CN108115672B - Motion control system and method of oblique wrist spraying robot - Google Patents
Motion control system and method of oblique wrist spraying robot Download PDFInfo
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- CN108115672B CN108115672B CN201611061699.8A CN201611061699A CN108115672B CN 108115672 B CN108115672 B CN 108115672B CN 201611061699 A CN201611061699 A CN 201611061699A CN 108115672 B CN108115672 B CN 108115672B
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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
- B25J9/1615—Programme controls characterised by special kind of manipulator, e.g. planar, scara, gantry, cantilever, space, closed chain, passive/active joints and tendon driven manipulators
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B05—SPRAYING OR ATOMISING IN GENERAL; APPLYING FLUENT MATERIALS TO SURFACES, IN GENERAL
- B05B—SPRAYING APPARATUS; ATOMISING APPARATUS; NOZZLES
- B05B13/00—Machines or plants for applying liquids or other fluent materials to surfaces of objects or other work by spraying, not covered by groups B05B1/00 - B05B11/00
- B05B13/02—Means for supporting work; Arrangement or mounting of spray heads; Adaptation or arrangement of means for feeding work
- B05B13/04—Means for supporting work; Arrangement or mounting of spray heads; Adaptation or arrangement of means for feeding work the spray heads being moved during spraying operation
- B05B13/0431—Means for supporting work; Arrangement or mounting of spray heads; Adaptation or arrangement of means for feeding work the spray heads being moved during spraying operation with spray heads moved by robots or articulated arms, e.g. for applying liquid or other fluent material to 3D-surfaces
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J11/00—Manipulators not otherwise provided for
- B25J11/0075—Manipulators for painting or coating
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Abstract
The invention discloses a motion control system and a motion control method of an oblique wrist spraying robot. The motion control method comprises the following steps: reading each joint value of the diagonal wrist spraying robot, recording Cartesian space information of the diagonal wrist spraying robot through kinematics positive solution, and storing the Cartesian space information; in the process of executing operation, the stored Cartesian space information is analyzed, the track is calculated, feasible solutions of joint values of all joints are obtained through an inverse calculation method, the feasible solutions are further screened according to the stored Cartesian space information to obtain unique and appropriate inverse solution results, and then the oblique wrist spraying robot is controlled to move to the target position corresponding to the inverse solution results. Through the mode, the problem of joint space and Cartesian space vector mapping of the oblique wrist spraying robot can be solved, the high precision and the real-time performance of the robot motion planning process are guaranteed, and the problem of non-closed solution of inverse kinematics caused by oblique wrist at the tail end is solved.
Description
Technical Field
The invention relates to the technical field of intelligent robots, in particular to a motion control system and method of an oblique wrist spraying robot.
Background
The existing kinematics methods of the oblique wrist spraying robot have the defects of poor efficiency, complex calculation, incomplete solution to the multi-solution problem and the like. If the Wu method requires more than 100s in the near symbol calculation process, the method cannot be used in a real-time robot operating system; the numerical iteration method has the advantages that the operation result is directly related to the initial value selection, and no means is provided for properly selecting the initial value to enable the obtained kinematics inverse solution result to be expected; the elimination method finally needs to solve all eigenvalues and corresponding eigenvectors of the high-order matrix, and the overhead for the matrix to calculate each eigenvalue is very large, and even 30 times of the overhead may be needed to accurately obtain the desired solution, which cannot be borne by the real-time control system of the robot.
The research and development level of the domestic spraying robot is in a relatively preliminary stage, the research and development level is limited by the kinematics modeling problem of the terminal oblique wrist, some manufacturers adopt orthogonal wrists to greatly reduce the difficulty of robot modeling, and meanwhile, many advantages of the oblique wrists are lost, so that the working space is small, the pipelines are easy to tie, and the problems are not solved fundamentally. The theoretical research of the inverse kinematics algorithm of the spraying robot in colleges and universities at home and abroad is perfect, but the practical effect is not good, most of the spraying robot is in a simulation stage, the operation time is above the second level, and the Wu method has the operation time of more than 100s and cannot be applied to the real-time control system of the industrial robot.
Disclosure of Invention
The invention mainly solves the technical problem of providing a motion control system and a motion control method of an oblique wrist spraying robot, which can solve the problem of joint space and Cartesian space vector mapping of the oblique wrist spraying robot, ensure high precision and real-time performance of a robot motion planning process and solve the problem of non-closed solution of inverse kinematics caused by oblique wrists at the tail end.
In order to solve the technical problems, the invention adopts a technical scheme that: provided is a motion control method of an oblique wrist painting robot, comprising the following steps: reading each joint value of the diagonal wrist spraying robot, recording Cartesian space information of the diagonal wrist spraying robot through a kinematics positive solution, and storing the Cartesian space information; in the process of executing operation, the stored Cartesian space information is analyzed, the track is calculated, feasible solutions of joint values of all joints are obtained through an inverse calculation method, the feasible solutions are further screened according to the stored Cartesian space information to obtain unique and appropriate inverse solution results, and then the oblique wrist spraying robot is controlled to move to the target position corresponding to the inverse solution results.
The method comprises the following steps of obtaining a feasible solution of joint values of each joint through an inverse solution method:
establishing a kinematic equation set for the oblique wrist spraying robot;
and obtaining a value of a high-order matrix corresponding determinant of one single joint as 0, solving the value of the joint according to the characteristic value of the high-order matrix, and substituting the rest joints into a null element by a kinematic equation set, wherein the unknown number of the equation set is the same as the degree of freedom of the oblique wrist spraying robot, and the equation number is twice of the degree of freedom.
The oblique wrist spraying robot has six degrees of freedom.
The method comprises the following steps of establishing a kinematic equation set for the oblique wrist spraying robot:
and modeling the oblique wrist spraying robot by adopting a D-H method so as to establish a kinematic equation set for the oblique wrist spraying robot.
The method comprises the following steps of obtaining a high-order matrix corresponding determinant of one single joint, wherein the value of the determinant is 0: and obtaining the value of the determinant corresponding to the high-order matrix of one of the single joints as 0 by a elimination method.
In order to solve the technical problem, the invention adopts another technical scheme that: there is provided a motion control system of an oblique wrist painting robot, the motion control system including: the reading module is used for reading each joint value of the oblique wrist spraying robot; the first analysis module is used for recording Cartesian space information of the oblique wrist spraying robot through kinematics positive solution; the storage module is used for storing the Cartesian space information; the second analysis module is used for analyzing the stored Cartesian space information in the operation executing process, calculating a track, obtaining feasible solutions of joint values of all joints through an inverse calculation method, and further screening the feasible solutions according to the stored Cartesian space information to obtain a unique and proper inverse solution result; and the control module is used for controlling the oblique wrist spraying robot to move to the target position corresponding to the inverse solution result.
The second analysis module specifically establishes a kinematic equation set for the oblique wrist spraying robot, further obtains a value of a high-order matrix corresponding determinant of one single joint as 0, obtains a value of the joint according to a characteristic value of the high-order matrix, and substitutes the kinematic equation set for elimination elements to obtain the rest joints, wherein an unknown number of the equation set is the same as the degree of freedom of the oblique wrist spraying robot, and the number of equations is twice of the degree of freedom.
The oblique wrist spraying robot has six degrees of freedom.
The second analysis module specifically adopts a D-H method to model the oblique wrist spraying robot so as to establish a kinematic equation set for the oblique wrist spraying robot.
The second analysis module obtains the value of the determinant corresponding to the high-order matrix of one of the single joints as 0 through a elimination method.
The invention has the beneficial effects that: the present invention provides a motion control system of an oblique wrist painting robot and a method thereof, which is different from the prior art, the method comprising the following steps: the method comprises the steps of firstly reading each joint value of the oblique wrist spraying robot, recording Cartesian space information of the oblique wrist spraying robot through kinematics positive solution, storing the Cartesian space information, resolving a track through resolving the stored Cartesian space information in the process of executing operation, obtaining a feasible solution of each joint value of each joint through an inverse solution method, further screening the feasible solution according to the stored Cartesian space information to obtain a unique and proper inverse solution result, and further controlling the oblique wrist spraying robot to move to a target position corresponding to the inverse solution result. Therefore, the method can solve the problem of joint space and Cartesian space vector mapping of the oblique wrist spraying robot, ensure high precision and real-time performance of a robot motion planning process and solve the problem of non-closed solution of inverse kinematics caused by oblique wrist at the tail end.
Drawings
Fig. 1 is a flowchart of a motion control method of an oblique wrist painting robot according to an embodiment of the present invention;
fig. 2 is a schematic structural diagram of a motion control system of an oblique wrist painting robot according to an embodiment of the present invention.
Detailed Description
Referring to fig. 1, fig. 1 is a flowchart illustrating a motion control method of an oblique wrist painting robot according to an embodiment of the present invention. As shown in fig. 1, the motion control method of the present embodiment includes the steps of:
step S1: reading each joint value of the oblique wrist spraying robot, recording Cartesian space information of the oblique wrist spraying robot through kinematics positive solution, and storing the Cartesian space information.
The step is executed in the teaching process of the oblique wrist spraying robot.
Step S2: in the process of executing operation, the stored Cartesian space information is analyzed, the track is calculated, feasible solutions of joint values of all joints are obtained through an inverse calculation method, the feasible solutions are further screened according to the stored Cartesian space information to obtain unique and appropriate inverse solution results, and then the oblique wrist spraying robot is controlled to move to the target position corresponding to the inverse solution results.
Specifically, a kinematic equation set is established for the oblique wrist spraying robot, and more specifically, the kinematic equation set is established for the oblique wrist spraying robot by modeling through a D-H method.
And then acquiring the value of the determinant corresponding to the high-order matrix of one of the single joints as 0, specifically acquiring the value of the determinant corresponding to the high-order matrix of one of the single joints as 0 by a negation method. And then, calculating the value of the joint according to the characteristic value, and substituting the rest joints into a null element by a kinematic equation set to obtain the rest joints, wherein the unknown number of the equation set is the same as the degree of freedom of the oblique wrist spraying robot, and the equation number is twice of the degree of freedom. For example, if the diagonal wrist spray robot has six degrees of freedom, the number of unknowns in the equation set is 6, and the number of equations is 12 (the number of effective elements in the homothetic matrix).
More specifically, the matrix equation is position (x)k，yk，zk) Angle of rotation (theta) with respect to the input member1，θ2，θ3，θ4) A system of non-linear equations in between. Because of the specificity of the tail end of the six-degree-of-freedom spraying robot, the inverse kinematics solution does not have a closed solution, and the resolution difficulty of the position reverse analysis by the analytical method is high, the numerical method is adopted in the embodiment for resolution.
The inverse matrix solving method of the linear equation set is only suitable for the coefficient matrix which is a reversible square matrix, and for the general linear equation set, the MP generalized inverse matrix can be applied to research and express the general solution of the linear equation set.
Expanding a quasi-Newton iteration method:
solving a nonlinear system of equations in a normal case, where the equation number is equal to the unknown number, for a nonlinear system of equations
fi(x0，x1，...，xn-1)＝0 i＝0，1，...，n-1
It is briefly described as
fi(X)＝0 i＝0，1，...，n-1
Wherein X is (X)0，x1，...，xn-1)T
It is assumed that,
and (4) performing the k-th iteration approximation on the nonlinear equation system. Then the k +1 th iteration value is calculated to obtain the Newton iteration format as X(k+1)＝X(k)-F(X(k))-1f(X(k)) Wherein:
F(X(k)) As a Jacobian matrix, i.e.
The definition of the combined MP inverse can be extended to the following conclusions:
for non-linear system of equations
fi(x0，x1，...，xn-1)＝0 i＝0，1，...，m-1
It is briefly described as
fi(X)＝0 i＝0，1，...，m-1
Wherein X is (X)0，x1，...，xn-1)T，
Suppose that
And (4) performing the k-th iteration approximation on the nonlinear equation system. Then the k +1 th iteration value is calculated to obtain the Newton iteration format as
X(k+1)＝X(k)-F(X(k))-f(X(k))
Wherein the content of the first and second substances,
F(X(k)) Is an extended generalized Jacobian matrix.
Defining function f (theta)
f1(Θ)＝D2s1s2-D4(c4(c1s3+c2c3s1)-s1s2s4)+D3s1s2-px
f2(Θ)＝-D4(c4(s1s3-c1c2c3)+c1s2s4)-D2c1s2-D3c1s2-py
f3(Θ)＝D1+D2c2+D3c2+D4(c2s4+c3c4s2)-pz
Wherein p isx，py，pzIs a constant and represents the position of the robot in a rectangular coordinate system (cartesian space).
When an iterative method is applied
f1(Θ)＝0
f2(Θ)＝0
f3(Θ)＝0
Then Θ is the numerical solution of the first four axes.
Jacobi matrix
J11＝(D2+D3)c1s2-D4(-s1s3c4+c1c2c3c4-c1s2s4)
J12＝(D2+D3)s1c2-D4(-s1s2c3c4-s1c2s4)
J13＝-D4(c1c3c4-s1c2s3c4)
J14＝-D4(-c1s3s4-s1c2c3s4-s1s2c4)
J21＝(D2+D3)s1s2-D4(c1s3c4+s1c2c3c4-s1s2s4)
J22＝-(D2+D3)c1c2-D4(+c1s2c3c4+c1c2s4)
J23＝-D4(s1c3c4+c1c2s3c4)
J24＝-D4(-s1s3s4+c1c2c3s4+c1s2c4)
J31＝0
J32＝-(D2+D3)s2+D4(-s2s4+c2c3c4)
J33＝+D4(-s2s3c4)
J34＝+D4(c2c4-s2c3s4)
The matrix J rows are full rank, wherein J is the minimum norm generalized inverse of the Jacobian matrix, and the iterative format of the extended quasi-Newton method is
Θ(k+1)＝Θ(k)-J-f(Θ)
The remaining joint values are solved, and the obtained front four joint values are only needed to be substituted.
Based on the foregoing, the invention combines a plurality of technical features such as kinematics, linear algebra and engineering calculation. The method comprises application mathematical means such as kinematics positive solution, MP matrix construction, extended quasi-Newton iteration method and the like. The oblique wrist spraying robot has six degrees of freedom, is different from a common six-degree-of-freedom robot, the tail end of the oblique wrist spraying robot adopts the oblique wrist, the included angle of the axes of two adjacent shafts of the rear three shafts is 60 degrees, and the axes of the three shafts of the rear end are not in a same point. The motion ranges of the three joints at the tail end are all-360 degrees, and the pipelines are not easy to knot and break due to the special structural characteristics. In an approximate semi-ellipsoid space taking a robot base as a center, the tail end of the robot can almost reach the space, and the working space range is extremely large. After the method is used, all poses in the whole space can be accurately mapped with joint spaces one by one. In the process of adopting motion planning, the method provided by the invention can be suitable for most planning modes, is high in calculation speed and high in precision, and can enable the tail end to pass through a singular point. In addition, the invention has good effect in the project of the new-loose 16kg load I-type spraying robot, high precision and high speed. The method of the embodiment integrates the elimination method and the iteration method, has the common advantages of the elimination method and the iteration method, obviously improves the efficiency, and improves the efficiency by about 30 times compared with the elimination method. The joint space precision of the calculation precision obtained by inverse solution can reach 0.0001 degree, the Cartesian space precision can reach 0.0001 millimeter level, and the precision limit of the existing robot core parts can be completely met.
The invention also provides a motion control system of the oblique wrist spraying robot, and the motion control system is applied to the motion control method. Please refer to fig. 2.
As shown in fig. 2, the motion control system 20 of the diagonal wrist painting robot of the present embodiment includes a reading module 21, a first analyzing module 22, a storage module 23, a second analyzing module 24, and a control module 25.
The reading module 21 is used for reading each joint value of the oblique wrist spraying robot.
The first analysis module 22 is used for recording Cartesian space information of the oblique wrist spraying robot through kinematics positive solution.
The storage module 23 is used for storing cartesian space information.
The second analysis module 24 is configured to, during an operation execution process, analyze the stored cartesian space information to calculate a trajectory and obtain a feasible solution of joint values of each joint through an inverse calculation method, and further screen the feasible solution according to the stored cartesian space information to obtain a unique and appropriate inverse solution result.
Specifically, the second analysis module 24 specifically establishes a kinematic equation set for the oblique wrist spraying robot, specifically, the oblique wrist spraying robot is modeled by using a D-H method, so as to establish the kinematic equation set for the oblique wrist spraying robot. And further acquiring the value of the determinant corresponding to the high-order matrix of one of the single joints as 0, specifically acquiring the value of the determinant corresponding to the high-order matrix of one of the single joints as 0 by a negation method. And then, calculating the value of the joint according to the characteristic value, and substituting the rest joints into a null element by a kinematic equation set to obtain the rest joints, wherein the unknown number of the equation set is the same as the degree of freedom of the oblique wrist spraying robot, and the equation number is twice of the degree of freedom. For example, if the diagonal wrist spray robot has six degrees of freedom, the number of unknowns in the equation set is 6, and the number of equations is 12 (the number of effective elements in the homothetic matrix).
The control module 25 is used for controlling the oblique wrist spraying robot to move to the target position corresponding to the inverse solution result.
Specific examples of motion control are described above and will not be described herein.
Therefore, the method can solve the problem of joint space and Cartesian space vector mapping of the oblique wrist spraying robot, ensure high precision and real-time performance of a robot motion planning process and solve the problem of non-closed solution of inverse kinematics caused by oblique wrist at the tail end.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes performed by the present specification and drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (6)
1. A motion control method of an oblique wrist painting robot is characterized by comprising the following steps:
reading each joint value of the diagonal wrist spraying robot, recording Cartesian space information of the diagonal wrist spraying robot through a kinematics positive solution, and storing the Cartesian space information;
in the process of executing operation, resolving a track by analyzing the stored Cartesian space information, obtaining feasible solutions of joint values of all joints by an inverse resolving method, further screening the feasible solutions according to the stored Cartesian space information to obtain unique and appropriate inverse solution results, and further controlling the oblique wrist spraying robot to move to a target position corresponding to the inverse solution results;
the step of obtaining a feasible solution of joint values of each joint by an inverse solution method includes:
establishing a kinematic equation set for the oblique wrist spraying robot;
obtaining a value of a high-order matrix corresponding determinant of one single joint as 0, obtaining a value of the joint according to a characteristic value of the high-order matrix, and substituting the rest joints into a vanishing element by a kinematic equation set, wherein an unknown number of the equation set is the same as the degree of freedom of the oblique wrist spraying robot, and the number of equations is twice of the degree of freedom;
the step of acquiring the value of the determinant corresponding to the high-order matrix of one of the single joints as 0 comprises the following steps:
obtaining the value of a determinant corresponding to a high-order matrix of one of the single joints as 0 by a elimination method;
the matrix equation of the oblique wrist spraying robot is a nonlinear equation set between a position and an input member corner, and the nonlinear equation set is solved by adopting a Jacobian matrix and an extended quasi-Newton iteration method.
2. The motion control method of claim 1, wherein the skewed wrist painting robot has six degrees of freedom.
3. The method of claim 1, wherein the step of establishing a set of kinematic equations for the skewed wrist painting robot comprises:
and modeling the oblique wrist spraying robot by adopting a D-H method so as to establish a kinematic equation set for the oblique wrist spraying robot.
4. A motion control system for an oblique wrist painting robot, the motion control system comprising:
the reading module is used for reading each joint value of the oblique wrist spraying robot;
the first analysis module is used for recording Cartesian space information of the oblique wrist spraying robot through kinematics positive solution;
the storage module is used for storing the Cartesian space information;
the second analysis module is used for analyzing the stored Cartesian space information in the operation executing process, calculating a track, obtaining feasible solutions of joint values of all joints through an inverse calculation method, and further screening the feasible solutions according to the stored Cartesian space information to obtain a unique and proper inverse solution result; the second analysis module specifically establishes a kinematic equation set for the oblique wrist spraying robot, further obtains a value of a high-order matrix corresponding determinant of one single joint as 0, obtains a value of the joint according to a characteristic value of the high-order matrix, and substitutes the kinematic equation set for elimination elements to obtain the rest joints, wherein an unknown number of the equation set is the same as the degree of freedom of the oblique wrist spraying robot, and the number of equations is twice of the degree of freedom; the second analysis module obtains the value of the determinant corresponding to the high-order matrix of one of the single joints as 0 through an elimination method; the matrix equation of the oblique wrist spraying robot is a nonlinear equation set between a position and an input component corner, and the second analysis module adopts a Jacobian matrix and an extended quasi-Newton iteration method to solve the nonlinear equation set;
and the control module is used for controlling the oblique wrist spraying robot to move to the target position corresponding to the inverse solution result.
5. The motion control system of claim 4, wherein the skewed wrist painting robot has six degrees of freedom.
6. The motion control system of claim 4, wherein the second analysis module specifically models the skewed wrist painting robot using a D-H method to establish a system of kinematic equations for the skewed wrist painting robot.
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