CN117921685B - Calibration method for co-positioning precision of double robots - Google Patents
Calibration method for co-positioning precision of double robots Download PDFInfo
- Publication number
- CN117921685B CN117921685B CN202410334586.9A CN202410334586A CN117921685B CN 117921685 B CN117921685 B CN 117921685B CN 202410334586 A CN202410334586 A CN 202410334586A CN 117921685 B CN117921685 B CN 117921685B
- Authority
- CN
- China
- Prior art keywords
- robot
- error
- double
- coordinate system
- matrix
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 78
- 239000011159 matrix material Substances 0.000 claims description 122
- 238000005070 sampling Methods 0.000 claims description 56
- 230000035945 sensitivity Effects 0.000 claims description 53
- 230000009466 transformation Effects 0.000 claims description 27
- 230000008569 process Effects 0.000 claims description 24
- 230000009977 dual effect Effects 0.000 claims description 23
- 239000013598 vector Substances 0.000 claims description 22
- 238000013528 artificial neural network Methods 0.000 claims description 17
- 238000003062 neural network model Methods 0.000 claims description 17
- 238000004364 calculation method Methods 0.000 claims description 16
- 238000010206 sensitivity analysis Methods 0.000 claims description 14
- 238000009826 distribution Methods 0.000 claims description 13
- 230000000694 effects Effects 0.000 claims description 8
- 210000002364 input neuron Anatomy 0.000 claims description 8
- 210000004205 output neuron Anatomy 0.000 claims description 8
- 230000008859 change Effects 0.000 claims description 7
- 238000013507 mapping Methods 0.000 claims description 6
- 238000005259 measurement Methods 0.000 claims description 6
- 238000010606 normalization Methods 0.000 claims description 6
- 238000005094 computer simulation Methods 0.000 claims description 5
- 238000002790 cross-validation Methods 0.000 claims description 5
- 238000004422 calculation algorithm Methods 0.000 claims description 4
- 238000000540 analysis of variance Methods 0.000 claims description 3
- 230000008878 coupling Effects 0.000 claims description 3
- 238000010168 coupling process Methods 0.000 claims description 3
- 238000005859 coupling reaction Methods 0.000 claims description 3
- 230000005484 gravity Effects 0.000 claims description 3
- 238000012163 sequencing technique Methods 0.000 claims description 3
- 230000008045 co-localization Effects 0.000 claims description 2
- 238000012545 processing Methods 0.000 description 19
- 238000004519 manufacturing process Methods 0.000 description 8
- 238000012549 training Methods 0.000 description 6
- 238000003860 storage Methods 0.000 description 4
- 238000013461 design Methods 0.000 description 3
- 238000010586 diagram Methods 0.000 description 3
- 238000001553 co-assembly Methods 0.000 description 2
- 238000000354 decomposition reaction Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 238000011065 in-situ storage Methods 0.000 description 2
- 210000002569 neuron Anatomy 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 230000026676 system process Effects 0.000 description 2
- 238000013459 approach Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004590 computer program Methods 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 230000004069 differentiation Effects 0.000 description 1
- 230000007246 mechanism Effects 0.000 description 1
- PKAHQJNJPDVTDP-UHFFFAOYSA-N methyl cyclopropanecarboxylate Chemical compound COC(=O)C1CC1 PKAHQJNJPDVTDP-UHFFFAOYSA-N 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 238000005498 polishing Methods 0.000 description 1
- 230000000750 progressive effect Effects 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 238000005507 spraying Methods 0.000 description 1
- 238000007619 statistical method Methods 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
- 238000010200 validation analysis Methods 0.000 description 1
- 238000012795 verification Methods 0.000 description 1
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1653—Programme controls characterised by the control loop parameters identification, estimation, stiffness, accuracy, error analysis
-
- 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
- B25J9/161—Hardware, e.g. neural networks, fuzzy logic, interfaces, processor
-
- 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
- B25J9/1661—Programme controls characterised by programming, planning systems for manipulators characterised by task planning, object-oriented languages
-
- 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
- B25J9/1692—Calibration of manipulator
Landscapes
- Engineering & Computer Science (AREA)
- Robotics (AREA)
- Mechanical Engineering (AREA)
- Automation & Control Theory (AREA)
- Physics & Mathematics (AREA)
- Artificial Intelligence (AREA)
- Evolutionary Computation (AREA)
- Fuzzy Systems (AREA)
- Mathematical Physics (AREA)
- Software Systems (AREA)
- Numerical Control (AREA)
- Manipulator (AREA)
Abstract
The invention relates to the technical field of dual-robot collaborative calibration, which solves the technical problem that the dual-robot collaborative positioning precision is low due to a plurality of residual errors which cannot be identified through a model in a dual-robot system, in particular to a calibration method of the dual-robot collaborative positioning precision.
Description
Technical Field
The invention relates to the technical field of cooperative calibration of double robots, in particular to a calibration method of cooperative positioning precision of double robots.
Background
Aerospace manufacturing is a high-technology industry in China and is in the top position of advanced equipment manufacturing industry. The large complex components are the overall configuration of the spacecraft, support, bear and transmit loads for all subsystem instruments and equipment, and high-quality and high-efficiency processing is a key for ensuring reliable operation of the spacecraft.
Typically, large complex components typically comprise hundreds of parts to be machined of various shapes, including a large number of two or more associated mounting brackets that subsequently need to be assembled with the same external load (e.g., space telescope, space robot, etc.), commonly referred to as a set of support bracket associated brackets of the type having dimensional constraints with respect to each other, with their mounting surfaces being associated mounting surfaces, so that a set of associated mounting surfaces has a high index of uniformity accuracy. When the distribution distance of a group of associated mounting brackets on the surface of a complex component is too large and exceeds the processing capacity of a single robot, the complex component is required to be cooperatively processed by a double-robot cooperative manufacturing system so as to meet the consistency precision required by design.
However, because errors generated in the movement process of the single robot are random, when the double-robot system processes a group of associated feature holes exceeding the working space of the single robot on the surface of a complex component, the control is improper, not only the high-precision positioning of the single-side robot cannot be completed, but also the positioning errors of the robots on two sides are extremely likely to be overlapped because the robots are finally positioned in the opposite directions of the target hole site, and finally the pose of the external loading equipment under the complex component coordinate system is deviated from the designed pose, and even the external loading equipment cannot be assembled smoothly.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a calibration method for the co-location precision of double robots, which solves the technical problem that the co-location precision of the double robots is lower due to a plurality of residual errors which cannot be identified through a model in the double robot system.
In order to solve the technical problems, the invention provides the following technical scheme: a calibration method of co-positioning precision of double robots comprises the following steps:
S1, acquiring the pose of sampling points of the double robots in a working space relative to respective base coordinate systems through a laser tracker, and recording joint rotation angle values of the double robots in each sampling point and coordinate measurement values of the corresponding laser tracker under the pose;
S2, constructing a double-robot co-location error model based on the coordinate system error and the connecting rod error, and determining uncertainty parameters of double-robot system errors in the double-robot co-location error model;
s3, constructing a sensitivity function, performing sensitivity analysis on uncertainty parameters of the double-robot co-location error model by combining the sensitivity function to obtain a sensitivity analysis result, and performing step-by-step joint identification on error sources of the double-robot co-location error model according to the sensitivity analysis result to obtain residual errors in the double-robot system;
s4, establishing a joint rotation angle-based residual error equation of the double robots according to the residual errors;
S5, constructing a BP neural network model by taking joint rotation angles of the double robots as input neurons and taking absolute positioning errors of the main robots and co-positioning errors of the double robots as output neurons;
S6, distributing optimal initial weights and thresholds for the BP neural network by adopting a K-layer folding cross-validation algorithm, and completing prediction of residual errors in the double-robot system;
And S7, fitting a residual error equation by adopting a BP neural network module, and correcting and compensating original parameters according to the fitting result of the BP neural network on the residual error so as to improve the co-positioning precision of the double robots.
