CN113894809A - Method for acquiring geometric parameters of kinematic model of industrial robot - Google Patents

Method for acquiring geometric parameters of kinematic model of industrial robot Download PDF

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CN113894809A
CN113894809A CN202111248261.1A CN202111248261A CN113894809A CN 113894809 A CN113894809 A CN 113894809A CN 202111248261 A CN202111248261 A CN 202111248261A CN 113894809 A CN113894809 A CN 113894809A
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CN113894809B (en
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俞涛
王新祥
陈志来
黄义
陆坤
王杰
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Csic Pride(nanjing)intelligent Equipment System Co ltd
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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    • B—PERFORMING OPERATIONS; TRANSPORTING
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Abstract

The invention discloses a method for acquiring geometric parameters of a kinematic model of an industrial robot, which comprises the following steps of 1, establishing a robot connecting rod transformation matrix; step 2, solving a final pose transformation matrix; step 3, establishing a robot tail end position component solving model; step 4, establishing a coefficient group model; step 5, laying reference points; step 6, establishing a coefficient matrix R; step 7, solving a coefficient matrix R; step 8, establishing a calibration equation; and 9, solving the length a of the connecting rod and the offset d of the connecting rod. The method has the characteristics of low cost, simplicity and convenience in operation, strong applicability and the like, can accurately solve the actual geometric parameters of the robot kinematics model on the premise of not depending on the theoretical geometric parameters of the robot kinematics model, and can better improve the absolute positioning accuracy of the robot.

Description

Method for acquiring geometric parameters of kinematic model of industrial robot
Technical Field
The invention relates to the technical field of industrial robots, in particular to a method for acquiring geometric parameters of a kinematic model of an industrial robot.
Background
The acquisition of kinematic parameters of a robot is one of key technologies for the practical application of robot technology. Generally, the industrial robot has high repeated positioning accuracy, but has low absolute positioning accuracy, and factors influencing the absolute positioning accuracy mainly include processing factors, assembly factors, environmental factors and the like. Research and practical application results show that the absolute accuracy error of the industrial robot is mainly caused by the geometric parameter error of the robot kinematic model, so that the correct geometric parameter of the robot kinematic model is obtained, and the absolute positioning accuracy of the robot can be obviously improved.
The acquisition of the geometric parameters of the robot kinematic model is mainly to use advanced measurement means or geometric constraints to solve accurate geometric parameters of the model based on the robot kinematic model, and in the actual solving process, the current mainstream method is to adopt a high-precision measurement system to carry out measurement calibration, cooperate with the known theoretical parameters of the robot kinematic model, establish an error model, obtain the error between the actual parameters and the theoretical parameters, and compensate. The measurement means generally adopts a laser tracker with high precision measurement, the price is high, and meanwhile, the whole measurement calibration process is complex and has high requirements on operator skills. For a large part of middle and small enterprises which are researched and developed by industrial robots and are matched with the enterprises in China, if high-precision laser tracker equipment is introduced by investment, large capital pressure is brought, and if the modes of leasing or measuring and calibrating service outsourcing and the like are adopted, the calibration cost also occupies about 10% of the cost of a single industrial robot. The high cost, the complex measuring process and the necessity of relying on the theoretical geometrical parameters of the kinematic model known by the industrial robot are common problems of the measuring systems.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for acquiring the geometric parameters of the kinematic model of the industrial robot aiming at the defects of the prior art, the method for acquiring the geometric parameters of the kinematic model of the industrial robot can conveniently and quickly improve the absolute positioning precision of the industrial robot, and is practical, simple to operate, low in cost, high in efficiency and independent of the theoretical parameters of the geometric model of the robot.
In order to solve the technical problems, the invention adopts the technical scheme that:
a method for acquiring geometric parameters of a kinematic model of an industrial robot comprises the following steps:
step 1, establishing a robot connecting rod transformation matrix: the industrial robot is an m-axis robot and is provided with m joints and m connecting rods; establishing a connecting rod transformation matrix of the ith connecting rod of the m-axis robot by using four geometric parameters of a kinematic model
Figure BDA0003321829100000011
Wherein i is more than or equal to 1 and less than or equal to m; the four geometric parameters are respectively a joint angle theta, a connecting rod torsion characteristic angle alpha, a connecting rod length a and a connecting rod offset d; when m is determined, the connecting rod torsion characteristic angle alpha is a given value; the link transformation matrixes corresponding to the m links are respectively as follows:
Figure BDA0003321829100000012
Figure BDA0003321829100000021
each connecting rod transformation matrix is a matrix with four rows and four columns.
