CN110722562A - Space Jacobian matrix construction method for machine ginseng number identification - Google Patents

Space Jacobian matrix construction method for machine ginseng number identification Download PDF

Info

Publication number
CN110722562A
CN110722562A CN201911029194.7A CN201911029194A CN110722562A CN 110722562 A CN110722562 A CN 110722562A CN 201911029194 A CN201911029194 A CN 201911029194A CN 110722562 A CN110722562 A CN 110722562A
Authority
CN
China
Prior art keywords
coordinate system
robot
joint
matrix
pose
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201911029194.7A
Other languages
Chinese (zh)
Other versions
CN110722562B (en
Inventor
严思杰
齐龙
陈新渡
徐小虎
褚尧
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Huazhong University of Science and Technology
Original Assignee
Huazhong University of Science and Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Huazhong University of Science and Technology filed Critical Huazhong University of Science and Technology
Priority to CN201911029194.7A priority Critical patent/CN110722562B/en
Publication of CN110722562A publication Critical patent/CN110722562A/en
Application granted granted Critical
Publication of CN110722562B publication Critical patent/CN110722562B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1607—Calculation of inertia, jacobian matrixes and inverses

Landscapes

  • Engineering & Computer Science (AREA)
  • Automation & Control Theory (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Manipulator (AREA)
  • Numerical Control (AREA)

Abstract

The invention discloses a space Jacobian matrix construction method for robot number identification, which comprises the steps of S100, constructing a robot kinematics model; s200, analyzing differential motion characteristics of the robot joint based on a robot kinematic model, and establishing a homogeneous transformation matrix between coordinate systems under the condition of differential motion; and S300, assuming that a certain joint coordinate system generates differential motion, establishing a virtual coordinate system corresponding to the joint on the basis, establishing a transformation matrix between the two, further calculating the actual pose of the tail end of the robot relative to a base coordinate system, comparing the actual pose with theory pose, obtaining the pose error of the tail end of the robot relative to the base coordinate system caused by the motion amount error of the joint coordinate system, and constructing a space Jacobian matrix of the robot. The method of the invention is a robot space Jacobian matrix construction method based on a differential transformation principle and a virtual coordinate system method, has lower time consumption, and can quickly construct the space Jacobian matrix of the robot.

