CN113325799A - Spot welding robot operation space smooth path planning method for curved surface workpiece - Google Patents

Spot welding robot operation space smooth path planning method for curved surface workpiece Download PDF

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CN113325799A
CN113325799A CN202110180287.0A CN202110180287A CN113325799A CN 113325799 A CN113325799 A CN 113325799A CN 202110180287 A CN202110180287 A CN 202110180287A CN 113325799 A CN113325799 A CN 113325799A
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coordinate system
spot
workpiece
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CN113325799B (en
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张邦成
赵航
尹晓静
柳虹亮
杨磊
孙建伟
常笑鹏
陈司昱
邵昱博
张子强
夏奇
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Changchun University of Technology
Faw Tooling Die Manufacturing Co Ltd
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Faw Tooling Die Manufacturing Co Ltd
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    • G05B19/00—Programme-control systems
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention discloses a spot welding robot operation space smooth path planning method for a curved surface workpiece. Modeling is carried out on the profile of the curved surface workpiece and the distribution of welding spots through a three-dimensional grid method, the shortest smooth obstacle avoidance path between the welding spots is generated through smooth processing by adopting an improved A-star algorithm and a uniform B spline subdivision algorithm, an optimal welding sequence is obtained through a multi-target elite simulated annealing genetic algorithm, and a joint space path corresponding to the current welding path is obtained through inverse kinematics solution according to a collision-free motion constraint condition of a welding clamp coordinate system and a welding spot coordinate system and a safe distance constraint condition of the welding clamp coordinate system and the profile of the curved surface workpiece. The invention has application reference value in the actual industry, can shorten the planning and debugging time of engineers, and can improve the working efficiency of the robot.

Description

Spot welding robot operation space smooth path planning method for curved surface workpiece
Technical Field
The invention relates to the technical field of robot welding, in particular to a planning method for a spot welding robot operation space smooth path of a curved workpiece.
Background
The automotive industry is a typical application area for spot welding robotic systems, where about 60% of the welding points of the body are performed by the robot. The spot welding robot has the advantages that the workpiece profile and the welding spots are distributed in a complex manner, so that the welding sequence of the welding spots is reasonably arranged, an excellent welding track planning scheme is obtained, and the spot welding robot has very important significance for saving welding time, reducing production cost and improving production efficiency. At present, a robot has a large space for application research, a welding engineer often depends on the experience of the welding engineer and a process card of a designer, the teaching engineer relies on long-time teaching and debugging of the teaching engineer, the theory cannot be optimized, and the method is contradictory to the automobile industry pursuing high production beat efficiency.
For a curved surface workpiece object with a complex space, how to automatically generate a smooth optimal path in an operation space is an urgent problem to be solved. The problem of the welding path between welding points and the problem of the welding sequence of the welding points have relative independence, and the optimization process is interdependent, however, most of the existing methods only consider the welding sequence of the welding points, and the global optimal solution of the welding path in the operation space cannot be obtained. In addition, most of the existing methods intensively study the path planning of the robot joint space, however, the spot welding operation needs high-precision positioning to achieve the compactness and compactness of a welding spot nugget, so that the requirement of welding strength is met, and therefore, the smooth path planning of the operation space with intuition, high efficiency and high operation precision is more reasonable.
The invention aims to realize the automatic generation of the welding line robot path instead of manual planning by using an intelligent algorithm in the actual engineering, find the optimal smooth path and improve the planning efficiency. The core of the white body welding spot path planning is a three-dimensional TSP problem, the Memetic algorithm combines neighborhood knowledge and a group-based search method, has the characteristic of a high-efficiency heuristic algorithm, increases the diversity of solutions compared with a group method (such as a genetic algorithm, an ant colony algorithm and the like), and has better ability of jumping out of local optimum.
Disclosure of Invention
The invention aims to solve the technical problem that the welding path length is shortened and the smoothness is improved by a spot welding robot welding path off-line planning method, and the method comprises four modules, namely a spot welding robot kinematics model module, a motion constraint condition module, an inter-welding point shortest smooth obstacle avoidance path planning module and an optimal welding point welding sequence planning module. Firstly, modeling is carried out through the profile of a curved surface workpiece and the distribution of welding points by a three-dimensional grid method, and an optimal path set among the welding points is generated by calling a shortest and smooth obstacle avoidance path planning module among the welding points; secondly, according to the optimal path set among the welding spots, calling an optimal welding spot welding sequence planning module to determine a welding spot welding sequence on the basis of considering the path length and smoothness to obtain a complete optimal welding spot welding path; secondly, according to the collision-free motion constraint condition of the welding tongs coordinate system and the welding spot coordinate system and the safe distance constraint condition of the welding tongs coordinate system and the profile of the curved surface workpiece, a homogeneous transformation matrix of the spot welding robot is obtained through the complete motion constraint closed chain of the motion constraint condition module; and finally, according to the obtained discrete points of the complete and optimal welding spot welding path, solving through inverse kinematics of a spot welding robot kinematics model module to obtain a spot welding robot joint angle change curve, namely a planned path in a joint space. Spot welding robot kinematics model module bagThe method comprises the steps of including a positive kinematics model and an inverse kinematics model, wherein the inverse kinematics model carries out inverse kinematics calculation of the robot according to a Pieper criterion, reversely solving joint variables of the front three joints according to the position of a wrist coordinate system, enabling the wrist to be equivalent to a z-y-z Euler angle rotation matrix, and reversely solving the rear three joint variables according to the front three joint variables; the motion constraint condition module determines a welding spot coordinate system according to the distance limit of a welding spot and an edge point of the profile of the curved surface workpiece, sets a collision-free motion constraint condition of the welding spot coordinate system and a safe distance constraint condition of the welding spot coordinate system and the profile of the curved surface workpiece according to the position and posture relation of the welding tongs, the welding spot and the profile of the curved surface workpiece, and establishes a complete motion constraint closed chain of the spot welding robot; the shortest and smooth obstacle avoidance path planning module among welding spots adopts an improved A-star algorithm to plan a welding path, and the included angle alpha and the included angle threshold alpha between the front node and the rear node are calculated0By comparison, if α ≧ α0Deleting redundant nodes to improve the path smoothness, smoothing the path by adopting a uniform B spline curve subdivision algorithm, and finally generating a shortest collision-free smooth path set between welding spots; on the basis of a genetic algorithm path planning method, an optimal welding spot welding sequence planning module takes the shortest path length and the highest path smoothness as an objective function, improves a mutation operator through a variable neighborhood search method, performs variable neighborhood search through four neighborhood structures of 'point insertion', 'exchange', '2-opt' and 'block insertion', combines an elite population strategy with a selection operator, provides more cross mutation operation opportunities for elite individuals, and finally jumps out of local search through a simulated annealing algorithm to obtain a global optimal solution of a welding path.
