrix error generated by an error factor into a robot tail end coordinate system;
after the second-order differential minor terms are ignored, differential errors of all the connecting rods are transmitted to an end coordinate system, and the accumulated sum of all the connecting rod errors in the end coordinate system is the robot error kinematic model;
s2, expanding the robot error kinematics model to a calibration system model;
the step S2 specifically comprises the following steps: combining an error matrix from a measuring device measuring coordinate system to a robot base coordinate system, an error matrix from a robot tail end flange coordinate system to the measuring device measuring coordinate system and a robot error kinematic model to obtain a calibration system model;
s3, inputting the actual position point location coordinates detected by the measuring device and the current joint gesture of the robot into a calibration system model for primary parameter identification, and obtaining the parameter value of a transformation matrix of a measuring part in the calibration system model;
the measurement part transforms matrix parameter values to include transformation matrix initial parameters from a measurement coordinate system of a measurement device to a robot base coordinate system and transformation matrix initial parameters from a robot tail end flange coordinate system to the measurement coordinate system of the measurement device;
the step of inputting the actual position point location coordinates detected by the measuring device and the current joint gesture of the robot into the calibration system model for preliminary parameter identification, and the step of obtaining the parameter value of the transformation matrix of the measuring part in the calibration system model specifically comprises the following steps:
inputting the actual position point position coordinates detected by the measuring device and the current joint gesture of the measured robot into a simplified calibration system model, and carrying out parameter identification by adopting an improved index optimization algorithm to obtain the parameters of a transformation matrix of a measurement part in the simplified calibration system model;
s4, performing sub-step parameter optimization by combining the theoretical parameter value of the robot and the parameter value of the transformation matrix of the measurement part to obtain a first calibration value of the kinematic parameter of the robot;
s5, when the first calibration value is within the error threshold range, taking the first calibration value as a final calibration value, otherwise, respectively correcting the theoretical parameter value of the robot and the parameter value of the transformation matrix of the measurement part through the first calibration value, and re-executing S4.
2. The method for quickly calibrating a robot according to claim 1, wherein the improved exponential optimization algorithm calculates a preset transformation matrix initial parameter value by using a least square method, and generates a random solution set by taking the value as a center, and simultaneously sets a population iteration mode as a distance between an average solution and an optimal solution in a current winner solution.
3. A method for rapid calibration of a robot according to claim 1, wherein the calibration system model is simplified to obtain a simplified calibration system model with the minimum average distance between the measurement point of the calibration system model and the theoretical calibration coordinate point as the process target.
4. A method for rapid calibration of a robot according to claim 3, wherein the objective function of the simplified calibration system model is expressed as:
；
in the method, in the process of the invention,coordinate values obtained by measuring the laser tracker; />For the theoretical calibration coordinate value under the condition of the same joint angle of the robot, < >>For the target value, N is a positive integer, and min () is a minimization function.
5. The method for quickly calibrating a robot according to claim 1, wherein the step S4 specifically comprises: substituting the theoretical parameter value of the robot and the parameter value of the transformation matrix of the measurement part into a calibration system model, and optimizing by adopting an iterative weighting LM algorithm to obtain a first calibration value.
6. A system for rapid calibration of a robot, comprising:
the input module is used for inputting various data required by the calibration of the robot;
the calibration module is used for carrying out the rapid calibration of the robot according to the method of any one of claims 1-5.
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Citations (11)
| 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 |
| KR20160007791A (en) * | 2014-06-30 | 2016-01-21 | 현대중공업 주식회사 | Calibration Method of Robot for Interventional treatment |
| WO2020134426A1 (en) * | 2018-12-29 | 2020-07-02 | 南京埃斯顿机器人工程有限公司 | Plane precision calibration method for industrial robot |
| WO2020237407A1 (en) * | 2019-05-24 | 2020-12-03 | 深圳配天智能技术研究院有限公司 | Method and system for self-calibrating robot kinematic parameter, and storage device |
| CN113119130A (en) * | 2021-04-28 | 2021-07-16 | 浙江大学 | Geometric error identification method for industrial robot |
| CN113160334A (en) * | 2021-04-28 | 2021-07-23 | 北京邮电大学 | Double-robot system calibration method based on hand-eye camera |
| CN114918920A (en) * | 2022-06-01 | 2022-08-19 | 浙江大学 | Industrial robot calibration method based on neural network and distance error model |
| CN115356986A (en) * | 2022-08-22 | 2022-11-18 | 电子科技大学 | Be-SA algorithm-based industrial robot absolute positioning precision improving method |
| DE102022130318A1 (en) * | 2021-12-06 | 2023-06-07 | Fanuc Corporation | AUTONOMOUS ROBUST ASSEMBLY PLANNING |
| CN116452648A (en) * | 2023-06-15 | 2023-07-18 | 武汉科技大学 | Point cloud registration method and system based on normal vector constraint correction |
-
2023
- 2023-12-05 CN CN202311649058.4A patent/CN117349990B/en active Active
Patent Citations (11)
| 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 |
| KR20160007791A (en) * | 2014-06-30 | 2016-01-21 | 현대중공업 주식회사 | Calibration Method of Robot for Interventional treatment |
| WO2020134426A1 (en) * | 2018-12-29 | 2020-07-02 | 南京埃斯顿机器人工程有限公司 | Plane precision calibration method for industrial robot |
| WO2020237407A1 (en) * | 2019-05-24 | 2020-12-03 | 深圳配天智能技术研究院有限公司 | Method and system for self-calibrating robot kinematic parameter, and storage device |
| CN113119130A (en) * | 2021-04-28 | 2021-07-16 | 浙江大学 | Geometric error identification method for industrial robot |
| CN113160334A (en) * | 2021-04-28 | 2021-07-23 | 北京邮电大学 | Double-robot system calibration method based on hand-eye camera |
| DE102022130318A1 (en) * | 2021-12-06 | 2023-06-07 | Fanuc Corporation | AUTONOMOUS ROBUST ASSEMBLY PLANNING |
| CN114918920A (en) * | 2022-06-01 | 2022-08-19 | 浙江大学 | Industrial robot calibration method based on neural network and distance error model |
| CN115356986A (en) * | 2022-08-22 | 2022-11-18 | 电子科技大学 | Be-SA algorithm-based industrial robot absolute positioning precision improving method |
| CN116452648A (en) * | 2023-06-15 | 2023-07-18 | 武汉科技大学 | Point cloud registration method and system based on normal vector constraint correction |
Non-Patent Citations (1)
| Title |
|---|
| 《基于协方差矩阵自适应进化策略的机器人手眼标定算法》;赵云涛;《计算机应用》;3325-3329 * |
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