Description

Space Jacobian matrix construction method for machine ginseng number identification
Technical Field
The invention belongs to the technical field of robot calibration, and particularly relates to a space Jacobian matrix construction method for robot number identification.
Background
The motion accuracy of an industrial robot plays a crucial role in the reliability of its use in production. The geometric parameter error of each connecting rod of the robot is the most main link causing the positioning error of the robot, mainly originates from the deviation between the actual geometric parameter and the theoretical parameter value of the connecting rod in the manufacturing and installation process, and is generally regarded as the system error.
The identification of geometric parameter errors of all connecting rods of the robot is an important means for improving the motion precision of the robot, the main work of parameter identification is to construct the conversion relation from the numerical errors of the robot to the tail end errors of the robot, the parameter identification is divided into two steps, firstly, the conversion relation G from the parameter errors of the robot to the joint coordinate system errors is constructediThen constructing a transformation relation J from the robot joint coordinate system error to the terminal errori(i.e., a spatial Jacobian matrix or an object Jacobian matrix). After the transformation relation from the robot parameter error to the tail end error is obtained, the parameter error value of the robot can be solved by methods such as a least square method and the like. In the existing method for constructing the space Jacobian matrix of the robot, the object Jacobian matrix of the robot is generally constructed firstly, and then the space Jacobian matrix is constructed by utilizing the transformation relation between the object Jacobian matrix and the space Jacobian matrix, so that the time consumption of a parameter identification algorithm is long, and the technical requirement of robot calibration is difficult to adapt.
Disclosure of Invention
Aiming at the defects or the improvement requirements in the prior art, the invention provides a space Jacobian matrix construction method for robot parameter identification, which is based on a differential transformation principle and a virtual coordinate system method, has lower time consumption compared with the traditional method, can quickly construct the space Jacobian matrix of the robot, and provides favorable conditions for realizing the parameter identification of the robot.
In order to achieve the above object, the present invention provides a spatial jacobian matrix construction method for robot parameter identification, comprising the following steps:
s100, analyzing the influence of the rod length, the torsion angle, the offset and the joint angle in the D-H model of the robot on the relationship between the connecting rod and the joint of the robot, calculating a homogeneous transformation matrix of the adjacent joints of the robot by using translation and rotation operators, and constructing a robot kinematics model;
s200, analyzing differential motion characteristics of the robot joint based on a robot kinematic model, and establishing a homogeneous transformation matrix between coordinate systems under the condition of differential motion;
and S300, assuming that a certain joint coordinate system generates differential motion, establishing a virtual coordinate system corresponding to the joint on the basis, establishing a transformation matrix between the two, further calculating the actual pose of the tail end of the robot relative to a base coordinate system, comparing the actual pose with theory pose, obtaining the pose error of the tail end of the robot relative to the base coordinate system caused by the motion amount error of the joint coordinate system, and constructing a space Jacobian matrix of the robot.
Further, in step S200, the establishing of the homogeneous transformation matrix includes the following specific steps:
s201: the amplitude of translation and rotation in differential motion is small, so that the angular operation of the robot is approximately processed in differential transformation, when the joint angle is small, sin theta is approximately equal to theta, and cos theta is approximately equal to 1;
s202: differential rotation motion delta from joint i-1 to joint i of robotxδyδz]TAnd translational motion d ═ dxdydz]TThe differential rotational movement δ ═ δxδyδz]TThe transformation matrix of (a) is:
Figure BDA0002249607730000021
wherein k is [ k ]xkykz]T,δx＝kxδθ,δy＝kyδθ,δz＝kzδθ；
The translational movement d ═ dxdydz]TThe corresponding transformation matrix is:
Figure BDA0002249607730000031
further, by differentiating the rotational motion and the translational motion, a total transformation matrix of the differential motion between the robot joint coordinate systems is constructed as follows:
Figure BDA0002249607730000032
further, step S200 further includes:
s203: introduction of an antisymmetric matrix [ δ ]:
Figure BDA0002249607730000033
further, S300 includes the following specific steps:
s301: analyzing the error form of the robot joint coordinate system, and introducing a virtual coordinate system to indicate the pose error of the joint coordinate system;
s302: solving a homogeneous transformation relation between the virtual coordinate system and the original joint coordinate system by utilizing a basic principle of a differential variation method;
s303: solving the pose relation of the robot tail end coordinate system relative to the base coordinate system after the virtual coordinate system is introduced, and comparing the pose relation with the in-situ pose relation to obtain the pose deviation of the robot tail end coordinate system;
s304: and constructing a space Jacobian matrix of the robot according to the pose deviation of the terminal coordinate system of the robot.
Further, the space jacobian matrix j (q) of the robot in S304 is:
Figure BDA0002249607730000034