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FIG. 1 is a schematic diagram of a six-degree-of-freedom robot and its link coordinates according to the present invention;
FIG. 2 is a schematic diagram of a redundant node discrimination method of the improved A-star algorithm of the present invention;
FIG. 3 is a schematic diagram of the mechanism of action of genetic operators of the integrated elite population strategy of the present invention;
FIG. 4 is a schematic diagram of a method for searching a variable neighborhood structure of a mutation operator according to the present invention;
FIG. 5 is a flow chart of a Memetic algorithm based path planning method of the present invention;
FIG. 6 is a schematic view of inter-pad routing for both the conventional and modified A-star algorithms of the present invention;
FIG. 7 is a schematic diagram of a conventional genetic algorithm based path planning according to the present invention;
FIG. 8 is a schematic diagram of the path planning based on the elite adaptive genetic algorithm of the present invention;
FIG. 9 is a schematic diagram of the path planning based on the multi-objective elite simulated annealing genetic algorithm of the present invention;
FIG. 10 is a fitness evolution curve of the present invention;
FIG. 11 is an objective function value evolutionary curve of the present invention;
FIG. 12 is a population fitness mean evolution curve of the present invention;
FIG. 13 is a population fitness variance evolutionary curve of the present invention;
FIG. 14 is a graph showing the change in joint angle of the spot welding robot according to the present invention;
FIG. 15 is a diagram of a spot welding robot kinematics model and an optimal spot weld path for a beam assembly on a rear seat of the present invention;
Detailed Description
The invention is described in further detail below with reference to figures 1-15,
as shown in fig. 1, the transformation matrix of the robot links is as follows:
Figure BDA0002941281520000031
in the formula, ai-1Is the length of the connecting rod, alphai-1Is the connecting rod torsion angle diIs the link offset, θiIs the joint angle. c thetaiRepresents cos θi，sθiDenotes sin θi，cαi-1Represents cos alphai-1，sαi-1Denotes sin αi-1。
Due to ai-1、αi-1、diAre all alreadyKnowing the parameters, the joint transformation matrix
Figure BDA00029412815200000314
Only with joint variables thetaiAccordingly, the following formulae are not specifically illustrated, ciRepresents cos θi，siDenotes sin θi。
The pose of the robot terminal coordinate system in the base coordinate is described by a homogeneous transformation matrix, and the robot kinematics forward solution expression is as follows:
Figure BDA0002941281520000032
wherein θ comprises (θ)1,θ2,θ3,θ4,θ5,θ6)，
Figure BDA00029412815200000315
A transformation matrix representing the base coordinate system and the joint 6 coordinate system,
Figure BDA0002941281520000033
Figure BDA0002941281520000034
respectively representing a transformation matrix between two adjacent coordinate systems,
Figure BDA0002941281520000035
representing transformation matrix of adjacent joint coordinate system and joint angle variable thetaiP is the position vector [ p ] of the end reference point relative to the base coordinate systemx,py,pz]T，[n o a]Attitude matrix being a relative base coordinate system of a terminal reference point
Figure BDA0002941281520000036
As the three joints of the wrist of most spot welding robots are intersected at the same point, the inverse kinematics calculation of the robot can be carried out according to the Pieper criterionAccording to the position of wrist coordinate system to solve the joint variable theta of the first three jointsi(i is 1,2,3), then according to the wrist posture coordinate and the first three calculated joint variables, the last three joint variables theta are reversely solvedi(i＝4,5,6)。
Since the wrist coordinate systems {4}, {5}, and {6} are common in origin, the position of the point in the base coordinate system can be obtained from the link transformation.
Figure BDA0002941281520000037
In the formula (I), the compound is shown in the specification,
Figure BDA0002941281520000038
is represented by [ p ]x,py,pz,1]T，
Figure BDA0002941281520000039
A transformation matrix representing the base coordinates and the joint 1 coordinate system,
Figure BDA00029412815200000310
a transformation matrix representing a joint 1 coordinate system and a joint 2 coordinate system,
Figure BDA00029412815200000311
a transformation matrix representing the joint 2 coordinate system and the joint 3 coordinate system, f1、f2And f3Are respectively denoted by f1＝a3c3-d4s3+a2、f2＝a3s3+d4c3 and f3＝0。
Continuing to use the homogeneous transformation matrix and substituting into the known matrix
Figure BDA00029412815200000312
Position vector px,py,pz,1]TTo obtain
Figure BDA00029412815200000313
In the formula, g1、g2And g3Are respectively represented as g1＝c2f1-s2f2+a1，g2＝f3And g3＝-s2f1-c2f2-f3。
From the geometric relationship and the above equation, [ p ]x,py,pz,1]TCan be written as
Figure BDA0002941281520000041
[px,py,pz,1]TThe position in the base coordinate system can also be expressed as:
Figure BDA0002941281520000042
in the formula, k1、k2And k3Are respectively represented by k1＝f1，k2＝-f2And
Figure BDA0002941281520000043
substituting the D-H parameter data into the D-H parameter data, and obtaining the D-H parameter data by the following equations (3) to (6):
Figure BDA0002941281520000044
in the formula (I), the compound is shown in the specification,
Figure BDA0002941281520000045
by substituting formulae (6) and (7) by g 20 and known
Figure BDA0002941281520000046
Coordinate [ p ]x,py,pz,1]TObtaining:
Figure BDA0002941281520000047
wherein the content of the first and second substances,
Figure BDA0002941281520000048
according to theta already solved above1、θ2And theta3Further, the target rotation matrix can be obtained
Figure BDA0002941281520000049
Thereby to obtain
Figure BDA00029412815200000410
In the formula (I), the compound is shown in the specification,
Figure BDA00029412815200000411
expressed as the last three joint variables θi(i is 4,5,6),
Figure BDA00029412815200000412
the first three joints thetai(i is 1,2,3) is the inverse of the attitude transformation matrix,
Figure BDA00029412815200000413
attitude matrix [ n o a ] of reference point relative to base coordinate system at tail end of robot]。
And (3) performing euler angle transformation on three axes of the wrist of the spot welding robot similarly to z-y-z to obtain:
Figure BDA00029412815200000414
in the formula (I), the compound is shown in the specification,
Figure BDA00029412815200000415
is when theta4Coordinate system {4} is at coordinate when 0Attitude in system {3}, Rzyz(θ4,θ5,θ6) Is the wrist equivalent z-y-z euler angular rotation matrix.
