CN109366486B - Flexible robot inverse kinematics solving method, system, equipment and storage medium - Google Patents

Flexible robot inverse kinematics solving method, system, equipment and storage medium Download PDF

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CN109366486B
CN109366486B CN201811137249.1A CN201811137249A CN109366486B CN 109366486 B CN109366486 B CN 109366486B CN 201811137249 A CN201811137249 A CN 201811137249A CN 109366486 B CN109366486 B CN 109366486B
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徐文福
刘天亮
牟宗高
梁斌
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Shenzhen Graduate School Harbin Institute of Technology
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    • 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
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/06—Programme-controlled manipulators characterised by multi-articulated arms
    • B25J9/065—Snake robots

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Abstract

The invention discloses a flexible robot inverse kinematics solving method, a system, equipment and a storage medium, wherein the flexible robot inverse kinematics solving method comprises the following steps: on the basis of the original degree of freedom of the flexible robot, adding a terminal virtual degree of freedom, wherein the terminal virtual degree of freedom is a terminal virtual movement degree of freedom and/or a terminal virtual rotation degree of freedom; wherein at least one terminal virtual degree of freedom is provided; acquiring a positive kinematic equation of the flexible robot after the virtual degree of freedom of the tail end is increased; acquiring a Jacobian matrix of the flexible robot according to the positive kinematics equation; and carrying out flexible robot inverse kinematics solution according to the Jacobian matrix. According to the method, the defect that effective solution often does not exist in a traditional inverse kinematics solving method is overcome by increasing the virtual degree of freedom of the tail end, and the possibility that the solution exists in the inverse kinematics solving of the flexible robot is improved.

Description

Flexible robot inverse kinematics solving method, system, equipment and storage medium
Technical Field
The invention relates to the field of robots, in particular to a flexible robot inverse kinematics solving method, system, equipment and storage medium.
Background
Compared with the traditional mechanical arm, the flexible robot has a slender trunk and redundant degree of freedom, and shows extremely strong flexibility in a complex and multi-obstacle environment, so that the flexible robot is widely applied to operation tasks of overhauling, maintaining, assembling and the like of large-scale equipment in the nuclear power field and the aerospace field. In these special narrow space environments, in many cases, it is only necessary that the end position of the flexible robot be reachable (i.e., in the case of a specified position (posture), there is a corresponding joint angle solution), and the posture range is reachable. However, in all the developed flexible robots, the joints are mostly composed of universal joint structures, so that each joint has only two degrees of freedom in pitch and yaw, and the degrees of freedom of the flexible robot as a whole are configured as P-Y-P …, and lack of the degree of freedom in roll, which leads to the following problems due to the limited attitude space:
(1) the flexible robot lacks a degree of freedom of rolling in the arrangement of the degrees of freedom, and when the degree of freedom of the flexible robot as a whole is limited, it is difficult to equate the movement of other joints to the rolling movement of the tip.
(2) In the case of flexible robot degrees of freedom redundancy, while it can be equivalent to a rolling motion of the tip by the motion of the remaining joints, it may not have a valid solution given some tip positions and poses.
(3) The motion of other joints is equivalent to the rolling motion of the tail end, and the operation effective length of the flexible robot is inevitably reduced to a certain extent.
In addition, the existing solution method for inverse kinematics of the flexible robot has the characteristic that the position can be reached, but the posture can be only partially reached, namely under the condition of specific target tail end position and posture in some special narrow space environments, an effective joint angle solution is difficult to find by using the traditional robot inverse kinematics numerical iteration method.
Disclosure of Invention
The present invention is directed to solving, at least to some extent, one of the technical problems in the related art. To this end, an object of the present invention is to provide a flexible robot inverse kinematics solution method, system, device, and storage medium for improving the possibility of a solution for flexible robot inverse kinematics solution.
