CN113807488B - Space position optimization method for robot system component of labeling machine - Google Patents
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Abstract
The method for optimizing the space position of the components of the labeling robot system comprises the following steps of: step 1, establishing a coordinate system of a labeling machine robot system; step 2, generating space coordinates of the labeling points; step 3, establishing a mathematical model for optimizing the spatial positions of the industrial robot and the label printer in the labeling robot system; and step 4, completing calculation by adopting an optimization algorithm. According to the method, a spatial position optimization mathematical model of a label printer and an industrial robot in a labeling robot system is established, a plurality of spatial points are randomly generated to simulate the spatial positions of a plurality of labeling points according to constraint conditions of labeling objects, the improvement of a particle swarm optimization algorithm is realized by applying non-linearly-changed inertia weight, learning factors and particle number, and the working efficiency of the labeling robot system is improved after the spatial positions of system components are optimized.
Description
Technical Field
The invention relates to a system component space position optimization method, in particular to a space position optimization method of an industrial robot and a label printer in a labeling robot system, and belongs to the technical field of industrial robots.
Background
With the rapid development of society, it has become more and more important to implement product information tracing through identity information tags. At present, the market of automatic labeling machines has been developed rapidly, but most labeling machines are difficult to realize industrial scenes that labeling positions are not fixed and labels are required to be prepared on line in real time, part of enterprises combine machine vision with robot technology to establish a labeling machine robot system, however, the spatial position relationship between a label printer and an industrial robot in the system is very important, and if the placing positions are unreasonable, the working efficiency and quality of the labeling machine robot system can be affected. The invention provides a space position optimization method of a part of a labeling robot system, which provides a technical foundation for the establishment of the labeling robot system.
Disclosure of Invention
Based on the above reasons, the invention provides a space position optimization method of a label printer and an industrial robot in a labeling robot system, so as to improve the working efficiency of the labeling robot system.
The invention discloses a method for optimizing the spatial position of a robot system component of a labeling machine, which comprises the following steps:
step 1, establishing a coordinate system of a labeling machine robot system, establishing a user coordinate system in a theoretical center of a station to be labeled, determining the postures of an industrial robot and a label printer according to the postures of the user coordinate system, and establishing the industrial robot coordinate system and the label printer coordinate system;
step 2, generating space coordinates of the labeling points, and randomly generating a plurality of space points to simulate the space positions of a plurality of labeling points according to constraint conditions of labeling objects;
step 3, establishing a mathematical model for optimizing the spatial positions of an industrial robot and a label printer in a labeler system, determining spatial position constraint conditions of the industrial robot and the label printer by taking the spatial positions of the industrial robot and the spatial positions of the label printer as design variables and combining the working space of the robot, taking the minimum joint angle total travel of the industrial robot as an objective function, converting a world coordinate pose matrix of a labeling point and all labeling points into a robot joint coordinate by utilizing an inverse kinematics analysis and solution expression of the industrial robot, calculating the joint angle total travel of the industrial robot by taking the sum of absolute values of joint angle change amounts of the robot moving from the labeling point to a single labeling point as the joint angle travel of the single labeling point, and summing the joint angle travel of all labeling points;
and step 4, completing calculation by adopting an optimization algorithm, and solving a mathematical model for optimizing the spatial positions of the industrial robot and the label printer in the robot system of the labeling machine by adopting the optimization algorithm to obtain the optimal spatial positions of the industrial robot and the label printer, wherein the industrial robot has the minimum total stroke of joint angles for labeling all labeling points.
The invention adopts an improved particle swarm optimization algorithm to complete the calculation of the space position optimization of the robot system component of the labeling machine, and improves the traditional particle swarm optimization algorithm as follows:
(1) Calculating inertial weight omega by using nonlinear variation Tanh function, wherein the calculation formula isWherein omega is min 、ω max Representing the minimum value of the inertia weight and the maximum value of the inertia weight, wherein K is the maximum iteration number, K is the current iteration number, lambda is the amplification coefficient, and mu is the translation coefficient;
(2) Individual learning factor c using asynchronously nonlinear varying learning factors 1 The calculation formula of (2) isWherein, c 1max 、c 1min The learning factors are the maximum individual learning factor and the minimum individual learning factor; social learning factor c 2 The calculation formula of (2) is +.>Wherein, c 2max 、c 2min Is the maximum social learning factor and the minimum social learning factor;
(3) The particle number n with nonlinear variation is adopted, and the calculation formula is thatWherein n is max Is the iterative maximum particle number; n is n min Is the iterative minimum number of particles.
