CN109304730B - Robot kinematic parameter calibration method based on laser range finder - Google Patents
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Abstract
The invention belongs to the technical field related to information measurement, and discloses a robot kinematic parameter calibration method based on a laser range finder, which comprises the following steps: (1) connecting a laser range finder to a robot to be calibrated, and placing a test flat plate in a working space of the robot; (2) determining a mapping relation between a robot tail end coordinate system and a robot base coordinate system and a mapping relation between a laser range finder coordinate system and the robot tail end coordinate system; (3) collecting a joint angle value corresponding to each movement of the robot and a reading value of the laser range finder; (4) obtaining a plurality of points, and determining kinematic parameter errors according to the coplanarity condition; (5) and compensating and calibrating the kinematic parameters of the robot, obtaining the kinematic parameter error again after calibration, comparing the kinematic parameter error with the last value, and further determining that the calibration is finished or re-calibrating. The method has the advantages of high measurement efficiency, simple operation, easy implementation and high accuracy.
Description
Technical Field
The invention belongs to the technical field related to information measurement, and particularly relates to a robot kinematic parameter calibration method based on a laser range finder.
Background
With the continuous expansion of the loading amount and the application range of industrial robots (hereinafter referred to as robots), the industry also puts higher demands on various aspects of the performance of the robots, particularly the pose accuracy of the robots, such as absolute positioning accuracy and repeated positioning accuracy. At present, the repeated positioning precision of an industrial robot is very high and can reach 0.1 millimeter, but the absolute positioning precision is very poor and can only reach the centimeter magnitude, and the precision can not meet the control requirement of an industrial field, so that the positioning precision of the robot is not high, and the error is larger because the geometric error of the robot in the processing, manufacturing and assembling processes is about 90 percent of the error. The robot kinematic parameter calibration is to obtain higher absolute positioning accuracy by identifying and compensating geometric errors of the robot, and is an effective way for improving the absolute positioning accuracy of the robot. The kinematics parameter calibration is generally divided into 4 steps of modeling, measuring, parameter identification and error compensation.
With the development of the field of robots, researchers at home and abroad propose a plurality of calibration methods for improving the precision of the robots, which mainly comprise the following five calibration methods:
the first method is to use the most extensive parameter calibration based on a position error model, measure the actual position of the tail end of the robot by an external measuring instrument, compare the actual position with the theoretical position of the robot, establish a position error differential equation by using the actual positions and the theoretical positions of a plurality of groups of points, and further solve an error parameter. Common measuring instruments such as a laser tracker, a three-coordinate measuring machine and the like are calibrated based on the model, and although the laser tracker and the three-coordinate measuring machine have high measuring precision, the laser tracker and the three-coordinate measuring machine are expensive, complex to operate and low in calibrating efficiency.
The second is parameter calibration based on a distance error model, and the method establishes an error model by utilizing the characteristic that the distances of any two points of the robot in the space in a robot coordinate system and a measurement coordinate system are equal, and further solves the kinematic parameter error. The conventional instruments of the method, such as a calibration device based on a pull-wire sensor and the like, and the calibration and measurement instruments industrially used by dynalog company are also based on the principle, but the instruments are expensive and complicated to operate.
The third method is a method using sensors, such as an inertial sensor plus a position sensor method, a laser sensor plus a PSD calibration device, and an image processing method based on an image sensor, however, this method adopts a calibration device which is complicated to operate, expensive, and not commercialized in a large scale.
And the fourth method is to use an artificial neural network for calibration, firstly, the method is used for obtaining a large amount of data of the parameter error of the robot and the joint angle of the robot, and the data is used as output and input parameters to train the neural network, so that when the robot moves to a certain position, the neural network can calculate the kinematic parameter error at the position and compensate the kinematic parameter error to a robot control system in real time. The method can realize real-time performance of error compensation, but the measurement workload is large.
