CN105773609A - Robot kinematics calibration method based on vision measurement and distance error model - Google Patents

Abstract

The invention discloses a robot kinematics calibration method based on visual measurement and a distance error model, comprising: establishing a corrected robot D-H model; a distance error model; establishing a robot kinematics calibration model; simultaneously calibrating hand-eye relationship and kinematic parameters ; Measuring the actual coordinate position of the end; Correcting the D-H parameters of the robot; Experimental verification. The robot kinematics calibration method based on visual measurement and distance error model provided by the present invention has the advantages of simplicity, high efficiency and quickness. The method simplifies the calibration model, which can greatly improve the positioning accuracy and distance accuracy of industrial robots. It is generally applicable to series articulated robots and has certain practical significance.

Description

A Robot Kinematics Calibration Method Based on Vision Measurement and Distance Error Model

technical field

The invention relates to the technical field of robot kinematics calibration, in particular to an industrial robot kinematics calibration method based on visual measurement and a distance error model.

Background technique

Since the world's first robot was produced, robots have played an increasingly important role in people's lives and production fields. In actual work, there is an error between the end pose of the robot obtained by the control software and the actual pose reached by the end of the robot. Generally speaking, the repetitive positioning accuracy of the robot is very high, while the absolute positioning accuracy of the robot is not too high. The reasons for the low absolute positioning accuracy of the robot include errors in production, handling, assembly, and joint transmission errors. However, in many areas of robot application, such as complex assembly, maintenance, welding, etc., due to their own characteristics, robots must be able to achieve sufficient precision. Therefore, how to overcome the influence of various factors and improve the absolute positioning accuracy of the robot as much as possible has become a key part of robot technology.

The absolute positioning accuracy is mainly affected by the accuracy of the connecting rod parameters in the robot kinematics model. Calibration technology can improve the absolute positioning accuracy of the robot by correcting the robot kinematics parameters. Therefore, it needs to be calibrated before the robot is used. At present, there are two main methods of robot kinematics calibration: kinematics loop method and axis measurement method. The kinematic loop method is a method to obtain the pose of the end of the robot through the measuring device, and obtain the joint parameters of the robot by solving the kinematic equation of the robot. Compared with the axis measurement method, the kinematic loop method has simple process, strong operability and higher precision.

In traditional calibration methods, measuring devices such as laser measuring instruments and three-coordinate measuring instruments are generally used to obtain the robot's end pose, which is expensive and complicated to operate. The use of visual measurement has the advantages of fast measurement speed and non-contact measurement. However, when the visual hand-eye calibration is performed, due to the use of the nominal value of the kinematic parameters of the robot, there is a repetition error in the calibrated pose.

Contents of the invention

Aiming at the above-mentioned problems in the prior art, the present invention proposes a robot kinematics calibration method based on visual measurement and a distance error model, which effectively improves the absolute positioning accuracy of industrial robots.

In order to achieve the above object, the technical solutions provided by the embodiments of the present invention are as follows:

A kind of robot kinematics calibration method based on visual measurement and distance error model, described method comprises the following steps:

S1, establish the corrected robot D-H model;

S2, distance error model;

S3. Establishing a robot kinematics calibration model;

S4. Simultaneous calibration of hand-eye relationship and kinematic parameters;

S5. Measurement of the actual coordinate position of the end;

S6, correcting robot D-H parameters and hand-eye relationship;

S7. Experimental verification, judging whether the accuracy requirements are met, if so, then the calibration ends, if not, re-select the position point, iterate the experimental results, and perform the calibration experiment again.

As a further improvement of the present invention, in the modified D-H kinematics model of the robot established in the step S1, the homogeneous transformation relationship matrix of the adjacent joint coordinate systems of the traditional D-H model is:

When the rotation axes of two adjacent joints are approximately parallel, it is necessary to introduce the rotation amount β on the y-axis to represent the modified D-H model, that is, the MDH model. The transformation matrix of the adjacent joint coordinate system is:

Among them, a is the length of the connecting rod, α is the rotation angle of the connecting rod, d is the offset distance of the connecting rod, θ is the joint angle, and β is the rotation angle around the y-axis.