The method for completing the optimization calculation of the space position of the robot system component of the labeling machine by adopting the improved particle swarm optimization algorithm comprises the following specific steps:
(1) initializing basic parameters of an optimized mathematical model of a robot system of a labeling machine, randomly initializing the center coordinates of labeling points and the positions and speeds of all particles, initializing individual optimal values, and taking the minimum value as a global optimal value;
(2) updating the number of particles that vary non-linearly;
(3) updating an asynchronous nonlinear variation learning factor, calculating nonlinear variation inertia weight by a Tanh function, updating positions and speeds of all particles, calculating joint rotation angle total journey of the industrial robot according to the kinematic analysis solution of the industrial robot, updating all particle fitness values, and updating a global optimal value and an individual optimal value;
(4) judging whether the iteration reaches the maximum iteration number, and if not, returning to the step (2).
The method has the beneficial effects that:
(1) The optimal spatial positions of the label printer and the industrial robot in the labeler system are solved by establishing a mathematical model for optimizing the spatial positions of the components of the labeler system and adopting an optimization algorithm, so that the working efficiency of the labeler system is improved;
(2) Randomly generating a plurality of space points to simulate the space positions of a plurality of labeling points according to the constraint conditions of the labeling objects;
(3) And the improvement of the particle swarm optimization algorithm is realized by applying the nonlinear variation inertia weight, the learning factor and the particle number, and the convergence accuracy and the optimization efficiency of the algorithm are improved.
Drawings
FIG. 1 is a schematic diagram of a labeler robot system used in the method of the present invention;
FIG. 2 is a coordinate system of a labeler robot system employed in the method of the present invention;
FIG. 3 is a flow chart of an improved particle swarm optimization algorithm of the present invention.
Detailed Description
The invention discloses a method for optimizing the spatial position of a robot system component of a labeling machine, which comprises the following steps:
step 1, establishing a coordinate system of a labeling machine robot system, establishing a user coordinate system in a theoretical center of a station to be labeled, determining the postures of an industrial robot and a label printer according to the postures of the user coordinate system, and establishing the industrial robot coordinate system and the label printer coordinate system;
step 2, generating space coordinates of the labeling points, and randomly generating a plurality of space points to simulate the space positions of a plurality of labeling points according to constraint conditions of labeling objects;
step 3, establishing a mathematical model for optimizing the spatial positions of an industrial robot and a label printer in a labeler system, determining spatial position constraint conditions of the industrial robot and the label printer by taking the spatial positions of the industrial robot and the spatial positions of the label printer as design variables and combining the working space of the robot, taking the minimum joint angle total travel of the industrial robot as an objective function, converting a world coordinate pose matrix of a labeling point and all labeling points into a robot joint coordinate by utilizing an inverse kinematics analysis and solution expression of the industrial robot, calculating the joint angle total travel of the industrial robot by taking the sum of absolute values of joint angle change amounts of the robot moving from the labeling point to a single labeling point as the joint angle travel of the single labeling point, and summing the joint angle travel of all labeling points;
and step 4, completing calculation by adopting an optimization algorithm, and solving a mathematical model for optimizing the spatial positions of the industrial robot and the label printer in the robot system of the labeling machine by adopting the optimization algorithm to obtain the optimal spatial positions of the industrial robot and the label printer, wherein the industrial robot has the minimum total stroke of joint angles for labeling all labeling points.
The invention adopts an improved particle swarm optimization algorithm to complete the calculation of the space position optimization of the robot system component of the labeling machine, and improves the traditional particle swarm optimization algorithm as follows:
(1) Calculating inertial weight omega by using nonlinear variation Tanh function, wherein the calculation formula isWherein omega is min 、ω max Representing the minimum value of the inertia weight and the maximum value of the inertia weight, wherein K is the maximum iteration number, K is the current iteration number, lambda is the amplification coefficient, and mu is the translation coefficient;
(2) Individual learning factor c using asynchronously nonlinear varying learning factors 1 The calculation formula of (2) isWherein, c 1max 、c 1min The learning factors are the maximum individual learning factor and the minimum individual learning factor; social learning factor c 2 The calculation formula of (2) is +.>Wherein, c 2max 、c 2min Is the maximum social learning factor and the minimum social learning factor;
(3) The particle number n with nonlinear variation is adopted, and the calculation formula is thatWherein n is max Is the iterative maximum particle number; n is n min Is the iterative minimum number of particles.