The fifth method is to calibrate the method for applying physical constraint to the tail end of the robot, such as surface constraint or spherical constraint, establish the surface constraint or spherical constraint equation of the tail end point, and further solve the kinematic parameter error, such as a planar constraint model proposed by Zhong et al (Zhong X L, Lewis J M, Francis L N. Autonomous robot simulation using a trigger probe [ J ]. Robotics and Autonomous systems,1996,18(4):395-410.), but the method is limited by manual operation, resulting in the problems of low measurement accuracy, low measurement efficiency and the like; as another example, the invention disclosed in china invention (CN104608129A) is a robot plane constraint calibration method, which utilizes a probe installed at the end of a robot and constrains the probe in a plane whose normal vector is parallel to the robot base coordinate axis, thereby implementing robot kinematic parameter calibration. When the method is used for calibration, the probe needs to be in contact with the calibration block, the calibration block moves due to the fact that the probe easily touches the calibration block, calibration needs to be conducted again, the motion range of a tail end point of the robot is small, all axes of the robot do not move fully, the calibration point is concentrated in a certain small area of a working space of the robot and is not distributed in the working space of the robot fully; meanwhile, because the coordinate system of the robot base cannot be displayed, the normal vectors of the three planes are difficult to be completely parallel to the coordinate system of the robot base when the calibration blocks are placed, so that a great error is generated during calculation, and even the solution cannot be realized.
Disclosure of Invention
Aiming at the defects or the improvement requirements in the prior art, the invention provides a robot kinematic parameter calibration method based on a laser range finder, which is researched and designed aiming at the robot kinematic parameter calibration method based on the working characteristics of the existing calibration method. The calibration tools needed by the robot kinematic parameter calibration method are the laser range finder and the test panel, the structure is simple, the installation is convenient, the operation is easy, the cost is low, the main measurement component is the laser range finder, and the calibration precision is ensured. In addition, the test flat plate is placed in the working space of the robot, so that the measurement space range of the robot can be effectively expanded, the sampling points are ensured to be uniformly distributed in the space, and the precision is favorably improved.
In order to achieve the aim, the invention provides a robot kinematic parameter calibration method based on a laser range finder, which comprises the following steps:
(1) respectively connecting a laser range finder and a computer to a robot to be calibrated, and simultaneously placing a test flat plate in a working space of the robot;
(2) determining a mapping relation between a robot tail end coordinate system and a robot base coordinate system and a mapping relation between a laser range finder coordinate system and the robot tail end coordinate system;
(3) controlling the movement of each axis of the robot, and acquiring the joint angle value of each axis corresponding to each movement and the reading value of the laser range finder by the computer to obtain a plurality of groups of measurement data;
(4) obtaining a plurality of points according to the obtained mapping relation and the plurality of groups of measurement data, and determining the kinematic parameter error of the robot according to the obtained plurality of points and the coplanarity condition;
(5) compensating and calibrating the kinematic parameters of the robot by using the obtained kinematic parameter errors, repeating the steps (2) to (4) after calibration to obtain the kinematic parameter errors again, comparing the kinematic parameter errors obtained in the previous and subsequent steps, and optimizing the calibration process and transferring to the step (2) if the calibrated kinematic parameter errors diverge; otherwise, the kinematic parameter error obtained for the second time is adopted to carry out compensation calibration on the kinematic parameter of the robot, and the calibration is completed.
Further, the homogeneous transformation matrix of the robot link coordinate system { i } with respect to the link coordinate system { i-1} is recorded as
Then:
in the formula, alphai，ai，θi，diEach represents a link rotation angle, a link length, a joint angle, and a link offset in a link coordinate system { i } (i ═ 1 … 6).
Further, the pose transformation matrix of the robot end coordinate system { E } relative to the robot base coordinate system { B }, and the like
Comprises the following steps:
in the formula (I), the compound is shown in the specification,
representing a pose transformation matrix of the connecting rod i relative to the connecting rod i-1; n, o, a is a unit vector of a robot terminal coordinate system { E }; p is a position vector of the origin of the coordinate system of the tail end of the robot relative to the origin of the coordinate system of the base of the robot; n, o, a and P are { alpha [)i，ai，θi，diFunction of 1 … 6.