Further, in step S2, the specific process includes the following steps:
s21, establishing a dual-robot co-location error model by using an actual coordinate transformation equation of a tool coordinate system of the slave robot relative to a tool coordinate system of the master robot, wherein the model is as follows:
In the above formula, toolTtool' and d toolTtool' are a theoretical coordinate transformation matrix and an error matrix between the robot tool coordinate system and the master robot tool coordinate system, respectively; a i and dA i are a theoretical coordinate transformation matrix and an error matrix between the i-1 th connecting rod coordinate system and the i-1 th connecting rod coordinate system, i= 1,2,3,4,5,6,1 ', 2', 3 ', 4', 5 ', 6';
S22, simplifying a double-robot co-location error model to obtain a double-robot co-location error matrix, wherein the method comprises the following steps:
toolΔtool'＝toolΔ6+6ΔM+MΔN+NΔ12+12Δtool'
In the above, toolΔtool' is a co-location error matrix from the robot tool coordinate system to the master robot tool coordinate system; toolΔ6 Error for the host robotic tool coordinate system; 6'Δtool' Is the tool coordinate system error of the slave robot; MΔN Modeling errors for a master-slave robot base coordinate system; 6ΔM Is the error of the connecting rod coordinate system of the host robot; NΔ6' Is the error of the connecting rod coordinate system of the slave robot;
S23, determining uncertainty parameters of a double-robot system error according to a double-robot co-location error matrix, wherein the uncertainty parameters comprise a double-robot tool coordinate system error, a double-robot base coordinate system modeling error and a double-robot connecting rod coordinate system error;
s24, rewriting a double-robot co-location error matrix into:
In the above-mentioned method, the step of, tooldtool' And toolδtoo' are translational and rotational differential amounts, respectively, of error from the robotic tool coordinate system to the master robotic tool coordinate system; m f and DeltaX f are respectively a double-robot system coordinate system error Jacobian matrix and an error column vector; m s and DeltaX s are respectively an error Jacobian matrix and an error column vector of the slave robot link coordinate system; m m and DeltaX m are respectively an error Jacobian matrix and an error column vector of a connecting rod coordinate system of the host robot; j is a master-slave robot cooperative error jacobian matrix considering multi-source errors; Δx is the column vector of all errors.
Further, in step S3, the specific process includes the following steps:
S31, constructing a sensitivity function by taking an uncertainty parameter as a variable, and obtaining a first-order sensitivity coefficient S i and a total sensitivity coefficient ST i for representing the influence degree of the uncertainty parameter on the total variance output by the double-robot co-location error model;
S32, dividing uncertainty parameters into main parameters and non-main parameters by taking the total sensitivity coefficient ST i as a limit with the ratio of 95%, wherein more than 95% of the uncertainty parameters are main parameters;
S33, summing the main parameters and marking as Sum (1-j)(STj), and defining the summed parameters as the main parameters when the specific gravity of the Sum parameter accounting for the overall sensitivity coefficient ST i is greater than or equal to 0.95, namely: sum (1-j)(STj)/Sum(STi) is more than or equal to 0.95;
S34, sequencing the coordinate system errors of the double-robot tool and the modeling errors of the double-robot base coordinate system and the coordinate system errors of the double-robot connecting rod according to Sum (1-j)(STj)/Sum(STi) not less than 0.95 in priority;
And S35, carrying out step-by-step joint identification on the error sources according to the priority order to obtain the residual error in the double-robot system.
Further, in step S31, the specific process includes the steps of:
s311, defining n uncertainty parameters of the double-robot system error, and writing into a function form taking the uncertainty parameters as variables, namely:
In the above-mentioned method, the step of, tooldtool' And toolδtoo' are translational and rotational differential amounts, respectively, of error from the robotic tool coordinate system to the master robotic tool coordinate system; f (DeltaX) represents an influence function of the uncertainty parameter on the co-location error of the double robots; Δx is a vector consisting of n uncertainty parameters;
s312, expressing the function taking the uncertainty parameter as a variable as a form of analysis of variance, namely:
In the above formula, f 0 (Δx) represents an expected value of f (Δx); fi (Δxi) represents the effect of the change in the ith parameter on the function value; f i,j(ΔXi,ΔXj) represents the effect of the common variation of the ith and j-th parameters on the function value; f 1,2,…,n(ΔX1,ΔX2,ΔX3,…,ΔXn) represents the influence of the common change of the 1 st to nth parameters on the function value;
S313, regarding all the input uncertainty parameters as continuous random variables, and calculating the variance of f (delta X), wherein the calculation formula of the variance of f (delta X) is as follows:
Wherein ,Di(f)＝Var[EX～i(f|ΔXi)];Di,j(f)＝Var[EX～(i,j)(f|ΔXi,ΔXj)]-Di(f)-Dj(f),X～i denotes all variables except Δx i, and X to (i, j) denote all variables except Δx i、ΔXj;
s314, carrying out normalization processing on a calculation formula of the f (delta X) variance, and representing the influence degree of the total variance output by the double-robot co-location error model;
S315, introducing an overall sensitivity coefficient ST i, and carrying out overall arrangement on the independent influence degree of delta X i on the positioning error and the influence degree of delta X i on the positioning error when the delta X i is coupled with other uncertain parameters;
S316, sampling n uncertainty parameters delta X to obtain m groups of random variables, and generating sampling matrixes delta A n×m and delta B n×m of the uncertainty parameters delta X;
S317, constructing a new matrix delta A B (i) according to the sampling matrices delta A n×m and delta B n×m, enabling the ith column in the new matrix delta A B (i) to be delta B i, and obtaining new matrices delta A B (i) and delta B A (i), wherein the new matrices delta A B (i) are as follows:
S318, determining the expected f 0 (delta A) and the variance D of the double-robot co-location error model; for the matrix Δa, the expected f 0 (Δa) and variance D of the dual robot co-location error model are:
the calculation formula for the expected f 0 (ΔA) is:
The calculation formula of the variance D is:
In the above formula, N is the total number of subintervals; f (delta A) j is the influence function of the ith column of the sampling matrix delta A of the uncertainty parameter delta X on the end positioning error of the double-robot system; f 2(ΔA)j is the square of the influence function of the ith column of the sampling matrix deltaa of the uncertainty parameter deltax on the end positioning error of the dual robot system; The desired square of the influence function of the sampling matrix deltaa of the uncertainty parameter deltax on the end positioning error of the dual robot system.
S319, a first-order sensitivity coefficient S i and an overall sensitivity coefficient ST i are defined according to the expected f 0 (Δa) and the variance D.
Further, in step S314, the formula of the normalization process is:
In the method, in the process of the invention, S i is a first-order variance ratio, defined as a first-order sensitivity coefficient of an uncertainty parameter DeltaX i, used for representing the influence degree of DeltaX i on the total variance of the model output; s i,j is a second order variance ratio, defined as a second order sensitivity coefficient of the uncertainty parameter Δx i,ΔXj, used to characterize the extent of influence of Δx i,ΔXj on the overall variance of the model output after coupling.
Further, in step S315, the expression of the overall sensitivity coefficient ST i is:
In the above formula, ST i is the overall sensitivity coefficient; s i is a first order variance ratio; s i,j is the second order variance ratio.
