CN114700954B - Six-degree-of-freedom industrial robot hole making rigidity optimization method - Google Patents
Six-degree-of-freedom industrial robot hole making rigidity optimization method Download PDFInfo
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- 238000004458 analytical method Methods 0.000 claims description 2
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- 238000006073 displacement reaction Methods 0.000 description 10
- 238000004364 calculation method Methods 0.000 description 7
- 238000003754 machining Methods 0.000 description 4
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- 230000036544 posture Effects 0.000 description 3
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Classifications
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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
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
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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
- B25J11/005—Manipulators for mechanical processing tasks
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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
- B25J9/1679—Programme controls characterised by the tasks executed
- B25J9/1687—Assembly, peg and hole, palletising, straight line, weaving pattern movement
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]
Abstract
The invention discloses a six-degree-of-freedom industrial robot hole making rigidity optimization method, which comprises the following steps of: according to the target hole site, determining the pose of the robot to be optimized, and enabling the robot to rotate around the axis of the end effector tool to obtain a limited reachable pose(i=1, 2, …, n), calculating the corner limit criterion of all reachable posespIndex of dexterityKCICoefficient of system stiffnessKAccording to the weight coefficient、、The rigidity performance optimization criterion of all the poses is obtained by synthesizing the obtained indexesgSelecting the pose with the optimal value corresponding to the reachable pose as the pose after rigidity optimizationThe method realizes the optimization of various processing pose, can improve the hole making precision of the robot, enhance the hole making stability of the robot and meet the application requirements of the six-degree-of-freedom industrial robot in hole making tasks.
Description
Technical Field
The invention relates to the technical field of rigidity optimization, in particular to a six-degree-of-freedom industrial robot hole-making rigidity optimization method.
Background
The current manufacturing industry has increasingly increased demands on production efficiency and cost, and six-degree-of-freedom industrial robots can process the same point in countless different postures by virtue of the redundant degrees of freedom. The unique flexibility and automation characteristics of industrial robots make them widely used in the field of drilling. However, the six-degree-of-freedom industrial robot has the structural characteristics that the rigidity is about 1/50 times that of a numerical control machine tool, and is easy to vibrate in the hole making process, so that the cutter is seriously worn, and the service life is shortened too rapidly. Meanwhile, machining vibration causes the reduction of hole making precision, the reduction of machining efficiency, even the occurrence of dangerous problems such as machining failure, tipping and the like, and the application prospect of the industrial robot in the field of hole making is severely limited. Therefore, mathematical analysis of the hole making rigidity of the six-degree-of-freedom industrial robot is an important precondition for improving the machining precision of the six-degree-of-freedom industrial robot, and has important practical significance for optimizing the hole making rigidity of the six-degree-of-freedom industrial robot.
Chinese patent CN 111702762a discloses a method for optimizing the working posture of an industrial robot, which establishes an industrial robot stiffness model, and adopts fairing processing to implement posture optimization of a processing track and a target point according to spatial feature points. Chinese patent CN 113894782a discloses a method and system for optimizing milling gesture of robot based on rigidity orientation, which divides stable processing space and potential chatter space by calculating main rigidity difference of tool nose, and determines space boundary where chatter occurs by redundancy angle, so as to realize stable processing on milling path.
Although the method realizes the enhancement of the processing stability on the processing track, the method does not leave a corner allowance for the industrial robot from the safety point of view, does not consider the dexterity of the robot in the processing movement, and mainly focuses on milling processing in the application field. Therefore, the processing stability of the industrial robot in the hole making field cannot be improved pertinently, and the movement dexterity and the movement safety of the robot cannot be considered to optimize the hole making processing rigidity.
Disclosure of Invention
In view of the above, the invention provides a six-degree-of-freedom industrial robot hole-making rigidity optimization method, aiming at the technical problem that the industrial robot dexterity and safety cannot be considered to realize hole-making rigidity optimization in the prior art.
The technical scheme of the invention is that the six-degree-of-freedom industrial robot hole making rigidity optimization method for realizing hole making rigidity optimization by considering the dexterity and safety of the industrial robot is provided, and the method comprises the following specific steps:
step one: determining the pose to be optimized of the robot by the target hole siteAt this time, the rotation angle of the robot around the axis direction of the end effector tool is +.>=0°, rotating the robot around the axis direction of the tool of the end effector by 1 ° as a step length to obtain a candidate pose, judging whether the pose is reachable, and if so, marking as reachable pose +.>Repeating the procedure to obtain a limited number +.>、 />、……、/>(n.ltoreq.300) up to->（ />) The number n of reached limit or reached pose reaches 300;
step two: setting the robot corner limit safety margin to 10%, and calculating all reachable pose(iRobot joint rotation angle limit criterion under =1, 2, …, n)pThe criterion reaches the maximum value near the joint limit of the corners, which indicates that the corners of the robot are all close to the limit, and the gradient is 0 at the joint limit far away from the corners, which indicates that the corners of the robot are all at the safe position;
the robot joint rotation angle limit criterion in the second steppThe specific calculation method of (2) is as follows:
wherein the method comprises the steps ofIs the joint rotation angle of the robot, subscriptiRepresent the firstiThe subscripts max and min respectively represent the maximum and minimum joint angles after 10% angle allowance is reserved;
step three: calculate all reachable poses(iRobot dexterity index under =1, 2, …, n)KCI；
The specific calculation method of the robot dexterity index KCI in the third step is as follows:
wherein the method comprises the steps ofIs a weighting matrix; />、/>Respectively representing an i-order identity matrix and a j-order identity matrix; />、/>The root mean square of the linear velocity and the angular velocity vector of the tail end of the robot body is respectively obtained. />Condition number for normalized Jacobian matrix;nthe number of joints of the robot;
step four: calculate all reachable poses(iRigidity coefficient of industrial robot hole making system under =1, 2, …, n)K；
Rigidity coefficient of industrial robot hole making system in the fourth stepKThe specific calculation method of (2) is as follows:
according to the relation between the stress, deformation and rigidity matrix of the tail end of the robot hole making system, the rigidity matrix of the tail end of the robot hole making system is segmented:
wherein the method comprises the steps offA force vector applied to the tail end of the robot;ma moment vector applied to the tail end of the robot;、/>、/>、/>the system comprises a force-linear displacement stiffness matrix, a force-angular displacement stiffness matrix, a moment-linear displacement stiffness matrix and a moment-angular displacement stiffness matrix of a robot hole making system;dthe deformation line displacement of the tail end of the robot is realized;δthe robot is deformed and angularly displaced at the tail end of the robot. Because the stress born by the tail end is far greater than the moment born by the tail end when the robot is used for making holes, the method can be simplified into:
if the robot end bears a force vectorfAs a unit vector, the above formula can be reduced to:
from the above, it is apparent that the stiffness of the robotic hole making system mathematically forms an ellipsoid, referred to as a stiffness ellipsoid. The stiffness ellipsoid describes in a physical sense the stiffness properties of the robotic hole making system.The matrix has 3 mutually orthogonal eigenvectors, the corresponding direction is the direction of the principal axis of the rigidity ellipsoid, and the corresponding eigenvalue is the length of the principal axis of the rigidity ellipsoid. Taking the length of a rigidity ellipsoid main shaft as the rigidity coefficient of an industrial robot hole making systemK：
Wherein the method comprises the steps ofK x 、K y 、K z The rigidity coefficients of the three directions under the flange coordinate system of the industrial robot hole making system are X, Y, Z respectively,λ 2 、λ 1 、λ 3 the lengths of the main axes of the ellipsoids of the rigidity in the corresponding directions are respectively;
step five: according top、KCI、KCalculate all reachable poses(iRigidity performance optimization criterion of robot pore-forming system under condition of (1, 2, …, n)gBy analyzing and comparing the rigidity performance optimization criteria under each reachable posegObtaining the optimal value thereofg max Corresponding reachable pose->Pose after rigidity optimization->。
Optionally, the stiffness performance optimization criterion of the industrial robot hole making system under each reachable pose is calculated as follows:
wherein the method comprises the steps of、/>、/>The joint rotation angle criterion after the unitization, the robot dexterity index and the rigidity coefficient of the industrial robot hole making system are respectively determined; />、/>、/>The weight coefficients of the three functions are considered to be equally important in the robot hole making process.
Compared with the prior art, the invention has the following advantages: by adopting the optimization method, the optimal processing pose can be obtained from the three aspects of robot movement dexterity, robot corner limit and robot system rigidity, the robot hole making precision is improved, meanwhile, the robot kinematic performance is kept excellent, and each corner is at a safe position, so that the defect of insufficient rigidity of the industrial robot is overcome, the hole making stability of the robot is enhanced, and the application requirements of the six-degree-of-freedom industrial robot in hole making tasks are met.
Drawings
FIG. 1 is an optimization effect diagram of a six-degree-of-freedom industrial robot hole making stiffness optimization method of the invention;
FIG. 2 is a schematic view of the angles of rotation of the pose before and after optimization of the method for optimizing the hole making rigidity of the six-degree-of-freedom industrial robot;
FIG. 3 is a graph showing the variation of the joint limit rotation angle criterion according to one embodiment of the present invention;
FIG. 4 is a graph showing the variation of the joint limit rotation angle criterion according to one embodiment of the present invention;
FIG. 5 is a graph showing the variation of the stiffness coefficient in the X direction of a joint according to an embodiment of the present invention;
FIG. 6 is a graph showing the variation of the Y-direction stiffness coefficient of a joint according to an embodiment of the present invention;
FIG. 7 is a graph showing the variation of the Z-direction stiffness coefficient of a joint according to one embodiment of the present invention;
FIG. 8 is a graph showing the variation of stiffness property optimization criteria according to one embodiment of the present invention;
Detailed Description
The invention will be further described with reference to the drawings and the specific examples.
The invention is intended to cover any alternatives, modifications, equivalents, and variations that fall within the spirit and scope of the invention. In the following description of preferred embodiments of the invention, specific details are set forth in order to provide a thorough understanding of the invention, and the invention will be fully understood to those skilled in the art without such details. Furthermore, the drawings of the present invention are not necessarily to scale, nor are they necessarily drawn to scale.
1-2, the six-degree-of-freedom industrial robot hole making rigidity optimization method for realizing hole making rigidity optimization by considering the dexterity and safety of the industrial robot comprises the following specific steps:
step one: determining the pose to be optimized of the robot by the target hole site At this time, the rotation angle of the robot around the axis direction of the end effector tool is +.>=0°, rotating the robot around the axis direction of the tool of the end effector by 1 ° as a step length to obtain a candidate pose, judging whether the pose is reachable, and if so, marking as reachable pose +.>Repeating the procedure to obtain a limited number +.>、/>、……、/>(n.ltoreq.300) up to->（ />) The number n of reached limit or reached pose reaches 300;
step two: setting the robot corner limit safety margin to 10%, and calculating all reachable pose(iRobot joint rotation angle limit criterion under =1, 2, …, n)pThe criterion reaches the maximum value near the joint limit of the corners, which indicates that the corners of the robot are all close to the limit, and the gradient is 0 at the joint limit far away from the corners, which indicates that the corners of the robot are all at the safe position;
the robot joint rotation angle limit criterion in the second steppThe specific calculation method of (2) is as follows:
wherein the method comprises the steps ofIs the joint rotation angle of the robot, subscriptiRepresent the firstiThe subscripts max and min respectively represent the maximum and minimum joint angles after 10% angle allowance is reserved;
step three: calculate all reachable poses(iRobot dexterity index under =1, 2, …, n)KCI；
The robot dexterity index in the third stepKCIThe specific calculation method of (2) is as follows:
wherein the method comprises the steps ofIs a weighting matrix; />、/>Respectively representi、jA rank identity matrix; />、/>The root mean square of the linear velocity and the angular velocity vector of the tail end of the robot body is respectively obtained. />Condition number for normalized Jacobian matrix;nthe number of joints of the robot;
step four: calculate all reachable poses(iRigidity coefficient of industrial robot hole making system under =1, 2, …, n)K；
Rigidity coefficient of industrial robot hole making system in the fourth stepKThe specific calculation method of (2) is as follows:
according to the relation between the stress, deformation and rigidity matrix of the tail end of the robot hole making system, the rigidity matrix of the tail end of the robot hole making system is segmented:
wherein the method comprises the steps offA force vector applied to the tail end of the robot;ma moment vector applied to the tail end of the robot;、/>、/>、/>the system comprises a force-linear displacement stiffness matrix, a force-angular displacement stiffness matrix, a moment-linear displacement stiffness matrix and a moment-angular displacement stiffness matrix of a robot hole making system;dthe deformation line displacement of the tail end of the robot is realized;δthe robot is deformed and angularly displaced at the tail end of the robot. Due to the machineWhen people make holes, the stress born by the tail end is far greater than the stress moment born by the tail end, and the above formula can be simplified into:
if the robot end bears a force vectorfAs a unit vector, the above formula can be reduced to:
from the above, it is apparent that the stiffness of the robotic hole making system mathematically forms an ellipsoid, referred to as a stiffness ellipsoid. The stiffness ellipsoid describes in a physical sense the stiffness properties of the robotic hole making system.The matrix has 3 mutually orthogonal eigenvectors, the corresponding direction is the direction of the principal axis of the rigidity ellipsoid, and the corresponding eigenvalue is the length of the principal axis of the rigidity ellipsoid. Taking the length of a rigidity ellipsoid main shaft as the rigidity coefficient of an industrial robot hole making systemK：
Wherein the method comprises the steps ofK x 、K y 、K z The rigidity coefficients of the three directions under the flange coordinate system of the industrial robot hole making system are X, Y, Z respectively,λ x 、λ y 、λ z the lengths of the main axes of the ellipsoids of the rigidity in the corresponding directions are respectively;
step five: according top、KCI、KCalculate all reachable poses(iRigidity performance optimization criterion of robot pore-forming system under condition of (1, 2, …, n)gAnalyzing and comparing each reachable poseThe following rigidity performance optimization criteriagSelecting the optimal valueg max Corresponding reachable pose->Pose after rigidity optimization->The method comprises the steps of carrying out a first treatment on the surface of the Rigidity performance optimization criterion of industrial robot hole making system under each reachable posegThe calculation is as follows:
wherein the method comprises the steps of、/>、/>The joint rotation angle criterion after the unitization, the robot dexterity index and the rigidity coefficient of the industrial robot hole making system are respectively determined; />、 />、 />The weight coefficients of the three functions are considered to be equally important in the robot hole making process;
the invention is further illustrated by the following specific examples.
To be optimized in pose=[-5.89°,21.93°,-7.47°,-0.30°,77.69°,85.85°] T For example, all reachable positions are obtained according to step one>、 />、……、/>(n is less than or equal to 300), calculating joint rotation angle limit criteria under all the reachable pose according to the second step, and as shown in a result shown in a figure 3, clearly expressing experimental results by taking angles of all the reachable pose as horizontal coordinates, wherein the reachable angle range is +.>The abscissa is used unless otherwise indicated.
Calculating all the robot dexterity indexes under the reachable pose according to the third stepKCIThe results are shown in FIG. 4. In the figure, P is the initial pose corresponding point, and 0.45 is the settingKCIA threshold above which the robot dexterity meets the optimization requirement.
Calculating rigidity coefficients of the industrial robot hole making system under all the reachable pose according to the fourth stepKThe results are shown in FIGS. 5-7. Pa in the figure represents the pose to be optimized.
According to step fiveη p =η KCI =η K =1 calculating the stiffness performance optimization criterion of the robot hole making system under all reachable positionsgThe results are shown in FIG. 8. In the figure, pa represents the pose to be optimized, and Pb represents the pose after optimization.
5 groups of optimization effect verification experiments are carried out on a 3mm aluminum plate, a drill bit with the diameter of 6mm and the feeding speed of 1mm/s are adopted, hole making experiments are respectively carried out at different spindle rotating speeds, the maximum error of the aperture is measured by an inside micrometer, and the experimental results are shown in table 1.
Table 1: pore diameter maximum error meter before and after rigidity optimization of pore-forming system
As shown in the table, the maximum error of the aperture after the rigidity of the hole making system is optimized is smaller than that before the rigidity is optimized, the maximum aperture error is not more than 0.05mm, the optimization method is effective, and the specific embodiment is finished.
The foregoing is illustrative of the preferred embodiments of the present invention, and is not to be construed as limiting the claims. The present invention is not limited to the above embodiments, and the specific structure thereof is allowed to vary. In general, all changes that come within the meaning and range of equivalency of the claims are to be embraced within their scope.
Claims (2)
1. The six-degree-of-freedom industrial robot hole making rigidity optimization method is characterized by comprising the following steps of:
step one: determining the pose to be optimized of the robot by the target hole siteAt this time, the rotation angle of the robot around the axis direction of the end effector tool is +.>=0°, rotating the robot around the axis direction of the tool of the end effector by 1 ° as a step length to obtain a candidate pose, judging whether the pose is reachable, and if so, marking as reachable pose +.>Repeating the procedure to obtain a limited number +.>、 />、……、 />(n.ltoreq.300) up to->（/>) The number n of reached limit or reached pose reaches 300;
step two: setting the robot corner limit safety margin to 10%, and calculating all reachable pose(iRobot joint rotation angle limit criterion under =1, 2, …, n)p；
Step three: calculate all reachable poses(iRobot dexterity index under =1, 2, …, n)KCI；
Step four: calculate all reachable poses(iRigidity coefficient of industrial robot hole making system under =1, 2, …, n)K；
Step five: according top、KCI、KCalculate all reachable poses(iRigidity performance optimization criterion of robot pore-forming system under condition of (1, 2, …, n)gComparing the rigidity performance optimization criteria under each reachable pose through comparison analysisgObtaining the optimal value thereofg max Corresponding reachable pose->Pose after rigidity optimization->。
2. The six-degree-of-freedom industrial robot hole making stiffness optimization method according to claim 1, wherein the stiffness performance optimization criterion of the industrial robot hole making system in the fifth step is calculated as follows:
wherein the method comprises the steps of、 />、 />The joint rotation angle criterion after the unitization, the robot dexterity index and the rigidity coefficient of the industrial robot hole making system are respectively determined; />、 />、 />Is->、 />、 />The weight coefficient of the three are equally important in the robot hole making process.
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| US20090098404A1 (en) * | 2007-10-16 | 2009-04-16 | Honda Motor Co., Ltd. | System for forming holes in metal sheet |
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