CN114523474B - Distance-limited industrial robot kinematic parameter estimation method - Google Patents
Distance-limited industrial robot kinematic parameter estimation method Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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Abstract
The invention discloses a kinematic parameter estimation method of an industrial robot, which comprises the following steps: 1. and (3) establishing a kinematic parameter estimation distance error model by combining the robot kinematic model, the tool coordinate system and the end pose relation of the robot, and 4, eliminating redundant parameters in the error model and optimizing the kinematic parameters of the industrial robot by using a Dog-Leg algorithm. According to the invention, through the consistency of the distances between two points in different coordinate systems, the pose relation from the coordinate system of the calibration measuring device to the base coordinate system of the robot is avoided, and the precision of the measuring system can be improved, so that the kinematic parameters of the industrial robot can be accurately estimated.
Description
Technical Field
The invention relates to the field of estimation of kinematic parameters of industrial robots, in particular to an estimation method of kinematic parameters of industrial robots based on relative distance limitation.
Background
The precision is one of important indexes for evaluating the performance of the industrial robot, and experimental researches show that among factors affecting the overall precision of the robot, the error caused by the deviation of the kinematic parameters accounts for about 65% -95% of the total error. The current method for improving the precision of the robot mainly comprises the steps of identifying actual kinematic parameters through a calibration method, and compensating and correcting theoretical parameters, so that the error of the robot is reduced.
When calibrating a robot using a commonly used three-dimensional measuring device, it is necessary to first know the coordinate transformation between the measurement coordinate system and the robot base coordinate system. However, in the process of establishing a robot base coordinate system, two axes obtained by rotation hardly meet the condition of being perpendicular to each other, the established coordinate system needs to be orthogonalized, so that coordinate transformation is difficult to accurately measure, and finally the accuracy of the whole measurement system is reduced.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an industrial robot kinematic parameter estimation method which can accurately compensate the kinematic parameter errors of an industrial robot so as to improve the kinematic accuracy of the industrial robot.
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
the invention relates to a kinematic parameter estimation method of an industrial robot, which is applied to the calibration process of the industrial robot, and a position measuring device is loaded at the tail end of the industrial robot; the method is characterized in that the method for estimating the kinematic parameters is carried out according to the following steps:
step 1, establishing an industrial robot base coordinate system O in a measurement range of the position measurement device B Robot end coordinate system O S Tool coordinate system O t And the measuring device coordinate system is set as the world coordinate system O W ；
Step 2, establishing a kinematic parameter model of the industrial robot;
step 2.1, establishing a joint coordinate system for each axis of the n-degree-of-freedom industrial robot output by the j-axis driving device, and establishing a pose relation T between the adjacent ith and (i+1) th joint coordinate systems through standard D-H parameters i ；i∈[1,j-1]；
Step 2.2, from the pose relationship T i Obtaining a robot end coordinate system O S Relative to the robot base coordinate system O B Pose relationship of (2) B T S ；
Step 3, tool coordinate System O t Is calibrated;
step 3.1, according to the pose relation among all joints of the industrial robot and the robot tail end coordinate system O S By single axis rotation to obtain robot end coordinate system O S Origin position of (2) and robot end coordinate system O S Is arranged in the Z-axis direction;
step 3.2, optimizing the objective function by using a least square method by taking the minimum distance between two points obtained by rotating the end effector of the industrial robot at different angles and the distance error between the two points obtained by the measuring device as the objective function, thereby obtaining a tool coordinate system O t With robot end coordinate system O S The pose relationship of (2) is recorded as S T t ；
Step 4, establishing a kinematic parameter estimation distance error model of the industrial robot;
step 4.1, passing through the robot terminal coordinate system O S Relative to the robot base coordinate system O B Pose relationship of (2) B T S And tool coordinate system O t Relative to the robot end coordinate system O S Pose relationship of (2) S T t Obtaining a tool coordinate system O by using the formula (1) t Relative to the robot base coordinate system O B Pose relationship of (2) B T t ：