Step 2, solving the final pose transformation matrix
Figure BDA0003321829100000022
The concrete solving formula is as follows:
Figure BDA0003321829100000023
step 3, establishing a robot tail end position component pxSolving the model: taking the straight line of the central axis of the mth connecting rod at the tail end as xAxial, then end position component pxIs the position component of the robot end in the x axis; assuming that the final pose transformation matrix obtained in the step 2
Figure BDA0003321829100000024
The value of the fourth column in the first row is v, then p is establishedxSolution model p ofxV; wherein v is a dependent variable about three independent variables of a joint angle theta, a connecting rod length a and a connecting rod offset d; the joint angle theta is an intermediate independent variable, and the length a and the offset d of the connecting rod are independent variables to be solved.
Step 4, establishing a coefficient group model r: for p established in step 3xSolving the model, and carrying out factorization to obtain a coefficient group model r consisting of coefficients of each to-be-solved independent variable; at this time, the coefficient group model r is a model including only the intermediate argument θ.
Step 5, laying reference points: laying a reference point P in the space of the motion range of the robot0And n reference points, wherein n is not less than the number of the independent variables to be solved; n reference points are respectively P1、P2、P3、…、Pn(ii) a And P is0、P1、P2、P3、…、PnThe horizontal and vertical coordinates of the frame are increased in sequence; reference point P1、P2、P3、…、PnTo a reference point of reference P0Are respectively D1、D2、D3、…、Dn。
Step 6, establishing a coefficient matrix R, wherein the specific expression is as follows:
R＝[R1、R2、R3、…、Rn]T
R1＝r1-r0
R2＝r2-r0
R3＝r3-r0
Rn＝rn-r0
in the formula, R1、R2、R3、…、RnAre respectively reference points P1、P2、P3、…、PnA relative coefficient set of (a); r is0As a reference point P0A coefficient group of (a), referred to as a reference coefficient group; r is1、r2、r3、…、rnAre respectively reference points P1、P2、P3、…、PnThe coefficient set of (2).
And 7, solving the coefficient matrix R, wherein the concrete solving method comprises the following steps.
Step 71, solving the reference coefficient group r0The method specifically comprises the following steps.
Step 71A, moving the tail end sharp point of the robot to a datum reference point P0。
Step 71B, obtaining a joint angle variable J0: the reference point P is obtained at the reference point by a joint encoder built in each joint0Joint angle variable J of time robot0(ii) a Variable J of joint angle0Including at the reference point P0Time m-1 joint angle theta of the joint.
Step 71C, solving the reference coefficient group r0: will obtain the joint angle variable J0Substituting the model into the coefficient group model r established in the step 4 to obtain a reference coefficient group r0。
Step 72, solving r1、r2、r3、…、rn: respectively moving the tail end sharp points of the robot to reference points P1、P2、P3、…、Pn(ii) a Repeating the step 71, and solving to obtain r1、r2、r3、…、rn。
Step 73, solving a coefficient matrix R: r obtained in step 710And r obtained in step 721、r2、r3、…、rnAnd substituting the coefficient matrix R established in the step 6 to obtain the coefficient matrix R with known quantity.
Step 8, establishing a calibration equation, specifically:
RX＝D
D＝[D1、D2、D3、…、Dn]T
in the formula, X is the column vector of all independent variables of the connecting rod length a and the connecting rod offset d to be solved.
Step 9, solving the length a and the offset d of the connecting rod: the coefficient matrix R solved in the step 7 and the D obtained in the step 51、D2、D3、…、Dn(ii) a And (4) sequentially substituting into the calibration equation established in the step (8), and respectively solving to obtain all the connecting rod lengths a and the connecting rod offsets d.
The industrial robot is a 6-axis robot with 6 joints and 6 connecting rods; the length a of each of the 6 connecting rods is a0、a1、a2、a3、a4、a5And a is a0＝a4＝a5So only a needs to be solved for1、a2、a3(ii) a The connecting rods d of the 6 connecting rods are respectively d1、d2、d3、d4、d5、d6And d is1＝d2＝d3＝d5So only d needs to be solved for4And d6The total to-be-solved independent variables are respectively a1、a2、a3、d4、d6(ii) a The joint angles theta of the 5 joints are respectively theta1、θ2、θ3、θ4、θ5、θ6。
The connecting rod torsion characteristic angles alpha of the 6 connecting rods are respectively alpha0、α1、α2、α3、α4、α5And then:
Figure BDA0003321829100000031
the link transformation matrices corresponding to the 6 links are respectively as follows:
Figure BDA0003321829100000032
and
Figure BDA0003321829100000033
wherein the content of the first and second substances,
Figure BDA0003321829100000034
the expression of (a) is:
Figure BDA0003321829100000035
in the formula, i is more than or equal to 1 and less than or equal to 6.