As a further improvement of the present invention, the step S2 to establish a distance error model specifically includes: the coordinates of the measured point at the end of the robot in the basic coordinate system are P _R (i), and the coordinates in the measurement coordinate system are P _RW (i) , the distance error between any two points can be expressed as:

Δd(i+1)＝|I _R (i+1)|-|I _RW (i+1)|

Here, |I _R (i+1)| represents the distance from point _PR (i) to _PR (i+1) on the actual trajectory of the robot; |I _RW (i+1)| represents the point _PRW on the robot command trajectory (i) Distance to P _RW (i+1).

The relationship between the distance error and position error between two adjacent points can be expressed as:

d _p (i) is the position deviation vector of a certain point in the basic coordinate system, d _p (i)=P _R (i)-P _RW (i).

The homogeneous transformation matrix of adjacent connecting rod coordinate system under the influence of connecting rod geometric parameter error will become The differential perturbation homogeneous matrix is:

Then the transformation matrix of the connecting rod at the end of the robot relative to the base coordinate system is:

in,

The calculation simplification obtains the error matrix as:

The first three items in the fourth column are robot positioning error dp[d _x d _y d _z ] ^T .

As a further improvement of the present invention, the formula of the robot kinematics calibration model in the step S3 is:

Here, Δd(i+1) is the distance error, and Δq is the robot kinematics parameter error.

As a further improvement of the present invention, the simultaneous calibration of hand-eye relationship and kinematic parameters in step S4 includes:

The distance between the actual distance d _W (i+1) between the position points where the robot actually moves and the distance d′ _W ( The relational expression of i+1) is:

The relationship between the distance d _R (i+1) of the point on the command trajectory of the robot and the distance d _W (i+1) between the point where the robot actually moves is:

The simultaneous calibration formula of hand-eye relationship and kinematic parameters is:

As a further improvement of the present invention, the step S5 is specifically:

In the working space of the robot, any n points are taken, and the coordinate value of each point is recorded, that is, the command track point P _RW (i). At the same time, the external parameter matrix M of each picture is obtained by using the CCD camera, and then the hand-eye calibration matrix X is obtained. Then the pose matrix of the robot end effector coordinate system relative to the world coordinate system is A=M ^-1 *X ^-1 , and the first three elements in the fourth column of the pose matrix A are the world coordinates of the robot end effector, namely The actual trajectory point P _R (i).

In order to reduce calculation rounding errors, an equidistance calibration model is used when taking points, so that the distance between two adjacent points on the robot trajectory is equal, then the distance error calibration model is simplified as:

As a further improvement of the present invention, the step S6 is specifically:

Substituting the command trajectory coordinate value corresponding to each specified point in step S5 and the corresponding actual trajectory coordinate value of the robot end measured by the CCD camera into the simultaneous calibration formula of the robot's hand-eye relationship and kinematic parameters in step S4, the composition A system of equations, rewrite the system of equations into a matrix form, and use the basic theory of generalized inverse matrix to obtain the least squares solution, that is, the error values of the geometric parameters of the robot's connecting rods Δa _i-1 , Δα _i-1 , Δd _i , Δθ _i , Δβ _i , and hand-eye relationship parameter error. The geometric parameter errors of the connecting rods are brought into each connecting rod for correction, and the hand-eye parameter errors are brought into the hand-eye matrix for correction.

As a further improvement of the present invention, the step S7 is:

Use the corrected geometric parameters of the connecting rod and the corrected hand-eye relationship matrix to obtain the corrected distance error, conduct experimental verification, analyze and calculate the results after the experiment, and judge whether the accuracy requirements are met. If yes, the calibration is over. If not, then Re-select the position point and perform the calibration experiment again.