In the formula (1), R 3×3 For the tool coordinate system O t Relative robot base coordinate system O B Is a rotation matrix of (a); p is p x ,p y ,p z Respectively represent the tool coordinate system O t Relative robot base coordinate system O B Translation vectors in the X, Y and Z axes;
step 4.2, when only the pose relationship is considered B T t Position vector p= (p) x ,p y ,p z ) T The reduced formula of formula (1) is obtained by using formula (2):
p＝g(θ,η′) (2)
in the formula (2), θ represents the rotation angle of each axis of the industrial robot, namely an input variable, and η' is a kinematic parameter to be estimated, namely a constant to be estimated; g represents a function of the position vector p obtained by θ and η';
relative to the robot base coordinate system O B Tool coordinate system O t The position vector of the nth position in the motion trail of the industrial robot is P n ＝(p x,n ,p y,n ,p z,n ) T ＝g(θ n ,η′)；θ n Each axis rotation angle indicating the nth position of the industrial robot;
relative to the measuring device coordinate system O W Tool coordinate system O t The n-th position in the measuring device is P' n ＝(p′ x,n ,p′ y,n ,p′ z,n ) T ；
Constructing a relative distance error function f of the nth configuration using (3) n (θ n ,η′)：
f n (θ n ,η′)＝||P n -P n-1 ||| 2 -||P′ n -P′ n-1 || 2 ＝||g(θ n ,η′)-g(θ n-1 ,η′)|| 2 -||P′ n -P′ n-1 || 2 (3)
In the formula (3), P n-1 Representation relative to a robot base coordinate system O B Tool coordinate system O t Position vector of n-1 th position in motion track of industrial robot, P' n-1 Representing the coordinate system O relative to the measuring device W Tool coordinate system O t Position of n-1 th bit in measuring device, θ n-1 Each axis rotation angle representing the n-1 th position of the industrial robot;
step 4.3, according to the relative distance error function f n (θ n Construction of an error function e (η')= [ f ] 1 (θ 1 ,η′),f 2 (θ 2 ,η′),…,f n (θ n ,η′),…,f m (θ m ,η′)] T M represents the number of sets of measurement data, so that a least squares objective function E (η') is constructed using equation (4):
step 5, removing redundant parameters which have no influence on the least square objective function E (eta ') in the estimated kinematic parameter eta' to obtain an effective estimated parameter eta;
step 6, estimating kinematic parameters of the industrial robot by utilizing a Dog-Leg algorithm;
defining k to represent the number of iterations, and letting k=0; defining the maximum iteration number as kmax;
initializing the confidence region radius of the kth iteration to be delta k Taking the robot theory D-H parameter as an effective estimation parameter eta of the kth iteration k Setting three control errors as e 1 ,e 2 ,e 3 ；
Step 6.1, calculating the relative distance error function f of the nth bit shape of the kth iteration n (θ n ,η k ) Corresponding jacobian matrix J n For m sets of data, by J n Constructing the kth iterationObjective function E (eta) k ) Jacobian matrix J (eta) k )＝[J 1 J 2 … J n … J m ] T Thereby constructing the descending direction of the kth iteration Gauss-Newton method
And descent direction of steepest descent method +.>
Step 6.2 if
Go to step 6.7, otherwise according to η k Solving the error function e (eta) of the kth iteration k ) If ||e (eta) k )|| 2 ≤e 3 Or the confidence region radius delta for the kth iteration k ≤e 2 (||η k ||+e 2 ) Turning to step 6.7, otherwise executing step 6.3;
step 6.3 when using
For the objective function E (eta k ) When the descent direction of the (1) is the descent direction of the steepest descent method, calculating the step length lambda of the kth iteration moving along the descent direction of the steepest descent method k And a proportional parameter beta k Thereby calculating the descending direction +.f of the Dog-Leg algorithm using equation (5)>
If it is
Go to step 6.7, otherwise go to step 6.4;
step 6.4, letting new kinematic parameters
Calculating the gain ratio ρ, if ρ>0, updating the effective estimated parameter eta of the k+1st iteration k+1 ＝η new The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, updating the effective estimated parameter eta of the k+1st iteration k+1 ＝η k ；
Step 6.5, updating the confidence region radius Δ of the kth iteration using (6) k Thereby obtaining the reliability region radius delta of the k+1st iteration k+1 ：
In the formula (6), σ represents a set threshold value;
step 6.6, after k+1 is assigned to k, judging whether k < kmax is satisfied, if so, turning to step 6.1, otherwise, executing step 6.7;
step 6.7, outputting the effective estimated parameter eta of the kth iteration k I.e. the required D-H parameter estimate.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention provides an accurate estimation algorithm for calibrating a robot by estimating the kinematic parameters of the robot by utilizing the Dog-Leg algorithm and by the consistency of the distances between two points in different coordinate systems; the pose relation from the coordinate system of the calibration measuring device to the robot base coordinate system is avoided, and the precision of the measuring system is improved, so that the kinematic parameters of the industrial robot are accurately estimated.