Further, in step S319, the first-order sensitivity coefficient S i is expressed as:
The overall sensitivity coefficient ST i is expressed as:
In the above formula, f (Δb) j is an influence function of the j-th column of the sampling matrix Δb of the uncertainty parameter on the end positioning error of the dual robot system; and exchanging the influence function of the j-th column after the i-th column on the end positioning error of the double-robot system for the sampling matrixes delta A and delta B of the uncertainty parameters.
Further, in step S316, the specific process includes the following steps:
S3161, let DeltaS i be the m sampling result sets of the uncertainty parameter DeltaX i, and calculate the corresponding probability distribution P i, wherein the calculation formula of the probability distribution P i is as follows:
Pi＝Fi(ΔSi)
In the above formula, F i is a mapping function;
S3162, mapping the value range of the uncertainty parameter DeltaX i to a probability interval of [0,1] through a F i () function, and equally dividing the probability interval into N subintervals;
s3163, defining random variable xi with value interval of [0,1] in each subinterval, and sampling the ith uncertain parameter delta S i according to the random variable xi to obtain a jth sampling value delta S ij;
S3164, forming a sample matrix delta S n×m according to a sampling value delta S ij, wherein after the uncertainty parameter delta X i is sampled, the sampling value can form a sample matrix delta S n×m;
s3165, generating sampling matrices Δa n×m and Δb n×m of the uncertain parameter Δx from the sample matrix Δs n×m. Further, in step S4, the residual error equation based on the joint rotation angle is as follows:
Em＝mbTmf -1wTmb -1wTmf'
In the above description, E m is the absolute positioning error matrix of the host robot in the dual-robot system, mbTmf is the theoretical coordinate transformation matrix of the flange coordinate system of the host robot relative to the base coordinate system, wTmb is the theoretical coordinate transformation matrix of the flange coordinate system of the host robot relative to the world coordinate system, wTmf' is the theoretical coordinate transformation matrix of the actually measured flange coordinate system of the laser tracker relative to the world coordinate system;
Erel＝mfTsf -1mf'Tsf'
in the above formula, E rel is a dual robot co-location error matrix, mfTsf and mf'Tsf' are a theoretical coordinate transformation matrix and an actual coordinate transformation matrix of the slave robot flange coordinate system relative to the master robot flange coordinate system.
Further, in step S5, the BP neural network model sequentially includes an input layer, a hidden layer, and an output layer, where each hidden layer includes a trainable parameter, a weight, a deviation, a nonlinear function, and a torrent layer;
The output neurons are absolute positioning errors of the host robots and co-positioning errors of the double robots, and joint corners of the double robots are used as input neurons.
By means of the technical scheme, the invention provides a calibration method for the co-positioning precision of the double robots, which has at least the following beneficial effects:
1. According to the invention, the multi-error sources of the double robots are subjected to step-by-step joint compensation through sensitivity analysis, a theoretical basis is provided for the identification sequence, the loss of precision caused by the complex identification sequence in data processing is avoided, finally, the identified residual errors are fitted by adopting the BP neural network, the identified geometric parameters and the training network are input into the double robot control system, and the co-location precision of the double robot system is more effectively improved.
2. According to the invention, the BP neural network is adopted to identify and compensate the residual errors which cannot be identified by the double-robot co-positioning error model, so that the requirements of absolute positioning precision of a single robot and co-positioning precision of the double robots in the double-robot co-assembly process of large complex components can be simultaneously met.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute a limitation on the application. In the drawings:
FIG. 1 is a flow chart of a calibration method of the dual robot co-location accuracy of the present invention;
FIG. 2 is a schematic diagram of a field layout of a dual robot system of the present invention;
FIG. 3 is a schematic diagram of a BP neural network model of the absolute positioning error of the master robot of the present invention;
FIG. 4 is a schematic diagram of a BP neural network model of the dual robot co-localization error of the present invention;
FIG. 5 is a graph showing the effect of the present invention on the residual error fit.
Detailed Description
In order that the above-recited objects, features and advantages of the present application will become more readily apparent, a more particular description of the application will be rendered by reference to the appended drawings and appended detailed description. Therefore, the realization process of how to apply the technical means to solve the technical problems and achieve the technical effects can be fully understood and implemented.
Aerospace manufacturing is a high-technology industry in China and is in the top position of advanced equipment manufacturing industry. The large complex components are the overall configuration of the spacecraft, support, bear and transmit loads for all subsystem instruments and equipment, and high-quality and high-efficiency processing is a key for ensuring reliable operation of the spacecraft. In recent years, the in-situ operation mode of the small-sized processing unit is developed, and the in-situ operation mode is applied to the operations of hole making, polishing, spraying, assembling and the like of a large-sized structural member, and compared with a large-sized gantry machine tool and a single robot manufacturing unit, the double-robot system has obvious advantages in the construction cost and time space distribution of a production line.
Typically, large complex components typically comprise hundreds of parts to be machined of various shapes, including a large number of two or more associated mounting brackets that subsequently need to be assembled with the same external load (e.g., space telescope, space robot, etc.), commonly referred to as a set of support bracket associated brackets of the type having dimensional constraints with respect to each other, with their mounting surfaces being associated mounting surfaces, so that a set of associated mounting surfaces has a high index of uniformity accuracy. When the distribution distance of a group of associated mounting brackets on the surface of a complex component is too large and exceeds the processing capacity of a single robot, the complex component is required to be cooperatively processed by a double-robot cooperative manufacturing system so as to meet the consistency precision required by design. Because errors generated in the movement process of a single robot are random, when a double-robot system processes a group of associated characteristic holes exceeding the working space of the single robot on the surface of a complex component, the control is improper, the high-precision positioning of a single-side robot cannot be completed, the positioning errors of two-side robots are likely to be overlapped due to the fact that the robots are finally positioned in the opposite directions of a target hole site, and finally the pose of the external loading equipment under the complex component coordinate system deviates from the design pose after the external loading equipment is installed, and even the external loading equipment cannot be assembled smoothly. Therefore, a high-precision calibration method for co-positioning precision needs to be applied to the double-robot system.
Patent application number CN202010031572.1 discloses a method, system, device storage medium for collaborative synchronization of two robots, based on two industrial robots, the method represents the base coordinates of the slave robot by adopting the base coordinate system of the master robot, and obtains the TCP coordinates of the slave robot in real time in combination with the first representation and the change of the TCP end of the master robot, and controls the slave robot in real time according to the obtained coordinates, so that the slave robot can follow the master robot in real time and realize high-precision synchronization.
Patent application number CN202110469546.1 discloses a calibration method of a double-robot system based on a hand-eye camera, which obtains a kinematic error matrix of the double-robot system by adopting an MCPC kinematic modeling method to obtain a kinematic parameter calibration value of the double-robot system and improve the operation precision of the double-robot system.
Literature "A Dual Quaternion-Based Approach for Coordinate Calibration of Dual Robots in Collaborative Motion,2020,5(3):4086-4093." researches a dual-robot cooperative motion coordinate calibration method based on hand-eye calibration, and provides a dual-quaternion-based dual-robot cooperative calibration method based on the same.
However, the above method has the following disadvantages:
(1) The double-robot cooperative error model is simple, the error source of the double-robot system is not analyzed, no deep discussion and research are made on the double-robot cooperative positioning error model, and the mechanism of errors generated when the double-robot processing system performs processing tasks is not analyzed;
(2) In the actual processing process, the double-robot system has a plurality of residual errors which cannot be identified through the model, the residual errors in the double-robot system are not identified by the method, and a solution for further improving the co-location precision of the double robots is lacking;
(3) Only the cooperative positioning precision of the double robots is explored, the absolute positioning precision of the double robots is not explored correspondingly, the requirements of actually processing two components with relevant dimensions cannot be met, and the method cannot be applied to actual processing.