Description of drawings

Fig. 1 is the specific flowchart of the robot kinematics calibration method based on vision measurement and distance error model of the present invention;

Fig. 2 is the D-H kinematics model diagram of six-axis industrial robot in the specific embodiment of the present invention;

Fig. 3 is the schematic diagram of the distance error model of the robot in the specific embodiment of the present invention;

Fig. 4 is the schematic diagram of the visual measurement process of the robot in the specific embodiment of the present invention;

Fig. 5 is the schematic diagram of the equidistance model when the robot vision collects points in the specific embodiment of the present invention;

detailed description

As shown in Figure 1, it is a flow chart of the robot kinematics calibration method based on visual measurement and distance error model, and the implementation of the present invention will be further described below according to the accompanying drawings and specific examples:

S1, establish the corrected robot D-H model;

The D-H model is the most basic robot kinematics model. It is a method to describe how to model the connecting rods and joints of the robot, and is widely applicable to any robot configuration. Figure 2 shows the D-H kinematics model diagram of a 6-axis robot, which contains four geometric parameters: link length a, link rotation angle α, link offset distance d, and joint angle θ. The homogeneous transformation relationship matrix of the adjacent joint coordinate system of the traditional D-H model connecting rod i-1 and connecting rod i is shown in the following formula (1):

However, when the rotation axes of two adjacent joints are approximately parallel, there will be certain errors. The ideal absolute parallelism does not exist in practice. Even if the rotation axes of the two joints have a small deviation from absolute parallelism, their common There is a huge error between the arbitrarily taken public perpendiculars when the line is absolutely parallel to the ideal. Therefore, it is necessary to introduce the rotation amount β on the y-axis to represent it to form a modified D-H model, that is, the MDH model. The transformation matrix of the adjacent joint coordinate system is shown in the following formula (2):

Among them, a is the length of the connecting rod, α is the rotation angle of the connecting rod, d is the offset distance of the connecting rod, θ is the joint angle, and β is the rotation angle around the y-axis.

S2, distance error model;

Figure 3 is a schematic diagram of the distance error model. The coordinates of the measured point at the end of the robot in the base coordinate system are P _R (i), and the coordinates in the measurement coordinate system are P _RW (i). Formula (3) is any two Point distance error model:

Δd(i+1)＝|I _R (i+1)|-|I _RW (i+1)| (3)

Here, |I _R (i+1)| represents the distance from point _PR (i) to _PR (i+1) on the actual trajectory of the robot; |I _RW (i+1)| represents the point _PRW on the robot command trajectory (i) Distance to P _RW (i+1).

The relationship between the distance error and position error between two adjacent points is shown in the following formula (4):

d _p (i) is the position deviation vector of a certain point in the basic coordinate system, d _p (i)=P _R (i)-P _RW (i).

Due to the deviation between the actual geometric parameters of the robot joints and the theoretical parameter values during the manufacturing and installation process, the homogeneous transformation matrix of the adjacent link coordinate system will become Formula (5) is the differential perturbation homogeneous matrix of adjacent connecting rods:

here,

The transformation matrix of the connecting rod at the end of the robot relative to the base coordinate system is shown in the following formula (6):

in,

Calculate and simplify to obtain the error matrix as shown in the following formula (7):

The first three items in the fourth column are robot positioning error dp=[d _x d _y d _z ] ^T

S3. Establishing a robot kinematics calibration model;

Figure 3 is a schematic diagram of the distance error model of the robot. For any two points of the robot in the three-dimensional space, although their coordinate values in the robot base coordinate system and the measurement coordinate system are different, the two points in the robot base coordinate system The distance in is the same as the distance in the survey coordinate system. Taking advantage of this feature, a robot distance error calibration model is established, and the formula is shown in (8):

Here, Δd( _i +1) is the distance error, Δq is the robot kinematics parameter error, and Bi is the coefficient matrix, which can be solved by S2.

S4. Simultaneous calibration of hand-eye relationship and kinematic parameters;

When performing visual measurement hand-eye calibration, due to the use of the nominal value of the robot kinematics parameters, there is a repetition error in the calibrated pose. The world coordinates of the point at the moved position are not exact, and this error must be taken into account. In the actual movement, the actual distance d _W (i+1) between the two positions of the robot and the distance d′ _W between the point where the robot actually moves to is calculated using the calibrated error hand-eye relationship matrix X The relational expression of (i+1) is:

The relationship between the distance d _R (i+1) of the point on the command trajectory of the robot and the distance d _W (i+1) between the point where the robot actually moves is:

Then the simultaneous calibration formula of hand-eye relationship and kinematic parameters is shown in formula (9):

S5. Measurement of the actual coordinate position of the end;

In the working space of the robot, randomly select n points, and record the coordinate value of each point, that is, the command trajectory point P _RW (i). At the same time, the external parameter matrix M of each picture is obtained by using the CCD camera, and then the hand-eye calibration result X is obtained. Then the pose matrix of the robot end effector coordinate system relative to the world coordinate system is A=M ^-1 *X ^-1 , and the first three elements in the fourth column of the pose matrix A are the world coordinates of the robot end effector, namely The actual trajectory point P _R (i), Fig. 4 is a schematic diagram of robot vision measurement.