In step 3, pxThe solution model of (a) is:
px＝v＝(-cosθ1sinθ2cosθ3-cosθ1cosθ2cosθ3)(cosθ4sinθ5d6+a3)
+(cosθ1sinθ2sinθ3-cosθ1 cosθ2cosθ3)(--cosθ5d6-d4)
-sinθ1sinθ4sinθ5d6-cosθ1sinθ2a2+cosθ1a1。
in step 4, the model p is solvedxThe expression after factorization is:
px＝cosθ1a1-cosθ1sinθ2a2-a3(cosθ1sinθ2cosθ3+cosθ1cosθ2sinθ3)
+d4(cosθ1cosθ2cosθ3-cosθ1sinθ2sinθ3)
+d6(cosθ1cosθ2cosθ3cosθ5-cosθ1sinθ2sinθ3cosθ5
-cosθ1sinθ2cosθ3cosθ4sinθ5-cosθ1cosθ2sinθ3cosθ4sinθ5
-sinθ1sinθ4sinθ5)
let the coefficient set model r be [ ra, rb, rc, rd, re ═ ra, rb, rc](ii) a Wherein ra, rb, rc, rd and re are respectively the independent variable a to be solved1、a2、a3、d4、d6The coefficient of (a); then:
ra＝cosθ1
rb＝-cosθ1sinθ2
rc＝-(cosθ1sinθ2cosθ3+cosθ1cosθ2sinθ3)
rd＝cosθ1 cosθ2 cosθ3-cosθ1 sinθ2sinθ3
re＝cosθ1cosθ2cosθ3 cosθ5-cosθ1 sinθ2sinθ3cosθ5-cosθ1sinθ2cosθ3cosθ4sinθ5-cosθ1cosθ2sinθ3 cosθ4sinθ5-sinθ1sinθ4sinθ5。
in step 71, the obtained reference coefficient set r is solved0Comprises the following steps:
r0＝[ra0，rb0，rc0，rd0，re0]
in step 72, the resulting r is solved1、r2、r3、…、rnComprises the following steps:
r1＝[ra1，rb1，rC1，rd1，re1]
r2＝[ra2，rb2，rc2，rd2，re2]
rn＝[ran，rbn，rcn，rdn，ren]
in the formula: ra (ra)0，rb0，rc0，rd0，re0Are respectively a reference point P0A (a)1、a2、a3、d4、d6The coefficient of (a).
ra1，rb1，rc1，rd1，re1Are respectively reference points P1A (a)1、a2、a3、d4、d6The coefficient of (a).
ra2，rb2，rc2，rd2，re2Are respectively reference points P2A (a)1、a2、a3、d4、d6The coefficient of (a).
ran，rbn，rcn，rdn，renAre respectively reference points PnA (a)1、a2、a3、d4、d6The coefficient of (a).
Then:
R1＝r1-r0＝[ra1-ra0，rb1-rb0，rc1-rc0，rd1-rd0，re1-re0]
R2＝r2-r0＝[ra2-ra0，rb2-rb0，rc2-rc0，rd2-rd0，re2-re0]
Rn＝rn-r0＝[ran-ra0，rbn-rb0，rcn-rc0，rdn-rd0，ren-re0]。
in step 71, in step 7, the expression of the coefficient matrix R obtained by solving is:
Figure BDA0003321829100000051
in step 71, the expression of the calibration equation established in step 8 is:
Figure BDA0003321829100000052
the invention has the following beneficial effects:
(1) and the cost is low: compared with expensive measuring tools such as a laser tracker, the invention does not bring economic pressure to users.
(2) The operation is simple and convenient: the whole solving process comprises a simple data sampling process, few operation steps and no higher skill requirement on a user.
(3) The applicability is strong: the solving method provided by the invention is suitable for all six-axis robots and seven-axis robots connected in series, is also suitable for four-axis SCARA robots, does not have strict requirements on the measurement environment, and is suitable for most industrial fields applied by industrial robots.
(4) And the error generation links are few: most of the existing robot kinematic parameter identification methods extract the tail end position component of the robot through the robot kinematic forward solution according to the connecting rod transformation matrix on the basis of the theoretical parameters of the original model, and calculate the error transfer matrix by using the full differential form of the position component.
(5) The actual parameters can be directly obtained without depending on theoretical parameters. In some application occasions, theoretical geometric parameters of a kinematic model of a robot body cannot be known, and other calibration methods depending on the known theoretical parameters cannot provide conditions for completing measurement calibration. The geometric constraints of the method provided by the invention are relative and accurate, and the actual geometric parameters can be directly obtained by solving, so that the kinematics calibration of the robot is completed.