Solving method for theta by using z-y-z Euler angle4、θ5And theta6。
Figure BDA00029412815200000416
In the formula, rij(i, j-1, 2,3) represents formula (9)
Figure BDA00029412815200000417
Elements of the matrix, where i is the rotation matrix
Figure BDA00029412815200000418
J is a rotation matrix
Figure BDA00029412815200000419
Number of columns of (theta)5The leading negative sign represents the y-axis and θ of the coordinate system {4}5The direction is opposite.
When the workpiece is a curved surface, the general formula can be expressed by a space curved surface equation:
F(x,y,z)＝0 (12)
Figure BDA00029412815200000420
is a welding point pi(xi,yi,zi) The unit normal vector of (1) is a welding point coordinate system { p }iZ-axis unit vector of
Figure BDA00029412815200000421
The set of edge points of the workpiece is { m }j}, edge point m of workpiecej(xdj,ydj,zdj) With the coordinates p of the welding spoti(xi,yi,zi) The vector between is represented as:
Figure BDA00029412815200000422
from the edge point { m of the workpiecejTo the welding point p on the curved surfacei(xi,yi,zi) Unit normal vector
Figure BDA00029412815200000423
The vector of (d) is represented as:
Figure BDA0002941281520000051
edge point m of workpiecej(xdj,ydj,zdj) To the welding point coordinate pi(xi,yi,zi) Unit normal vector
Figure BDA0002941281520000052
The shortest distance of
Figure BDA0002941281520000053
The corresponding vector can be expressed as:
Figure BDA0002941281520000054
edge point m of workpiecej(xdj,ydj,zdj) To the welding point pi(xi,yi,zi) As the coordinate system of the welding point { p }iThe x-axis unit vector of } is given by:
Figure BDA0002941281520000055
coordinate system of welding spot { piY-axis unit vector of }:
Figure BDA0002941281520000056
base coordinate and welding spot coordinate system { p }iThe homogeneous transformation matrix of }:
Figure BDA0002941281520000057
and transforming a matrix by the soldering turret and the spot welding robot:
Figure BDA0002941281520000058
the axis of the C-shaped servo welding tongs is perpendicular to the cutting surface of the workpiece at the coordinate position of the welding spot to ensure that the nugget is compact, and the method comprises the following steps:
Figure BDA0002941281520000059
the complete motion constraint closed chain is represented as:
Figure BDA00029412815200000510
the A-star algorithm is a graph search algorithm, the current node is analyzed through the cost of an initial node and a nearby node and heuristic evaluation from the node to a target node, and the cost function of the A-star algorithm is as follows:
f(n)＝g(n)+h(n) (23)
wherein n represents the current node, f (n) is an evaluation function of the initial node, the node and the target node of the spot welding robot, g (n) is the real cost between the initial node and a certain node of the state environment, and h (n) is the budget cost in the process from the current node to the target node.
The distance between the welding tongs and the workpiece is greater than the safe distance, and the following steps are carried out:
H(R,W)-dsafe≥0 (24)
wherein R and W represent a robot respectivelyEnd effector and workpiece, indicating that the robot has no collision with the workpiece, wherein dsafeIndicating the safe distance of the robot end effector from the workpiece.
Selecting Euclidean distance as a cost function of h (n), wherein the function expression is as follows:
Figure BDA00029412815200000511
in the formula (x)n,yn,zn) Represents the center coordinate of the current node, (x)g,yg,zg) Representing the target node center coordinates.
As shown in FIG. 2, which is a schematic diagram of the method for judging the redundant nodes of the improved A-star algorithm, 8 expansion nodes exist in the adjacent area on a grid map, and a spot welding robot is limited by the traveling direction to keep a safe distance d from the surface of a workpiecesafeRemoving redundant nodes, and backtracking nodes n according to the path obtained by backtrackingstPointing to a current node n on the surface of the workpiececForm a vector
Figure BDA0002941281520000061
Current node ncAnd subsequent node nsForm a vector
Figure BDA0002941281520000062
By calculation of
Figure BDA0002941281520000063
And
Figure BDA0002941281520000064
the included angle alpha between the two nodes is removed to form a redundant node ncVector of motion
Figure BDA0002941281520000065
Sum vector
Figure BDA0002941281520000066
The angle α therebetween is calculated as follows:
Figure BDA0002941281520000067
α0is a vector
Figure BDA0002941281520000068
And vector
Figure BDA0002941281520000069
Alpha is not less than alpha0Then, the node n is determinedcAre redundant nodes.
