CN105773609A - Robot kinematics calibration method based on vision measurement and distance error model - Google Patents
Robot kinematics calibration method based on vision measurement and distance error model Download PDFInfo
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Abstract
The invention discloses a robot kinematics calibration method based on visual measurement and a distance error model, which comprises the following steps: establishing a corrected D-H model of the robot; a distance error model; establishing a robot kinematics calibration model; calibrating the hand-eye relationship and the kinematic parameters at the same time; measuring the actual coordinate position of the tail end; correcting the D-H parameters of the robot; and (5) experimental verification. The robot kinematics calibration method based on the vision measurement and distance error model has the advantages of simplicity, high efficiency and quickness, adopts a non-contact measurement mode of vision detection, simultaneously considers the repeated error of hand-eye calibration, simplifies the calibration model by utilizing an equidistant model mode, can greatly improve the positioning accuracy and distance accuracy of the industrial robot, is generally suitable for the serial joint type robot, and has certain practical significance.
Description
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
Since the first robot in the world has been generated, robots play an increasingly important role in the fields of human life and production. In actual work, an error exists between the terminal pose of the robot obtained through the control software and the actual pose reached by the terminal of the robot. Generally, the precision of the repeated positioning of the robot is high, while the precision of the absolute positioning of the robot is not too high. The reasons for the low absolute positioning accuracy of the robot include errors in production, transportation and assembly, joint transmission errors and the like. However, in many fields of application of robots, such as complex assembly, maintenance, welding, etc., due to their own characteristics, it is required that the robot must be able to achieve sufficient accuracy. Therefore, how to overcome the influence of various factors and improve the absolute positioning accuracy of the robot as much as possible becomes a key part in the robot technology.
The absolute positioning precision is mainly influenced by the precision of the parameters of the connecting rod in the robot kinematic model, and the calibration technology can improve the absolute positioning precision of the robot by correcting the kinematic parameters of the robot. Therefore, the robot needs to be calibrated before it is used. At present, the robot kinematics calibration method mainly comprises two methods: kinematic loop methods and axis measurements. The kinematics loop method is a method for obtaining the pose of the tail end of the robot through a measuring device and obtaining the joint parameters of the robot through solving a kinematics equation of the robot. Compared with an axis measurement method, the kinematic loop method is simple in process, strong in operability and higher in precision.
In the traditional calibration method, measuring devices such as a laser measuring instrument, a three-coordinate measuring instrument and the like are generally used when the terminal pose of the robot is obtained, so that the cost is high, and the operation is complex. The visual measurement has the advantages of high measurement speed, non-contact measurement and the like. However, when the vision hand-eye calibration is performed, since the nominal value of the kinematic parameter of the robot is used, the calibrated pose has repeated errors.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a robot kinematics calibration method based on visual measurement and a distance error model, and the absolute positioning accuracy of an industrial robot is effectively improved.
In order to achieve the above purpose, the technical solutions provided by the embodiments of the present invention are as follows:
a robot kinematics calibration method based on visual measurement and a distance error model comprises 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, iterating the experimental result, and performing the calibration experiment again.
As a further improvement of the present invention, in the step S1, in the step of establishing the modified robot D-H kinematic model, 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, 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.
As a further improvement of the present invention, 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 PR(i) The coordinate in the measuring coordinate system is PRW(i) The distance error between any two points can be expressed as:
Δd(i+1)＝|IR(i+1)|-|IRW(i+1)|
here, | IR(i +1) | represents a point P on the actual trajectory of the robotR(i) To PR(ii) a distance of (i + 1); iRW(i +1) | represents a point P on the robot instruction trackRW(i) To PRW(i + 1).
The relationship between the distance error and the position error between two adjacent points can be expressed as:
dp(i) for a positional deviation vector of a point in the base coordinate system, dp(i)＝PR(i)-PRW(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:
wherein,
the error matrix obtained by calculation simplification is:
wherein the first three terms of the fourth column are robot positioning errors dp [ d ]xdydz]T。
As a further improvement of the present invention, the formula of the robot kinematics calibration model in step S3 is:
here, Δ d (i +1) is a distance error, and Δ q is a robot kinematic parameter error.
As a further improvement of the present invention, the calibrating the hand-eye relationship and the kinematic parameters in step S4 includes:
actual distance d between the points to which the robot actually movesW(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 trackR(i +1) distance d from the point of the position to which the robot actually movesWThe relationship between (i +1) is:
the simultaneous calibration formula of the hand-eye relationship and the kinematic parameters is as follows:
as a further improvement of the present invention, the step S5 specifically includes:
in the working space of the robot, any n points are taken, and the coordinate value of each point is recorded, namely the instruction track point PRW(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 matrix 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 of the fourth column of the pose matrix A, i.e.As world coordinates of the robot end-effector, i.e. said actual trajectory point PR(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 is simplified as follows:
as a further improvement of the present invention, the step S6 specifically includes:
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 roboti-1，Δαi-1，Δdi，Δθi，ΔβiAnd 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.
As a further improvement of the present invention, 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.
Drawings
FIG. 1 is a detailed flowchart of the robot kinematics calibration method based on the vision measurement and distance error model according to the present invention;
FIG. 2 is a D-H kinematics model diagram of a six-axis industrial robot according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a distance error model of a robot according to an embodiment of the present invention;
FIG. 4 is a schematic view of a vision measurement process of a robot according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of an equidistant model of a robot during visual point acquisition according to an embodiment of the present invention;
Detailed Description
Fig. 1 is a block flow diagram of a robot kinematics calibration method based on a vision measurement and a distance error model, and the following describes the implementation of the present invention according to the accompanying drawings and specific examples:
s1, establishing a corrected D-H model of the robot;
the D-H model is the most basic robot kinematics model, is a method for describing how to model the connecting rods and joints of the robot, and is widely applicable to any robot configuration. Fig. 2 is a diagram of a D-H kinematic model of a 6-axis robot, which includes 4 geometric parameters: the length a of the connecting rod, the rotating angle alpha of the connecting rod, the offset distance d of the connecting rod and the joint angle theta. The homogeneous transformation relation matrix of the adjacent joint coordinate systems of the connecting rod i-1 and the connecting rod i of the traditional D-H model is shown as the following formula (1):
however, when the rotation axes of two adjacent joints are approximately parallel, a certain error exists, the ideal absolute parallel does not exist in practice, and even if the deviation of the rotation axes of the two joints from the absolute parallel is small, a great error exists between the common perpendicular line of the two joints and the arbitrarily-taken common perpendicular line when the two joints are perfectly parallel. Therefore, it is necessary to introduce the rotation amount β on the y-axis to represent, and construct a modified D-H model, i.e. an MDH model, the transformation matrix of the adjacent joint coordinate systems is shown in the following formula (2):
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.
S2, a distance error model;
FIG. 3 is a schematic diagram of a distance error model, where the coordinate of the measured point at the end of the robot in the base coordinate system is PR(i) The coordinate in the measuring coordinate system is PRW(i) Equation (3) is a distance error model for any two points:
Δd(i+1)＝|IR(i+1)|-|IRW(i+1)| (3)
here, | IR(i +1) | represents a point P on the actual trajectory of the robotR(i) To PR(ii) a distance of (i + 1); iRW(i +1) | represents a point P on the robot instruction trackRW(i) To PRW(i + 1).
The relationship between the distance error and the position error between two adjacent points is shown in the following formula (4):
dp(i) for a positional deviation vector of a point in the base coordinate system, dp(i)＝PR(i)-PRW(i)。
Homogeneous transformation matrix of adjacent link coordinate system due to deviation between actual geometric parameter and theoretical parameter value of robot joint in manufacturing and installation processWill become intoEquation (5) is a differential disturbance homogeneous matrix of adjacent links:
here, ,
the transformation matrix of the robot tail end connecting rod relative to the basic coordinate system is shown as the following formula (6):
wherein,
the error matrix obtained by the calculation simplification is shown as the following formula (7):
wherein the first three terms in the fourth column are robot positioning errors dp ═ dxdydz]T
S3, establishing a robot kinematics calibration model;
as shown in fig. 3, which is a schematic diagram of a robot distance error model, for any two points in a three-dimensional space of a robot, although coordinate values of the two points in a robot base coordinate system and a measurement coordinate system are different, the distance between the two points in the robot base coordinate system and the distance between the two points in the measurement coordinate system are the same. By utilizing the characteristic, a robot distance error calibration model is established, and the following formula (8) is shown:
where Δ d (i +1) is a distance error, Δ q is a robot kinematic parameter error, BiAs a coefficient matrix, it can be solved by S2.
S4, calibrating the hand-eye relationship and the kinematic parameters at the same time;
when the vision measurement hand-eye calibration is carried out, due to the fact that the nominal value of the kinematic parameter of the robot is used, the calibrated pose has repeated errors, the world coordinates of the point of the position, corresponding to the point on the instruction track, where the robot actually moves, on the obtained actual track of the robot end effector are not accurate, and the errors need to be taken into account. The actual distance d between two points of the robot in the actual movementW(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 trackR(i +1) distance d from the point of the position to which the robot actually movesWThe relationship between (i +1) is:
the formula for calibrating the hand-eye relationship and the kinematic parameters simultaneously is shown as the following formula (9):
s5, measuring the actual coordinate position of the tail end;
in the working space of the robot, randomly selecting n points, and recording the coordinate value of each point, namely the instruction track point PRW(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 PR(i) Fig. 4 is a schematic view of robot vision measurement.
In order to reduce the rounding error, an equidistant calibration model is adopted when the points are taken, fig. 5 is a schematic diagram of the equidistant point-taking model, so that the distances between two adjacent points on the motion trajectory of the robot are equal, and the distance error calibration model can be simplified into formula (10):
s6, correcting the D-H parameters and the hand-eye relationship of the robot;
and 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 measured by the CCD camera corresponding to the instruction track coordinate value into the robot eye relationship and kinematic parameter simultaneous calibration formula in the step S4.
Obtaining n-1 equations from n points to form an equation set;
the equation set is rewritten into a matrix form, and the least square solution is obtained by adopting the basic theory of the generalized inverse matrix, namelyGeometric parameter error value delta a of each connecting rod of roboti-1，Δαi-1，Δdi，Δθi，ΔβiAnd 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.
S7, experimental verification
And (4) calculating 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 distance error meets the requirement, judging whether the robot meets the precision requirement, if so, finishing calibration, otherwise, returning to the step S5, calculating other experimental data points, and carrying out calibration experiment again until the precision requirement is met.
According to the robot kinematics calibration method based on the vision measurement and the distance error model, the kinematics model is more accurate by constructing the corrected 5-parameter D-H model. The robot error model is constructed by adopting a kinematics loop method, so that the method is simple, efficient and high in universality. When the coordinates of the actual point position are obtained, a visual measurement mode is adopted, and the method has the advantages of high measurement speed, non-contact measurement and the like. The simultaneous calibration of the hand-eye relationship and the kinematic parameters avoids repeated errors and greatly improves the calibration precision.
In conclusion, the robot kinematics calibration method based on the vision measurement and the distance error model has the advantages of simplicity, practicability, high efficiency and rapidness, is generally suitable for serial joint robots, and can greatly improve the positioning accuracy and the distance accuracy of the industrial robot.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention; various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in 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 PR(i) The coordinate in the measuring coordinate system is PRW(i) The distance error between any two points can be expressed as:
Δd(i+1)＝|IR(i+1)|-|IRW(i+1)|
here, | IR(i +1) | represents a point P on the actual trajectory of the robotR(i) To PR(i + 1). IRW(i +1) | represents a point P on the robot instruction trackRW(i) To PRW(i + 1).
The relationship between the distance error and the position error between two adjacent points can be expressed as:
wherein d isp(i) For a positional deviation vector of a point in the base coordinate system, dp(i)＝PR(i)-PRW(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 iΔi
here, ,
the error matrix obtained by calculation simplification is:
wherein the first three terms in the fourth column are robot positioning errors dp ═ dxdydz]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 movesW(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 trackR(i +1) distance d from the point of the position to which the robot actually movesWThe 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 PRW(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 PR(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 roboti-1，Δαi-1，Δdi，Δθi，ΔβiAnd 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.
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