(6) The invention solves the overdetermined equation to obtain the actual valueGeometric parameter (a)1，a2，a3，d4，d6) And replacing theoretical parameters, and accurately acquiring geometric parameters of the kinematic model to improve the absolute positioning precision of the robot.
Drawings
Fig. 1 shows a schematic diagram of an industrial robot according to the invention comprising an independent variable to be solved.
FIG. 2 is a schematic diagram showing the arrangement positions of the reference points.
Among them are:
10. a robot; 11. a first joint rotation center; 12. a second joint rotation center; 13. a third joint center of rotation; 14. a fourth joint rotation center; 15. a fifth joint rotation center; 16. a terminal cusp.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific preferred embodiments.
In the description of the present invention, it is to be understood that the terms "left side", "right side", "upper part", "lower part", etc., indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and that "first", "second", etc., do not represent an important degree of the component parts, and thus are not to be construed as limiting the present invention. The specific dimensions used in the present example are only for illustrating the technical solution and do not limit the scope of protection of the present invention.
The industrial robot is an m-axis robot and is provided with m-1 joints and m connecting rods. In the present embodiment, as shown in fig. 1, the robot 10 is preferably an m-6 axis robot having 6 joints and 6 links.
The joint centers of the 5 joints are a first joint rotation center 11, a second joint rotation center 12, a third joint rotation center 13, a fourth joint rotation center 14 and a fifth joint rotation center 15, respectively.
The 6 connecting rods are respectively a 1 st connecting rod, a 2 nd connecting rod, a 3 rd connecting rod, a 4 th connecting rod, a 5 th connecting rod and a 6 th connecting rod which are connected in sequence. The 1 st connecting rod is arranged on the base, and the tail end of the 6 th connecting rod is a tail end sharp point 16.
The robot kinematics model has four geometric parameters, namely a joint angle theta, a connecting rod torsion characteristic angle alpha, a connecting rod length a and a connecting rod offset d.
When m is determined, the characteristic angle α of the connecting rod twist is a given value, and when m is 6 in the present embodiment, the characteristic angles α of the connecting rod twist of 6 connecting rods are α from the 1 st connecting rod to the 6 th connecting rod respectively0、α1、α2、α3、α4、α5And then:
Figure BDA0003321829100000061
the link lengths a of the 6 links from the 1 st link to the 6 th link are a0、a1、a2、a3、a4、a5And a is a0＝a4＝a5So only a needs to be solved for1、a2、a3。
The connecting rod d of the 6 connecting rods from the 1 st connecting rod to the 6 th connecting rod is d1、d2、d3、d4、d5、d6And d is1＝d2＝d3＝d5So only d needs to be solved for4And d6The total to-be-solved independent variables are respectively a1、a2、a3、d4、d6。
The joint angles θ of the 5 joints from the 1 st joint to the 5 th joint are θ1、θ2、θ3、θ4、θ5、θ6. Because the tail end joint, namely the 6 th joint, does not relate to the length of the connecting rod and the offset of the connecting rod, theta is not related to6As a calculation factor, only θ needs to be considered1、θ2、θ3、θ4、θ5。
A method for acquiring geometric parameters of a kinematic model of an industrial robot comprises the following steps.
Step 1, establishing a robot connecting rod transformation matrix
Establishing a connecting rod transformation matrix of the ith connecting rod of the m-axis robot by using four geometric parameters of a kinematic model
Figure BDA0003321829100000071
The link transformation matrixes corresponding to the m links are respectively as follows:
Figure BDA0003321829100000072
each connecting rod transformation matrix is a matrix with four rows and four columns. Wherein the content of the first and second substances,
Figure BDA0003321829100000073
the specific expression of (A) is as follows:
Figure BDA0003321829100000074
wherein i is not less than 1 and not more than m, and i is not less than 1 and not more than 6 in the embodiment.