In order to reduce calculation rounding errors, an equidistant calibration model is used when taking points. Figure 5 is a schematic diagram of the equidistant point collection model, so that the distance between two adjacent points on the robot trajectory is equal, and the distance error calibration model can be simplified into the formula (10):

S6, correcting robot D-H parameters and hand-eye relationship;

Substitute the command trajectory coordinate value corresponding to each designated point in step S5 and the corresponding actual trajectory coordinate value of the end of the robot measured by the CCD camera into the simultaneous calibration formula of robot hand-eye relationship and kinematic parameters in step S4.

Obtain n-1 equations from n points to form an equation system;

Rewrite the equations into a matrix form, and use the basic theory of generalized inverse matrices to obtain the least squares solution, that is, the error values of the geometric parameters of each connecting rod of the robot Δa _i-1 , Δα _i-1 , Δd _i , Δθ _i , Δβ _i , And hand-eye relationship parameter error. The geometric parameter errors of the connecting rods are brought into each connecting rod for correction, and the hand-eye parameter errors are brought into the hand-eye matrix for correction.

S7. Experimental verification

Calculate the corrected distance error by using the corrected connecting rod geometric parameters and the corrected hand-eye relationship matrix, conduct experimental verification, analyze and calculate the results after the experiment, determine whether the distance error meets the requirements, and judge whether the robot meets the accuracy requirements, and if so, then The calibration is finished, if not, return to step S5, obtain another experimental data point, and perform the calibration experiment again until the accuracy requirement is met.

The above robot kinematics calibration method based on visual measurement and distance error model makes the kinematics model more accurate by constructing a modified 5-parameter D-H model. The kinematics loop method is used to construct the robot error model, which is simple, efficient and highly versatile. When obtaining the coordinates of the actual point position, the method of visual measurement is adopted, which has the advantages of fast measurement speed and non-contact measurement. The simultaneous calibration of hand-eye relationship and kinematic parameters avoids repeated errors and greatly improves the calibration accuracy.

In summary, the robot kinematics calibration method based on visual measurement and distance error model provided by the present invention has the advantages of simplicity, practicality, high efficiency, and quickness, and is generally applicable to serial joint robots, which can greatly improve the positioning accuracy and distance of industrial robots. precision.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention; for those skilled in the art, the present invention may have various modifications and changes. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims (8)

1. A robot kinematics calibration method based on visual measurement and a distance error model is characterized by comprising the following steps:

s1, establishing a corrected D-H model of the robot;

s2, a distance error model;

s3, establishing a robot kinematics calibration model;

s4, calibrating the hand-eye relationship and the kinematic parameters at the same time;

s5, measuring the actual coordinate position of the tail end;

s6, correcting the D-H parameters and the hand-eye relationship of the robot;

and S7, performing experimental verification, judging whether the precision requirement is met, if so, finishing calibration, otherwise, reselecting the position point, and performing the calibration experiment again.

2. The method according to claim 1, wherein in the step S1, in the modified D-H kinematics model of the robot, the homogeneous transformation relation matrix of the coordinate systems of the adjacent joints in the conventional D-H model is:

when the rotation axes of two adjacent joints are approximately parallel, the rotation amount beta on the y axis needs to be introduced to represent, and a modified D-H model, namely an MDH model, is formed, then the transformation matrix of the coordinate systems of the adjacent joints is:

wherein a is the length of the connecting rod, alpha is the rotating angle of the connecting rod, d is the offset distance of the connecting rod, theta is the joint angle, and beta is the rotating angle around the y axis.