Figure BDA00029412815200000610
Wherein r isαIs the deletion of a redundant node ncThe discriminant function of (1). If alpha.gtoreq.alpha0Then the redundant node n is deletedc(ii) a Otherwise, the node n is reservedc。
After the redundant node removing operation, m + n +1 nodes n on the path of the spot welding roboti(i is 0,1,2, … m + n), smoothing the path by adopting a uniform B-spline curve subdivision algorithm to obtain the shortest path between the welding points, wherein the mathematical expression of the B-spline curve is as follows:
Figure BDA00029412815200000611
where t is 0 ≦ 1, i is 0,1,2, …, m, the B-spline curve is piecewise defined, given m + n +1 nodes ni(i＝0,1,2,…m+n)，Pi+kFor the position vector of each node, a parameter curve of m +1 segments n times can be defined.
Fk,n(t) is an n-th order B-spline basis function expressed as
Figure BDA00029412815200000612
Wherein t is more than or equal to 0 and less than or equal to 1，k＝0,1,2,…,n，
Figure BDA00029412815200000613
Representing the combined operation in the probability theory, and connecting the whole curve formed by all the curve segments to be called an n-order B-spline curve.
The objective function of the robot path planning is that the path between every two welding points and the shortest and the whole path have the highest smoothness.
Individual x traversing all weld pathsiThe sum of the lengths of (a) and (b) is expressed as:
Figure BDA00029412815200000614
in the formula IijIs the shortest path between the welding points obtained by the improved A-star algorithm, and n is the number of the path sections passing between the welding points.
Individual x traversing all weld pathsiThe path smoothness objective function expression of (1) is:
Figure BDA00029412815200000615
m and n are the number of turns and the number of segments of the path between the welding points, α is the angle between the front and rear nodes, tαIs an angle-dependent coefficient.
Figure BDA00029412815200000616
Figure BDA00029412815200000617
Is a path length matrix, the elements in the matrix representing the path length between two pads, where n is the number of pads and the value L between two padsjkAnd LkjNot necessarily equal.
Figure BDA0002941281520000071
MCiIs a path smoothness matrix, the elements in the matrix representing the path smoothness between two welds, CkjAnd CjkThe values of (a) are not necessarily equal.
Converting the multi-objective problem into a single-objective optimization problem, wherein an objective function is as follows:
gi＝ω1Li+ω2Si (34)
wherein, ω is1、ω2Weight coefficients, ω, representing path length and degree of smoothing, respectively1≥0，ω2Not less than 0 and omega1+ω2＝1。
The fitness function is used for measuring the excellent degree of an individual capable of achieving an optimal solution in optimization calculation, and the fitness function of the individual in the population is as follows:
Figure BDA0002941281520000072
wherein k iscAnd kdThe larger the value of (A), the greater the number of individuals xiThe higher the selection probability of (2), the use of roulette selection to represent the individual xiA probability is selected.
Figure BDA0002941281520000073
Wherein N is the size of the population and the individual xiHas an accumulated probability of
Figure BDA0002941281520000074
The probability of being selected in the roulette selection method is proportional to the fitness of the roulette selection method, and the method has the basic idea that: generating a random number gamma e [0,1 ∈ ]]And calculateRelative fitness value of an individual, if qi-1＜γ≤qiThen the ith individual is selected to the next generation.
As shown in FIG. 3, the concrete action mechanism of the strategy is that the elite population strategy is combined with the selection operator, so that the convergence rate of the genetic algorithm can be accelerated, the evolution direction of the population can be improved, and the pop of the t generation population can be improvedtOf individual xiSorting the fitness and sorting the poptDivided into elite sets Et(X) and the common set St(X) two sub-populations, selected in Elite set Et(X) and the common Individual set St(X), through cross and mutation operations, selecting the individuals with the highest fitness to form a new elite set Et(X)。
As shown in fig. 4, four domain structures of dynamic neighborhood search are constructed according to a path planning target, a dynamic neighborhood search algorithm is designed to improve the mutation operation of the genetic algorithm, and the four neighborhood structures of "point insertion", "exchange", "2-opt" and "block insertion" are used to perform neighborhood-variable search to expand the search range, so as to obtain a locally optimal solution, and enable the solution to jump out of local optimal. FIG. 4a illustrates an "insert" neighborhood search defined as the transfer of a segment of consecutive nodes from a current path to another path, selecting a segment of consecutive nodes r1R is to1A position of the global insertion path; FIG. 4b illustrates a "block-switched" neighborhood search defined as the selection of a segment of consecutive nodes from each of two different paths for location switching; FIG. 4c illustrates a "2-opt" neighborhood search defined by selecting two arbitrary non-adjacent points in a path and reversing the order of all points (including the two points) between the two points; FIG. 4d shows a "point exchange" neighborhood search, defined as the exchange of the positions of two genes.
After the cross operation and the mutation operation, the new individual objective function value LnewAnd the objective function value L of parent individualoldMaking a comparison if the new individual objective function value LnewThe traditional genetic algorithm gives up the replacement of a new individual with a parent individual, so that the traditional genetic algorithm is trapped in local optimization and can jump out after multiple iterationsAnd (4) optimizing, and increasing the speed of searching the optimal solution by the algorithm by introducing a simulated annealing algorithm.
Adopting an importance sampling method under the Metropolis criterion, and obtaining a target value L at the temperature tnew＜LoldUpdating the population, replacing the parent individuals with the new individuals, and if the objective function value L is obtainednew＞LoldAnd introducing a simulated annealing idea to accept new individuals with a certain probability.
Figure BDA0002941281520000075
Wherein k isbFor the Boltzmann constant, the system will tend to an equilibrium state of lower energy over multiple iterations.
As shown in fig. 5, which is a flowchart of a path planning method based on a Memetic algorithm of the present invention, first, an initial population, an initial temperature, and an elite set are set, an improved a-star algorithm is used to generate a path set between welding points, then, an individual objective function is calculated, a fitness function is established, an elite strategy improvement selection operation is performed, a variation operation is performed by a variable neighborhood search method, and finally, a simulated annealing algorithm is used to jump out a local optimal solution, and iteration is performed using the local optimal solution as a starting point until a solution satisfying an optimization objective is obtained, and a genetic process is terminated, thereby obtaining a final global optimal solution.