Based on the technical problems in the prior art, please refer to fig. 1-5, a specific implementation of the present embodiment is shown, and the present embodiment combines sensitivity analysis on the basis of establishing a dual-robot co-location error model, performs step-by-step joint identification on the dual-robot co-location error model, and simultaneously constructs a dual-robot residual error BP neural network model for residual errors after step-by-step joint identification of the dual-robot system, so as to further identify residual errors after step-by-step joint identification, and improve dual-robot co-location accuracy. Therefore, the embodiment provides a calibration method for the co-positioning precision of the double robots, and the residual errors which cannot be identified by the co-positioning error model of the double robots are identified and compensated by adopting the BP neural network, so that the absolute positioning precision of the single robot and the co-positioning precision requirement of the double robots in the co-assembly process of the double robots of large complex components can be simultaneously met. The method comprises the following steps:
S1, acquiring the pose of a sampling point of a double robot in a working space relative to a respective base coordinate system through a laser tracker, recording the joint rotation angle value of the double robot at each sampling point and the coordinate measurement value of the corresponding laser tracker under the pose, dividing the double robot into a master robot and a slave robot, selecting a double robot layout as shown in fig. 2 according to an actual processing scene, constructing a double robot processing system by utilizing laser tracker measuring equipment, constructing a measuring field, establishing the respective base coordinate system and flange coordinate system of a master robot and a slave robot, establishing the working space of the double robot for collaborative processing based on the actual working condition, planning the working space of the double robot for collaborative processing, then performing random sampling according to the sampling points in the working space of the double robot, recording the joint angle of the double robot at each sampling point and the coordinate measurement value of the corresponding laser tracker, and recording the coordinate value of the double robot at the corresponding measuring point.
It should be noted that: latin hypercube sampling (Latin Hypercube Sampling, LHS) is a statistical method used to generate random samples with a given distribution. This method is often used for sampling in a multi-dimensional parameter space, such as the working space of a robot.
The base coordinate system is a rectangular coordinate system which takes the robot mounting base as a reference and is used for describing the motion of the robot body; the flange coordinate system is used for describing the tail end position of the robot motion system, the basic coordinate system of the tail end of the robot, and the tail end of the robot is the center of the flange; the tool coordinate system is used for describing the position condition of the tool mounted at the front end of the flange, and the tool coordinate and the flange coordinate are coincident by default.
S2, constructing a double-robot co-location error model based on the coordinate system error and the connecting rod error, and determining uncertainty parameters of double-robot system errors in the double-robot co-location error model; in step S2, the specific process includes the following steps:
s21, establishing a dual-robot co-location error model by using an actual coordinate transformation equation of a tool coordinate system of the slave robot relative to a tool coordinate system of the master robot, wherein the model is as follows:
In the above formula, toolTtool' and d toolTtool' are a theoretical coordinate transformation matrix and an error matrix between the robot tool coordinate system and the master robot tool coordinate system, respectively; a i and dA i are a theoretical coordinate transformation matrix and an error matrix between the i-1 th link coordinate system and the i-th link coordinate system, i=
1,2,3,4,5,6,1`,2`,3`,4`,5`,6`；
S22, simplifying a double-robot co-location error model to obtain a double-robot co-location error matrix, wherein the method comprises the following steps:
toolΔtool'＝toolΔ6+6ΔM+MΔN+NΔ12+12Δtool'
In the above, toolΔtool' is a co-location error matrix from the robot tool coordinate system to the master robot tool coordinate system; toolΔ6 Error for the host robotic tool coordinate system; 6'Δtool' Is the tool coordinate system error of the slave robot; MΔN Modeling errors for a master-slave robot base coordinate system; 6ΔM Is the error of the connecting rod coordinate system of the host robot; NΔ6' Is the error of the connecting rod coordinate system of the slave robot;
S23, determining uncertainty parameters of a double-robot system error according to a double-robot co-location error matrix, wherein the uncertainty parameters comprise a double-robot tool coordinate system error, a double-robot base coordinate system modeling error and a double-robot connecting rod coordinate system error;
After the dual-robot co-location error model is established, a dual-robot co-location error matrix is obtained through a simplified model, and the co-location error of the dual-robot system is obtained through the co-location error matrix and is derived from the dual-robot tool coordinate system error, the dual-robot base coordinate system modeling error and the dual-robot connecting rod coordinate system error.
S24, rewriting a double-robot co-location error matrix into:
In the above-mentioned method, the step of, tooldtool' And toolδtoo' are translational and rotational differential amounts, respectively, of error from the robotic tool coordinate system to the master robotic tool coordinate system; m f and DeltaX f are respectively a double-robot system coordinate system error Jacobian matrix and an error column vector; m s and DeltaX s are respectively an error Jacobian matrix and an error column vector of the slave robot link coordinate system; m m and DeltaX m are respectively an error Jacobian matrix and an error column vector of a connecting rod coordinate system of the host robot; j is a master-slave robot cooperative error jacobian matrix considering multi-source errors; Δx is the column vector of all errors.
The error Jacobian matrix generated by the error of the tool coordinate system and the base coordinate system of the double robot system can be obtained by establishing an error model of the tool coordinate system and the base coordinate system of the double robot system; therefore, the double robot system is divided into a main robot and a slave robot, wherein the connecting rod homogeneous transformation matrix of the main robot is a process from the tail end to the base, and the slave robot is a process from the base to the tail end, and when only the connecting rod coordinate system error caused by the D-H parameter is considered, the connecting rod coordinate system error expression is obtained through partial differentiation, so that the error Jacobian matrix of the double robot system caused by the D-H parameter error is obtained.
S3, constructing a sensitivity function, performing sensitivity analysis on uncertainty parameters of the double-robot co-location error model by combining the sensitivity function to obtain a sensitivity analysis result, and performing step-by-step joint identification on error sources of the double-robot co-location error model according to the sensitivity analysis result to obtain residual errors in the double-robot system; in step S3, the specific process includes the following steps:
S31, constructing a sensitivity function by taking an uncertainty parameter as a variable, and obtaining a first-order sensitivity coefficient S i and a total sensitivity coefficient ST i for representing the influence degree of the uncertainty parameter on the total variance output by the double-robot co-location error model;
In this embodiment, uncertainty parameters such as error sources including a tool coordinate system, a base coordinate system, and a link parameter are extracted, sensitivity analysis is performed, and if there are n uncertainty parameters in the error of the dual robot system, the uncertainty parameters can be written as a function with the uncertainty parameters as variables, so in step S31, the specific process includes the following steps:
s311, defining n uncertainty parameters of the double-robot system error, and writing into a function form taking the uncertainty parameters as variables, namely:
In the above-mentioned method, the step of, tooldtool' And toolδtoo' are translational and rotational differential amounts, respectively, of error from the robotic tool coordinate system to the master robotic tool coordinate system; f (DeltaX) represents an influence function of the uncertainty parameter on the co-location error of the double robots; Δx is a vector consisting of n uncertainty parameters;
s312, expressing the function taking the uncertainty parameter as a variable as a form of analysis of variance, namely:
In the above formula, f 0 (Δx) represents an expected value of f (Δx); fi (Δxi) represents the effect of the change in the ith parameter on the function value; f i,j(ΔXi,ΔXj) represents the effect of the common variation of the ith and j-th parameters on the function value; f 1,2,…,n(ΔX1,ΔX2,ΔX3,…,ΔXn) represents the influence of the common change of the 1 st to nth parameters on the function value;
S313, regarding all the input uncertainty parameters as continuous random variables, and calculating the variance of f (delta X), wherein the calculation formula of the variance of f (delta X) is as follows:
Wherein ,Di(f)＝Var[EX～i(f|ΔXi)];Di,j(f)＝Var[EX～(i,j)(f|ΔXi,ΔXj)]-Di(f)-Dj(f),X～i denotes all variables except Δx i, and X to (i, j) denote all variables except Δx i、ΔXj;
S314, carrying out normalization processing on a calculation formula of the f (delta X) variance, wherein the calculation formula is used for representing the influence degree of the total variance output by the double-robot co-location error model, and the normalization processing formula is as follows:
In the method, in the process of the invention, S i is a first-order variance ratio, defined as a first-order sensitivity coefficient of an uncertainty parameter DeltaX i, used for representing the influence degree of DeltaX i on the total variance of the model output; s i,j is a second-order variance ratio, defined as a second-order sensitivity coefficient of an uncertainty parameter DeltaX i,ΔXj, used for representing the influence degree of DeltaX i,ΔXj on the total variance of the model output after coupling;
The first order variance ratio of the sensitivity function is defined herein as the first order sensitivity coefficient of the uncertainty parameter, which characterizes the extent to which the uncertainty parameter affects the overall variance of the model output. The second order variance ratio of the sensitivity function is defined as the second order sensitivity coefficient of the uncertainty parameter, and is used for representing the influence degree of the total variance of the model output.