3. The method according to claim 1, wherein the step S2 of establishing the distance error model specifically includes: the coordinate of the measured point at the tail end of the robot in the basic coordinate system is P_R(i) The coordinate in the measuring coordinate system is P_RW(i) The distance error between any two points can be expressed as:

Δd(i+1)＝|I_R(i+1)|-|I_RW(i+1)|

here, | I_R(i +1) | represents a point P on the actual trajectory of the robot_R(i) To P_R(i + 1). I_RW(i +1) | represents a point P on the robot instruction track_RW(i) To P_RW(i + 1).

The relationship between the distance error and the position error between two adjacent points can be expressed as:

wherein d is_p(i) For a positional deviation vector of a point in the base coordinate system, d_p(i)＝P_R(i)-P_RW(i)。

Homogeneous transformation matrix of adjacent connecting rod coordinate systems under influence of geometric parameter errors of connecting rodsWill become intoThe differential perturbation homogeneous matrix is:

the transformation matrix of the robot end link with respect to the base coordinate system is:

dT₀ ⁱ＝T₀ ¹Δ₁T₁ ⁱ+T₀ ²Δ₂T₂ ⁱ+T₀ ³Δ₃T₃ ⁱ+T₀ ⁴Δ₄T₄ ⁱ+T₀ ⁵Δ₅T₅ ⁱ+...+T₀ ⁱΔ_i

here, ,

the error matrix obtained by calculation simplification is:

wherein the first three terms in the fourth column are robot positioning errors dp ═ d_xd_yd_z]^T。

4. The method according to claim 3, wherein the formula of the robot kinematics calibration model in the step S3 is as follows:

here, Δ d (i +1) is a distance error, and Δ q is a robot kinematic parameter error.

5. The method according to claim 4, wherein the calibrating the hand-eye relationship and the kinematic parameters in step S4 simultaneously comprises: actual distance d between the points to which the robot actually moves_W(i +1) and a distance d 'from a point at which the robot actually moves, which is calculated using the calibrated error hand-eye relationship matrix X'_W(i +1) is represented by the following relationship:

distance d of points on robot command track_R(i +1) distance d from the point of the position to which the robot actually moves_WThe relationship between (i +1) is:

the simultaneous calibration formula of the hand-eye relationship and the kinematic parameters is as follows:

6. the method according to claim 5, wherein the step S5 is specifically: in the working space of the robot, selecting n points, recording the coordinate value of each point, namely the command trackLocus P_RW(i) In that respect And simultaneously, solving an external parameter matrix M of each picture by using a CCD camera, and then solving a hand-eye calibration result X. The pose matrix of the robot end effector coordinate system relative to the world coordinate system is a ═ M^-1*X^-1The first three elements in the fourth column of the pose matrix A are the world coordinates of the robot end effector, namely the actual track point P_R(i)。

In order to reduce the calculation rounding error, an equidistant calibration model is adopted during point taking, so that the distances between two adjacent points on the motion trail of the robot are equal, and the distance error calibration model can be simplified as follows:

7. the method according to claim 6, wherein the step S6 is specifically: substituting the instruction track coordinate value corresponding to each designated point in the step S5 and the actual track coordinate value of the robot tail end obtained by the measurement of the CCD camera corresponding to the instruction track coordinate value in the step S4 into the robot eye relation and kinematic parameter simultaneous calibration formula in the step S4 to form an equation set, rewriting the equation set into a matrix form, and solving a least square solution by adopting the basic theory of a generalized inverse matrix, namely solving the least square solution, namely the error value delta a of the geometric parameter of each connecting rod of the robot_i-1，Δα_i-1，Δd_i，Δθ_i，Δβ_iAnd hand-eye relationship parameter errors. And the geometric parameter errors of the connecting rods are brought into each connecting rod for correction, and the hand-eye parameter errors are brought into the hand-eye matrix for correction.

8. The method according to claim 7, wherein the step S7 is: and (3) solving the corrected distance error by using the corrected geometric parameters of the connecting rod and the corrected hand-eye relation matrix, carrying out experimental verification, analyzing and calculating the result after the experiment, judging whether the precision requirement is met, if so, finishing the calibration, otherwise, reselecting the position point, and carrying out the calibration experiment again.