The method for completing the optimization calculation of the space position of the robot system component of the labeling machine by adopting the improved particle swarm optimization algorithm comprises the following specific steps:
(1) initializing basic parameters of an optimized mathematical model of a robot system of a labeling machine, randomly initializing the center coordinates of labeling points and the positions and speeds of all particles, initializing individual optimal values, and taking the minimum value as a global optimal value;
(2) updating the number of particles that vary non-linearly;
(3) updating an asynchronous nonlinear variation learning factor, calculating nonlinear variation inertia weight by a Tanh function, updating positions and speeds of all particles, calculating joint rotation angle total journey of the industrial robot according to the kinematic analysis solution of the industrial robot, updating all particle fitness values, and updating a global optimal value and an individual optimal value;
(4) judging whether the iteration reaches the maximum iteration number, and if not, returning to the step (2).
The invention is applicable to the labeler robot system shown in fig. 1, and comprises a pressure supply unit 1, a control unit 2, a vision unit 3, a label printer 4 and an industrial robot 5. The labeling robot system is used for labeling the end faces of the bundled bars of the bundled bar weighing stations of the special steel bar finishing production line, and the spatial positions of the industrial robot and the label printer in the system are optimized by adopting the method.
1 establishing a coordinate System of a labeler robot System
The coordinate system of the labeler robot system is shown in fig. 2. A label printer of the labeling robot system is a ZT410 printing and stripping integrated industrial printer of zebra, and an ER7L-C10 six-degree-of-freedom industrial robot of Epstein-Barr is selected as an industrial robot. Taking theoretical plane of integral end face of bundled bar as X w -Y w A plane. Because the maximum diameter of one bundle of bars is not more than 360mm, the bundle of bar supports are horizontally arranged, and the center of the maximum diameter of the bundle of bars is taken as the originO w With X being horizontal to the right w In the positive direction, with Y being the vertical upward direction w In the forward direction, a user coordinate system is established. With the center of a flange plate of a fixed base of an industrial robot as an origin O 0 X of industrial robot coordinate system 0 X of axis and user coordinate system w Axis direction is consistent, Z of industrial robot coordinate system 0 Y of axis and user coordinate system w The axial directions are consistent, and an industrial robot coordinate system is established. With the center point of the label printed by the label printer as the origin O p X of label printer coordinate system p X of axis and industrial robot coordinate system 0 Axis direction is consistent, Z of label printer coordinate system p Z of axis and industrial robot coordinate system 0 The axial directions are consistent.
2 establishing the center coordinates of each bar in the bundle of bars
Maximum non-level degree of end faces of bunched bars in an industrial site is 20mm, maximum bunching diameter of the bunched bars is 360mm, and center coordinates P of the bars are determined under the constraint condition b ＝[x b ，y b ，z b ] T The range under the user coordinate system is: -160mm<x b <160mm， -160mm<y b <160mm，-20mm<z b <0mm. In order to ensure that after the placement positions of the industrial robot and the label printer are fixed, labeling points of each rod in a bundle of rods are in an industrial robot working space, space point simulation rod center coordinates are randomly generated through a Monte Carlo method, and N=2000 space point simulation rod center coordinates are randomly generated through a unirnd function in a MATLAB environment:
steel_center(:,1)＝unifrnd(-160,160,[1,N])；
steel_center(:,2)＝unifrnd(-160,160,[1,N])；
steel_center(:,3)＝unifrnd(0,0,[1,N])。
3 establishing mathematical model for optimizing spatial positions of industrial robot and label printer in labeler robot system
The vision unit in the labeler robot system is arranged right in front of the bar. In order to avoid blocking the camera view, the industrial robot is placed on the left side of the bar, and the label printer is placed on the workerThe right side of the industrial robot. The end effector of the industrial robot was 300mm long with a total compression stroke of 50mm. In order to ensure the safety of the equipment, in a user coordinate system Z w The ER7L-C10 industrial robot at the position of 340mm of the shaft is labeled through linear motion, the compression stroke of the end effector is 40mm, and the linear motion distance of the industrial robot during labeling is 80mm. The maximum working radius of the ER7L-C10 industrial robot is 910mm, and in order to ensure that the bundled bars and the label printer are in the working space of the robot, the spatial position P of the industrial robot is defined by comprehensively considering the structure and the working mode of the industrial robot r ＝[x 1 ， y 1 ，z 1 ] T The range under the user coordinate system is: -620mm<x 1 <-200mm，-640mm<y 1 <-200mm， 200mm<z 1 <700mm; label printer spatial position P p ＝[x 2 ，y 2 ，z 2 ] T The range under the industrial robot coordinate system is: 600mm<x 2 <1000mm，-400mm<y 2 <400mm，0mm<z 2 <600mm。
When the industrial robot is labeled, the axial direction of the end operator is perpendicular to the end face of the bar, the axial direction of the end operator is perpendicular to the label surface when the industrial robot is labeled, and the world coordinate pose matrix T of the industrial robot, from which the robot moves to a labeling point, is determined through experiments p The method comprises the following steps:
industrial robot world coordinate pose matrix T for taking punctuation t The method comprises the following steps:
positive kinematics analysis of ER7L-C10 industrial robot, according to robot connecting rod information provided by ER7L-C10 robot manufacturer, robot connecting rod angle theta 1 ＝0°，θ 2 ＝90°，θ 3 ＝0°，θ 4 ＝0°，θ 5 ＝0°，θ 6 =0°, and the robot D-H parameters are determined as shown in the table1.
TABLE 1 robot D-H parameters
Homogeneous transformation matrix general formula A between two adjacent coordinate systems of ER7L-C10 industrial robot by standard D-H parameter method n The method comprises the following steps:
wherein s is n Representing sin theta n ，c n Representing cos theta n ，s 23 Representation sin (θ) 2 +θ 3 )，c 23 Represent cos (θ) 2 +θ 3 ) Based on the D-H parameter, A is obtained 0 -A 6 The transformation matrix is:
transform matrix A uniformly 1 -A 6 Obtaining homogeneous transformation matrix T from base to TCP of ER7L-C10 industrial robot by continuous multiplication 6 The method comprises the following steps:
in the method, in the process of the invention,
n x ＝s 1 c 4 s 6 -c 1 s 4 s 6 c 23 +s 1 s 4 c 5 c 6 +c 1 c 4 c 5 c 6 c 23 -c 1 s 5 c 6 s 23 ；
n y ＝-c 1 c 4 s 6 -s 1 s 4 s 6 c 23 -c 1 s 4 c 5 c 6 +s 1 c 4 c 5 c 6 c 23 -s 1 s 5 c 6 s 23 ；
n z ＝s 5 c 6 c 23 +c 4 c 5 c 6 s 23 -s 4 s 6 s 23 ；
o x ＝s 1 c 4 c 6 -c 1 s 4 c 6 c 23 -s 1 s 4 c 5 s 6 -c 1 c 4 c 5 s 6 c 23 +c 1 s 5 s 6 s 23 ；
o y ＝s 6 c 1 s 4 c 5 -s 1 c 4 c 5 s 6 c 23 +s 1 s 5 s 6 s 23 -c 1 c 4 c 6 -s 1 s 4 c 6 c 23 ；
o z ＝-s 5 s 6 c 23 -c 4 c 5 s 6 s 23 -s 4 c 6 s 23 ；
a x ＝s 1 s 4 s 5 +c 1 c 4 s 5 c 23 +c 1 c 5 s 23 ；
a y ＝s 1 c 5 s 23 -c 1 s 4 s 5 +s 1 c 4 s 5 c 23 ；
a z ＝c 4 s 5 s 23 -c 23 c 5 ；
p x ＝d 3 s 1 +a 1 c 1 +d 4 c 1 s 23 +a 2 c 1 c 2 +d 6 c 1 c 5 s 23 +a 3 c 1 c 23 +d 6 c 1 c 5 c 23 +d 6 s 1 s 4 s 5 +d 6 c 1 c 4 s 5 c 23 ；
p y ＝a 1 s 1 -d 3 c 1 +d 4 s 1 s 23 +a 2 s 1 c 2 +d 6 s 1 c 5 s 23 -d 6 c 1 s 4 s 5 +a 3 s 1 s 23 +d 6 s 1 c 4 s 5 c 23 ；
p z ＝d 1 -d 4 c 23 +a 3 s 23 +a 2 s 2 -d 6 c 5 c 23 +d 6 c 4 s 5 s 23 。
and writing an industrial robot positive kinematics ER7L_C10_zhengjie.m function according to the calculated positive kinematics analytic solution in the MATLAB environment.
ER7L-C10 industrial robot inverse kinematics analysis, separation variable method in analysis method is applied to realize analysis solution of robot inverse kinematics, and theta is realized according to structural characteristics of the robot ER7L-C10 5 When it is zero, it is necessary to discuss the joint angle θ in case of cases 4 And theta 6 Solution, therefore, the joint angle θ is first solved 1 、θ 2 、θ 3 Solving the joint angle theta 4 、θ 5 、θ 6 。
Homogeneous transformation matrix T of ER7L-C10 industrial robot 6 Left-hand matrix A 1 -1 Right multiplication matrix A 6 -1 The method can obtain:
solving for joint angle θ according to the above 1 、θ 2 、θ 3 The method comprises the following steps:
θ 3 ＝θ 23 -θ 2 (6)
wherein:
m 2 ＝p z -d 1 -a z d 6 ；m 1 ＝p x c 1 -a 1 +p y s 1 -a y d 6 s 1 -a x d 6 c 1 ；
m 3 ＝(d 4 2 +a 3 2 +m 1 2 +m 2 2 -a 2 2 )/2；
homogeneous transformation matrix T of ER7L-C10 industrial robot 6 Left-hand matrix A 1 -1 The left-hand matrix A 2 -1 The left-hand matrix A 3 -1 The method can obtain:
when theta is as 5 When the joint angle is not equal to 0, solving the joint angle theta according to the above formula 4 、θ 5 、θ 6 The method comprises the following steps:
θ 5 ＝±arccos(s 23 (a x c 1 +a y s 1 )-a z c 23 ) (8)
homogeneous transformation matrix T of ER7L-C10 industrial robot 6 Left-hand matrix A 1 -1 The method can obtain:
when theta is as 5 When equal to 0, θ 46 Represents θ 4 +θ 6 Solving for joint angle θ according to the above 46 The method comprises the following steps:
due to the joint angle theta of the robot 5 When the value is equal to 0, the axes of the robots 4, 5 and 6 are coaxial, and the robots are at singular points and theta 4 And theta 6 There are infinite solutions, so here solve for θ 4 And theta 6 Joint angle sum, passing angle theta 46 Calculate the joint angle θ 4 And theta 6 ，θ 4 And theta 6 There are three selection solutions for the solution,
(1) Reading the current angle value of the 6-axis of the ER7L-C10 industrial robot as the joint angle theta 6 And then theta 4 Has a value of θ 46 -θ 6 ；
(2) Reading the current angle value of the 4-axis of the ER7L-C10 industrial robot as the joint angle theta 4 And then theta 6 Has a value of θ 46 -θ 4 ；
(3) Artificial given joint angle theta 4 Solving for θ 6 Is a value of (2); or given joint angle theta 6 Solving for θ 4 Is a value of (2).
To sum up, ER7L_C10 industrial robot θ 1 ，θ 2 ，θ 3 ，θ 4 ，θ 5 ，θ 6 All feasible solutions of (2) are obtained and inverse kinematics is analyzedThe solution combination arrangement has 16 possible solutions, and the inverse solution selection solution is realized according to the 'minimum travel method' rule. Angle of articulation theta 5 When the robot is equal to 0 robot singular, the solution is selected by the mode one. In the MATLAB environment, the industrial robot inverse kinematics ER7L_C10_fanjie.m and ER7L_C10_readmessage.m functions were written.
The space position optimization is realized by the principle of minimum total joint rotation angle travel of the robot when the bundled bars are labeled. Converting world coordinate pose matrixes of the mark taking points and all the mark pasting points into robot joint coordinates by using an inverse kinematics analytic solution expression of the industrial robot, calculating the change amount of each joint angle of the robot moving from the mark taking points to the mark pasting points, summing absolute values of the change amounts of each joint angle to obtain the joint angle total travel of each bar in the mark pasting process, wherein the joint angle total travel of the industrial robot is the sum of the joint angle total travel of each bar in a bundle of bars, solving the minimum value of the joint angle total travel of the industrial robot by using an optimization algorithm, and optimally designing a mathematical model as follows:
wherein f is the minimum fitness value of all particles; n represents the number of the bundle of bars; θ 1j Labeling each joint corner of the points; θ 2j Taking the joint angles of the punctuation, wherein j=1, 2, … and 6; i=1, 2, …, N.