in the formula: j. the design is a squareliAnd JaiRespectively representing the amount of translation and the amount of rotation of the end effector due to the unit amount of joint motion of the joint i.
Further, in S301, a transformation matrix of the robot end joint n with respect to the base coordinate system is described as
Figure BDA0002249607730000041
Figure BDA0002249607730000042
In the formula:
Figure BDA0002249607730000043
respectively representing transformation matrixes of the coordinate systems n, i and n relative to the coordinate systems 0, 0 and i;
Figure BDA0002249607730000044
respectively representThe rotation matrix of (1);0Pi0、iPn0、0Pn0respectively represent
Figure BDA0002249607730000046
Is determined.
Further, in S302, assuming that the coordinate system i reaches the virtual coordinate system i ' after undergoing differential motion, the coordinate system n moves to n ', and at this time, the transformation matrix of the coordinate system n ' with respect to the base coordinate system is
Figure BDA0002249607730000047
Figure BDA0002249607730000048
In the formula:
Figure BDA0002249607730000049
respectively representing transformation matrices of the coordinate systems i, i ', n ' relative to the coordinate systems o, i ';
Figure BDA00022496077300000410
respectively represent
Figure BDA00022496077300000411
The rotation matrix of (1);0Pi0、iPi′0、i′Pn′0respectively represent
Figure BDA00022496077300000412
Is determined.
Further, in S303, the pose deviation of the robot end coordinate system is:
0Dni＝[0dni T 0δni T]T
wherein the content of the first and second substances,0dniis a positional deviation equal to the position of the origin of the coordinate system n in the final state under the base coordinate system0Pno' subtracting the position of the origin of the coordinate system n in the initial state under the base coordinate system0Pno；0δniIn order to be the attitude deviation,
Figure BDA00022496077300000413
Figure BDA00022496077300000414
to represent
Figure BDA00022496077300000415
The rotation matrix of (2).
Further, in S100, the robot kinematic model is a transformation matrix of the robot link coordinate system i with respect to the link coordinate system i-1:
Figure BDA00022496077300000416
wherein: a isi-1Is the length of the connecting rod i-1; alpha is alphai-1Is the torsion angle of the connecting rod i-1; diThe offset distance of the connecting rod i relative to the connecting rod i-1 is shown; thetaiThe rotation angle of the connecting rod i relative to the connecting rod i-1 around the axis i; rot (x, alpha)i-1) Representing the rotation angle alpha around the x-axis of the coordinate systemi-1The corresponding homogeneous transformation matrix is specifically as follows:
Figure BDA0002249607730000051
Trans(x,ai-1) Representing the x-axis translation distance a around the coordinate systemi-1The corresponding homogeneous transformation matrix is specifically as follows:
Rot(z,θi) Representing the angle of rotation theta around the z-axis of the coordinate systemiThe corresponding homogeneous transformation matrix is specifically
Figure BDA0002249607730000053
Trans(z,di) Representing a translation distance d around the z-axis of the coordinate systemiThe corresponding homogeneous transformation matrix is specifically as follows:
Figure BDA0002249607730000054
in general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
1. the construction method of the space Jacobian matrix of the robot is based on the differential transformation principle and the virtual coordinate system method, has lower time consumption compared with the traditional method, can quickly construct the space Jacobian matrix of the robot, and provides favorable conditions for realizing parameter identification of the robot.
2. The space Jacobian matrix construction method analyzes the characteristic of differential motion of the robot joint by utilizing the basic principle of differential transformation, establishes a homogeneous transformation matrix between coordinate systems under the condition of differential motion, understands the generation of errors as the result of the differential motion of the coordinate systems, conveniently establishes a mathematical description method of the errors of the coordinate systems, and lays a foundation for solving the end pose errors.
3. The method for constructing the space Jacobian matrix establishes a virtual coordinate system corresponding to the joint, deduces a transformation matrix between the virtual coordinate system and the joint, further calculates the actual pose of the tail end of the robot relative to a base coordinate system, compares the actual pose with the theory pose, and constructs the space Jacobian matrix of the robot.
Drawings
FIG. 1 is a flowchart of a spatial Jacobian matrix construction method for robot parameter identification according to an embodiment of the present invention;
FIG. 2 is a schematic illustration of a robot linkage according to an embodiment of the present invention;
FIG. 3 is a schematic diagram illustrating the connection between the links according to an embodiment of the present invention;
FIG. 4 is a schematic diagram illustrating a coordinate system of a robot link according to an embodiment of the present invention;
FIG. 5 is a flowchart of solving a homogeneous transformation matrix based on a differential transformation method according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of a differential transformation process in an embodiment of the present invention;
FIG. 7 is a schematic diagram of differential motion of joint coordinate system and virtual coordinate system according to an embodiment of the present invention;
FIG. 8 is a flowchart of constructing a spatial Jacobian matrix based on a virtual coordinate system method according to an embodiment of the present invention.
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.
As shown in fig. 1, an embodiment of the present invention provides a method for constructing a space jacobian matrix for robot parameter identification, including the following steps:
s100: and establishing a kinematic model of the robot based on a D-H method. Analyzing the influence of the rod length a, the torsion angle alpha, the offset D and the joint angle theta on the relation between the robot connecting rod and the joint in the D-H model; calculating a homogeneous transformation matrix of adjacent joints of the robot by using translation and rotation operators, thereby obtaining a kinematic model of the robot;
s200: a homogeneous transformation matrix between coordinate systems under the condition of differential motion is deduced by using the basic principle of differential transformation. Analyzing the characteristic of differential motion of the robot joint, and establishing a homogeneous transformation matrix between coordinate systems under the condition of differential motion;
s300: and deducing a robot space Jacobian matrix formula by using a virtual coordinate system method. Assuming that a certain joint coordinate system generates differential motion, establishing a virtual coordinate system corresponding to the joint on the basis, deducing a transformation matrix between the two, further calculating the actual pose of the tail end of the robot relative to a base coordinate system, and comparing the actual pose with the theory of principle pose to finally construct a space Jacobian matrix of the robot.
Specifically, the method comprises the following steps:
(1) and establishing a kinematic model of the robot based on a D-H method.
As shown in FIG. 2, the link i-1 is formed by the joint axis i-1 and the common normal line length a of the joint axis ii-1And the angle alpha between the two axesi-1And (4) determining. a isi-1A length called link i-1, whose direction is defined as pointing from joint i-1 to joint i; alpha is alphai-1Referred to as the torsion angle of the link i-1, is oriented as a parallel line from the axis i-1 to the axis i about the common normal.
As shown in fig. 3, there is a joint axis between adjacent links, and accordingly, each joint axis has two common normal lines perpendicular to it, and the distance between the two common normal lines (links) is called the offset distance of the links, and is denoted as diRepresenting the offset distance of the connecting rod i relative to the connecting rod i-1; the angle between these two common normal lines (connecting rods) is called the joint angle, and is denoted as θiAnd represents the rotation angle of the link i about the axis i with respect to the link i-1.
As shown in fig. 4, in order to determine the relative movement and the pose relationship between the links of the robot, a coordinate system is fixed to each link. The coordinate system is called a base coordinate system fixed to the base (link 0), and the coordinate system is called a coordinate system i fixed to the link i.
For the intermediate coordinate system i, z is specifiediThe shaft and the joint axis i are collinear and point to any direction;x thereofiShaft and aiCollinear, pointing from joint i to i +1, when aiWhen equal to 0, take xi＝±zi+1×zi(ii) a It y isiThe axes are determined according to the right hand rule; origin o of the coordinate systemiIs taken at xiAnd ziAt the intersection of (a) when z isi+1、ziAt the time of intersection, oiTaken at the intersection point, when zi+1、ziIn parallel, oiIs taken ati+1Where 0.
For the head and tail link coordinate systems, the z-axis of the coordinate system 0 is generally specified in the direction of the joint axis 1, and when the joint variable 1 is zero, the coordinate systems 0, 1 coincide. The end link coordinate system is specified similarly to coordinate system 0, with x being chosen for the revolute joint nnSuch that when thetanWhen equal to 0, xn、xn-1Coincidence, selection of origin of coordinate system n being such that d n0; for the mobile joint n, a coordinate system n is defined by θnIs equal to 0, and when dnWhen equal to 0, xn、xn-1And (4) overlapping.
Based on the above establishment method of the robot link coordinate system, the link coordinate system i can be regarded as the link coordinate system i-1 transformed by:
(a) around xi-1Rotation of the shaft alphai-1An angle; (b) along xi-1Axial movement ai-1(ii) a (c) Around ziAxis of rotation thetaiAn angle; (d) along ziAxial movement di。
According to the kinematics principle of the robot, the transformation matrix of the robot link coordinate system i relative to the link coordinate system i-1 can be obtained by the following formula:
Figure BDA0002249607730000081
wherein: a isi-1Is the length of the connecting rod i-1; alpha is alphai-1Is the torsion angle of the connecting rod i-1; diThe offset distance of the connecting rod i relative to the connecting rod i-1 is shown; thetaiThe rotation angle of the connecting rod i relative to the connecting rod i-1 around the axis i; rot (x, alpha)i-1) Representing the rotation angle alpha around the x-axis of the coordinate systemi-1Corresponding homogeneous transformationThe matrix is specifically as follows:
Figure BDA0002249607730000082
Trans(x,ai-1) Representing the x-axis translation distance a around the coordinate systemi-1The corresponding homogeneous transformation matrix is specifically as follows:
Figure BDA0002249607730000091
Rot(z,θi) Representing the angle of rotation theta around the z-axis of the coordinate systemiThe corresponding homogeneous transformation matrix is specifically
Figure BDA0002249607730000092
Trans(z,di) Representing a translation distance d around the z-axis of the coordinate systemiThe corresponding homogeneous transformation matrix is specifically as follows:
Figure BDA0002249607730000093
the method specifically comprises the following steps:
Figure BDA0002249607730000094
the modeling method is adopted to establish a kinematic model of the robot.
(2) Fundamental principle of differential transformation