The technical scheme adopted by the invention is as follows: a flexible robot inverse kinematics solving method comprises the following steps:
on the basis of the original degree of freedom of the flexible robot, the virtual degree of freedom of the tail end is increased; at least one terminal virtual degree of freedom is set, and the terminal virtual degree of freedom is a terminal virtual movement degree of freedom and/or a terminal virtual rotation degree of freedom;
acquiring a positive kinematic equation of the flexible robot after the virtual degree of freedom of the tail end is increased;
acquiring a Jacobian matrix of the flexible robot according to the positive kinematics equation;
and carrying out flexible robot inverse kinematics solution according to the Jacobian matrix.
And further, performing inverse kinematics solution on the flexible robot according to the Jacobian matrix and a numerical iteration method.
The other technical scheme adopted by the invention is as follows: a flexible robot inverse kinematics solution system, comprising:
the terminal virtual degree of freedom increasing unit is used for increasing the terminal virtual degree of freedom on the basis of the original degree of freedom of the flexible robot; at least one terminal virtual degree of freedom is set, and the terminal virtual degree of freedom is a terminal virtual movement degree of freedom and/or a terminal virtual rotation degree of freedom;
the positive kinematic equation acquisition unit is used for acquiring the positive kinematic equation of the flexible robot after the virtual degree of freedom of the tail end is increased;
the Jacobian matrix obtaining unit is used for obtaining a Jacobian matrix of the flexible robot according to the positive kinematics equation;
and the inverse kinematics solving unit is used for solving the inverse kinematics of the flexible robot according to the Jacobian matrix.
Further, the inverse kinematics solving unit carries out inverse kinematics solution on the flexible robot according to the Jacobian matrix and a numerical iteration method.
The other technical scheme adopted by the invention is as follows: a flexible robot inverse kinematics solution apparatus comprising:
at least one processor; and the number of the first and second groups,
a memory communicatively coupled to the at least one processor; wherein the content of the first and second substances,
the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the flexible robot inverse kinematics solution method.
The other technical scheme adopted by the invention is as follows: a computer-readable storage medium having stored thereon computer-executable instructions for causing a computer to perform the flexible robot inverse kinematics solution method.
The invention has the beneficial effects that:
according to the inverse kinematics solving method, system, equipment and storage medium for the flexible robot, the defect that effective solution often does not exist in the traditional inverse kinematics solving method is overcome by increasing the virtual degree of freedom of the tail end, and the possibility that the solution exists in the inverse kinematics solving of the flexible robot is improved.
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FIG. 1 is a schematic diagram of an embodiment of a terminal virtual degree of freedom of a flexible robot according to an inverse kinematics solution method of the flexible robot in the present invention;
FIG. 2 is a schematic diagram of an embodiment of a coordinate system DH of a flexible robot arm according to an inverse kinematics solution method of the flexible robot in the present invention;
fig. 3 is a flowchart of a method of a flexible robot according to an embodiment of the present invention.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict.
Example 1
In the embodiment, in order to solve the problem that the flexible robot lacks a rolling degree of freedom in the degree of freedom configuration, the problem that an effective solution is difficult to solve when the terminal position posture is given by using a traditional iteration method exists; the flexible robot inverse kinematics solving method comprises the following steps:
on the basis of the original degree of freedom of the flexible robot, the virtual degree of freedom of the tail end is increased;
acquiring a positive kinematic equation of the flexible robot with the increased terminal virtual degree of freedom;
acquiring a Jacobian matrix of the flexible robot according to a positive kinematics equation;
and carrying out inverse kinematics solution on the flexible robot according to the Jacobian matrix.
It can be known that, on the basis of the degrees of freedom of the flexible arm robot, the terminal functions such as the camera view angle or the task restriction (such as the task of grabbing things) are virtualized into additional degrees of freedom, and the limit of the joint is the restriction range of the camera view angle or the task, so that the solution possibility of the flexible arm robot under any given terminal position posture is increased. Compared with the traditional inverse kinematics solving method of the flexible robot, the method equivalently reduces the dimension of the terminal constraint of the flexible robot, expands the solving search range of the flexible robot, has the characteristics of more solving quantity and high iteration efficiency, and can be widely applied to the inverse kinematics solving of the flexible robot. Referring to fig. 1, fig. 1 is a schematic diagram of a specific embodiment of a terminal virtual degree of freedom of a flexible robot according to an inverse kinematics solution method of the flexible robot in the present invention; using the flexible robot shown in fig. 1 for grasping an article; in this embodiment, the flexible robot has 2n degrees of freedom, belongs to a redundant robot, and is composed of n joints, each joint has 2 mutually perpendicular degrees of freedom (such as the Y axis and the Z axis in fig. 1), and the degree of freedom in the X direction is added as a terminal virtual degree of freedom.