Further, the transformation matrix of the laser range finder coordinate system relative to the robot end coordinate system is:
further, if the laser range finder is a one-dimensional sensor, the position transformation matrix of the laser beam projection point relative to the laser range finder coordinate system is as follows:
in the formula, l is the measuring distance of the laser range finder.
Further, the homogeneous coordinate of the laser beam projection point on the test flat plate under the robot base standard system { B } is:
Further, Δ ρ ═ Δ a1 … Δa6 Δd1 … Δd6 Δα1 … Δα6 Δθ1 … Δθ6 Δl]Wherein, Δ αi、Δdi、Δαi、Δθi(i ═ 1 … 6) are the error values between the theoretical kinematic parameters and the actual kinematic parameters, respectively.
Further, in step (4), a plurality of points are determined from the obtained plurality of sets of measurement data; and then, coplanar forming three vectors formed by four points in the plane to obtain an equation meeting the coplanar condition, forming an equation by four points in sequence to obtain an equation set comprising a plurality of equations, and solving the equation set by adopting a least square method to obtain the kinematic parameter error of the robot.
Further, the kinematic parameter errors obtained twice before and after are respectively delta rho and delta rho2If | | | Δ ρ | < | | | Δ ρ | |2And if yes, the calibrated kinematic parameter error is diverged.
Further, the computer is connected to the robot and the laser range finder, and is used for collecting robot joint angle data and laser range finder measurement data and processing the data.
Generally, compared with the prior art, the robot kinematic parameter calibration method based on the laser range finder provided by the invention has the following beneficial effects:
1. the calibration tools needed by the kinematic parameter calibration method are the laser range finder and the test panel, the structure is simple, the installation is convenient, the operation is easy, the cost is low, the main measurement component is the laser range finder, and the calibration precision is ensured;
2. the test flat plate is placed in the working space of the robot, so that the measuring space range of the robot can be effectively expanded, the sampling points are ensured to be uniformly distributed in the space, and the precision is improved;
3. the testing flat plate is used for component plane constraint conditions, and the tail end of the robot is not actually contacted with the testing flat plate in the calibration process, so that the calibration precision is ensured;
4. plane constraint under the coplanar condition is adopted, multiple conversions between a plurality of measurement coordinate systems and a robot base coordinate system are avoided, the calculated amount and error sources are effectively reduced, and the calibration accuracy is ensured.
Drawings
Fig. 1 is a schematic flow chart of a robot kinematic parameter calibration method based on a laser range finder according to a preferred embodiment of the present invention;
FIG. 2 is a calibration diagram of a robot calibrated by the method for calibrating kinematic parameters of the robot based on the laser range finder in FIG. 1;
fig. 3 is a schematic plan view of the test plate involved in the robot of fig. 2.
The same reference numbers will be used throughout the drawings to refer to the same or like elements or structures, wherein: 1-a robot body, 11-a tail end flange, 2-a connecting mechanism, 3-a laser range finder, 4-a test panel and 5-a computer.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Referring to fig. 1 and 2, in the method for calibrating kinematic parameters of a robot based on a laser range finder according to the preferred embodiment of the present invention, the method for calibrating kinematic parameters of a robot is simple to operate, the price of the adopted calibration equipment is low, and the high precision of the kinematic parameter calibration is ensured.
The robot kinematic parameter calibration method based on the laser range finder mainly comprises the following steps:
firstly, respectively connecting a laser range finder 3 and a computer 5 to a robot to be calibrated, and simultaneously placing a test flat plate 4 in a working space of the robot. The robot includes robot body 1, connect in robot body's terminal flange 11 and connect in terminal flange 11's coupling mechanism 2, robot body 1 connect in computer 5, coupling mechanism 2 fixed connection laser range finder 3. The smooth surface of the test flat plate 4 faces upwards, and the flatness of the smooth surface is one level or more than one level. The laser beam emitted by the laser range finder 3 is irradiated on the smooth surface of the test flat plate 4, and the distance between the laser beam and the test flat plate 4 is kept within the measuring range of the laser range finder 3. And the computer 5 is used for acquiring joint angle data of the robot and distance data measured by the laser range finder 3. In this embodiment, the test plate 4 is disposed on the damping component to prevent the rotation of the motor of the robot during the measurement process and the interference of the vibration noise of the measurement site; during the measurement process, the included angle between the laser beam and the normal vector of the smooth surface of the test flat plate 4 is less than 60 ℃.