Fig. 6a and 6b are schematic diagrams of inter-welding-point path planning of the conventional a-star algorithm and the improved a-star algorithm of the present invention, respectively, and the safe altitude distance is set to 2.5mm for collision-free path optimization of the welding robot. In order to verify the improved A-star algorithm, the starting point and the end point of the path are respectively set as (1,1,7.5) and (10.5,5.5,2.8), the number of corner turns can be effectively reduced by removing redundant nodes and smoothing, the path length is reduced from 14.7135dm to 13.9875dm, and the smoothness degree of the path between welding points of the improved A-star algorithm is 0.27888.
As shown in fig. 7, 8 and 9, which are schematic diagrams of path planning of a conventional genetic algorithm, an elite adaptive genetic algorithm and an elite simulated annealing genetic algorithm based on a multi-objective function, respectively, the population sizes of the three genetic algorithms are set asp s40, the iteration number is 1000, and the initial parameter of the traditional genetic algorithm and the elite adaptive genetic algorithm is set as the cross probability pc0.9 and a mutation probability pmSetting the initial parameter of the elite simulated annealing genetic algorithm as the initial temperature T as 0.10The attenuation factor μ is 0.96 at 50. Compared with the traditional genetic algorithm and the elite adaptive genetic algorithm, the planned path length 42.0799dm of the elite simulated annealing genetic algorithm is smaller than the planned path length 84.9788dm of the traditional genetic algorithm and the planned path length 69.3153dm of the elite adaptive genetic algorithm; the planned path smoothness 0.63613 is less than the conventional genetic algorithm planned path length 1.5725 and the elite adaptive genetic algorithm planned path length 1.4472.
FIG. 10 and FIG. 11 show a comparison graph of an evolution curve of objective function values and a comparison graph of an evolution curve of fitness, respectively, in which a conventional genetic algorithm and an elite adaptive genetic algorithm are finally trapped in local optima, the conventional genetic algorithm optimizes a path by using a fixed basic cross mutation operator, the elite adaptive genetic algorithm adopts an adaptive cross mutation operator for adjustment, the conventional genetic algorithm and the elite adaptive genetic algorithm lack a regional capability of jumping out of the local optimal solution, the elite simulated annealing genetic algorithm adopts a variable neighborhood search algorithm for mutation operation, while maintaining population individual diversity, a search region is increased, the simulated annealing algorithm improves the capability of jumping out of the local optimal solution, the convergence rate is superior to that of the conventional genetic algorithm and the elite adaptive algorithm, the global optimal solution is reached when the number of iterations is about 150, and the comparison result shows that the objective function values of the elite simulated annealing genetic algorithm are reduced by 47.8% compared with the objective function values of the conventional genetic algorithm, the reduction of the objective function value of the adaptive genetic algorithm is 39.3 percent.
Fig. 12 and 13 show a population fitness variance evolution curve comparison graph and a population fitness mean evolution curve comparison graph, respectively, in the early stage of population evolution, the population individual diversity of the elite simulated annealing genetic algorithm is better, the traditional genetic algorithm and the elite adaptive genetic algorithm do not reach the global optimal solution, and in the late stage of population evolution, compared with the traditional genetic algorithm, the fitness mean and the variance of the elite adaptive genetic algorithm are larger, and the elite adaptive genetic algorithm has stronger global search capability.
As shown in fig. 14, a change curve of the joint angle of the spot welding robot reflects a change relationship of the joint angle along with discrete points of a path in a process of moving the robot along a path of a welding point, and a three-dimensional curved workpiece constrains a closed chain according to a complete motion of a base coordinate system, a robot end coordinate system, a welding point coordinate system and a welding clamp coordinate system in a working space of the spot welding robot to obtain an expected position and a posture of the robot end coordinate system relative to the base coordinate system, so that a required position and a required posture of a joint variable are obtained by solving through inverse kinematics, and no position mutation exists in a moving process and a motion constraint condition is met.
FIG. 15 shows a kinematic model of a spot welding robot and an optimal welding point path diagram of a beam assembly on a back row seat according to the present invention, wherein a D-H (Denavit-hartenberg matrix) method is adopted to establish the spot welding robot model, and D1、d4The offset of the connecting rod of the shoulder and the forearm of the spot welding robot, a1、a2And a3The length of the connecting rod of the shoulder and the big arm, respectively, consider a3Has important significance for analyzing the elbow singularity of the robot, wherein the connecting rod torsion angle of each connecting rod is alpha1＝-90°、α2＝0°、α3＝-90°、α4＝90°、α5＝-90°、α6The θ value of each joint is a joint variable, which is 0 °. And calling a shortest smooth obstacle avoidance path planning module among welding spots and an optimal welding spot welding sequence planning module to generate an optimal path of a beam assembly on the back-row seat, wherein the optimal collision-free smooth path consists of 1122 discrete path points, and calling a spot welding robot kinematic model module and a motion constraint condition module to generate the spot welding robot joint angle change curve of fig. 14.

Claims (6)

1. A spot welding robot operation space smooth path planning method for a curved surface workpiece is characterized by comprising a spot welding robot kinematics model module, a motion constraint condition module, an inter-welding point shortest smooth obstacle avoidance path planning module and an optimal welding point welding sequence planning module, wherein firstly, modeling is carried out through a three-dimensional grid method curved surface workpiece profile and welding point distribution, and an inter-welding point shortest smooth obstacle avoidance path planning module is called to generate an inter-welding point optimal path set; secondly, according to the optimal path set among the welding spots, calling an optimal welding spot welding sequence planning module to determine a welding spot welding sequence on the basis of considering the path length and smoothness to obtain a complete optimal welding spot welding path; secondly, according to the collision-free motion constraint condition of the welding tongs coordinate system and the welding spot coordinate system and the safe distance constraint condition of the welding tongs coordinate system and the profile of the curved surface workpiece, a homogeneous transformation matrix of the spot welding robot is obtained through the complete motion constraint closed chain of the motion constraint condition module; and finally, according to the obtained discrete points of the complete and optimal welding spot welding path, solving through inverse kinematics of a spot welding robot kinematics model module to obtain a spot welding robot joint angle change curve, namely a planned path in a joint space.