In this embodiment, the link transformation matrices corresponding to 6 links are respectively:
Figure BDA0003321829100000075
and
Figure BDA0003321829100000076
according to alpha0、α1、α2、α3、α4、α5Value, this embodiment transformation matrix of the first link of the industrial robot to the robot base
Figure BDA0003321829100000077
Comprises the following steps:
Figure BDA0003321829100000078
in the same way, the second connecting rod is oppositeTransforming matrices in the first link
Figure BDA0003321829100000079
Comprises the following steps:
Figure BDA00033218291000000710
third link relative to second link transformation matrix
Figure BDA00033218291000000711
Comprises the following steps:
Figure BDA00033218291000000712
the fourth link transforms the matrix relative to the third link
Figure BDA0003321829100000081
Comprises the following steps:
Figure BDA0003321829100000082
fifth link relative to fourth link transformation matrix
Figure BDA0003321829100000083
Comprises the following steps:
Figure BDA0003321829100000084
matrix transformation of sixth link relative to fifth link
Figure BDA0003321829100000085
Comprises the following steps:
Figure BDA0003321829100000086
step 2, solving the final bitPosture transformation matrix
Figure BDA0003321829100000087
The concrete solving formula is as follows:
Figure BDA0003321829100000088
in the present embodiment, it is preferred that,
Figure BDA0003321829100000089
in actual calculation, firstly
Figure BDA00033218291000000810
Is converted into
Figure BDA00033218291000000811
And
Figure BDA00033218291000000812
by multiplying, i.e. by first determining
Figure BDA00033218291000000813
And
Figure BDA00033218291000000814
then:
Figure BDA00033218291000000815
wherein
Figure BDA00033218291000000816
The representation is a matrix of the pose angle state of the tail end of the robot under a world coordinate system, and the specific meaning of each letter is the prior art and is not explained one by one; p is a radical ofx，py，pzRespectively representing cartesian coordinate values of the robot tip in a world coordinate system.
In this embodiment, the method for establishing the world coordinate system xoy includes: when each joint of the robot is used as a zero position, the straight line of the central axis of the mth connecting rod at the tail end is taken as an x axis, a point on the x axis departing from the tip point at the tail end is taken as an original point o, the left side direction or the right side direction of the mth connecting rod passing through the original point o and being perpendicular to the x axis is taken as a y axis, and the forward direction of the tip point at the tail end is taken as the positive direction of the x axis, as shown in fig. 2.
Step 3, establishing a robot tail end position component pxSolving model
Taking the straight line where the central axis of the mth connecting rod at the tail end is located as an x axis, the component p of the position of the tail end isxIs the x-axis position component of the robot tip.
Assuming that the final pose transformation matrix obtained in the step 2
Figure BDA00033218291000000817
The value of the fourth column in the first row is v, then p is establishedxSolution model p ofxV; wherein v is a dependent variable about three independent variables of a joint angle theta, a connecting rod length a and a connecting rod offset d; the joint angle theta is an intermediate independent variable, and the length a and the offset d of the connecting rod are independent variables to be solved.
In this embodiment, pxThe solution model of (a) is:
px＝v＝(-cosθ1 sinθ2 cosθ3-cosθ1 cosθ2 cosθ3)(cosθ4sinθ5 d6+a3)
+(cosθ1sinθ2sinθ3-cosθ1 cosθ2cosθ3)(-cosθ5d6-d4)
-sinθ1sinθ4sinθ5 d6-cosθ1sinθ2 a2+cosθ1 a1。
step 4, establishing a coefficient group model r
For p established in step 3xSolving the model, and carrying out factorization to obtain a coefficient group model r consisting of coefficients of each to-be-solved independent variable; this is achieved byThe coefficient set model r is a model that includes only the intermediate argument θ.
In the present embodiment, the model p is solvedxThe expression after factorization is:
px＝cosθ1a1-cosθ1 sinθ2a2-a3(cosθ1sinθ2 cosθ3+cosθ1 cosθ2sinθ3)
+d4(cosθ1cosθ2cosθ3-cosθ1sinθ2sinθ3)
+d6(cosθ1cosθ2cosθ3cosθ5-cosθ1sinθ2sinθ3cosθ5
-cosθ1sinθ2cosθ3cosθ4sinθ5-cosθ1cosθ2sinθ3cosθ4sinθ5
-sinθ1sinθ4sinθ5)
let the coefficient set model r be [ ra, rb, rc, rd, re ═ ra, rb, rc](ii) a Wherein ra, rb, rc, rd and re are respectively the independent variable a to be solved1、a2、a3、d4、d6The coefficient of (a); then:
ra＝cosθ1
rb＝-cosθ1sinθ2
rc is one (cos θ)1sinθ2 cosθ3+cosθ1 cosθ2 sinθ3)
rd＝cosθ1 cosθ2 cosθ3-cosθ1 sinθ2 sinθ3
re＝cosθ1cosθ2cosθ3 cosθ5-cosθ1 sinθ2sinθ3cosθ5-cosθ1sinθ2cosθ3cosθ4sinθ5-cosθ1cosθ2sinθ3 cosθ4sinθ5-sinθ1sinθ4sinθ5。
Step 5, laying reference points
Laying a reference point P in the space of the motion range of the robot0And n reference points, wherein n is not less than the number of the independent variables to be solved, and n is greater than 5 in the embodiment.
n reference points are respectively P1、P2、P3、…、Pn(ii) a And P is0、P1、P2、P3、…、PnAre sequentially increased, as shown in fig. 2, reference point P1、P2、P3、…、PnTo a reference point of reference P0Are respectively D1、D2、D3、…、Dn。
Step 6, establishing a coefficient matrix R, wherein the specific expression is as follows:
R＝[R1、R2、R3、…、Rn]T
R1＝r1-r0
R2＝r2-r0
R3＝r3-r0
Rn＝rn-r0
in the formula, R1、R2、R3、…、RnAre respectively reference points P1、P2、P3、…、PnA relative coefficient set of (a); r is0As a reference point P0A coefficient group of (a), referred to as a reference coefficient group; r is1、r2、r3、…、rnAre respectively reference points P1、P2、P3、…、PnThe coefficient set of (2).
And 7, solving the coefficient matrix R, wherein the concrete solving method comprises the following steps.
Step 71, solving reference coefficientGroup r0The method specifically comprises the following steps.
Step 71A, moving the tail end sharp point of the robot to a datum reference point P0。
Step 71B, obtaining a joint angle variable J0: the reference point P is obtained at the reference point by a joint encoder built in each joint0Joint angle variable J of time robot0(ii) a Variable J of joint angle0Including at the reference point P0Time m-1 joint angle theta of the joint.
In the present embodiment, it is preferred that,
J0＝[θ1，θ2，θ3，θ4，θ5]
step 71C, solving the reference coefficient group r0: will obtain the joint angle variable J0Substituting the model into the coefficient group model r established in the step 4 to obtain a reference coefficient group r0：
r0＝[ra0，rb0，rc0，rd0，re0]
Step 72, solving r1、r2、r3、…、rn: respectively moving the tail end sharp points of the robot to reference points P1、P2、P3、…、Pn(ii) a Repeating the step 71, and solving to obtain r1、r2、r3、…、rn：
r1＝[ra1，rb1，rc1，rd1，re1]
r2＝[ra2，rb2，rc2，rd2，re2]
r3＝[ra3，rb3，rc3，rd3，re3]
rn＝[ran，rbn，rcn，rdn，ren]
In the formula: ra (ra)0，rb0，rc0，rd0，re0Are respectively a radicalQuasi-reference point P0A (a)1、a2、a3、d4、d6The coefficient of (a).
ra1，rb1，rc1，rd1，re1Are respectively reference points P1A (a)1、a2、a3、d4、d6The coefficient of (a).
ra2，rb2，rc2，rd2，re2Are respectively reference points P2A (a)1、a2、a3、d4、d6The coefficient of (a).
ra3，rb3，rc3，rd3，re3Are respectively reference points P3A (a)1、a2、a3、d4、d6The coefficient of (a).
ran，rbn，rcn，rdn，renAre respectively reference points PnA (a)1、a2、a3、d4、d6The coefficient of (a).
Step 73, solving a coefficient matrix R: r obtained in step 710And r obtained in step 721、r2、r3、…、rnSubstituting into the coefficient matrix R established in the step 6 to obtain the coefficient matrix R with known quantity, namely R1、R2、…、RnThe specific expressions of (a) are respectively:
R1＝r1-r0＝[ra1-ra0，rb1-rb0，rc1-rc0，rd1-rd0，re1-re0]
R2＝r2-r0＝[ra2-ra0，rb2-rb0，rc2-rc0，rd2-rd0，re2-re0]
Rn＝rn-r0＝[ran-ra0，rbn-rb0，rcn-rc0，rdn-rd0，ren-re0]。
thus, the solved coefficient matrix R has the expression:
Figure BDA0003321829100000111
step 8, establishing a calibration equation, specifically:
RX＝D
D＝[D1、D2、D3、…、Dn]T
in the formula, X is the column vector of all independent variables of the connecting rod length a and the connecting rod offset d to be solved.
In this embodiment, the expression of the established calibration equation is:
Figure BDA0003321829100000112
step 9, solving the length a and the offset d of the connecting rod: the coefficient matrix R solved in the step 7 and the D obtained in the step 51、D2、D3、…、Dn(ii) a And (4) sequentially substituting into the calibration equation established in the step (8), and respectively solving to obtain all the connecting rod lengths a and the connecting rod offsets d, namely the actual geometric parameter values of the robot kinematic model.
Although the preferred embodiments of the present invention have been described in detail, the present invention is not limited to the details of the embodiments, and various equivalent modifications can be made within the technical spirit of the present invention, and the scope of the present invention is also within the scope of the present invention.

Claims (9)

1. A method for acquiring geometric parameters of a kinematic model of an industrial robot is characterized by comprising the following steps: the method comprises the following steps:
step 1, establishing a robot connecting rod transformation matrix: the industrial robot is an m-axis robotThe device is provided with m joints and m connecting rods; establishing a connecting rod transformation matrix of the ith connecting rod of the m-axis robot by using four geometric parameters of a kinematic model
Figure FDA0003321829090000011
Wherein i is more than or equal to 1 and less than or equal to m; the four geometric parameters are respectively a joint angle theta, a connecting rod torsion characteristic angle alpha, a connecting rod length a and a connecting rod offset d; when m is determined, the connecting rod torsion characteristic angle alpha is a given value; the link transformation matrixes corresponding to the m links are respectively as follows:
Figure FDA0003321829090000012
Figure FDA0003321829090000013
each connecting rod transformation matrix is a matrix with four rows and four columns;
step 2, solving the final pose transformation matrix
Figure FDA0003321829090000014
The concrete solving formula is as follows:
Figure FDA0003321829090000015
step 3, establishing a robot tail end position component pxSolving the model: taking the straight line where the central axis of the mth connecting rod at the tail end is located as an x axis, the component p of the position of the tail end isxIs the position component of the robot end in the x axis; assuming the final pose transformation moment drop obtained in the step 2
Figure FDA0003321829090000016
The value of the fourth column in the first row is v, then p is establishedxSolution model p ofxV; wherein v is a dependent variable about three independent variables of a joint angle theta, a connecting rod length a and a connecting rod offset d; the joint angle theta is an intermediate independent variable, and the length a and the offset d of the connecting rod are independent variables to be solved;
step 4, buildingVertical coefficient set model r: for p established in step 3xSolving the model, and carrying out factorization to obtain a coefficient group model r consisting of coefficients of each to-be-solved independent variable; at this time, the coefficient group model r is a model including only the intermediate argument θ;
step 5, laying reference points: laying a reference point P in the space of the motion range of the robot0And n reference points, wherein n is not less than the number of the independent variables to be solved; n reference points are respectively P1、P2、P3、…、Pn(ii) a And P is0、P1、P2、P3、…、PnThe horizontal and vertical coordinates of the frame are increased in sequence; reference point P1、P2、P3、…、PnTo a reference point of reference P0Are respectively D1、D2、D3、…、Dn；
Step 6, establishing a coefficient matrix R, wherein the specific expression is as follows:
R＝[R1、R2、R3、…、Rn]T
R1＝r1-r0
R2＝r2-r0
R3＝r3-r0
Rn＝rn-r0
in the formula, R1、R2、R3、…、RnAre respectively reference points P1、P2、P3、…、PnA relative coefficient set of (a); r is0As a reference point P0A coefficient group of (a), referred to as a reference coefficient group; r is1、r2、r3、…、rnAre respectively reference points P1、P2、P3、…、PnA coefficient group of (1);
and 7, solving the coefficient matrix R, wherein the concrete solving method comprises the following steps:
step 71, solving the reference coefficient group r0The method specifically comprises the following steps:
step 71A, moving the tail end sharp point of the robot to a datum reference point P0；
Step 71B, obtaining a joint angle variable J0: the reference point P is obtained at the reference point by a joint encoder built in each joint0Joint angle variable J of time robot0(ii) a Variable J of joint angle0Including at the reference point P0Joint angle theta of m-1 joints;
step 71C, solving the reference coefficient group r0: will obtain the joint angle variable J0Substituting the model into the coefficient group model r established in the step 4 to obtain a reference coefficient group r0；
Step 72, solving r1、r2、r3、…、rn: respectively moving the tail end sharp points of the robot to reference points P1、P2、P3、…、Pn(ii) a Repeating the step 71, and solving to obtain r1、r2、r3、…、rn；
Step 73, solving a coefficient matrix R: r obtained in step 710And r obtained in step 721、r2、r3、…、rnSubstituting the coefficient matrix R established in the step 6 to obtain the coefficient matrix R with known quantity;
step 8, establishing a calibration equation, specifically:
RX＝D
D＝[D1、D2、D3、…、Dn]T
in the formula, X is the column vector of all independent variable connecting rod lengths a and connecting rod offsets d to be solved;
step 9, solving the length a and the offset d of the connecting rod: the coefficient matrix R solved in the step 7 and the D obtained in the step 51、D2、D3、…、Dn(ii) a And (4) sequentially substituting into the calibration equation established in the step (8), and respectively solving to obtain all the connecting rod lengths a and the connecting rod offsets d.
2. Industrial robot kinematics model according to claim 1The method for acquiring the parameters is characterized by comprising the following steps: the industrial robot is a 6-axis robot with 6 joints and 6 connecting rods; the length a of each of the 6 connecting rods is a0、a1、a2、a3、a4、a5And a is a0＝a4＝a5So only a needs to be solved for1、a2、a3(ii) a The connecting rods d of the 6 connecting rods are respectively d1、d2、d3、d4、d5、d6And d is1＝d2＝d3＝d5So only d needs to be solved for4And d6The total to-be-solved independent variables are respectively a1、a2、a3、d4、d6(ii) a The joint angles theta of the 6 joints are respectively theta1、θ2、θ3、θ4、θ5、θ6。
3. The method for acquiring geometrical parameters of a kinematic model of an industrial robot according to claim 2, characterized in that: the connecting rod torsion characteristic angles alpha of the 6 connecting rods are respectively alpha0、α1、α2、α3、α4、α5And then:
Figure FDA0003321829090000031
4. method for obtaining geometrical parameters of a kinematic model of an industrial robot according to claim 3, characterized in that: the link transformation matrices corresponding to the 6 links are respectively as follows:
Figure FDA0003321829090000032
and
Figure FDA0003321829090000033
wherein the content of the first and second substances,
Figure FDA0003321829090000034
the expression of (a) is:
Figure FDA0003321829090000035
in the formula, i is more than or equal to 1 and less than or equal to 6.
5. The method for obtaining geometric parameters of a kinematic model of an industrial robot according to claim 4, characterized in that: in step 3, pxThe solution model of (a) is:
Figure FDA0003321829090000036
6. the method for acquiring geometrical parameters of a kinematic model of an industrial robot according to claim 5, characterized in that: in step 4, the model p is solvedxThe expression after factorization is:
Figure FDA0003321829090000037
let the coefficient set model r be [ ra, rb, rc, rd, re ═ ra, rb, rc](ii) a Wherein ra, rb, rc, rd and re are respectively the independent variable a to be solved1、a2、a3、d4、d6The coefficient of (a); then:
ra＝cosθ1
rb＝-cosθ1sinθ2
rc＝-(cosθ1sinθ2cosθ3+cosθ1cosθ2sinθ3)
rd＝cosθ1cosθ2cosθ3-cosθ1sinθ2sinθ3
re＝cosθ1cosθ2cosθ3cosθ5-cosθ1sinθ2sinθ3cosθ5-cosθ1sinθ2cosθ3cosθ4sinθ5-cosθ1cosθ2sinθ3cosθ4sinθ5-sinθ1sinθ4sinθ5。
7. the method for obtaining geometric parameters of a kinematic model of an industrial robot according to claim 6, characterized in that: in step 71, the obtained reference coefficient set r is solved0Comprises the following steps:
r0＝[ra0，rb0，rc0，rd0，re0]
in step 72, the resulting r is solved1、r2、r3、…、rnComprises the following steps:
r1＝[ra1，rb1，rc1，rd1，re1]
r2＝[ra2，rb2，rc2，rd2，re2]
rn＝[ran，rbn，rcn，rdn，ren]
in the formula: ra (ra)0，rb0，rc0，rd0，re0Are respectively a reference point P0A (a)1、a2、a3、d4、d6The coefficient of (a);
ra1，rb1，rc1，rd1，re1are respectively reference points P1A (a)1、a2、a3、d4、d6The coefficient of (a);
ra2，rb2，rc2，rd2，re2are respectively reference points P2A (a)1、a2、a3、d4、d6The coefficient of (a);
ran，rbn，rcn，rdn，renare respectively reference points PnA (a)1、a2、a3、d4、d6The coefficient of (a);
then:
R1＝r1-r0＝[ra1-ra0，rb1-rb0，rc1-rc0，rd1-rd0，re1-re0]
R2＝r2-r0＝[ra2-ra0，rb2-rb0，rc2-rc0，rd2-rd0，re2-re0]
Rn＝rn-r0＝[ran-ra0，rbn-rb0，rcn-rc0，rdn-rd0，ren-re0]。
8. the method for acquiring geometrical parameters of a kinematic model of an industrial robot according to claim 7, characterized in that: in step 71, in step 7, the expression of the coefficient matrix R obtained by solving is:
Figure FDA0003321829090000041
9. the method for acquiring geometrical parameters of a kinematic model of an industrial robot according to claim 8, characterized in that: in step 71, the expression of the calibration equation established in step 8 is:
Figure FDA0003321829090000042
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