As a further improvement of the technical scheme, the inverse kinematics solution of the flexible robot is carried out according to a Jacobian matrix and a numerical iteration method. Virtual freedom degree is added to the flexible robot, task constraint is met, and solution possibility and iteration efficiency are improved. Compared with the traditional inverse kinematics solution method, the method has the advantages of high solution possibility, high iteration efficiency, better fit with the task environment of the flexible robot and the like, and is more suitable for solving the inverse kinematics of the flexible robot.
The flexible robot inverse kinematics solution method is specifically described as follows:
first, to advance the flexible robot armAnd (4) performing kinematics analysis and solution, and establishing a D-H coordinate system. Although the D-H coordinate method is a general method in robotics, the current D-H coordinate system is established according to different rules and does not form a uniform standard, and the D-H coordinate method is mostly established according to personal habits. In this embodiment, a D-H coordinate system (as shown in FIG. 2) is established according to the improved D-H coordinate system rule, and a D-H parameter table is obtained as shown in Table 1. The D-H coordinate system establishment rule is as follows: ziThe axis of the shaft being in the direction of the axis of the i-th joint, XiAxis perpendicular to ZiAxial and directed away from ZiThe direction of the axis; y isiThe axes are established according to the rules of the right-hand coordinate system.
Figure GDA0003114368500000041
TABLE 1 Flexible arm DH parameters table
According to the D-H coordinate system establishment rule and the D-H parameter table, a homogeneous transformation matrix can be obtained in sequence:
Figure GDA0003114368500000042
Figure GDA0003114368500000043
Figure GDA0003114368500000051
and sequentially multiplying the homogeneous transformation matrixes to obtain the representation of the No. 21 coordinate system in the No. 1 coordinate system, namely solving the positive kinematics of the mechanical arm:
1T21＝1T2□2T3…20T21＝f(θ1,θ2,…,θ20)，
and T is a homogeneous transformation matrix corresponding to the tail end pose X.
And then, on the basis of the original degree of freedom of the flexible robot, according to the characteristics of the constraint range of a terminal camera or a task and the like, adding a plurality of terminal virtual degrees of freedom, wherein the terminal virtual degrees of freedom are terminal virtual mobile degrees of freedom or terminal virtual rotary degrees of freedom, and the terminal virtual degrees of freedom can correspond to a virtual mobile joint or a rotary joint. The terminal virtual freedom degree is at least one, and preferably, the terminal virtual freedom degree can be 2 or more than 2 terminal virtual movement freedom degrees or terminal virtual rotation freedom degrees or a mixture of the two, so that the solution of the inverse kinematics can be more matched with the characteristics of the terminal virtual movement freedom degree or the terminal virtual rotation freedom degree or the mixture of the two, and the solution of the inverse kinematics can be more matched with the constraint range of the task. The positive kinematic equation can be expressed as:
Figure GDA0003114368500000052
wherein the content of the first and second substances,
Figure GDA0003114368500000053
to increase the total variable of the joint after the virtual degree of freedom of the tail end; theta and f1(theta) respectively representing the original joint variable and the original positive kinematic equation of the flexible robot;
Figure GDA0003114368500000054
and
Figure GDA0003114368500000055
joint variables and positive kinematic equations corresponding to the terminal virtual degrees of freedom, respectively, the extreme constraints of which correspond to the camera view or the constraint range of the task, i.e.
Figure GDA0003114368500000056
The terminal virtual degree of freedom participates in the inverse kinematics solution process of the flexible robot and does not participate in the actual motion control of the flexible robot. According to the terminal virtual degree of freedom, the kinematic equation of the flexible robot and the Jacobian matrix, the positive kinematic equation of the flexible robot after the terminal virtual degree of freedom is increased can be expressed as:
X＝f(Θ)；
from the positive kinematic equation, the two-sided differential can be found:
Figure GDA0003114368500000057
where J (Θ) is the New Jacobian matrix for a flexible robot, which can further be expressed as:
Figure GDA0003114368500000058
wherein J (theta) is an original Jacobian matrix of the flexible robot,
Figure GDA0003114368500000059
and the Jacobian matrix corresponding to the end virtual degree of freedom part. e.g. of the typeiIs a unit vector of the joint rotation axis, riThe vector from the center of the joint rotation axis to the end of the arm.
By adding the virtual freedom degree of the tail end to the flexible robot, the possibility that the inverse kinematics solution of the flexible robot has a solution is increased, and a group of inverse solutions meeting the task constraint condition can be found quickly, and referring to fig. 3, fig. 3 is a flow chart of a method of a specific embodiment of the flexible robot inverse kinematics solution method in the invention; wherein, thetaiThe joint angles corresponding to all joints of the flexible robot,
Figure GDA0003114368500000061
for joint variables corresponding to the terminal virtual degree of freedom (joint) of the flexible robot, the specific solving process comprises the following steps:
(1) initial joint angle Θ for a given iteration0Desired end pose Xd(position and posture are abbreviated as pose).
(2) The number of iterations i of the current loop is set to 0.
(3) From positive kinematic equation
Figure GDA0003114368500000062
Calculating initial flexible robot end pose X0And further obtaining the pose difference value of the terminal pose under the current condition and the expected terminal pose as follows: Δ X0＝Xd-X0＝Xd-f(Θ0)。
(4) From the current joint angle, the current Jacobian matrix J (Θ) is calculated from the Jacobian matrix formula described above.
(5) Further obtaining the position and pose error of the tail end and the error mapped to the joint angle through a Jacobian matrix: delta thetai＝J+(Θi)ΔXiWherein J+(Θi) Is the pseudo-inverse of the Jacobian matrix J (Θ).
(6) Updating the Joint Angle Θi+1＝Θi+ΔΘi。
(7) Updating the pose X of the tip in the case of the updated new joint anglei+1＝f(Θi+1) And a pose difference Δ X from the expected posei+1。
(8) Judging whether the end pose difference is less than a set value, namely norm (delta X)i+1) E is less than or equal to epsilon, if the condition is satisfied, the iteration is ended, thetai+1Is the final solution of the joint angle; otherwise, the next step is carried out.
(9) Comparing the values of i if i ≦ imaxThen the next step is taken, otherwise the iteration ends and the equation does not have a proper solution.
(10) The iteration number i is i + 1.
(11) And (4) repeating the steps (4) to (10) until the iteration is finished.
Example 2
A flexible robot inverse kinematics solution system, comprising:
the terminal virtual degree of freedom increasing unit is used for increasing the terminal virtual degree of freedom on the basis of the original degree of freedom of the flexible robot;
the positive kinematic equation acquisition unit is used for acquiring a positive kinematic equation of the flexible robot after the virtual degree of freedom of the tail end is increased;
the Jacobian matrix acquisition unit is used for acquiring a Jacobian matrix of the flexible robot according to a positive kinematics equation;
and the inverse kinematics solving unit is used for solving the inverse kinematics of the flexible robot according to the Jacobian matrix.
Further, the inverse kinematics solving unit carries out inverse kinematics solving on the flexible robot according to the Jacobian matrix and a numerical iteration method. The terminal virtual degree of freedom is a terminal virtual movement degree of freedom and/or a terminal virtual rotation degree of freedom.
The specific working process of the flexible robot inverse kinematics solution system refers to the description of embodiment 1, and is not repeated.
Example 3
A flexible robot inverse kinematics solution apparatus comprising:
at least one processor; and the number of the first and second groups,
a memory communicatively coupled to the at least one processor; wherein the content of the first and second substances,
the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the flexible robot inverse kinematics solution method.
The specific description of the inverse kinematics solution method of the flexible robot refers to the description of embodiment 1, and is not repeated.
Example 4
A computer-readable storage medium having stored thereon computer-executable instructions for causing a computer to perform the flexible robot inverse kinematics solution method.
The specific description of the inverse kinematics solution method of the flexible robot refers to the description of embodiment 1, and is not repeated.
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (4)

1. The flexible robot inverse kinematics solving method is characterized by comprising the following steps of:
on the basis of the original degree of freedom of the flexible robot, the virtual degree of freedom of the tail end is increased; at least one terminal virtual degree of freedom is set, and the terminal virtual degree of freedom is a terminal virtual movement degree of freedom and/or a terminal virtual rotation degree of freedom;
acquiring a positive kinematic equation of the flexible robot after the virtual degree of freedom of the tail end is increased; wherein the positive kinematic equation is:
Figure FDA00032633382900000110
Figure FDA00032633382900000111
to increase the total variable of the joint after the virtual degree of freedom of the tail end; theta and f1(theta) respectively representing the original joint variable and the original positive kinematic equation of the flexible robot;
Figure FDA00032633382900000112
and
Figure FDA00032633382900000113
joint variables and positive kinematic equations corresponding to the terminal virtual degrees of freedom, respectively, the extreme constraints of which correspond to the camera view or the constraint range of the task, i.e.
Figure FDA0003263338290000011
Acquiring a Jacobian matrix of the flexible robot according to the positive kinematics equation; wherein the Jacobian matrix is
Figure FDA0003263338290000012
J (theta) is an original Jacobian matrix of the flexible robot,
Figure FDA0003263338290000013
and the Jacobian matrix corresponding to the end virtual degree of freedom part. e.g. of the typeiIs a unit vector of the joint rotation axis, riA vector from the center of the joint rotation axis to the end of the arm;
and solving the inverse kinematics of the flexible robot according to the Jacobian matrix and a numerical iteration method.
2. A flexible robot inverse kinematics solution system, comprising:
the terminal virtual degree of freedom increasing unit is used for increasing the terminal virtual degree of freedom on the basis of the original degree of freedom of the flexible robot; at least one terminal virtual degree of freedom is set, and the terminal virtual degree of freedom is a terminal virtual movement degree of freedom and/or a terminal virtual rotation degree of freedom;
the positive kinematic equation acquisition unit is used for acquiring the positive kinematic equation of the flexible robot after the virtual degree of freedom of the tail end is increased; wherein the positive kinematic equation is:
Figure FDA0003263338290000014
Figure FDA0003263338290000015
to increase the total variable of the joint after the virtual degree of freedom of the tail end; theta and f1(theta) respectively representing the original joint variable and the original positive kinematic equation of the flexible robot;
Figure FDA0003263338290000016
and
Figure FDA0003263338290000017
joint variables and positive kinematic equations corresponding to the terminal virtual degrees of freedom, respectively, the extreme constraints of which correspond to the camera view or the constraint range of the task, i.e.
Figure FDA0003263338290000018
The Jacobian matrix obtaining unit is used for obtaining a Jacobian matrix of the flexible robot according to the positive kinematics equation; wherein the Jacobian matrix is
Figure FDA0003263338290000019
J (theta) is an original Jacobian matrix of the flexible robot,
Figure FDA0003263338290000021
and the Jacobian matrix corresponding to the end virtual degree of freedom part. e.g. of the typeiIs a unit vector of the joint rotation axis, riA vector from the center of the joint rotation axis to the end of the arm;
and the inverse kinematics solving unit is used for solving the inverse kinematics of the flexible robot according to the Jacobian matrix and a numerical iteration method.
3. A flexible robot inverse kinematics solution apparatus, comprising:
at least one processor; and the number of the first and second groups,
a memory communicatively coupled to the at least one processor; wherein the content of the first and second substances,
the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the flexible robot inverse kinematics solution method of claim 1.
4. A computer-readable storage medium storing computer-executable instructions for causing a computer to perform the flexible robot inverse kinematics solution method of claim 1.
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