2. A spot welding robot operation space smooth path planning method for a curved surface workpiece according to claim 1, characterized in that the spot welding robot kinematics model module comprises a forward kinematics part and a reverse kinematics part, the robot reverse kinematics calculation is carried out according to Pieper criterion, the reverse kinematics mainly comprises two steps, firstly, joint variables of the first three joints are reversely solved according to the position of a wrist coordinate system, and as the three axes of the wrists of a plurality of spot welding robots are similar to z-y-z Euler angle transformation, the wrists are equivalent to a z-y-z Euler angle rotation matrix, and then, the three joint variables of the second three joints are reversely solved according to the three joint variables.
Since the wrist link coordinate systems {4}, {5}, and {6} are co-origin, the position of the point in the base coordinate system can be obtained from the link transformation.
Figure FDA0002941281510000011
In the formula (I), the compound is shown in the specification,
Figure FDA0002941281510000012
is represented by [ p ]x,py,pz,1]T，
Figure FDA0002941281510000013
A transformation matrix representing the base coordinates and the joint 1 coordinate system,
Figure FDA0002941281510000014
a transformation matrix representing a joint 1 coordinate system and a joint 2 coordinate system,
Figure FDA0002941281510000015
a transformation matrix representing the joint 2 coordinate system and the joint 3 coordinate system, f1、f2And f3Are respectively denoted by f1＝a3c3-d4s3+a2、f2＝a3s3+d4c3 and f3＝0。
Continuing to use the homogeneous transformation matrix and substituting into the known matrix
Figure FDA0002941281510000016
Position vector px,py,pz,1]TTo obtain
Figure FDA0002941281510000017
In the formula, g1、g2And g3Are respectively represented as g1＝c2f1-s2f2+a1，g2＝f3And g3＝-s2f1-c2f2-f3。
From the geometric relationship and the above equation, [ p ]x,py,pz,1]TCan be written as
Figure FDA0002941281510000018
[px,py,pz,1]TThe position in the base coordinate system can also be expressed as:
Figure FDA0002941281510000019
in the formula, k1、k2And k3Are respectively represented by k1＝f1，k2＝-f2And
Figure FDA0002941281510000021
substituting the D-H parameter data into the D-H parameter data, and obtaining the D-H parameter data by the following formulas (1) to (4):
Figure FDA0002941281510000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002941281510000023
by substituting formula (5) and formula (4) by g20 and known
Figure FDA0002941281510000024
Coordinate [ p ]x,py,pz,1]TObtaining:
Figure FDA0002941281510000025
wherein the content of the first and second substances,
Figure FDA0002941281510000026
according to theta already solved above1、θ2And theta3Further, the target rotation matrix can be obtained
Figure FDA0002941281510000027
Thereby to obtain
Figure FDA0002941281510000028
In the formula (I), the compound is shown in the specification,
Figure FDA0002941281510000029
expressed as the last three joint variables θi(i is 4,5,6),
Figure FDA00029412815100000210
the first three joints thetai(i is 1,2,3) is the inverse of the attitude transformation matrix,
Figure FDA00029412815100000211
attitude matrix [ n o a ] of reference point relative to base coordinate system at tail end of robot]。
And (3) performing euler angle transformation on three axes of the wrist of the spot welding robot similarly to z-y-z to obtain:
Figure FDA00029412815100000212
in the formula (I), the compound is shown in the specification,
Figure FDA00029412815100000213
is when theta4When 0, the coordinate system {4} is in the coordinate system {3}, Rzyz(θ4,θ5,θ6) Is the wrist equivalent z-y-z euler angular rotation matrix.
Solving method for theta by using z-y-z Euler angle4、θ5And theta6。
Figure FDA00029412815100000214
In the formula, rij(i, j-1, 2,3) represents a compound of formula (7)
Figure FDA00029412815100000215
Elements of the matrix, where i is the rotation matrix
Figure FDA00029412815100000216
J is a rotation matrix
Figure FDA00029412815100000217
Number of columns of (theta)5The leading negative sign represents the y-axis and θ of the coordinate system {4}5The direction is opposite.
3. The method for planning the smooth path of the operation space of the spot welding robot facing the curved surface workpiece according to claim 1, wherein the motion constraint module assumes { m } points from the edge of the workpiecejTo the welding point p on the curved surfacei(xi,yi,zi) Unit normal vector
Figure FDA00029412815100000218
Vector of (2)
Figure FDA00029412815100000219
To correspond to the shortest distance
Figure FDA00029412815100000220
Edge point m of the workpiecej(xdj,ydj,zdj) To the welding point pi(xi,yi,zi) Unit vector of
Figure FDA00029412815100000221
As coordinate system of the welding spot { piX-axis of the (Z), normal vector in units of curved surface
Figure FDA00029412815100000222
As a coordinate system of the spot of welding { p }iDetermining a coordinate system of the welding point { p } according to the right-hand rule on the z axis of the welding point { p }iThe y-axis of
Figure FDA00029412815100000223
And establishing a complete motion constraint closed chain of the spot welding robot and the welding spot according to the position and posture relation of the welding spot and the profile of the curved surface workpiece, the collision-free motion constraint condition of the welding spot coordinate system and the safe distance constraint condition of the welding spot coordinate system and the profile of the curved surface workpiece.
Figure FDA00029412815100000224
Is a welding point pi(xi,yi,zi) The unit normal vector of (1) is a welding point coordinate system { p }iZ-axis unit vector of
Figure FDA00029412815100000225
The set of edge points of the workpiece is { m }j}, edge point m of workpiecej(xdj,ydj,zdj) With the coordinates p of the welding spoti(xi,yi,zi) The vector between is represented as:
Figure FDA0002941281510000031
from the edge point { m of the workpiecejTo the welding point p on the curved surfacei(xi,yi,zi) Unit normal vector
Figure FDA0002941281510000032
The vector of (d) is represented as:
Figure FDA0002941281510000033
edge point m of workpiecej(xdj,ydj,zdj) To the welding point coordinate pi(xi,yi,zi) Unit normal vector
Figure FDA0002941281510000034
The shortest distance of
Figure FDA0002941281510000035
The corresponding vector can be expressed as:
Figure FDA0002941281510000036
edge point m of workpiecej(xdj,ydj,zdj) To the welding point pi(xi,yi,zi) As the coordinate system of the welding point { p }iThe x-axis unit vector of } is given by:
Figure FDA0002941281510000037
coordinate system of welding spot { piY-axis unit vector of }:
Figure FDA0002941281510000038
base coordinate and welding spot coordinate system { p }iThe homogeneous transformation matrix of }:
Figure FDA0002941281510000039
and transforming a matrix by the soldering turret and the spot welding robot:
Figure FDA00029412815100000310
the axis of the C-shaped servo welding tongs is perpendicular to the cutting surface of the workpiece at the coordinate position of the welding spot to ensure that the nugget is compact, and the method comprises the following steps:
Figure FDA00029412815100000311
the complete motion constraint closed chain is represented as:
Figure FDA00029412815100000312
the distance between the welding tongs and the workpiece is greater than the safe distance, and the following steps are carried out:
H(R,W)-dsafe≥0 (20)
wherein R and W represent the robot end effector and the workpiece, respectively, and dsafeIndicating a safe distance between the two.
4. The method for planning the smooth path of the spot welding robot operating space for the curved surface workpiece according to claim 1, wherein the module for planning the shortest smooth obstacle-avoiding path between the welding spots determines the safety distance d between the welding tongs and the workpiece in order to ensure that the welding tongs and the workpiece do not affect each other during the welding process of the curved surface workpiecesafeModeling a structured environment by a three-dimensional grid method, adopting an A-star algorithm with Euclidean distance as a cost function, and calculating a vector included angle alpha between front and rear nodes and an included angle threshold alpha0By comparison, if α ≧ α0And deleting the redundant nodes to improve the path smoothness, and smoothing the path by adopting a uniform B spline curve subdivision algorithm to finally generate the shortest collision-free smooth path set among the welding spots.
Backtracking node nstPointing to a current node n on the surface of the workpiececForm a vector
Figure FDA0002941281510000041
Current node ncAnd subsequent node nsForm a vector
Figure FDA0002941281510000042
By calculation of
Figure FDA0002941281510000043
And
Figure FDA0002941281510000044
the included angle alpha between the two nodes is removed to form a redundant node ncComprises the following steps:
Figure FDA0002941281510000045
α0is a vector
Figure FDA0002941281510000046
And vector
Figure FDA0002941281510000047
When alpha is more than or equal to alpha0Then, the node n is determinedcFor redundant nodes are:
Figure FDA0002941281510000048
wherein r isαIs the deletion of a redundant node ncIf α ≧ α0Then the redundant node n is deletedcOtherwise, the node n is reservedc。
After the redundant node removing operation, m + n +1 nodes n on the path of the spot welding roboti(i is 0,1,2, … m + n), smoothing the path by adopting a uniform B-spline curve subdivision algorithm to obtain the shortest path between the welding points, wherein the mathematical expression of the B-spline curve is as follows:
Figure FDA0002941281510000049
wherein t is 0-1, i is 0,1,2, …, m, BThe bar curve is defined in segments, given m + n +1 nodes
Figure FDA00029412815100000414
Pi+kFor the position vector of each node, a parameter curve of m +1 segments n times can be defined.
Fk,n(t) is an n-th order B-spline basis function, and the expression is as follows:
Figure FDA00029412815100000410
wherein t is 0. ltoreq. t.ltoreq.1, k is 0,1,2, …, n,
Figure FDA00029412815100000411
representing the combined operation in the probability theory, and connecting the whole curve formed by all the curve segments to be called an n-order B-spline curve.
5. The method for planning the smooth path of the operation space of the spot welding robot for the curved workpiece according to claim 1, wherein the optimal welding spot welding sequence planning module adopts a multi-objective elite simulated annealing genetic algorithm to optimize and solve the welding spot welding sequence, an objective function of the algorithm is path length and smoothness, the mutation operation adopts four neighborhood structures of 'point insertion', 'exchange', '2-opt' and 'block insertion' to perform variable neighborhood search, the introduced elite strategy provides a larger cross mutation operation opportunity for elite individuals, and finally, the simulated annealing algorithm is adopted to jump out a local optimal solution to obtain a global optimal solution.
Individual x traversing all weld pathsiThe path smoothness objective function expression of (1) is:
Figure FDA00029412815100000412
in the formula IijIs the shortest path between the welding points obtained by the improved A-star algorithm, and n is the number of paths passing between the welding points.
Individual x traversing all weld pathsiThe path smoothness objective function expression of (1) is:
Figure FDA00029412815100000413
m and n are the number of turn angles and the number of path segments between the welding points, alpha is the angle between the front and rear nodes, tαIs an angle-dependent coefficient.