4 adopting improved particle swarm optimization algorithm to complete calculation
The application optimization is realized by an improved particle swarm optimization algorithm for optimizing the spatial arrangement positions of the industrial robot and the label printer, and the speed and the position of particles in the traditional particle swarm optimization algorithm are updated by comparing the individual optimal value and the global optimal value of the particles.
Wherein ω is an inertial weight, and k is a current iteration number; id = 1,2, …, n; c 1 、c 2 Learning factors for individuals and social learning factors; r is (r) 1 、r 2 Is [0-1]Random numbers within the range; p is p id k Is the optimal value of the individual; g id k Is a global optimum; v id k The flight speed of the particle id in the kth iteration is the flight speed; x is X id k Is the position of the particle id at the kth iteration.
The parameters of the traditional particle swarm algorithm are improved as follows:
(1) Nonlinear dynamic adjustment of inertial weights
The magnitude of the inertial weight ω has a large impact on the particle swarm search for the globally optimal solution. And a Tanh function is adopted as an inertial weight calculation formula. When the algorithm starts to execute, by giving a larger value to ω, the algorithm can perform better search in a constraint condition at a larger speed at the initial stage of iteration, so that the algorithm can converge towards a global optimal solution with a larger probability, and as the algorithm executes, ω is gradually reduced, so that the solution of the optimization problem can be weighted between the global optimal and the local optimal to obtain an optimal fitness value.
Wherein omega is min 、ω max Representing the minimum and maximum values of the inertial weights; k is the total number of iterations; lambda is the amplification factor; μ is the translation coefficient.
(2) Asynchronous change learning factor adjustment
Individual learning factor c 1 And social learning factor c 2 The particles are controlled to move towards the individual and global optimal solutions, and the calculation efficiency of an optimization algorithm can be improved by applying a dynamically-changing learning factor, so that the calculation result of the algorithm can be greatly prevented from being trapped into the local optimal solution. Trigonometric functions are introduced as learning factors for asynchronous nonlinear changes. By applying larger individual learning factors and smaller societies earlier in the algorithmThe factors can be learned, so that the algorithm can fully search solutions around the particles, smaller individual learning factors and larger social learning factors are applied in the later period of algorithm optimization, and the particles are close to the globally optimal solution.
Wherein, c 1max 、c 1min Learning factors for maximum and minimum individuals; c 2max 、c 2min Is the maximum and minimum social learning factor.
(3) Nonlinear decreasing particle number
The optimization of the spatial positions of the industrial robot and the label printer takes longer time by adopting the traditional particle swarm optimization algorithm, because 2000 bars randomly generated by adopting the Monte Carlo method need larger particle number to realize the iterative solution of the particle swarm. The number of particles per iteration remains unchanged, resulting in a longer iterative calculation, thus suggesting a non-linear decrease in the number of particles.
Wherein n is max Is the iterative maximum particle number; n is n min Is the iterative minimum number of particles.
Total number of iterations k=200, calculation parameters: parameters in formula (16), λ=8, μ=1, ω min ＝0.4，ω max =0.8; parameters in formula (17), c 1min ＝0.5，c 1max =2.5; parameter c in equation (18) 2min ＝0.5，c 2max =2.5; parameters in formula (19), n max ＝150， n min ＝50，μ＝1.1。
The proposed improved particle swarm optimization algorithm realizes the updating of inertia weight, learning factor and particle number through formulas (16), (17), (18) and (19), and a flow chart of the improved particle swarm optimization algorithm for solving the optimal spatial positions of the industrial robot and the label printer is shown in fig. 3.