2. According to the method, the parameters used in the objective function are analyzed, the calibration of redundant parameters and unnecessary parameters is removed, and the efficiency and the robustness of an estimation algorithm are improved;
3. the method comprises the steps of independently calibrating position parameters of a tool coordinate system by using a single-axis rotation method, and removing coupling interference of the position parameters of the tool coordinate system relative to the tail end of the robot on the identification of geometrical parameters of the robot; thereby ensuring that the estimated kinematic parameters are the optimal values of the kinematic parameters of the industrial robot, but not the optimal values of a tool coordinate system and an industrial robot combined system;
4. according to the invention, mathematical modeling is performed by utilizing the robot kinematics parameters, so that the whole working space of the robot is obtained, and a proper measuring position is selected in the working space, so that the calibrated robot kinematics parameters are ensured to be applicable to all working points, the problem of excessive optimization is avoided, and the feasibility and the effectiveness of calibrating the robot by using the Dog-Leg algorithm are ensured.
Detailed Description
In the embodiment, the kinematic parameter estimation of the industrial robot based on the relative distance limitation is applied to the calibration process of the industrial robot, and a position measuring device is carried on an end effector of the industrial robot; the kinematic parameter estimation system is composed of an industrial robot kinematic parameter error identification model, a position measuring device tool coordinate system calibration module and a robot kinematic parameter error compensation module;
the method comprises the steps that an industrial robot has kinematic parameter errors due to assembly, manufacturing and other problems, and a robot kinematic parameter error model is built according to theoretical kinematic parameters of the industrial robot and a kinematic model of the robot; and obtaining a parameter error estimation model according to the relation between the kinematic parameter error model and the pose of the tool coordinate system and the robot end effector, and carrying out parameter error compensation by using the parameter error estimation model.
The position measuring device tool coordinate system is carried on an end effector of an industrial robot, a laser tracker can be used as the position measuring device for the industrial robot, the coordinate system of the laser tracker is a world coordinate system, a target ball of the laser tracker is fixed at the tail end of the robot, the geometric center point of the target ball is used as the origin of the tool coordinate system, the position relation between the tool coordinate system and the end effector coordinate system of the robot can be calibrated by using a single-axis rotation method, and the relative distance relation between two points in the motion track of the robot in the robot base coordinate system and the world coordinate system can be measured according to the target ball.
The industrial robot kinematic parameter error compensation module is based on an industrial robot parameter error identification model and a position measuring device tool coordinate system calibration module, and utilizes a nonlinear optimization algorithm to compensate kinematic error parameters.
In this embodiment, a kinematic parameter estimation method of an industrial robot may measure a motion distance error of an end effector by using a position measurement device; the kinematic parameter error can be compensated in the estimation process, so that the kinematic accuracy of the industrial robot is improved; specifically, the method for estimating the kinematic parameters of the industrial robot is carried out according to the following steps:
step 1, in the measuring range of a position measuring device, wherein the position measuring device can use a laser tracker, a three-coordinate measuring machine and the like, the accuracy of the position measuring device is generally required to be higher than that of a robot; in a kinematic parameter estimation system, an industrial robot base coordinate system O is established B Robot end coordinate system O S For a general industrial robot, a robot base coordinate system O B The origin position of the X-axis is defined at the intersection point of the horizontal plane where the J2 axis is positioned and the J1 axis, the X-axis is forward in the Z-axis direction, and the Y-axis is determined according to the right-hand rule; for a general industrial robot, robot tip coordinate system O S The origin of the (2) is the origin of the J6 axis of the industrial robot, and the X axis and the Z axis of the J6 axis are rotated 180 degrees according to the Y axis of the J6 axis to obtain a robot terminal coordinate system O S The X-axis and Z-axis directions of the robot end coordinate system O S The Y-axis direction of the Y-axis is the same as the Y-axis direction of the J6-axis; establishing a tool coordinate system O t Tool coordinate system O t The origin of (a) is the geometric center point of the measuring device, X, Y and the direction of the Z axis and the end coordinate system O of the robot S Is the same in direction; and the measuring device coordinate system is set as the world coordinate system O W ；
Step 2, establishing a kinematic parameter model of the industrial robot;
step 2.1, for the industrial robot with n degrees of freedom output by the j-axis driving device, establishing a joint coordinate system for each axis of the industrial robot, and establishing a pose relation T between the adjacent ith and (i+1) th joint coordinate systems through standard D-H parameters i ；i∈[1,j-1]；
Step 2.2, from the pose relationship T i Obtaining a robot end coordinate system O S Relative to a robot-based coordinate systemO B Pose relationship of (2) B T S ；
Step 3, tool coordinate System O t Is calibrated;
step 3.1, according to the pose relation among all joints of the industrial robot and the robot tail end coordinate system O S By rotating only one axis of the industrial robot, a set of points can be obtained, which lie in the same plane, and the plane equation in which the points lie is obtained using a least squares fit; then using the constraint condition that the points are equal to the axis distance to obtain a fitting circle, wherein the center position of the fitting circle is the space position of the axis, and the rotation axis can be obtained by adding the direction vector of the plane equation to the position of the axis, thereby obtaining the robot terminal coordinate system O S Is the Z axis of (2); along the robot end coordinate system O through the intersection of two axes of rotation S Is moved by a certain distance in the Z-axis direction to obtain a robot terminal coordinate system O S Origin position of (2);
step 3.2, using the minimum distance error between two points obtained by rotating the end effector of the industrial robot at different angles and the distance error between the two same points obtained by the measuring device as an objective function, and optimizing the objective function by using a least square method to obtain a tool coordinate system O t With robot end coordinate system O S The pose relationship of (2) is recorded as S T t ；
Step 4, establishing a kinematic parameter estimation distance error model of the industrial robot;
step 4.1, passing through the robot terminal coordinate system O S Relative to the robot base coordinate system O B Pose relationship of (2) B T S And tool coordinate system O t Relative to the robot end coordinate system O S Pose relationship of (2) S T t Obtaining a tool coordinate system O by using the formula (1) t Relative to the robot base coordinate system O B Pose relationship of (2) B T t ：
In the formula (1), R 3×3 ＝(n x ,n y ,n z ) T ,(o x ,o y ,o z ) T ,(a x ,a y ,a z ) T For the tool coordinate system O t Relative robot base coordinate system O B Is a rotation matrix of (a); p is p x ,p y ,p z Respectively represent the tool coordinate system O t Relative robot base coordinate system O B Translation vectors in the X, Y and Z axes;
step 4.2, when only the pose relationship is considered B T t Position vector p= (p) x ,p y ,p z ) T The reduced formula of formula (1) is obtained by using formula (2):
p＝g(θ,η′) (2)
in the formula (2), θ represents the rotation angle of each axis of the industrial robot, namely an input variable, and η' is a kinematic parameter to be estimated, namely a constant to be estimated; g represents a function of the position vector p obtained by θ and η';
relative to the robot base coordinate system O B Tool coordinate system O t The position vector of the nth position in the motion trail of the industrial robot is P n ＝(p x,n ,p y,n ,p z,n ) T ＝g(θ n ,η′)；θ n Each axis rotation angle indicating the nth position of the industrial robot;
relative to the measuring device coordinate system O W Tool coordinate system O t The n-th position in the measuring device is P' n ＝(p′ x,n ,p′ y,n ,p′ z,n ) T ；
Constructing a relative distance error function f of the nth configuration using (3) n (θ n ,η′)：
f n (θ n ,η′)＝||P n -P n-1 ||| 2 -||P′ n -P′ n-1 || 2 ＝||g(θ n ,η′)-g(θ n-1 ,η′)|| 2 -||P′ n -P′ n-1 || 2 (3)
In the formula (3), P n-1 Representation relative to robot baseStandard series O B Tool coordinate system O t Position vector of n-1 th position in motion track of industrial robot, P' n-1 Representing the coordinate system O relative to the measuring device W Tool coordinate system O t Position of n-1 th bit in measuring device, θ n-1 Each axis rotation angle representing the n-1 th position of the industrial robot;
step 4.3, according to the relative distance error function f n (θ n Construction of an error function e (η')= [ f ] 1 (θ 1 ,η′),f 2 (θ 2 ,η′),…,f n (θ n ,η′),…,f m (θ m ,η′)] T M represents the number of sets of co-measured data, thereby constructing a least squares objective function E (η') using equation (4):
step 5, removing redundant parameters which have no influence on the least square objective function E (eta ') in the estimated kinematic parameter eta' to obtain an effective estimated parameter eta;
step 6, estimating kinematic parameters of the industrial robot by utilizing a Dog-Leg algorithm;
defining k to represent the number of iterations, and letting k=0; defining the maximum iteration number as kmax;
initializing the confidence region radius of the kth iteration to be delta k Taking the robot theory D-H parameter as an effective estimation parameter eta of the kth iteration k Setting three control errors as e 1 ,e 2 ,e 3 ；
Step 6.1, calculating the relative distance error function f of the nth bit shape of the kth iteration n (θ n ,η k ) Corresponding jacobian matrix J n For m sets of data, by J n Constructing an objective function E (eta) of the kth iteration k ) Jacobian matrix J (eta) k )＝[J 1 J 2 … J n … J m ] T Thereby constructing the descending direction of the kth iteration Gauss-Newton method
And descent direction of steepest descent method +.>
Step 6.2 if
Go to step 6.7, otherwise according to η k Solving the error function e (eta) of the kth iteration k ) If ||e (eta) k )|| 2 ≤e 3 Or the confidence region radius delta for the kth iteration k ≤e 2 (||η k ||+e 2 ) Turning to step 6.7, otherwise executing step 6.3;
step 6.3 when using
For the objective function E (eta k ) When the descent direction of the (1) is the descent direction of the steepest descent method, calculating the step length lambda of the kth iteration moving along the descent direction of the steepest descent method k And a proportional parameter beta k For the proportional parameter beta k It needs to meet->
Calculating the descent direction of the Dog-Leg algorithm using (5)
If it is
Go to step 6.7, otherwise go to step 6.4;
step 6.4, letting new kinematic parameters
Calculating the gain ratio ρ, if ρ>0, updating the effective estimated parameter eta of the k+1st iteration k+1 ＝η new The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, updating the effective estimated parameter eta of the k+1st iteration k+1 ＝η k ；
Step 6.5, updating the confidence region radius Δ of the kth iteration using (6) k Thereby obtaining the reliability region radius delta of the k+1st iteration k+1 ：
In the formula (6), σ represents a set threshold value;
step 6.6, after k+1 is assigned to k, judging whether k < kmax is satisfied, if so, turning to step 6.1, otherwise turning to step 6.7;
step 6.7, outputting the effective estimated parameter eta of the kth iteration k I.e. the required D-H parameter estimate.
Claims (1)
1. The kinematic parameter estimation method of the industrial robot is applied to the calibration process of the industrial robot, and a position measuring device is loaded at the tail end of the industrial robot; the method is characterized by comprising the following steps of:
step 1, establishing an industrial robot base coordinate system O in a measurement range of the position measurement device B Robot end coordinate system O S Tool coordinate system O t And the measuring device coordinate system is set as the world coordinate system O W ；
Step 2, establishing a kinematic parameter model of the industrial robot;
step 2.1, establishing a joint coordinate system for each axis of the n-degree-of-freedom industrial robot output by the j-axis driving device, and establishing a pose relation T between the adjacent ith and (i+1) th joint coordinate systems through standard D-H parameters i ；i∈[1,j-1]；
Step 2.2, from the pose relationship T i Obtaining a robot end coordinate system O S Relative to the robot base coordinate system O B Pose relationship of (2) B T S ；
Step 3, tool coordinate System O t Is calibrated;
step 3.1, according to the pose relation among all joints of the industrial robot and the robot tail end coordinate system O S By single axis rotation to obtain robot end coordinate system O S Origin position of (2) and robot end coordinate system O S Is arranged in the Z-axis direction;
step 3.2, optimizing the objective function by using a least square method by taking the minimum distance between two points obtained by rotating the end effector of the industrial robot at different angles and the distance error between the two points obtained by the measuring device as the objective function, thereby obtaining a tool coordinate system O t With robot end coordinate system O S The pose relationship of (2) is recorded as S T t ；
Step 4, establishing a kinematic parameter estimation distance error model of the industrial robot;
step 4.1, passing through the robot terminal coordinate system O S Relative to the robot base coordinate system O B Pose relationship of (2) B T S And tool coordinate system O t Relative to the robot end coordinate system O S Pose relationship of (2) S T t Obtaining a tool coordinate system O by using the formula (1) t Relative to the robot base coordinate system O B Pose relationship of (2) B T t ：
In the formula (1), R 3×3 For the tool coordinate system O t Relative robot base coordinate system O B Is a rotation matrix of (a); p is p x ,p y ,p z Respectively represent the tool coordinate system O t Relative robot base coordinate system O B Translation vectors in the X, Y and Z axes;
step 4.2, when only the pose is consideredRelationship of B T t Position vector p= (p) x ,p y ,p z ) T The reduced formula of formula (1) is obtained by using formula (2):
p＝g(θ,η′) (2)
in the formula (2), θ represents the rotation angle of each axis of the industrial robot, namely an input variable, and η' is a kinematic parameter to be estimated, namely a constant to be estimated; g represents a function of the position vector p obtained by θ and η';
relative to the robot base coordinate system O B Tool coordinate system O t The position vector of the nth position in the motion trail of the industrial robot is P n ＝(p x,n ,p y,n ,p z,n ) T ＝g(θ n ,η′)；θ n Each axis rotation angle indicating the nth position of the industrial robot;
relative to the measuring device coordinate system O W Tool coordinate system O t The n-th position in the measuring device is P n ′＝(p′ x,n ,p′ y,n ,p z ′ ,n ) T ；
Constructing a relative distance error function f of the nth configuration using (3) n (θ n ,η′)：
f n (θ n ,η′)＝||P n -P n-1 ||| 2 -||P n ′-P n ′ -1 || 2 ＝||g(θ n ,η′)-g(θ n-1 ,η′)|| 2 -||P n ′-P n ′ -1 || 2 (3)
In the formula (3), P n-1 Representation relative to a robot base coordinate system O B Tool coordinate system O t Position vector of n-1 th position in motion trail of industrial robot, P n ′ -1 Representing the coordinate system O relative to the measuring device W Tool coordinate system O t Position of n-1 th bit in measuring device, θ n-1 Each axis rotation angle representing the n-1 th position of the industrial robot;
step 4.3, according to the relative distance error function f n (θ n Error of eta') structureDifference function e (η')= [ f 1 (θ 1 ,η′),f 2 (θ 2 ,η′),…,f n (θ n ,η′),…,f m (θ m ,η′)] T M represents the number of sets of measurement data, so that a least squares objective function E (η') is constructed using equation (4):
step 5, removing redundant parameters which have no influence on the least square objective function E (eta ') in the estimated kinematic parameter eta' to obtain an effective estimated parameter eta;
step 6, estimating kinematic parameters of the industrial robot by utilizing a Dog-Leg algorithm;
defining k to represent the number of iterations, and letting k=0; defining the maximum iteration number as kmax;
initializing the confidence region radius of the kth iteration to be delta k Taking the robot theory D-H parameter as an effective estimation parameter eta of the kth iteration k Setting three control errors as e 1 ,e 2 ,e 3 ；
Step 6.1, calculating the relative distance error function f of the nth bit shape of the kth iteration n (θ n ,η k ) Corresponding jacobian matrix J n For m sets of data, by J n Constructing an objective function E (eta) of the kth iteration k ) Jacobian matrix J (eta) k )＝[J 1 J 2 …J n …J m ] T Thereby constructing the descending direction of the kth iteration Gauss-Newton method
And descent direction of steepest descent method +.>
Step 6.2 if
Go to step 6.7, otherwise according to η k Solving the error function e (eta) of the kth iteration k ) If ||e (eta) k )|| 2 ≤e 3 Or the confidence region radius delta for the kth iteration k ≤e 2 (||η k ||+e 2 ) Turning to step 6.7, otherwise executing step 6.3;
step 6.3 when using
For the objective function E (eta k ) When the descent direction of the (1) is the descent direction of the steepest descent method, calculating the step length lambda of the kth iteration moving along the descent direction of the steepest descent method k And a proportional parameter beta k Thereby calculating the descending direction +.f of the Dog-Leg algorithm using equation (5)>
If it is
Go to step 6.7, otherwise go to step 6.4;
step 6.4, letting new kinematic parameters
Calculating gain ratio ρ, if ρ > 0, updating effective estimation parameter η of the (k+1) th iteration k+1 ＝η new The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, updating the effective estimated parameter eta of the k+1st iteration k+1 ＝η k ；
Step 6.5, updating the confidence region radius Δ of the kth iteration using (6) k Thereby obtaining the reliability region radius delta of the k+1st iteration k+1 ：
In the formula (6), σ represents a set threshold value;
step 6.6, after k+1 is assigned to k, judging whether k is smaller than kmax, if yes, turning to step 6.1, otherwise, executing step 6.7;
step 6.7, outputting the effective estimated parameter eta of the kth iteration k I.e. the required D-H parameter estimate.
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| CN109465829A (en) * | 2018-12-12 | 2019-03-15 | 南京工程学院 | A kind of industrial robot geometric parameter discrimination method based on transition matrix error model |
| CN110160554A (en) * | 2019-04-30 | 2019-08-23 | 东南大学 | A kind of single-shaft-rotation Strapdown Inertial Navigation System scaling method based on optimizing method |
| 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 |
| CN112318498A (en) * | 2020-09-23 | 2021-02-05 | 天津大学 | Industrial robot calibration method considering parameter coupling |
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| CN109465829A (en) * | 2018-12-12 | 2019-03-15 | 南京工程学院 | A kind of industrial robot geometric parameter discrimination method based on transition matrix error model |
| 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 |
| CN110160554A (en) * | 2019-04-30 | 2019-08-23 | 东南大学 | A kind of single-shaft-rotation Strapdown Inertial Navigation System scaling method based on optimizing method |
| CN112318498A (en) * | 2020-09-23 | 2021-02-05 | 天津大学 | Industrial robot calibration method considering parameter coupling |
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