Converting the multi-objective problem into a single-objective optimization problem, wherein an objective function is as follows:
gi＝ω1Li+ω2Ci (27)
wherein, ω is1、ω2Weight coefficients, ω, representing path length and degree of smoothing, respectively1≥0，ω2Not less than 0 and omega1+ω2＝1。
The elite population strategy is combined with the selection operator, so that the convergence speed of the genetic algorithm can be accelerated, the evolution direction of the population is improved, and the population pop of the t generation is subjected totOf individual xiSorting the fitness and sorting the poptDivided into elite sets Et(X) and the common set St(X) two sub-populations, selected in Elite set Et(X) and the common Individual set St(X), through cross and mutation operations, selecting the individuals with the highest fitness to form a new elite set Et(X)。
Constructing the following four neighborhoods according to a path planning target, designing a dynamic neighborhood search algorithm for improving the mutation operation of a genetic algorithm, performing neighborhood-variant search by using four neighborhood structures of 'point insertion', 'exchange', '2-opt' and 'block insertion' to expand the search range of the genetic algorithm, obtaining a local optimal solution, and enabling the solution to jump out of local optimal, wherein the first neighborhood structure is 'insertion' operation defined as that a certain section of continuous section is subjected to 'insertion' operationThe point is transferred from the current path to another path, and a section of continuous node r is selected1R is to1A position of the global insertion path; the second neighborhood structure is a 'block switching' operation, which is defined as that a section of continuous nodes are respectively selected from two different paths to carry out position switching; the third neighborhood structure is 2-opt operation, which is defined as selecting any two points which are not adjacent in a certain path and reversing all the points (including the two points) between the two points; the fourth neighborhood structure is the "point exchange" operation, which is defined as the exchange of the positions of two genes.
After the cross operation and the mutation operation, the new individual objective function value LnewAnd the objective function value L of parent individualoldComparing to obtain new individual objective function value LnewAnd the traditional genetic algorithm abandons the replacement of a new individual for a parent individual, falls into local optimization, and accelerates the speed of searching an optimal solution by introducing a simulated annealing algorithm.
Adopting an importance sampling method under the Metropolis criterion, and obtaining a target value L at the temperature tnew＜LoldIf so, updating the population, and replacing the parent individuals with the new individuals; if the value of the objective function Lnew＞LoldAnd introducing a simulated annealing idea to accept new individuals with a certain probability.
Figure FDA0002941281510000051
Wherein k isbFor Boltzmann constants, after repeated for many times, the system tends to an equilibrium state with lower energy, a local optimal solution is jumped out by using a simulated annealing algorithm, and the genetic process is terminated until a solution meeting an optimization target is obtained, so that a final global optimal solution is obtained.
6. A spot welding robot operation space smooth path planning method for curved surface workpieces according to claim 1, characterized in that a spot welding robot model is established by a D-H (Denavit-hartenberg matrix) method, D1、d4Respectively shoulder and forearm of spot welding robotOffset of connecting rod, a1、a2And a3The length of the connecting rod of the shoulder and the big arm, respectively, consider a3Has important significance for analyzing the elbow singularity of the robot, wherein the connecting rod torsion angle of each connecting rod is alpha1＝-90°、α2＝0°、α3＝-90°、α4＝90°、α5＝-90°、α6The θ value of each joint is a joint variable, which is 0 °. And planning an optimal smooth path at the tail end of the spot welding robot in an operation space, calling a shortest smooth obstacle avoidance path planning module among welding spots and an optimal welding spot welding sequence planning module to obtain motion path point data at the tail end, sequentially selecting the motion path point data, and calling a kinematics model module and a motion constraint condition module to obtain a joint angle corresponding to the current motion path point data.
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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113885535A (en) * 2021-11-25 2022-01-04 长春工业大学 Impact-constrained robot obstacle avoidance and time optimal trajectory planning method
CN114474043A (en) * 2021-12-20 2022-05-13 埃夫特智能装备股份有限公司 Method for realizing visual intelligent spraying of bedside
CN117601136A (en) * 2024-01-24 2024-02-27 济宁鲁鑫工程机械有限公司 Automatic welding robot path planning method and system
CN117733308A (en) * 2024-02-19 2024-03-22 浙江大学 Ultrasonic welding robot path planning method and device
CN117733308B (en) * 2024-02-19 2024-05-17 浙江大学 Ultrasonic welding robot path planning method and device

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101059919A (en) * 2007-05-31 2007-10-24 上海交通大学 General-purpose electromechnical equipment motion control demonstration and reproducing system
CN101648376A (en) * 2009-09-11 2010-02-17 北京理工大学 Method and device for controlling robot operations
CN102310258A (en) * 2010-06-30 2012-01-11 株式会社安川电机 Robot system
CN111496427A (en) * 2020-05-27 2020-08-07 长春工业大学 Safe and efficient robot end tool servo spot welding gun parking equipment

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101059919A (en) * 2007-05-31 2007-10-24 上海交通大学 General-purpose electromechnical equipment motion control demonstration and reproducing system
CN101648376A (en) * 2009-09-11 2010-02-17 北京理工大学 Method and device for controlling robot operations
CN102310258A (en) * 2010-06-30 2012-01-11 株式会社安川电机 Robot system
CN111496427A (en) * 2020-05-27 2020-08-07 长春工业大学 Safe and efficient robot end tool servo spot welding gun parking equipment

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
一汽模具制造有限公司,尚校,杜海,杨 磊,孟德峰,宋洋洲,姜善娟,毛柏明: "焊装生产线的节拍分析及优化", 《汽车工艺与材料》 *
姜大伟，张昊，张邦成，孙建伟: "仿人机器人行走系统运动学算法的研究", 《武汉理工大学学报》 *
邢天羿，刘春明，张邦成，谭海东: "微小型救援机械手的正、逆运动学仿真分析", 《长春工业大学学报》 *

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113885535A (en) * 2021-11-25 2022-01-04 长春工业大学 Impact-constrained robot obstacle avoidance and time optimal trajectory planning method
CN113885535B (en) * 2021-11-25 2023-09-12 长春工业大学 Impact constraint robot obstacle avoidance and time optimal track planning method
CN114474043A (en) * 2021-12-20 2022-05-13 埃夫特智能装备股份有限公司 Method for realizing visual intelligent spraying of bedside
CN117601136A (en) * 2024-01-24 2024-02-27 济宁鲁鑫工程机械有限公司 Automatic welding robot path planning method and system
CN117601136B (en) * 2024-01-24 2024-04-02 济宁鲁鑫工程机械有限公司 Automatic welding robot path planning method and system
CN117733308A (en) * 2024-02-19 2024-03-22 浙江大学 Ultrasonic welding robot path planning method and device
CN117733308B (en) * 2024-02-19 2024-05-17 浙江大学 Ultrasonic welding robot path planning method and device

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