And step two, determining the mapping relation between the robot tail end coordinate system and the robot base coordinate system and the mapping relation between the laser range finder coordinate system and the robot tail end coordinate system. Specifically, the kinematics model of the robot is established, and common modeling methods of the kinematics model of the robot include a classical DH method, a 5-parameter MDH method, a CPC model, an S model, a POE model and the like, and the classical DH method is most widely applied in the field of industrial robots compared with other modeling methods because the principle is simple and easy to understand, and the DH model of the robot is established by adopting the classical DH method in the embodiment.
The DH model establishes a spatial coordinate system of the links of the robot by establishing a joint coordinate system on each link joint of the industrial robot and characterizing each link with four parameters. Obtaining a homogeneous transformation matrix of a robot connecting rod coordinate system { i } relative to a connecting rod coordinate system { i-1} through a DH model and recording the homogeneous transformation matrix as
Then:
in the formula, alphai，ai，θi，diEach represents a link rotation angle, a link length, a joint angle, and a link offset in DH model parameters of a link coordinate system { i } (i ═ 1 … 6).
Pose transformation matrix of robot end coordinate system { E } relative to robot base coordinate system { B }
Comprises the following steps:
in the formula (I), the compound is shown in the specification,
representing a pose transformation matrix of the connecting rod i relative to the connecting rod i-1; n, o, a is a unit vector of a robot end coordinate system { E }, and P is a robot end coordinate systemA position vector of the origin relative to the origin of the robot base coordinate system; n, o, a and P are { alpha [)i，ai，θi，diFunction of 1 … 6. In this embodiment, the robot end coordinate system { E } is a coordinate system established with the center of an end flange of the robot, and the robot base coordinate system { B } is a coordinate system established with the center of a base of the robot; the laser range finder coordinate system { T } is a coordinate system established on the laser range finder 3, and its origin of coordinates is set at the exit point of the laser beam.
The transformation matrix of the laser range finder coordinate system relative to the robot tail end coordinate system is as follows:
the laser range finder 3 is a one-dimensional sensor, and the laser beam is projected on the test flat plate 4, so that the position transformation matrix of the laser beam projection point relative to the laser range finder coordinate system is as follows:
in the formula, l is the measuring distance of the laser range finder.
The homogeneous coordinate of the laser beam transmission point under the robot base coordinate system { B } is as follows:
the differential error expression of the robot end point is as follows:
Pa-Pn＝J·Δρ (6)
in the formula, PaIndicating the actual position of the end point, PnRepresenting the theoretical position of the end point, J represents a 3 × 25 matrix of error coefficients, i.e.:
Δ ρ is a 25 × 1 vector of geometric error parameters, i.e.:
Δρ＝[Δα1 … Δα6 Δd1 … Δd6 Δα1 … Δα6 Δθ1 … Δθ6 Δl] (8)
wherein, Delta alphai、Δdi、Δαi、Δθi(i ═ 1 … 6) are the error values between the theoretical kinematic parameters and the actual kinematic parameters, respectively.
And step three, controlling the movement of each axis of the robot, and acquiring the joint angle value of each axis corresponding to each movement and the reading value of the laser range finder 3 by the computer to obtain a plurality of groups of measurement data. Specifically, each axis of the robot is controlled to move, the tail end of the robot drives the laser range finder 3 to move for multiple times in a large range, the laser beam emitted by the laser range finder 3 is kept projected on the test flat plate 5 while the robot moves, and the reading value l of the laser range finder 3 at the moment is recorded when the robot stops moving every timeiAnd the joint angle value q of each axis of the robot at the momenti＝{θ1，θ2，θ3，θ4，θ5，θ6Recording as a set of measurement data; the measurement is repeated to obtain n sets of measurement data, where n is equal to or greater than 25+3, and n is 50 in the present embodiment.
And step four, obtaining the same number of points according to the obtained multiple groups of data and the mapping relation, and determining the kinematic parameter error according to the obtained points and the coplanarity condition. 50 points P can be obtained from 50 sets of data obtained by equation (5)i(xi yi zi)i∈[0，50]Namely:
combining equation (6) and equation (9) yields:
in the formula, Pi aRepresenting the actual position of the ith point; pi nIndicates the nominal position of the ith point, JiRepresenting a differential Jacobian coefficient matrix at the ith point; [ …]TRepresenting a matrix transposition.
The difference vector normalization of equation (11) yields:
three vectors can be formed by four points in the plane, and the three vectors satisfy the coplanar condition to obtain formula (13):
expanding equation (13) and truncating the second and higher order terms yields:
note the book
HiΔρ+Xi＝0 (15)
four points form an equation in the form of equation (15), and if 50 points form an equation for 4 points in sequence, then a system of 47 equations can be constructed:
HΔρ+X＝0 (16)
wherein H ═ H1，H2，…H47]T，X＝[X1，X2，…X47]T。
Solving the overdetermined equation (16) by adopting a least square method to obtain:
Δρ＝-H-1·X (17)
the obtained result is the kinematic parameter error.
Step five, compensating and calibrating the kinematic parameters of the robot by using the obtained kinematic parameter errors, repeating the step two to the step four after calibration to obtain the kinematic parameter errors again, comparing the kinematic parameter errors obtained twice before and after, and optimizing the calibration process and transferring to the step two if the calibrated kinematic parameter errors diverge; otherwise, the kinematic parameter error obtained for the second time is adopted to carry out compensation calibration on the kinematic parameter of the robot, and the calibration is completed.
Specifically, the obtained kinematic parameter error is compensated into a kinematic model to perform compensation calibration on the kinematic parameter of the robot, and then the steps from the second step to the fourth step are repeated to obtain a new kinematic parameter error which is recorded as delta rho2。
Then, the magnitude of the kinematic parameter error obtained twice before and after the comparison is made, if | | Δ ρ | > | Δ ρ |2If | l, the kinematic parameter error Δ ρ obtained for the second time is output2Compensating and calibrating the kinematic parameters of the robot by using the kinematic parameter errors obtained for the second time; if | | | Δ ρ | < | | | Δ ρ | |2If the calibrated kinematic parameter error diverges, a larger error exists in the second operation process or the kinematic parameter error obtained for the first time is wrong, the kinematic model and the solving process (calibration process) should be optimized, and the process goes to step two until the kinematic parameter error meeting the requirement is obtained.
Referring to fig. 3, a projection point of the laser range finder 3 on the test board 5 in a certain posture is denoted as a point P1, and a reading l of the laser range finder 3 at this time is recorded1And joint angle q1＝{θ1，θ2，θ3，θ4，θ5，θ6Changing the pose of the robot, repeating the previous process, and obtaining P2, P3, P4, … Pn and n groups of data. The data of 4 points of the N points can form an equation, the data of P1, P2, P3 and P4 can form a first equation, and the data of P2, P3, P4 and P5 can form a second equation; of the n points, 4 points in sequence form an equation, the total number of the equations is (n-3), and because 25 unknown error parameters exist, the operation should be ensured to be (n-3)>25。
According to the robot kinematic parameter calibration method based on the laser range finder, provided by the invention, the calibration tools required by the kinematic parameter calibration method are the laser range finder and the test flat plate, the structure is simple, the installation is convenient, the operation is easy, the cost is low, the main measurement component is the laser range finder, and the calibration precision is ensured. In addition, the test flat plate is placed in the working space of the robot, so that the measurement space range of the robot can be effectively expanded, the sampling points are ensured to be uniformly distributed in the space, and the precision is favorably improved.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A robot kinematic parameter calibration method based on a laser range finder is characterized by comprising the following steps:
(1) respectively connecting a laser range finder and a computer to a robot to be calibrated, and simultaneously placing a test flat plate in a working space of the robot;
(2) determining a mapping relation between a robot tail end coordinate system and a robot base coordinate system and a mapping relation between a laser range finder coordinate system and the robot tail end coordinate system;
(3) controlling the movement of each axis of the robot, and acquiring the joint angle value of each axis corresponding to each movement and the reading value of the laser range finder by the computer to obtain a plurality of groups of measurement data;
(4) obtaining a plurality of points according to the obtained mapping relation and the plurality of groups of measurement data, and determining the kinematic parameter error of the robot according to the obtained plurality of points and the coplanarity condition;
(5) compensating and calibrating the kinematic parameters of the robot by using the obtained kinematic parameter errors, repeating the steps (2) to (4) after calibration to obtain the kinematic parameter errors again, comparing the kinematic parameter errors obtained in the previous and subsequent steps, and optimizing the calibration process and transferring to the step (2) if the calibrated kinematic parameter errors diverge; otherwise, the kinematic parameter error obtained for the second time is adopted to carry out compensation calibration on the kinematic parameter of the robot, and the calibration is completed.
2. The robot kinematics parameter calibration method based on the laser range finder as claimed in claim 1, characterized in that: the homogeneous transformation matrix of the robot link coordinate system { i } relative to the link coordinate system { i-1} is recorded as
Then:
in the formula, alphai，ai，θi，diEach represents a link rotation angle, a link length, a joint angle, and a link offset in a link coordinate system { i } (i ═ 1 … 6).
3. The robot kinematics parameter calibration method based on the laser range finder as claimed in claim 2, characterized in that: a pose transformation matrix of the robot end coordinate system { E } relative to the robot base coordinate system { B }
Comprises the following steps:
in the formula, n, o and a are unit vectors of a robot terminal coordinate system { E }; p is a position vector of the origin of the coordinate system of the tail end of the robot relative to the origin of the coordinate system of the base of the robot; n, o, a and P are { alpha [)i，ai，θi，diFunction of 1 … 6.
4. The robot kinematics parameter calibration method based on the laser range finder as claimed in claim 3, characterized in that: the transformation matrix of the laser range finder coordinate system relative to the robot tail end coordinate system is as follows:
5. the robot kinematics parameter calibration method based on the laser range finder as claimed in claim 4, characterized in that: the laser range finder is a one-dimensional sensor, and the position transformation matrix of the laser beam projection point relative to the laser range finder coordinate system is as follows:
in the formula, l is the measuring distance of the laser range finder.
6. The robot kinematics parameter calibration method based on the laser range finder as claimed in claim 5, characterized in that: the homogeneous coordinate of the laser beam projection point on the test flat plate under the robot base system { B } is as follows:
7. The robot kinematics parameter calibration method based on the laser range finder as claimed in claim 6, characterized in that: Δ ρ ═ Δ a1 … Δa6 Δd1 … Δd6 Δα1 … Δα6 Δθ1 … Δθ6 Δl]Wherein, Δ αi、Δdi、Δαi、Δθi(i ═ 1 … 6) are the error values between the theoretical kinematic parameters and the actual kinematic parameters, respectively.
8. The method for calibrating the kinematic parameters of a robot based on a laser rangefinder according to any of claims 1 to 7, characterized in that: in the step (4), a plurality of points are determined according to the obtained multiple groups of measurement data; and then, coplanar forming three vectors formed by four points in the plane to obtain an equation meeting the coplanar condition, forming an equation by four points in sequence to obtain an equation set comprising a plurality of equations, and solving the equation set by adopting a least square method to obtain the kinematic parameter error of the robot.
9. The method for calibrating the kinematic parameters of a robot based on a laser rangefinder according to any of claims 1 to 7, characterized in that: the kinematic parameter errors obtained in two times are respectively delta rho and delta rho2If | | | Δ ρ | < | | | Δ ρ | |2And if yes, the calibrated kinematic parameter error is diverged.
10. The method for calibrating the kinematic parameters of a robot based on a laser rangefinder according to any of claims 1 to 7, characterized in that: and the computer is connected to the robot and the laser range finder, and is used for acquiring the joint angle data of the robot and the measurement data of the laser range finder and processing the data.
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