S315, introducing an overall sensitivity coefficient ST i, and combining the independent influence degree of DeltaX i on the positioning error and the influence degree of DeltaX i on the positioning error when coupled with other uncertain parameters, wherein the overall sensitivity coefficient ST i has the expression:
In the above formula, ST i is the overall sensitivity coefficient; s i is a first order variance ratio; s i,j is a second order variance ratio;
s316, sampling n uncertainty parameters delta X to obtain m groups of random variables, and generating sampling matrixes delta A n×m and delta B n×m of the uncertainty parameters delta X, wherein in the step S316, the specific process comprises the following steps:
S3161, let DeltaS i be the m sampling result sets of the uncertainty parameter DeltaX i, and calculate the corresponding probability distribution P i, wherein the calculation formula of the probability distribution P i is as follows:
Pi＝Fi(ΔSi)
In the above formula, F i is a mapping function;
S3162, mapping the value range of the uncertainty parameter DeltaX i to a probability interval of [0,1] through a F i (& gt) function, and equally dividing the probability interval into N subintervals;
S3163, defining random variable xi with value interval of [0,1] in each subinterval, and sampling the ith uncertain parameter delta S i according to the random variable xi to obtain a jth sampling value delta S ij; here, the j-th sampling value Δs ij of the i-th uncertainty parameter Δs i can be regarded as a probability distribution value for selecting one point as an uncertainty parameter in the j-th subinterval, and thus the calculation formula of the probability distribution value Δs ij is:
In the above-mentioned method, the step of, Representing the inverse of F i (.).
S3164, according to the sampling values Δs ij, a sample matrix Δs n×m is formed, and after the sampling of the uncertainty parameter Δx i is completed, the sampling values may form a sample matrix Δs n×m as follows:
S3165, generating sampling matrices Δa n×m and Δb n×m of the uncertain parameter Δx from the sample matrix Δs n×m as follows:
S317, constructing a new matrix delta A B (i) according to the sampling matrices delta A n×m and delta B n×m, enabling the ith column in the new matrix delta A B (i) to be delta B i, and obtaining new matrices delta A B (i) and delta B A (i), wherein the new matrices delta A B (i) are as follows:
S318, determining the expected f 0 (delta A) and the variance D of the double-robot co-location error model; for the matrix Δa, the expected f 0 (Δa) and variance D of the dual robot co-location error model are:
the calculation formula for the expected f 0 (ΔA) is:
The calculation formula of the variance D is:
In the above formula, N is the total number of subintervals; f (delta A) j is the influence function of the ith column of the sampling matrix delta A of the uncertainty parameter delta X on the end positioning error of the double-robot system; f 2(ΔA)j is the square of the influence function of the ith column of the sampling matrix deltaa of the uncertainty parameter deltax on the end positioning error of the dual robot system; The desired square of the influence function of the sampling matrix deltaa of the uncertainty parameter deltax on the end positioning error of the dual robot system.
S319, defining a first-order sensitivity coefficient S i and an overall sensitivity coefficient ST i according to the expected f 0 (delta A) and the variance D;
The first order sensitivity coefficient S i is expressed as:
The overall sensitivity coefficient ST i is expressed as:
In the above formula, f (Δb) j is an influence function of the j-th column of the sampling matrix Δb of the uncertainty parameter on the end positioning error of the dual robot system; and exchanging the influence function of the j-th column after the i-th column on the end positioning error of the double-robot system for the sampling matrixes delta A and delta B of the uncertainty parameters. /(I)
According to the embodiment, based on error source and sensitivity analysis in the double-robot system, step-by-step joint identification is performed on the double-robot co-location error model, so that the double-robot co-location error is reduced.
S32, dividing uncertainty parameters into main parameters and non-main parameters by taking the total sensitivity coefficient ST i as a limit with the ratio of 95%, wherein more than 95% of the uncertainty parameters are main parameters;
S33, summing the main parameters and marking as Sum (1-j)(STj), and defining the summed parameters as the main parameters when the specific gravity of the Sum parameter accounting for the overall sensitivity coefficient ST i is greater than or equal to 0.95, namely: sum (1-j)(STj)/Sum(STi) is more than or equal to 0.95;
S34, sequencing the coordinate system errors of the double-robot tool and the modeling errors of the double-robot base coordinate system and the coordinate system errors of the double-robot connecting rod according to Sum (1-j)(STj)/Sum(STi) not less than 0.95 in priority;
S35, carrying out step-by-step joint identification on error sources according to priority order to obtain residual errors in the double-robot system, analyzing redundancy of error parameters of the double-robot system based on a sensitivity algorithm, further determining uncertain distribution characteristics of the parameter errors and sensitivity of positioning errors, determining an optimal identification sequence, and improving parameter error identification accuracy of the double-robot system.
Specifically, the error sources are subjected to step-by-step joint identification according to priority ranking, a minimum identifiable parameter set is obtained through singular value decomposition, and correlations among uncertain parameters are calculated through simulation, so that all parameter combinations which cannot be identified at the same time are found out.
When n groups of robot end error vectors are acquired, the dimension of the Jacobian matrix J is as followsTo identify linearly related columns in the J matrix, a square matrix d=j T J can be constructed, singular value decomposition of D is performed, matrix D expressed as:
Where V 1 is a 55 xr matrix, V 2 is a 55× (55-r) matrix, and Σ is an r×r diagonal matrix.
Then, DV 2 is expressed as:
Where D 1 is a 55 Xr matrix, D 2 is a 55X (55-r) matrix, V 21 is a r (55-r) matrix, and V 22 is a (55-r) x (55-r) matrix. D 2 is related to D 1, and the first r columns in the permutation matrix P satisfying this condition may represent non-redundant parameter errors in the uncertainty parameter Δx, i.e. residual errors in the dual robot system.
In the embodiment, the actual sampling point data is adopted for step-by-step joint identification, the obtained uncertainty parameter error is used for correcting the double-robot co-location error model, the co-location error of the double robots is predicted and compensated, and the optimal identification result is obtained by adopting a step-by-step joint identification method after main parameters and non-main parameters are divided according to sensitivity.
S4, establishing a joint rotation angle-based residual error equation of the double robots according to residual errors, wherein the residual error equation consists of a host robot absolute positioning error matrix E m and a double robot cooperative positioning error matrix E rel in a double robot system, so that in the step, the difference value between the actual coordinates and ideal coordinates of the main robots is obtained by recording the joint rotation angle value of each sampling point of the main robots and corresponding laser tracker coordinate measurement values, the difference value is regarded as the absolute positioning residual error of the main robots, the absolute positioning residual error of the main robots is obtained by step joint identification, and a main robot absolute positioning error matrix is constructed and can be obtained by deriving a host robot nominal FLANGE coordinate system FLANGE master, a host robot actual FLANGE coordinate system FLANGE master', a WORLD coordinate system $WORLD and a host robot BASE coordinate system $BASE master, namely the expression of the host robot absolute positioning error matrix E m in the double robot system is as follows:
Em＝mbTmf -1wTmb -1wTmf'
Wherein mbTmf is a nominal homogeneous transformation matrix of a nominal flange coordinate system of the host robot relative to a base coordinate system of the main robot, wTmb is a homogeneous transformation matrix of the base coordinate system of the host robot relative to a measurement coordinate system of the laser tracker, and wTmf' is a homogeneous transformation matrix of an actual flange coordinate system of the main robot measured by the laser tracker relative to the laser tracker.
The absolute positioning error matrix E m of the main robot is rewritten into the form of an error vector epsilon m, namely:
εm＝[εx,εy,εz,εa,εb,εc]m T
Wherein epsilon m is the absolute positioning error vector of the host robot, epsilon x,εy,εz,εa,εb,εc is the six-dimensional error vector in the x, y, z, a, b and c directions respectively.
For the co-location residual error of the dual robots through step joint identification, a dual robot co-location error matrix is constructed, which can be derived from a laser tracker coordinate system $WORLD, a host robot nominal FLANGE coordinate system $FLANGE master, a slave robot nominal FLANGE coordinate system $FLANGE slave, a host robot actual FLANGE coordinate system $FLANGE master', a slave robot actual FLANGE coordinate system $FLANGE slave', a host robot BASE coordinate system $BASE master, and a slave robot BASE coordinate system $BASE slave, namely, the dual robot co-location error matrix E rel is:
Erel＝mfTsf -1mf'Tsf'
Wherein E rel is a dual robot co-location error matrix, mfTsf and mf'Tsf' are a theoretical coordinate transformation matrix and an actual coordinate transformation matrix of the flange coordinate system of the slave robot relative to the flange coordinate system of the master robot.
The matrix of the compensating pose of the double-robot co-positioning error matrix is mfTsfcomp＝wErel -1mfTsf, and the double-robot co-positioning error matrix E rel is rewritten into the form of an error vector, namely:
εrel＝[εx,εy,εz,εa,εb,εc]rel T
Wherein epsilon rel is a double-robot co-location error vector, epsilon x,εy,εz,εa,εb,εc is an x, y, z, a, b and c-direction six-dimensional error vector respectively.
S5, constructing a BP neural network model by taking joint angles of the double robots as input neurons and taking absolute positioning errors of the main robots and co-positioning errors of the double robots as output neurons, wherein in the step, the BP neural network model is divided into two parts as shown in fig. 3 and 4, and the BP neural network model of the main robots is respectively constructed and constructed to fit residual errors of the main robots, wherein the input neurons are joint angles of the main robots, and the absolute positioning errors of the main robots are the output neurons, as shown in fig. 3.
And (3) constructing a dual-robot co-location error BP neural network model to fit the dual-robot residual error, wherein the input neuron is a dual-robot joint corner, and the dual-robot co-location error is an output neuron, as shown in fig. 4.
The dual-robot BP neural network model sequentially comprises an input layer, a hidden layer and an output layer, wherein each hidden layer comprises a trainable parameter, a weight, a deviation, a nonlinear function and a torrent layer;
The output neurons are absolute positioning errors of the host robots and co-positioning errors of the double robots, and joint corners of the double robots are used as input neurons.
S6, training the BP neural network model to finish prediction of residual errors in the double-robot system, wherein the prediction is specifically as follows: and (3) distributing optimal initial weights and thresholds for the BP neural network by adopting a K-layer folding cross-validation algorithm, acquiring each parameter value when the convergence speed is the fastest by adjusting the number of hidden layers, the number of neurons of each layer, the number of rounds and the batch, and taking the joint rotation angle of the double robots as input to obtain a predicted joint rotation angle error, thereby completing the prediction of the residual error of the double robot system. Therefore, the weight of the neural network is designed according to the number of hidden layers, the number of neurons at each layer, the number of rounds and batches, so that the convergence speed of the neural network is the fastest.
The training of the BP neural network model comprises the following procedures: dividing a double-robot BP neural network data set S into K disjoint subsets by using a K-fold cross validation function, taking K-1 subsets in the data set S as training sets each time, and taking the remaining set as a prediction validation set, acquiring the optimal parameters of the BP neural network through the cross validation function, and carrying out normalization processing on input parameters and output parameters before selecting the training sets and the test sets, so that the convergence of a model is improved, and the equal importance of all joint angles as the input parameters is ensured; at the same time, it is ensured that all output features contribute the same to minimizing the loss function.
And S7, fitting a residual error equation by adopting a BP neural network model, correcting and compensating original parameters according to a fitting result of the BP neural network to the residual error, inputting the obtained neural network model into a double-robot control system to improve the co-location precision of the double robots, and specifically, inputting the obtained neural network model into the double-robot control system to improve the co-location precision of the double robots. As shown in fig. 5, the verification result of the method of merging error model step-by-step joint identification with neural network residual error identification in this embodiment can be obviously seen.
The invention is based on the dual-robot co-location error model, analyzes the error source which generates main influence in the dual-robot co-location error model in combination with sensitivity analysis, considers the influence of residual errors which cannot pass modeling in the dual-robot system on the dual-robot co-location precision, and finally fits the identified residual errors by adopting a BP neural network, so that the identified geometric parameters and the training network are input into the control system, and the co-location precision of the dual-robot is more effectively improved.
Those of ordinary skill in the art will appreciate that all or a portion of the steps in a method of implementing an embodiment described above may be implemented by a program to instruct related hardware, and thus, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
In this specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different manner from other embodiments, so that the same or similar parts between the embodiments are referred to each other. For each of the above embodiments, since it is substantially similar to the method embodiment, the description is relatively simple, and reference should be made to the description of the method embodiment for relevant points.
The foregoing embodiments have been presented in a detail description of the invention, and are presented herein with a particular application to the understanding of the principles and embodiments of the invention, the foregoing embodiments being merely intended to facilitate an understanding of the method of the invention and its core concepts; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.
Claims (2)
1. The calibration method for the co-positioning precision of the double robots is characterized by comprising the following steps of:
S1, acquiring the pose of sampling points of the double robots in a working space relative to respective base coordinate systems through a laser tracker, and recording joint rotation angle values of the double robots in each sampling point and coordinate measurement values of the corresponding laser tracker under the pose;
s2, constructing a double-robot co-location error model based on a coordinate system error and a connecting rod error, and determining uncertainty parameters of a double-robot system error in the double-robot co-location error model, wherein in the step S2, the specific process comprises the following steps:
s21, establishing a dual-robot co-location error model by using an actual coordinate transformation equation of a tool coordinate system of the slave robot relative to a tool coordinate system of the master robot, wherein the model is as follows:
；
In the above-mentioned method, the step of, And/>A theoretical coordinate transformation matrix and an error matrix between the robot tool coordinate system and the host robot tool coordinate system respectively; /(I)And/>Respectively is/>Number connecting rod coordinate System to/>Theoretical coordinate transformation matrix and error matrix between number-connecting rod coordinate systems,/>；
S22, simplifying a double-robot co-location error model to obtain a double-robot co-location error matrix, wherein the method comprises the following steps:
；
In the above-mentioned method, the step of, A co-location error matrix from the robot tool coordinate system to the master robot tool coordinate system; /(I)Error for the host robotic tool coordinate system; /(I)Is the tool coordinate system error of the slave robot; /(I)Modeling errors for a master-slave robot base coordinate system; /(I)Is the error of the connecting rod coordinate system of the host robot; /(I)Is the error of the connecting rod coordinate system of the slave robot;
S23, determining uncertainty parameters of a double-robot system error according to a double-robot co-location error matrix, wherein the uncertainty parameters comprise a double-robot tool coordinate system error, a double-robot base coordinate system modeling error and a double-robot connecting rod coordinate system error;
s24, rewriting a double-robot co-location error matrix into:
；
In the above-mentioned method, the step of, In/>And/>A translation differential amount and a rotation differential amount, respectively, of error between the robot tool coordinate system to the master robot tool coordinate system; /(I)And/>The system coordinate system error Jacobian matrix and the error column vector of the double robot system are respectively; /(I)And/>The error Jacobian matrix and the error column vector are respectively from the robot connecting rod coordinate system; /(I)And/>The error Jacobian matrix and the error column vector of the connecting rod coordinate system of the host robot are respectively; /(I)The method is a master-slave robot cooperative error Jacobian matrix considering multi-source errors; /(I)Column vectors composed of all errors;
S3, constructing a sensitivity function, performing sensitivity analysis on uncertainty parameters of the double-robot co-location error model by combining the sensitivity function to obtain a sensitivity analysis result, and performing step-by-step joint identification on error sources of the double-robot co-location error model according to the sensitivity analysis result to obtain residual errors in the double-robot system; in step S3, the specific process includes the following steps:
S31, constructing a sensitivity function by taking the uncertainty parameter as a variable to obtain a first-order sensitivity coefficient for representing the influence degree of the uncertainty parameter on the total variance output by the double-robot co-location error model Overall sensitivity coefficient/>; In step S31, the specific process includes the steps of:
S311, defining n uncertainty parameters of the double-robot system error, and writing into a function form taking the uncertainty parameters as variables, namely:
；
In the above-mentioned method, the step of, In/>And/>A translation differential amount and a rotation differential amount, respectively, of error between the robot tool coordinate system to the master robot tool coordinate system; /(I)The influence function of the uncertainty parameter on the co-positioning error of the double robots is represented; /(I)Is a vector consisting of n uncertainty parameters;
s312, expressing the function taking the uncertainty parameter as a variable as a form of analysis of variance, namely:
；
In the above-mentioned method, the step of, Representation/>Is a desired value of (2); /(I)Representing the effect of the change of the ith parameter on the function value; /(I)The influence of the common change of the ith parameter and the jth parameter on the function value is represented; Representing the effect of the common variation of the 1 st to nth parameters on the function value;
S313, regarding all input uncertainty parameters as continuous random variables, and calculating Variance of (v)The variance is calculated as:
；
In the above-mentioned method, the step of, ；/>，Representation of the division/>All variables except,/>Representation of the division/>、/>All variables except;
S314, pair of The variance calculation formula is normalized and used for representing the influence degree of the total variance output by the double-robot co-location error model, and the normalization formula is as follows:
；
In the method, in the process of the invention, ，/>，/>Is a first order variance ratio defined as uncertainty parameter/>For characterizing/>The degree of influence of the model output total variance; /(I)Is the second order variance ratio, defined as uncertainty parameter/>For characterizing/>The degree of influence of the total variance of the model output after coupling;
s315, introducing an overall sensitivity coefficient Will/>Independent influence degree and/>, on positioning errorsThe influence degree of positioning errors is comprehensively arranged when the positioning error is coupled with other uncertain parameters, and the total sensitivity coefficient/>The expression of (2) is:
；
In the above-mentioned method, the step of, Is the overall sensitivity coefficient; /(I)Is the first order variance ratio; /(I)Is the second order variance ratio;
s316 for n uncertainty parameters Sampling to obtain m groups of random variables and generating uncertainty parameters/>Sampling matrix/>And/>; In step S316, the specific process includes the following steps:
S3161 and the order Is uncertainty parameter/>And calculates the corresponding probability distribution/>Probability distribution/>The calculation formula of (2) is as follows: /(I)；
In the above-mentioned method, the step of,Is a mapping function;
S3162, parameter of uncertainty The value range of (1) is passed/>Mapping of functions to/>The probability interval is equally divided into N sub-intervals;
S3163 defining a value interval in each sub-interval as Random variable/>And according to random variable/>For the i < th > uncertain parameter/>Sampling to obtain the j-th sampling value/>；
S3164, according to the sampled valueComposition of sample matrix/>At completion uncertainty parameter/>After sampling of (a), the sampled values form a sample matrix/>；
S3165, according to the sample matrixGenerating uncertainty parameters/>Sampling matrix/>And/>；
S317 according to the sampling matrixAnd/>Constructing a new matrix/>Let the new matrix/>The ith column of (a)Obtaining a new matrix/>And/>The following are provided:
；
S318, determining expectation of a dual-robot co-location error model And variance D; for matrix/>Expected/>, dual robot co-localization error modelThe sum of variances D are:
it is desirable to The calculation formula of (2) is as follows: /(I)；
The calculation formula of the variance D is:；
in the above formula, N is the total number of subintervals; is uncertainty parameter/> Sampling matrix/>The influence function of the ith column of (2) on the positioning error of the tail end of the double-robot system; /(I)Is uncertainty parameter/>Sampling matrix/>The square of the function of the influence of column i on the end positioning error of the dual robot system; /(I)Is uncertainty parameter/>Sampling matrix/>To the desired square of the influence function of the end positioning error of the dual robot system;
S319, according to the expectations And variance D defines a first order sensitivity coefficient/>Overall sensitivity coefficient/>First order sensitivity coefficient/>Expressed as:
；
Overall sensitivity coefficient Expressed as: /(I)；
In the above-mentioned method, the step of,Sampling matrix/>, which is an uncertainty parameterThe j-th column of (2) influences the function of the positioning error of the tail end of the double-robot system; /(I)Sampling matrix/>, which is an uncertainty parameterAnd/>Exchanging the influence function of the j column after the i column on the positioning error of the tail end of the double-robot system;
S32, using the uncertainty parameter as the overall sensitivity coefficient The ratio of 95% is defined as a limit and divided into main parameters and non-main parameters, wherein more than 95% is the main parameter;
S33, summing the main parameters and recording as And define its overall sensitivity coefficient/>When the specific gravity of (2) is greater than or equal to 0.95, the summed parameters are the main parameters, namely: /(I)；
S34, according toThe method comprises the steps of performing priority ranking on a double-robot tool coordinate system error, a double-robot base coordinate system modeling error and a double-robot connecting rod coordinate system error;
S35, carrying out step-by-step joint identification on error sources according to priority sequencing to obtain residual errors in the double-robot system;
S4, establishing a joint rotation angle-based residual error equation of the double robots according to the residual errors, wherein the joint rotation angle-based residual error equation is as follows:
；
In the above-mentioned method, the step of, Is an absolute positioning error matrix of a host robot in a double-robot system,/>Is a theoretical coordinate transformation matrix of a flange coordinate system of the host robot relative to a base coordinate system, and is a matrix of a theoretical coordinate transformation of a flange coordinate system of the host robot relative to the base coordinate systemIs a theoretical coordinate transformation matrix of a flange coordinate system of the host robot relative to a world coordinate system, and is a matrix of a theoretical coordinate transformation matrix of a flange coordinate system of the host robot relative to the world coordinate systemA theoretical coordinate transformation matrix of the flange coordinate system measured by the laser tracker relative to the world coordinate system;
；
In the above-mentioned method, the step of, For a double robot co-location error matrix,/>And/>The system comprises a theoretical coordinate transformation matrix and an actual coordinate transformation matrix which are relative to a host robot flange coordinate system from the robot flange coordinate system;
S5, constructing a BP neural network model by taking joint rotation angles of the double robots as input neurons and taking absolute positioning errors of the main robots and co-positioning errors of the double robots as output neurons;
S6, distributing optimal initial weights and thresholds for the BP neural network by adopting a K-layer folding cross-validation algorithm, and completing prediction of residual errors in the double-robot system;
And S7, fitting a residual error equation by adopting a BP neural network module, and correcting and compensating original parameters according to the fitting result of the BP neural network on the residual error so as to improve the co-positioning precision of the double robots.
2. The calibration method according to claim 1, characterized in that in step S5, the BP neural network model comprises an input layer, a hidden layer and an output layer in sequence, each hidden layer comprising trainable parameters, weights, deviations, nonlinear functions and a torrent layer;
The output neurons are absolute positioning errors of the host robots and co-positioning errors of the double robots, and joint corners of the double robots are used as input neurons.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202410334586.9A CN117921685B (en) | 2024-03-22 | 2024-03-22 | Calibration method for co-positioning precision of double robots |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202410334586.9A CN117921685B (en) | 2024-03-22 | 2024-03-22 | Calibration method for co-positioning precision of double robots |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN117921685A CN117921685A (en) | 2024-04-26 |
| CN117921685B true CN117921685B (en) | 2024-05-24 |
Family
ID=90761411
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202410334586.9A Active CN117921685B (en) | 2024-03-22 | 2024-03-22 | Calibration method for co-positioning precision of double robots |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN117921685B (en) |
Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20090060752A (en) * | 2007-12-10 | 2009-06-15 | 현대중공업 주식회사 | Robot calibration method with joint stiffness parameters for the enhanced positioning accuracy |
| CN103240591A (en) * | 2012-02-03 | 2013-08-14 | 佳能株式会社 | Assembly equipment and assembly method |
| CN105034008A (en) * | 2015-09-15 | 2015-11-11 | 南京航空航天大学 | Intelligent flexible production line with double robot cooperative automatic assembling and operation method for same |
| CN109414813A (en) * | 2016-06-29 | 2019-03-01 | 应用材料公司 | The method and system of misalignment correction is provided in robot |
| CN111687827A (en) * | 2020-06-22 | 2020-09-22 | 南京航空航天大学 | Control method and control system for coordinating and operating weak rigid member by two robots |
| CN113636348A (en) * | 2021-08-05 | 2021-11-12 | 张莉 | Glass transfer system for building installation |
| CN114714348A (en) * | 2022-03-17 | 2022-07-08 | 浙江大学 | Industrial robot absolute positioning precision improving method |
| CN114905511A (en) * | 2022-05-12 | 2022-08-16 | 南京航空航天大学 | Industrial robot assembly error detection and precision compensation system calibration method |
| CN114918920A (en) * | 2022-06-01 | 2022-08-19 | 浙江大学 | Industrial robot calibration method based on neural network and distance error model |
-
2024
- 2024-03-22 CN CN202410334586.9A patent/CN117921685B/en active Active
Patent Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20090060752A (en) * | 2007-12-10 | 2009-06-15 | 현대중공업 주식회사 | Robot calibration method with joint stiffness parameters for the enhanced positioning accuracy |
| CN103240591A (en) * | 2012-02-03 | 2013-08-14 | 佳能株式会社 | Assembly equipment and assembly method |
| CN105034008A (en) * | 2015-09-15 | 2015-11-11 | 南京航空航天大学 | Intelligent flexible production line with double robot cooperative automatic assembling and operation method for same |
| CN109414813A (en) * | 2016-06-29 | 2019-03-01 | 应用材料公司 | The method and system of misalignment correction is provided in robot |
| CN111687827A (en) * | 2020-06-22 | 2020-09-22 | 南京航空航天大学 | Control method and control system for coordinating and operating weak rigid member by two robots |
| CN113636348A (en) * | 2021-08-05 | 2021-11-12 | 张莉 | Glass transfer system for building installation |
| CN114714348A (en) * | 2022-03-17 | 2022-07-08 | 浙江大学 | Industrial robot absolute positioning precision improving method |
| CN114905511A (en) * | 2022-05-12 | 2022-08-16 | 南京航空航天大学 | Industrial robot assembly error detection and precision compensation system calibration method |
| CN114918920A (en) * | 2022-06-01 | 2022-08-19 | 浙江大学 | Industrial robot calibration method based on neural network and distance error model |
Non-Patent Citations (3)
| Title |
|---|
| 双工业机器人协调运动中的标定 方法与轨迹规划研究;李孟虔;硕士学位论文;20210531;第1-102页 * |
| 双机器人标定方法研究及协调仿真;李文广;硕士学位论文;20110331;第1-93页 * |
| 基于参数与非参数模型结合的双臂机器人协作定位精度提升方法;白明等;《机器人》;20230531;第第45卷卷(第第3期期);第276-286页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN117921685A (en) | 2024-04-26 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111964575B (en) | Digital twin modeling method for milling of mobile robot | |
| CN108908327B (en) | Robot positioning error grading compensation method | |
| Huang et al. | Kinematic calibration of a 6-DOF hybrid robot by considering multicollinearity in the identification Jacobian | |
| Wu et al. | Geometric calibration of industrial robots using enhanced partial pose measurements and design of experiments | |
| Klimchik et al. | Identification of the manipulator stiffness model parameters in industrial environment | |
| CN111590581A (en) | Positioning compensation method and device for robot | |
| Li et al. | Measurement method for volumetric error of five-axis machine tool considering measurement point distribution and adaptive identification process | |
| CN106777656B (en) | Industrial robot absolute accuracy calibration method based on PMPSD | |
| CN112558547B (en) | Quick optimization method for geometric error compensation data of translational shaft of five-axis numerical control machine tool | |
| CN112697041B (en) | Monte carlo method-based pre-evaluation method for measurement accuracy of assembly pose | |
| CN112109084A (en) | Terminal position compensation method based on robot joint angle compensation and application thereof | |
| CN115648228B (en) | Industrial robot multi-source error compensation method, device, equipment and storage medium | |
| Cao et al. | Pose error compensation based on joint space division for 6-DOF robot manipulators | |
| CN114147726A (en) | Robot calibration method combining geometric error and non-geometric error | |
| CN113580148A (en) | Parallel robot kinematics calibration method based on equivalent kinematic chain | |
| CN112643658A (en) | Calibration method for adaptive error modeling of series robot based on SIR dimension reduction DH model | |
| CN114714348A (en) | Industrial robot absolute positioning precision improving method | |
| Wang et al. | Uncertainty evaluation and optimization of INS installation measurement using Monte Carlo Method | |
| Gao et al. | Kinematic calibration of industrial robots based on distance information using a hybrid identification method | |
| Song et al. | Calibration of a Stewart platform by designing a robust joint compensator with artificial neural networks | |
| Miao et al. | A two-step method for kinematic parameters calibration based on complete pose measurement—verification on a heavy-duty robot | |
| CN112720480B (en) | Robot track correction method and system based on grading errors | |
| CN117921685B (en) | Calibration method for co-positioning precision of double robots | |
| CN113211436B (en) | Six-degree-of-freedom series robot error calibration method based on genetic algorithm | |
| CN110427686B (en) | Large rigid body displacement parameter calculation method considering constraint conditions |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |