CN109746915B - Kinematics method for improving absolute positioning precision of industrial robot - Google Patents
Kinematics method for improving absolute positioning precision of industrial robot Download PDFInfo
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Abstract
The invention relates to a kinematics method for improving the absolute positioning accuracy of an industrial robot, which comprises the following steps of S1: establishing an error model of the robot's geometric parameters Ag, collecting the pose error Delta X of the robot's end, and adopting an identification methodIdentifying the DH geometric parameter error delta of the robot; s2: nominal inverse kinematics algorithm modules f are respectively designed in the robot controller‑1Positive kinematic algorithm X with geometric parameter error Δ AgEThe module and a module for calculating a robot geometric Jacobian matrix J algorithm; s3: the robot controller realizes a compensation kinematics algorithm by a method of combining nominal inverse kinematics, homogeneous transformation positive kinematics with error parameters and joint space deviation inverse solution by using geometric Jacobian. The invention adopts Jacobian mapping to joint space deviation for robot attitude errors caused by geometric error parameters, and combines the Jacobian mapping with nominal inverse kinematics to realize a kinematics algorithm for improving absolute positioning accuracy.
Description
Technical Field
The invention relates to the technical field of industrial robots, in particular to a kinematics method for improving the absolute positioning accuracy of an industrial robot.
Background
The industrial robot has poor absolute positioning precision due to various inevitable factors such as manufacturing geometric parameter errors in the machining and assembling process, flexibility of connecting rods and joints, backlash of speed reducers and the like, wherein the geometric parameter errors are main sources of errors of the tail end of the robot. The calibration of the industrial robot and the corresponding compensation algorithm are an effective way for improving the absolute positioning accuracy of the robot. In order to enable an industrial robot to meet more accurate fine operation and directly apply an off-line programming simulation program to a field and match an actual geometric kinematics model of the robot with a model in a simulation environment consistently, a kinematics method for improving the absolute positioning accuracy of the robot needs to be designed to compensate related errors.
An error compensation method for an industrial robot is disclosed in a Chinese patent No. CN201710811069, and mainly comprises the steps of calculating the tail end force of the robot through a dynamic model, solving the flexible offset of the stress state of the tail end of the robot by combining a rigidity matrix of gravity and inertia force, repeatedly and iteratively correcting the tail end pose data of the robot through acceptable errors, and finally solving joint input variables through inverse kinematics. The patent mainly compensates the end pose error caused by the elastic deformation of each part of the robot by a dynamic model and a rigidity matrix method. Errors caused by elastic deformation can be effectively compensated by the method. But geometric errors are a major source of robot tip errors.
European patent EP1250986a2 discloses in 2001 a kinematic method for compensating elastic deformations. US5162713 discloses in 1992 a method of first determining rod length errors and joint variable errors in geometric parameters of a SCARA robot, then jointly solving these errors and a nominal inverse solution for new modified cartesian coordinates, and finally using the modified cartesian coordinates as input of an inverse solution of the robot, thereby obtaining compensated robot joint variables. The patent only aims at compensating partial geometric parameter errors of the SCARA industrial robot, the application range is limited, and the compensation precision is also limited.
Disclosure of Invention
In order to avoid and solve the technical problems and effectively improve the absolute positioning accuracy of the robot, the invention considers the geometric error which is the main factor influencing the absolute positioning accuracy, and provides a kinematics method for improving the absolute positioning accuracy of the industrial robot.
The technical problem to be solved by the invention is realized by adopting the following technical scheme:
a kinematics method for improving the absolute positioning accuracy of an industrial robot comprises the following steps:
s1: firstly, establishing an error model of the robot's geometric parameter Ag, collecting the pose error Delta X of the robot's tail end in the working space of the robot, and identifying the robot's DH geometric parameter error Delta X by adopting an identification method; the kinematic relationship between the robot end position X and the joint variable q is:
X＝f(q,ɡ) (1)
considering the geometric error Δ Ag, the kinematic relationship between the robot tip position and the joint variables is:
X+ΔX＝f(q,ɡ+Δɡ) (2)
by the relations (1) and (2), the relationship between the pose error Δ X and the geometric parameter error Δ pg at the robot tip is established as follows:
ΔX＝Η(ɡ)Δɡ (3)
wherein, the Η (Ag) is an error identification Jacobian matrix, and after the joint position of the robot is known, the actual value of the matrix can be obtained; therefore, by detecting the robot end pose error, the joint error Δ Ag can be obtained through the relation (3).
S2: nominal inverse kinematics algorithm modules f are respectively designed in the robot controller-1Positive kinematic algorithm X with geometric parameter error Δ AgEThe module and a module for calculating a robot geometric Jacobian matrix J algorithm;
s3: when the robot controller converts the command value X of Cartesian spaceCWhen the robot controller is issued, the robot controller realizes a compensation kinematics algorithm by a method of combining nominal inverse kinematics, homogeneous transformation positive kinematics with error parameters and joint space deviation inverse solution by using geometric Jacobian.
As a further description of the present invention, the step S3 specifically includes the following steps:
s31: solving Cartesian space pose instruction value X through nominal inverse kinematics modelCCorresponding nominal values theta of all joints;
s32: then substituting the nominal joint value obtained by the previous step into a positive kinematics model considering the geometric error, and solving the Cartesian coordinate value X of the geometric errorE；
S33: solving the cartesian coordinate error value Δ X ═ XC-XE；
S34: passing through the Jacobian matrix J of the joint position q at that time, and inverting J-1Jointly solving the deviation value delta q of each axis corresponding to the joint space with the delta X obtained in the step S33;
s35: compensating each joint coordinate value q as q + δ q;
s36: substituting the joint coordinate value compensated by S35 into positive kinematics considering geometric error, and solving Cartesian coordinate value X compensated by the jointE；
S37: calculating the error between the Cartesian coordinate command value and the compensated Cartesian coordinate valueC-XEComparing the magnitude of the error with a specified Cartesian coordinate allowable error delta; if true, proceed to S38, otherwise proceed to S34;
s38: the joint coordinate value q of the latest compensation in S35 is issued to the position controller of each axis.
As a further explanation of the present invention, in steps S31 and S32 of S3, the corrected cartesian coordinate values including the geometric error are calculated using the robot nominal inverse solution, as follows:
XE＝f(q,ɡ+Δɡ) (4)。
as a further explanation of the present invention, at S34 of step S3, the pose error in cartesian space is mapped to joint variables by the geometric jacobian matrix J as follows:
δq＝J-1(q)·ΔX (5)。
the invention has the beneficial effects that: the method comprises the steps of analyzing a kinematic model and a kinematic error model of the industrial robot, establishing a positive kinematic model with error parameters by introducing geometric error parameters into positive kinematics, and estimating the terminal pose of the robot by using the model. After accurate geometric parameters are obtained, the robot end pose error is mapped to joint space variables by using a geometric Jacobian matrix, and errors of all DH geometric parameters on the robot end pose are compensated by using the joint variables. The invention adopts an iterative method, can obtain the joint variable meeting the Cartesian space error threshold, realizes the precision requirement of the error threshold, and lays a foundation for the robot to realize the refined operation.
Drawings
The invention is further illustrated with reference to the following figures and examples.
FIG. 1 is a block diagram of a control system of the present invention;
FIG. 2 is a flow chart of a method of the present invention;
FIG. 3 is a schematic view of a kinematic model joint coordinate system of an experimental six-axis industrial robot according to the present invention;
FIG. 4 is a diagram illustrating the comparison of the position errors of the robot ends before and after the kinematic compensation according to the present invention;
the labels in the figure are: 1. a tail end position error curve before absolute positioning accuracy is improved; 2. and (5) a tail end position error curve after the absolute positioning precision is improved.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further explained below.
As shown in fig. 1 to 4, a kinematic method for improving the absolute positioning accuracy of an industrial robot includes the following steps:
s1: firstly, establishing an error model of the robot's geometric parameter Ag, collecting the pose error Delta X of the robot's tail end in the working space of the robot, and identifying the robot's DH geometric parameter error Delta X by adopting an identification method; the kinematic relationship between the robot end position X and the joint variable q is:
X＝f(q,ɡ) (1)
considering the geometric error Δ Ag, the kinematic relationship between the robot tip position and the joint variables is:
X+ΔX＝f(q,ɡ+Δɡ) (2)
by the relations (1) and (2), the relationship between the pose error Δ X and the geometric parameter error Δ pg at the robot tip is established as follows:
ΔX＝Η(ɡ)Δɡ (3)
wherein, the Η (Ag) is an error identification Jacobian matrix, and after the joint position of the robot is known, the actual value of the matrix can be obtained; therefore, by detecting the robot end pose error, the joint error Δ Ag can be obtained through the relation (3).
S2: nominal inverse kinematics algorithm modules f are respectively designed in the robot controller-1Positive Ag errorKinematic algorithm XEThe module and a module for calculating a robot geometric Jacobian matrix J algorithm;
s3: when the robot controller converts the command value X of Cartesian spaceCWhen the robot controller is issued, the robot controller realizes a compensation kinematics algorithm by a method of combining nominal inverse kinematics, homogeneous transformation positive kinematics with error parameters and joint space deviation inverse solution by using geometric Jacobian. The absolute positioning accuracy of the robot in the Cartesian space is improved.
The method specifically comprises the following steps;
s31: solving Cartesian space pose instruction value X through nominal inverse kinematics modelCCorresponding nominal values theta of all joints;
s32: then substituting the nominal joint value obtained by the previous step into a positive kinematics model considering the geometric error, and solving the Cartesian coordinate value X of the geometric errorE；
S33: solving the cartesian coordinate error value Δ X ═ XC-XE；
S34: passing through the Jacobian matrix J of the joint position q at that time, and inverting J-1Jointly solving the deviation value delta q of each axis corresponding to the joint space with the delta X obtained in the step S33;
s35: compensating each joint coordinate value q as q + δ q;
s36: substituting the joint coordinate value compensated by S35 into positive kinematics considering geometric error, and solving Cartesian coordinate value X compensated by the jointE；
S37: calculating the error between the Cartesian coordinate command value and the compensated Cartesian coordinate valueC-XEComparing the magnitude of the error with a specified Cartesian coordinate allowable error delta; if true, proceed to S38, otherwise proceed to S34;
s38: the joint coordinate value q of the latest compensation in S35 is issued to the position controller of each axis.
At S31 and S32 of step S3, the modified cartesian coordinate values including the geometric error are calculated using the robot nominal inverse solution, as follows:
XE＝f(q,ɡ+Δɡ) (4)。
at S34 of step S3, the pose error in cartesian space is mapped to joint variables by the geometric jacobian matrix J as follows:
δq＝J-1(q)·ΔX (5)。
in order to facilitate a further understanding of the invention, specific examples are set forth below.
The experimental system used a six-axis industrial robot with a coordinate system as shown in fig. 3 (wherein X, Y, Z represents the coordinate axes) and DH nominal parameters and identification error parameters in the coordinate system as shown in tables 1 and 2, and identified geometric error parameters using a laser tracker, and verified the method using a robot controller.
TABLE 1 six-axis robot DH nominal parameters for experiments
TABLE 2 six-axis robot DH identification error parameter for experiment
| i | Δai | Δαi | Δdi | Δθi | Δβi |
| 1 | -0.2863 | 0.0145 | 0 | 0 | - |
| 2 | 0.4227 | 0.0159 | -0.16 | -0.9157 | 0.0289 |
| 3 | 0.0914 | 0.0183 | 0 | 0.3103 | - |
| 4 | 0.0089 | 0.0272 | 0.2785 | -1.2409 | - |
| 5 | -0.1453 | 0.0676 | 0.7922 | -0.0749 | - |
| 6 | 0 | 0 | 0 | 0 | - |
Wherein, a in Table 1iFor the length, alpha, of each linkiFor each joint torsion angle, diOffset for each link, thetaiFor each joint angle, betaiThe deflection angle between the parallel joints around the y axis; the parameters in table 2 are error parameters after error identification of the parameters in table 1.
The kinematics steps of six-axis industrial machine for improving absolute positioning accuracy in the experiment refer to the process. The practical effect of using kinematic methods to improve absolute positioning accuracy is shown in table 3 and fig. 4.
TABLE 3 comparison of absolute positioning accuracy of six-axis robot used in experiments before and after improvement
| Index (I) | Minimum value | Mean value | Maximum value | |
| Before lifting | 0.2870 | 0.5754 | 1.0811 | |
| After lifting | 0.0706 | 0.2779 | 0.5887 |
After comparison, the maximum value of the pose error of the Cartesian space coordinate of the robot is reduced from 1.0811mm to 0.5887mm before and after the geometric error is compensated, the pose error is reduced by 45.54%, the effectiveness of the kinematics method of absolute positioning lifting is proved, the accurate motion control of the robot is facilitated, and the robot can meet some high-precision application occasions.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are merely illustrative of the principles of the invention, but that various changes and modifications may be made without departing from the spirit and scope of the invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (4)
1. A kinematics method for improving the absolute positioning accuracy of an industrial robot is characterized by comprising the following steps: the method comprises the following steps:
s1: firstly, establishing an error model of the robot's geometric parameter Ag, collecting the pose error Delta X of the robot's tail end in the working space of the robot, and identifying the robot's DH geometric parameter error Delta X by adopting an identification method; the kinematic relationship between the robot end position X and the joint variable q is:
X＝f(q,ɡ) (1)
considering the geometric error Δ Ag, the kinematic relationship between the robot tip position and the joint variables is:
X+ΔX＝f(q,ɡ+Δɡ) (2)
by the relations (1) and (2), the relationship between the pose error Δ X and the geometric parameter error Δ pg at the robot tip is established as follows:
ΔX＝Η(ɡ)Δɡ (3)
wherein, the Η (Ag) is an error identification Jacobian matrix, and after the joint position of the robot is known, the actual value of the matrix can be obtained; therefore, the joint error delta Ag can be obtained through the relation (3) by detecting the terminal pose error of the robot;
s2: nominal inverse kinematics algorithm modules f are respectively designed in the robot controller-1Positive kinematic algorithm X with geometric parameter error Δ AgEThe module and a module for calculating a robot geometric Jacobian matrix J algorithm;
s3: when the robot controller converts the command value X of Cartesian spaceCWhen the robot controller is issued, the robot controller realizes a compensation kinematics algorithm by a method of combining nominal inverse kinematics, homogeneous transformation positive kinematics with error parameters and joint space deviation inverse solution by using geometric Jacobian.
2. A kinematic method for improving the absolute positioning accuracy of an industrial robot according to claim 1, characterized in that: the S3 specifically includes the following steps:
s31: solving Cartesian space pose instruction value X through nominal inverse kinematics modelCCorresponding nominal values theta of all joints;
s32: then substituting the nominal joint value obtained by the previous step into a positive kinematics model considering the geometric error, and solving the Cartesian coordinate value X of the geometric errorE；
S33: solving the cartesian coordinate error value Δ X ═ XC-XE；
S34: passing through the Jacobian matrix J of the joint position q at that time, and inverting J-1Jointly solving the deviation value delta q of each axis corresponding to the joint space with the delta X obtained in the step S33;
s35: compensating each joint coordinate value q as q + δ q;
s36: substituting the joint coordinate value compensated by S35 into positive kinematics considering geometric error, and solving Cartesian coordinate value X compensated by the jointE；
S37: calculating the error between the Cartesian coordinate command value and the compensated Cartesian coordinate valueC-XEComparing the magnitude of the error with a specified Cartesian coordinate allowable error delta; if true, proceed to S38, otherwise proceed to S34;
s38: the joint coordinate value q of the latest compensation in S35 is issued to the position controller of each axis.
3. A kinematic method for improving the absolute positioning accuracy of an industrial robot according to claim 2, characterized in that: at S31 and S32 of step S3, the modified cartesian coordinate values including the geometric error are calculated using the robot nominal inverse solution, as follows:
XE＝f(q,ɡ+Δɡ) (4)。
4. a kinematic method for improving the absolute positioning accuracy of an industrial robot according to claim 2, characterized in that: at S34 of step S3, the pose error in cartesian space is mapped to joint variables by the geometric jacobian matrix J as follows:
δq＝J-1(q)·ΔX (5)。
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