The specific calculation process under the MATLAB environment comprises the following steps:
(1) initializing parameter variable values of a particle swarm optimization algorithm, initializing spatial position constraint ranges of an industrial robot and a label printer, and randomly initializing the position and the speed of particles according to a rand (nmax, 1) function;
number of variables: narvs=6;
social learning factor maximum: c11 =2.5;
social learning factor minimum: c12 =0.5;
individual learning factor maximum: c21 =2.5;
individual learning factor minimum: c22 =0.5;
maximum value of inertial weight: wmax=0.8;
inertial weight minimum: wmin=0.4;
total number of iterations: k=200;
maximum speed of particle: vmax=15;
amplification factor: lmd=8;
translation coefficient: dis_n=1.1;
iterative maximum particle count: nmax=150;
iterative minimum particle count: nmin=50;
industrial robot X coordinate range:
robot_x_max＝-200；robot_x_min＝-620；
y coordinate range of industrial robot:
robot_y_max＝-200；robot_y_min＝-640；
z coordinate range of industrial robot
robot_z_max＝700；robot_z_min＝200；
Label printer X coordinate range
printer_x_max＝1000；printer_x_min＝600；
Label printer Y coordinate range
printer_y_max＝400；printer_y_min＝-400；
Z coordinate range of label printer
printer_z_max＝600；printer_z_min＝0；
Initializing the spatial positions of the industrial robot and the label printer:
robot_x＝robot_x_min+(robot_x_max-robot_x_min).*rand(nmax,1)；
robot_y＝robot_y_min+(robot_y_max-robot_y_min).*rand(nmax,1)；
robot_z＝robot_z_min+(robot_z_max-robot_z_min).*rand(nmax,1)；
printer_x＝printer_x_min+(printer_x_max-printer_x_min).*rand(nmax,1)；
printer_y＝printer_y_min+(printer_y_max-printer_y_min).*rand(nmax,1)；
printer_z＝printer_z_min+(printer_z_max-printer_z_min).*rand(nmax,1)；
position_pso＝[robot_x,robot_y,robot_z,printer_x,printer_y,printer_z]；
initializing the speed of the particles:
v＝-vmax+2*vmax.*rand(nmax,narvs)。
calculating fitness fit (ii) according to an industrial robot joint angle total stroke calculation Function object_function (step_center, position_pso, ii) and a calculation Function angle f (step_x, step_y, step_z) of the single rod industrial robot moving from a punctuation point to a punctuation point, and initializing a particle swarm global optimum value gbest and an individual optimum value pbest:
pbest＝position_pso；
ind＝find(fit＝＝min(fit),1)；
gbest＝position_pso(ind,:)。
initializing the center coordinates of each bar in the bundle of bars, namely, a step_center:
steel_center(:,1)＝unifrnd(-160,160,[1,N])；
steel_center(:,2)＝unifrnd(-160,160,[1,N])；
steel_center(:,3)＝unifrnd(0,0,[1,N])。
(2) updating the number of particles n according to formula (19);
n＝round(nmin+(nmax-nmin)*(1-(exp(lmd*(2*d/K-dis_n))-exp(lmd*(-(2*d/K-dis_n))))/(exp(lm d*(2*d/K-dis_n))+exp(lmd*(-(2*d/K-dis_n)))))/2)；
[fit,index]＝sort(fit)；
(3) the speed, position, inertial weight, and learning factor of the particles are updated according to equations (14), (15), (16), (17), and (18), fitness is updated according to functions object_function and angle Function, and global and individual optimal values are updated.
And updating inertia weight:
w＝wmin+(wmax-wmin)*(1-(exp(lmd*(2*d/K-1))-exp(lmd*(-(2*d/K-1))))/(exp(lmd*(2*d/K-1) )+exp(lmd*(-(2*d/K-1)))))/2。
individual learning factor update:
c1＝c12+(c11-c12)*cos((d/K)*pi/2)。
social learning factor update:
c2＝c21-(c21-c22)*cos((d/K)*pi/2)。
and (5) updating the speed:
v(i,:)＝w*v(i,:)+c1*rand(1)*(pbest(index(i),:)-position_pso(index(i),:))+c2*rand(1)*(gbest-posit ion_pso(index(i),:))。
and (3) position updating:
position_pso(index(i),:)＝position_pso(index(i),:)+v(i,:)。
calculating temp_sum according to a calculation function of the single rod industrial robot moving from the mark taking point to the mark pasting point:
temp_sum＝temp_sum+AngleFunction(position(i,1),position(i,2),position(i,3))。
calculating fit (index (i)) according to the joint rotation angle total travel function of the industrial robot:
fit(index(i))＝Object_Function(steel_center,position_pso,index(i))。
the optimal fitness function of the d-th iteration is as follows:
fitnessbest(d)＝Object_Function(steel_center,gbest,1)。
(4) and (3) performing the step (2) and the step (3) through K iterations to calculate the minimum value of the total joint rotation angle travel of the industrial robot, and obtaining the optimal space placement positions of the industrial robot and the label printer, wherein the calculation result of the improved particle swarm optimization algorithm is shown in the table 2.
TABLE 2 particle swarm optimization results
Claims (1)
1. The method for optimizing the spatial position of the components of the labeling robot system is characterized in that the labeling robot system adopted by the method comprises a pressure supply unit (1), a control unit (2), a visual unit (3), a label printer (4) and an industrial robot (5), and the method comprises the following steps:
step 1, establishing a coordinate system of a labeling machine robot system, establishing a user coordinate system in a theoretical center of a station to be labeled, determining the postures of an industrial robot and a label printer according to the postures of the user coordinate system, and establishing the industrial robot coordinate system and the label printer coordinate system;
step 2, generating space coordinates of the labeling points, and randomly generating a plurality of space points to simulate the space positions of a plurality of labeling points according to constraint conditions of labeling objects;
step 3, establishing a mathematical model for optimizing the spatial positions of the industrial robot and the label printer in the labeling robot system so as to realize the spatial positions of the industrial robotPr=[x 1 ，y 1 ，z 1 ] T And label printer spatial locationP p =[x 2 ，y 2 ，z 2 ] T For designing variables, determining space position constraint conditions of an industrial robot and a label printer by combining a working space of the robot, taking the minimum total joint rotation angle travel of the industrial robot as an objective function, converting world coordinate pose matrixes of the punctuation and all the punctuation into robot joint coordinates by utilizing an inverse kinematics analytic solution expression of the industrial robot, and calculating each joint rotation of the robot from the punctuation to a single punctuationThe sum of absolute values of the angle change amounts is the joint angle travel of a single labeling point, and the joint angle travel of all labeling points is summed to obtain the joint angle total travel of the industrial robot;
step 4, completing calculation by adopting an optimization algorithm, solving a mathematical model of space position optimization of an industrial robot and a label printer of a labeling robot system by adopting the optimization algorithm, obtaining the optimal space positions of the industrial robot and the label printer with the minimum total stroke of joint angles of labeling points of all labeling accomplished by the industrial robot, completing calculation of space position optimization of a part of the labeling robot system by adopting an improved particle swarm optimization algorithm, and improving the traditional particle swarm optimization algorithm as follows:
(1) Calculating inertial weights with nonlinear varying Tanh functionsωThe calculation formula isIn which, in the process,ω min 、ω max representing the minimum and maximum values of inertial weights,Kfor the maximum number of iterations to be performed,kfor the current number of iterations,λin order to amplify the coefficient of the power,µis a translation coefficient;
(2) Learning factor using asynchronous nonlinear variation, individual learning factorc 1 The calculation formula of (2) isIn which, in the process,c 1max 、c 1min the learning factors are the maximum individual learning factor and the minimum individual learning factor; social learning factorc 2 The calculation formula of (2) is +.>In which, in the process,c 2max 、c 2min is the maximum social learning factor and the minimum social learning factor;
(3) Using non-linearly varying particle numbersnThe calculation formula isIn which, in the process,n max is the iterative maximum particle number;n min is the iterative minimum particle number;
the method for completing the optimization calculation of the space position of the robot system component of the labeling machine by adopting the improved particle swarm optimization algorithm comprises the following specific steps:
(1) initializing basic parameters of an optimized mathematical model of a robot system of a labeling machine, randomly initializing the center coordinates of labeling points and the positions and speeds of all particles, initializing individual optimal values, and taking the minimum value as a global optimal value;
(2) updating the number of particles that vary non-linearly;
(3) updating an asynchronous nonlinear variation learning factor, calculating nonlinear variation inertia weight by a Tanh function, updating positions and speeds of all particles, calculating joint rotation angle total journey of the industrial robot according to the kinematic analysis solution of the industrial robot, updating all particle fitness values, and updating a global optimal value and an individual optimal value;
(4) judging whether the iteration reaches the maximum iteration number, and if not, returning to the step (2).
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