The basic principle of the differential transformation method is shown in fig. 5, because the translation and rotation amplitude is small in the differential motion, the differential transformation is used for carrying out approximation processing on the angle operation, namely sin theta is approximately equal to theta, cos theta is approximately equal to 1, after the approximation processing, a homogeneous transformation matrix between a coordinate system before and after the differential motion can be further deduced, the composition of the homogeneous transformation matrix is observed, wherein the rotation matrix is an antisymmetric matrix corresponding to the differential rotation quantity, and the antisymmetric matrix is introduced to simplify the representation of the homogeneous transformation matrix. The basic principle of the differential transformation method is specifically described below with reference to the drawings.
As shown in fig. 6, it is assumed that coordinate system B initially coincides with coordinate system a, and then B sequentially undergoes differential rotational motion δ [ δ ] with respect to axδyδz]TAnd translational motion d ═ dxdydz]TTo B'. According to the kinematics principle of the robot, the rotation transformation matrix for rotating theta angles around the x axis, the y axis and the z axis sequentially comprises the following steps:
Figure BDA0002249607730000101
Figure BDA0002249607730000102
Figure BDA0002249607730000103
when θ is small, the following equation can be approximated:
sinθ＝θ,cosθ＝1 (10)
then δ is ═ δ for the differential rotational movement of B relative to axδyδz]TThe differential rotation about each single axis can be transformed into:
Figure BDA0002249607730000104
Figure BDA0002249607730000106
the total transformation of the differential rotational motion can be seen as a composite action of the above three transformations, as shown in equation (11). Wherein, the equivalent rotation axis k ═ kxkykz]TEquivalent differential rotation angles delta theta and deltax，δy，δzThe relationship between them is:
δx＝kxδθ，δy＝kyδθ，δz＝kzδθ (14)
Figure BDA0002249607730000111
multiplication of the differential rotation transformation matrix conforms to the commutative law, i.e. the operator Rot (x, δ)x)、Rot(y,δy)、Rot(z,δz) The order of (A) can be arbitrarily changed.
For the convenience of subsequent calculation, the differential rotation transformation matrix is expanded into a 4-order homogeneous transformation matrix as follows:
Figure BDA0002249607730000112
when B generates differential rotation motion relative to A, the B generates translational motion d ═ d relative to Axdydz]TThe transformation matrix corresponding to the translational motion is:
Figure BDA0002249607730000113
since B always performs a differential motion with respect to A (reference frame), the left-hand rule is used to calculate the overall transformation matrix, and the differential motion [ dTδT]TThe corresponding overall transformation matrix is:
Figure BDA0002249607730000114
in practical calculations, we tend to change δ to [ δ ═ δxδyδz]TIs denoted as [ delta ]]It can be expressed as:
Figure BDA0002249607730000121
then
Figure BDA0002249607730000122
Can be expressed as:
Figure BDA0002249607730000123
in the formula: delta is [ delta ]xδyδz]T，d＝[dxdydz]TAnd E is a 3-order identity matrix.
(3) Method for deducing space Jacobian matrix formula of robot by using virtual coordinate system method
In the embodiment of the invention, a space Jacobian matrix of the robot is constructed based on a virtual coordinate system method, as shown in FIG. 8, firstly, the error forms (position errors and attitude errors) of the robot joint coordinate system are analyzed, the generation of the errors is understood as the result of differential motion of the robot joint coordinate system, and the virtual coordinate system is introduced to show the pose errors of the joint coordinate system. Then, by utilizing the basic principle of a differential variation method, the homogeneous transformation relation between the virtual coordinate system and the original joint coordinate system (error-free theoretical coordinate system) is solved, the pose relation of the tail end coordinate system of the robot relative to the base coordinate system after the virtual coordinate system is introduced is further deduced and compared with the in-situ pose relation (error-free theoretical pose relation), the pose deviation of the tail end coordinate system of the robot is obtained, the composition of the pose deviation is observed, and the space Jacobian matrix of the robot can be constructed. The basic principle of constructing the robot space Jacobian matrix based on the virtual coordinate system method is specifically described below in conjunction with the accompanying drawing.
The robot kinematics defines that the velocity Jacobian matrix J (q) of the robot represents the velocity vector of the slave joint
Figure BDA0002249607730000124
To the operating velocity vector
Figure BDA0002249607730000125
Linear mapping of (2). Since velocity can be considered as differential motion per unit time, the velocity jacobian can be considered as a jointA transformation matrix between the differential motion dq of the space to the differential motion D of the operating space. The object Jacobian matrix of the robot is a conversion matrix of the motion amount error of the joint to the motion amount error of the tail end relative to the theoretical pose (relative to the coordinate system of a tail end tool); the space Jacobian matrix is a conversion matrix from the joint motion amount error to the motion amount error of the end relative to the base coordinate system (expressed relative to the base coordinate system). The object Jacobian matrix and the space Jacobian matrix of the robot can be mutually converted. Namely, it is
D＝J(q)dq (21)
Further, J (q) may be expressed in blocks as
Figure BDA0002249607730000131
In the formula: j. the design is a squareliAnd JaiRespectively representing the amount of translation and the amount of rotation of the end effector due to the unit amount of joint motion of the joint i. End differential motion amount D ═ DTδT]TWhen expressed in the end tool coordinate system, the corresponding Jacobian matrix is noted asTJ (q), referred to as object Jacobian matrix; d ═ DTδT]TWhen expressed in the base coordinate system, the corresponding jacobian matrix is denoted as j (q), and is called a spatial jacobian matrix.
Here, assume D-H parameters a corresponding to the joint coordinate system ii-1，αi-1，diAnd thetaiA minute variation amount deltaa is generatedi-1，Δαi-1，ΔdiAnd Δ θiResulting in a differential rotation delta of the coordinate system i with respect to its theoretical poseiAnd a differential translation amount diI.e. producing a differential movement Di＝[di Tδi T]TThe differential motion causes the robot end coordinate system n to perform differential motion, so that the pose of the coordinate system n relative to the base coordinate system (coordinate system 0) changes.
As shown in FIG. 7, in the initial state, a transformation matrix of the robot end joint n with respect to the base coordinate system is represented as
Figure BDA0002249607730000138
According to the kinematics principle of the robot, the following relations exist:
Figure BDA0002249607730000132
in the formula:
Figure BDA0002249607730000133
respectively representing transformation matrices of the coordinate systems n, i and n relative to the coordinate systems o, o and i;
Figure BDA0002249607730000134
respectively representThe rotation matrix of (1);0Pi0、iPn0、0Pn0respectively represent
Figure BDA0002249607730000136
Is determined.
Assume that coordinate system i has reached coordinate system i '(virtual coordinate system) after differential motion, and accordingly coordinate system n has moved to n'. In this case, the transformation matrix of the coordinate system n' with respect to the base coordinate system is denoted as
Figure BDA0002249607730000137
Then:
Figure BDA0002249607730000141
because the pose of the coordinate system n relative to the coordinate system i is always kept unchanged in the process, the pose of the coordinate system n relative to the coordinate system i is always kept unchanged
Figure BDA0002249607730000142
Substituting formula (25) for formula (24) to obtain:
Figure BDA0002249607730000143
from the foregoing, it can be seen that the transformation matrix of the coordinate system i' with respect to the coordinate system iCan be obtained by differential transformation, knowing the magnitude of the differential motion as Di＝[di Tδi T]TAnd then:
Figure BDA0002249607730000144
substitution of equation (27) into (25) yields:
Figure BDA0002249607730000145
in particular, in the formula:and0Piocorresponding to the corresponding elements in formula (23).
Will be provided withRecord as
Figure BDA0002249607730000148
The equations (28) and (29) correspond to equal ones and are obtained:
Figure BDA00022496077300001410
so far, we only need to use that in formula (28)And in formula (23)
Figure BDA0002249607730000152
Comparing to obtain differential motion D of joint coordinate system ii＝[di Tδi T]TResulting in a pose deviation of the end coordinate system n with respect to the base coordinate system0Dni＝[0dni T 0δni T]TWherein0dniIn order to be a positional deviation,0δniis the attitude deviation.
For positional deviation0dniIn the calculation, we only need to use the position of the origin of the coordinate system n in the final state in the base coordinate system0Pno' subtracting the position of the origin of the coordinate system n in the initial state under the base coordinate system0PnoNamely, it can be obtained from formula (31):
Figure BDA0002249607730000153
for attitude deviation0δniThe calculation of (2) can be known from the analysis formula (30),
Figure BDA0002249607730000154
by
Figure BDA0002249607730000155
Left ride
Figure BDA0002249607730000156
This is obtained by indicating that the terminal coordinate system n is differentially rotated with respect to the base coordinate system based on the initial attitude, and the differential rotation amount is known from the equation (20)0δniComprises the following steps:
Figure BDA0002249607730000157
the following equations (32), (33) are arranged in a matrix form:
Figure BDA0002249607730000158
comparing with the formula (22), it can be known that:
Figure BDA0002249607730000159
from this, the spatial jacobian matrix of the robot can be obtained by using the formula (22). It is worth mentioning that it is possible to show,0Dnisince the description is given under the robot base coordinate system, the space jacobian matrix of the robot is obtained according to the formula (22).
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 space Jacobian matrix construction method for machine parameter identification is characterized by comprising the following steps:
s100, analyzing the influence of the rod length, the torsion angle, the offset and the joint angle in the D-H model of the robot on the relationship between the connecting rod and the joint of the robot, calculating a homogeneous transformation matrix of the adjacent joints of the robot by using translation and rotation operators, and constructing a robot kinematics model;
s200, analyzing differential motion characteristics of the robot joint based on a robot kinematic model, and establishing a homogeneous transformation matrix between coordinate systems under the condition of differential motion;
and S300, assuming that a certain joint coordinate system generates differential motion, establishing a virtual coordinate system corresponding to the joint on the basis, establishing a transformation matrix between the two, further calculating the actual pose of the tail end of the robot relative to a base coordinate system, comparing the actual pose with theory pose, obtaining the pose error of the tail end of the robot relative to the base coordinate system caused by the motion amount error of the joint coordinate system, and constructing a space Jacobian matrix of the robot.
2. The method for constructing space Jacobian matrix for machine-generated numerical identification as claimed in claim 1, wherein in step S200, the establishment of the homogeneous transformation matrix comprises the following specific steps:
s201: the amplitude of translation and rotation in differential motion is small, so that the angular operation of the robot is approximately processed in differential transformation, when the joint angle is small, sin theta is approximately equal to theta, and cos theta is approximately equal to 1;
s202: differential rotation motion delta from joint i-1 to joint i of robotxδyδz]TAnd translational motion d ═ dxdydz]TThe differential rotational movement δ ═ δxδyδz]TThe transformation matrix of (a) is:
Figure FDA0002249607720000011
wherein k is [ k ]xkykz]T,δx＝kxδθ,δy＝kyδθ,δz＝kzδθ；
The translational movement d ═ dxdydz]TThe corresponding transformation matrix is:
Figure FDA0002249607720000021
3. the method for constructing a spatial Jacobian matrix for robot parameter identification according to claim 2, wherein a total transformation matrix of differential motion between robot joint coordinate systems is constructed by differentiating rotational motion and translational motion as follows:
4. the method of claim 2, wherein the step S200 further comprises:
s203: introduction of an antisymmetric matrix [ δ ]:
Figure FDA0002249607720000023
5. the method for constructing space Jacobian matrix for machine parameter identification according to claim 1, wherein S300 comprises the following steps:
s301: analyzing the error form of the robot joint coordinate system, and introducing a virtual coordinate system to indicate the pose error of the joint coordinate system;
s302: solving a homogeneous transformation relation between the virtual coordinate system and the original joint coordinate system by utilizing a basic principle of a differential variation method;
s303: solving the pose relation of the robot tail end coordinate system relative to the base coordinate system after the virtual coordinate system is introduced, and comparing the pose relation with the in-situ pose relation to obtain the pose deviation of the robot tail end coordinate system;
s304: and constructing a space Jacobian matrix of the robot according to the pose deviation of the terminal coordinate system of the robot.
6. The method of claim 5, wherein the space Jacobian matrix J (q) of the robot in S304 is:
Figure FDA0002249607720000031
in the formula: j. the design is a squareliAnd JaiRespectively representing the amount of translation and the amount of rotation of the end effector due to the unit amount of joint motion of the joint i.
7. Machine according to claim 5A space Jacobian matrix construction method for identifying the number of the ginseng is characterized in that in S301, a transformation matrix of a robot tail end joint n relative to a base coordinate system is recorded as
Figure FDA0002249607720000032
Figure FDA0002249607720000033
In the formula:
Figure FDA0002249607720000034
respectively representing transformation matrixes of the coordinate systems n, i and n relative to the coordinate systems 0, 0 and i;
Figure FDA0002249607720000035
respectively represent
Figure FDA0002249607720000036
The rotation matrix of (1);0Pi0、iPn0、0Pn0respectively represent
Figure FDA0002249607720000037
Is determined.
8. The method of claim 5, wherein in step S302, if the coordinate system i reaches the virtual coordinate system i ' after differential motion, the coordinate system n moves to n ', and the transformation matrix of the coordinate system n ' relative to the base coordinate system is the same as the transformation matrix of the base coordinate system
Figure FDA0002249607720000038
Figure FDA0002249607720000039
In the formula:
Figure FDA00022496077200000310
respectively representing transformation matrices of the coordinate systems i, i ', n ' relative to the coordinate systems o, i ';
Figure FDA00022496077200000311
respectively represent
Figure FDA00022496077200000312
The rotation matrix of (1);0Pi0、iPi′0、i′Pn′0respectively represent
Figure FDA00022496077200000313
Is determined.
9. The method of constructing a spatial Jacobian matrix for machine parameter identification as claimed in claim 5, wherein in S303, the pose deviation of the robot end coordinate system is:
0Dni＝[0dni T0δni T]T
wherein the content of the first and second substances,0dniis a positional deviation equal to the position of the origin of the coordinate system n in the final state under the base coordinate system0Pno' subtracting the position of the origin of the coordinate system n in the initial state under the base coordinate system0Pno；0δniIn order to be the attitude deviation,
Figure FDA0002249607720000041
Figure FDA0002249607720000042
to representThe rotation matrix of (2).
10. The method of claim 1, wherein in S100, the robot kinematics model is a transformation matrix of a robot link coordinate system i relative to a link coordinate system i-1:
Figure FDA0002249607720000044
wherein: a isi-1Is the length of the connecting rod i-1; alpha is alphai-1Is the torsion angle of the connecting rod i-1; diThe offset distance of the connecting rod i relative to the connecting rod i-1 is shown; thetaiThe rotation angle of the connecting rod i relative to the connecting rod i-1 around the axis i; rot (x, alpha)i-1) Representing the rotation angle alpha around the x-axis of the coordinate systemi-1The corresponding homogeneous transformation matrix is specifically as follows:
Figure FDA0002249607720000045
Trans(x,ai-1) Representing the x-axis translation distance a around the coordinate systemi-1The corresponding homogeneous transformation matrix is specifically as follows:
Figure FDA0002249607720000046
Rot(z,θi) Representing the angle of rotation theta around the z-axis of the coordinate systemiThe corresponding homogeneous transformation matrix is specifically
Figure FDA0002249607720000047
Trans(z,di) Representing a translation distance d around the z-axis of the coordinate systemiThe corresponding homogeneous transformation matrix is specifically as follows:
Figure FDA0002249607720000051
CN201911029194.7A 2019-10-28 2019-10-28 Space Jacobian matrix construction method for machine ginseng number identification Active CN110722562B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201911029194.7A CN110722562B (en) 2019-10-28 2019-10-28 Space Jacobian matrix construction method for machine ginseng number identification

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201911029194.7A CN110722562B (en) 2019-10-28 2019-10-28 Space Jacobian matrix construction method for machine ginseng number identification

Publications (2)

Publication Number Publication Date
CN110722562A true CN110722562A (en) 2020-01-24
CN110722562B CN110722562B (en) 2021-03-09

Family

ID=69222226

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201911029194.7A Active CN110722562B (en) 2019-10-28 2019-10-28 Space Jacobian matrix construction method for machine ginseng number identification

Country Status (1)

Country Link
CN (1) CN110722562B (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111360836A (en) * 2020-04-02 2020-07-03 易思维（杭州）科技有限公司 Robot calibration method for optimizing identification parameters
CN113160334A (en) * 2021-04-28 2021-07-23 北京邮电大学 Double-robot system calibration method based on hand-eye camera
CN113752253A (en) * 2021-08-16 2021-12-07 常州大学 Parameter optimization method for continuum robot
WO2022205941A1 (en) * 2021-03-31 2022-10-06 深圳市优必选科技股份有限公司 Motion control method and apparatus, and robot control device and readable storage medium

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070146371A1 (en) * 2005-12-22 2007-06-28 Behzad Dariush Reconstruction, Retargetting, Tracking, And Estimation Of Motion For Articulated Systems
CN103085069A (en) * 2012-12-17 2013-05-08 北京邮电大学 Novel robot kinematics modeling method
CN106097390A (en) * 2016-06-13 2016-11-09 北京理工大学 A kind of robot kinematics's parameter calibration method based on Kalman filtering
WO2017129200A1 (en) * 2016-01-28 2017-08-03 MAX-PLANCK-Gesellschaft zur Förderung der Wissenschaften e.V. A system for real-world continuous motion optimization and control
CN107369167A (en) * 2017-07-20 2017-11-21 江南大学 A kind of robot self-calibrating method based on biplane constraint error model
CN107443382A (en) * 2017-09-12 2017-12-08 清华大学 Industrial robot structure parameter error recognizes and compensation method

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070146371A1 (en) * 2005-12-22 2007-06-28 Behzad Dariush Reconstruction, Retargetting, Tracking, And Estimation Of Motion For Articulated Systems
CN103085069A (en) * 2012-12-17 2013-05-08 北京邮电大学 Novel robot kinematics modeling method
WO2017129200A1 (en) * 2016-01-28 2017-08-03 MAX-PLANCK-Gesellschaft zur Förderung der Wissenschaften e.V. A system for real-world continuous motion optimization and control
CN106097390A (en) * 2016-06-13 2016-11-09 北京理工大学 A kind of robot kinematics's parameter calibration method based on Kalman filtering
CN107369167A (en) * 2017-07-20 2017-11-21 江南大学 A kind of robot self-calibrating method based on biplane constraint error model
CN107443382A (en) * 2017-09-12 2017-12-08 清华大学 Industrial robot structure parameter error recognizes and compensation method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
夏天: "工业机器人运动学标定及误差分析研究", 《中国优秀硕士学位论文全文数据库》 *
杜亮: "六自由度工业机器人定位误差参数辨识及补偿方法的研究", 《中国博士学位论文全文数据库》 *

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111360836A (en) * 2020-04-02 2020-07-03 易思维（杭州）科技有限公司 Robot calibration method for optimizing identification parameters
CN111360836B (en) * 2020-04-02 2021-04-09 易思维（杭州）科技有限公司 Robot calibration method for optimizing identification parameters
WO2022205941A1 (en) * 2021-03-31 2022-10-06 深圳市优必选科技股份有限公司 Motion control method and apparatus, and robot control device and readable storage medium
CN113160334A (en) * 2021-04-28 2021-07-23 北京邮电大学 Double-robot system calibration method based on hand-eye camera
CN113160334B (en) * 2021-04-28 2023-04-25 北京邮电大学 Dual-robot system calibration method based on hand-eye camera
CN113752253A (en) * 2021-08-16 2021-12-07 常州大学 Parameter optimization method for continuum robot

Also Published As

Publication number Publication date
CN110722562B (en) 2021-03-09

Similar Documents

Publication Publication Date Title
CN110722562B (en) Space Jacobian matrix construction method for machine ginseng number identification
CN107589934B (en) Solving method for inverse kinematics analytic solution of joint type mechanical arm
CN109895101B (en) Unique solution method for inverse kinematics numerical value of joint type mechanical arm
CN110757454B (en) Path planning method and device for cooperative rotation of double robots
CN110757450B (en) Shoulder joint rehabilitation robot parameter calibration method
CN107995885B (en) Coordinate system calibration method, system and device
CN107717993B (en) Efficient and convenient simple robot calibration method
CN111055273B (en) Two-step error compensation method for robot
WO2018188276A1 (en) Error modeling method for tail-end space curve trajectory of six-degree-of-freedom robot
CN110421566B (en) Robot precision compensation method based on approximation degree weighted average interpolation method
CN108621162A (en) A kind of manipulator motion planning method
CN105773620A (en) Track planning and control method of free curve of industrial robot based on double quaternions
CN103481288B (en) A kind of 5 articulated robot end-of-arm tooling posture control methods
JPH0820894B2 (en) Industrial robot operation control method
CN113580148B (en) Parallel robot kinematics calibration method based on equivalent kinematic chain
CN111844005B (en) 2R-P-2R-P-2R mechanical arm motion planning method applied to tunnel wet spraying
CN104991448B (en) A kind of kinematic method for solving of submarine mechanical arm based on configuration plane
CN114161425B (en) Error compensation method for industrial robot
Li et al. Solving inverse kinematics model for 7-DoF robot arms based on space vector
CN109866224B (en) Robot jacobian matrix calculation method, device and storage medium
CN111958602B (en) Real-time inverse solution method for wrist offset type 6-axis robot
CN112643658A (en) Calibration method for adaptive error modeling of series robot based on SIR dimension reduction DH model
CN111283682A (en) Geometric projection solution of forward kinematics of 4-UPU four-degree-of-freedom parallel robot
CN108638060B (en) Method for analyzing and rejecting redundant parameters in multi-degree-of-freedom machine ginseng number calibration
Mei et al. Calibration of a 6-DOF industrial robot considering the actual mechanical structures and CNC system

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant