CN115122338A - Multi-robot cooperation arc welding task planning method based on multi-objective optimization - Google Patents
Multi-robot cooperation arc welding task planning method based on multi-objective optimization Download PDFInfo
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- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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Abstract
The invention discloses a multi-robot cooperation arc welding task planning method based on multi-objective optimization, which specifically comprises the following steps: describing and analyzing the multi-robot cooperation arc welding task, processing the input welding seam information, and adding labels of the robot, the synchronous, the asynchronous and the welding direction; selecting decision variables and optimization targets, setting constraint conditions, and modeling the multi-robot welding task allocation problem into a multivariable, multi-constraint and multi-target optimization problem; and designing new crossover and mutation operators aiming at the established optimization model, and solving by using a multi-objective genetic algorithm to obtain the welding sequence of each robot so as to complete task allocation. The method effectively solves the problem that tasks are difficult to distribute due to the fact that a plurality of welding seams are numerous, actual welding constraints are complex, a plurality of robot systems are constrained and the like when the plurality of robots are used for welding large-scale complex components, effectively improves the solving efficiency and the global optimization capability of the algorithm, and has wider application prospects.
Description
Technical Field
The invention belongs to the field of multi-robot cooperative welding for large-scale complex components, and particularly relates to a multi-robot cooperative arc welding task planning method based on multi-objective optimization.
Background
With the development of robot technology, industrial robots have been widely used in various industries of industrial production, such as welding, carrying, polishing, and other fields. In the manufacturing process of large and complex components, a large number of welding seams exist, the sizes of the welding seams are generally large, and complex welding process constraints exist, so that the welding quality is high. At present, manual welding is adopted, the efficiency is low, the welding quality is poor, and in addition, the damage to the body of a worker is easily caused by a severe working environment. Therefore, the introduction of industrial robots instead of manual welding is an inevitable option for the manufacture of large complex components. The existing robot working at an independent station has limited operability and flexibility and cannot meet the welding of numerous large-scale complex welding seams; the cooperative robot system formed by two or more robots has stronger operation capability, more flexible system structure, stronger cooperative capability and the like, can complete the work which can not be completed or is difficult to complete by a single robot, and is very suitable for cooperatively welding large and complex components. Therefore, how to use the multi-robot system to realize the automatic welding of large-scale complex components has important research significance and practical value, and the task allocation is the premise and the basis of the automatic operation of the multi-robot system.
At present, most of robot systems in workshop sites adopt a manual teaching programming mode to provide preset tracks for robots, the efficiency of the mode is very low, the preset tracks must be known, and increasingly complex task requirements are difficult to meet. The method is used for multi-robot cooperative welding for large complex components, a large number of welding seams and complex constraint conditions exist, and a specific algorithm needs to be designed to distribute reasonable welding tasks and welding tracks for each robot. Aiming at the task planning problem of multi-robot cooperative welding, the current research mostly models the problem as a traveler or a plurality of travelers, selects optimization targets such as welding time, welding track length or welding balance and the like, and adopts intelligent optimization algorithms such as a genetic algorithm, a particle swarm algorithm, an ant colony algorithm and the like to solve. However, in the existing research of multi-point-to-point welding task, the welding process constraints such as synchronous welding, safe time, welding direction and the like are considered a little, and often only one of the optimization targets is concerned or a plurality of targets are combined into one target for optimization by a weighting method, so that the comprehensive consideration of the plurality of optimization targets is lacked; in addition, when the welding task planning problem of a large-scale complex component is solved, the traditional intelligent optimization algorithm is low in solving efficiency and easy to fall into local optimization.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a multi-robot cooperation arc welding task planning method based on multi-objective optimization.
The invention discloses a multi-robot cooperative arc welding task planning method based on multi-objective optimization, which comprises the following steps of:
step 1: describing and analyzing the multi-robot cooperation arc welding task, processing the input welding seam information, and adding the labels of the robot, the synchronous, the asynchronous and the welding direction.
Step 2: selecting decision variables and optimization targets, setting constraint conditions, and modeling the multi-robot welding task allocation problem into a multivariable, multi-constraint and multi-target optimization problem.
And step 3: and designing new crossover and mutation operators aiming at the established optimization model, and solving by using a multi-objective genetic algorithm to obtain the welding sequence of each robot so as to complete task allocation.
The step 1 specifically comprises the following steps:
s11: description and analysis of multi-robot cooperation arc welding task:
the essence of the multi-robot cooperation welding task allocation problem is that tasks are efficiently and orderly completed on the premise of meeting various constraints and welding quality; define robot set R ═ R 1 ,r 2 ,...,r n ]Where n is the number of robots, r i Is the ith robot, i 1, 2.., n; defining weld set W ═ W 1 ,w 2 ,...,w m ]Where m is the number of welds, w j For the jth weld, j 1,2,.. m, the welding and idle speeds of the robot are v, respectively m And v n (ii) a Limited by the initial position and the working space, each robot can only weld part of the welding seams in a specific area, and the cooperation and competition relationship among multiple robots inevitably occurs, so the welding seams in the set W are divided into dedicated welding seams of each robot and competitive welding seams of multiple robots; definition robot r i The exclusive weld set of
Wherein s is k ∈[1,m]And no repeated elements, k belongs to [1, | r i |]，|r i L is robot r i The number of exclusive welding seams is possessed; defining a competitive weld set as C ═ C 1 ,c 2 ,...,c l ]Wherein
After optimization, the welding line sequence finally distributed by each robot is
S12: adding the labels of the robot, the synchronous, the asynchronous and the welding direction for the welding seam:
definition of weld information structure W inf Wherein W is inf (i).w＝w i Is the ith welding line, and the starting point and the end point of the ith welding line are respectively W inf (i).start＝[x 1 ,y 1 ,z 1 ]And W inf (i).end＝[x 2 ,y 2 ,z 2 ]，W inf (i).robot＝r j Indicates that the weld belongs to the jth robot, W inf (i) L-l denotes the length of the weld; w is a group of inf (i).syn＝[1,r j ]Showing the weld and r j The weld belongs to a synchronous weld, which requires welding to start and end simultaneously, W inf (i) Syn ═ 0 indicates that the weld does not belong to a synchronized weld; w is a group of inf (i).asyn＝[1,r j ]Showing the weld and r j The welding seam belongs to an asynchronous welding seam, and the welding of another welding seam can be carried out only after the welding of one welding seam is finished, W inf (i) Asyn ═ 0 means that the weld does not belong to an asynchronous weld; w inf (i) D-1 indicates that the welding direction of the weld is from the starting point to the end point, W inf (i) And d-0 indicates that the welding direction of the weld is from the end point to the start point.
The step 2 specifically comprises the following steps:
s21: selection of decision variables:
set x ═ x 1 ,x 2 ,...,x m ]Each element in (1) represents the ID of the weld as a decision variable, x, of the optimization model m ∈[1,m]The values are required to be integers without loss or repetition.
S22: selection of constraint conditions:
(1) constraint phi of synchronous welding 1 : in order to ensure the welding quality, some welding seams need synchronous welding, namely the start time and the end time of two welding seams and the welding direction are consistent, and for the two synchronous welding seams w i And w j Need to satisfy
ts i ＝ts j ，te i ＝te j ，d i ＝d j Where i, j is E [1, m ∈ ]]
ts i Is a weld seam w i Start time of (te) i To its end time, d i Is its welding direction.
(2) Asynchronous welding constraint phi 2 : to prevent weld distortion or robot collisions, some welds need to be welded at different times, for two asynchronous welds w i And w j Need to satisfy
te i ＜ts j ||te j ＜ts i Where i, j is E [1, m ∈ ]]
(3) Constraint of welding direction phi 3 : due to the requirement of welding process, certain welding seams need to be welded according to a specific direction, and for a welding seam w with welding direction constraint i Need to satisfy
(4) Spatial accessibility constraint phi of each robot 4 : for any one robot r i A weld allocated to it must be within its reachable space, otherwise the weld cannot be completed; set up robot r j Has an accessible space of R j (q j ) Wherein q is j Is a robot r j The range of joint vector of is
w i (r j )∈R j (q k ) Where i ∈ [1, m ]],j∈[1,n]
(5) Collision constraint phi between robots 5 : let the space occupied by the workpiece be R w Robot r i And r j The space occupied by the pose is R i (q i ) And R j (q j ) Then there is
S23: selection of the objective function:
(1) robot waiting time Tw: for a set of simultaneous welds w i1 And w j1 When one robot reaches one of the welding lines w first i1 While, it needs waiting time Tw 1 Rear sum w j1 Welding together; for a set of asynchronous welds w i2 And w j2 If w is i2 Starting welding first, requiring a waiting time Tw 2 After start weld w j2 The welding of (a) and, therefore,
(2) idle distance Dn of robot: ith robot r i Assigned welding path P i ＝[w p1 ,w p2 ,...,w pri ]Wherein p is k ∈S i ∪C i And therefore, the first and second electrodes are,
s24: establishing an optimization model:
and (3) integrating the decision variables, the constraint conditions and the objective function to establish a multi-constraint and multi-objective optimization model as follows:
the step 3 specifically comprises the following steps:
s31: initialization:
before optimization is carried out by using a multi-objective genetic algorithm, an initialization population needs to be generated; definition robot r i The exclusive weld set of
Wherein s is k ∈[1,m]And no repeated elements, k belongs to [1, | r i |]，|r i L is robot r i The number of exclusive welding seams is possessed, and m is the total number of the welding seams; defining the competitive weld set as C ═ C 1 ,c 2 ,...,c l ]Wherein
n is the number of robots; when the starting point is fixed, a start is defined i Is a robot r i A starting point of (2)
After other welding seams in the welding line are randomly arranged
For a competitive weld c l When the robot is in the working space of a plurality of robots, the robot is randomly distributed to one of the robots; when the starting point is not fixed, the starting point is to be
After the welding lines in the middle are randomly arranged, the components are formed
Also, for the competitive weld c l When the robot is in the working space of a plurality of robots, the robot is randomly distributed to one of the robots; finally, obtaining an individual P of the initialized population 0 (i)＝[x 1 ,x 2 ,...,x n ]Until an initialization population P of size N is obtained 0 。
S32: and (3) calculating a fitness function:
calculating the total waiting time Tw and the total idle load distance Dn of the multi-robot system aiming at the condition that synchronous welding seams and asynchronous welding seams exist simultaneously; for population P t Carrying out pareto stratification on individuals in the test sample by adopting a rapid non-dominated sorting method, wherein the individuals at the f < th > layer are superior to the individuals at the f +1 < th > layer; for individuals on the same layer, calculating the crowdedness degree Cd (j) of each individual according to the values of objective functions Tw and Dn, wherein j is epsilon [1, N]Individuals with a large crowding value are better than individuals with a small crowding value; therefore, the pareto layer number f and the individual congestion value Cd are selected together as the fitness function value.
S33: selecting operation:
in order to keep the excellent characteristics of the population in the evolution process, selecting a better N/2 individual as a parent population parpop according to a fitness function for subsequent evolution operation; for individuals on different pareto surfaces, preferentially selecting individuals with a lower number of layers; for individuals on the same pareto surface, the preference for individuals with a greater crowdedness ensures that the distribution of individuals on the pareto surface is as uniform as possible, up to a sufficient number N/2 of individuals.
S34: and (3) cross operation:
in order to increase the diversity of individuals in the population, N/4 individuals in a parental population are selected as parents, and N/4 individuals are selected as parents; randomly selecting an individual from the parent and the mother, randomly generating cross points, and then exchanging the gene segments of the parent and the mother to generate an N/2 offspring population kindspop 1.
S35: mutation operation:
firstly, randomly selecting an individual in a parent, and then randomly selecting two gene segments to exchange, so that the individual diversity is increased, and the offspring population kindspop2 is generated.
S36: elite individual retention strategy:
in order not to lose the good characteristics in the evolution process, the parents and the offspring are merged and then individual selection is performed again, namely P t ' partopp @ kindspop1 @ kindspop2, after non-dominated sorting, new populations P are selected t ＝P t ' (1: N) and continue with the next iteration.
S37: termination conditions were as follows:
and when the maximum iteration times or the maximum calculation times of the objective function are reached, stopping iteration of the population, and outputting the current pareto approximate optimal solution as an approximate optimal allocation scheme of the multi-robot welding task.
The beneficial technical effects of the invention are as follows:
the invention effectively solves the problem that tasks are difficult to distribute due to numerous welding lines, actual welding constraints and complex self constraints of a multi-robot system when the multi-robot aims at the welding of large-scale complex components by modeling the multi-robot cooperative welding problem as a multivariable, multi-constraint and multi-target optimization problem and then using an improved multi-target genetic algorithm to solve, effectively improves the solving efficiency and the global optimization capability of the algorithm compared with other methods, and has wider application prospect.
Drawings
FIG. 1 is a main flow diagram of the process of the present invention;
FIG. 2 is a schematic diagram of three robots welding a large complex component;
FIG. 3 is a flow chart of a multi-robot cooperative welding task allocation multi-objective optimization model building method according to the present invention;
FIG. 4 is a flow chart of the method for solving an optimization model based on the multi-objective genetic algorithm.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The invention discloses a multi-robot cooperation arc welding task planning method based on multi-objective optimization, which has the flow shown in figure 1 and specifically comprises the following steps:
1. the problem description of multi-robot task allocation for welding large-scale complex components is oriented.
The invention aims at the multi-robot cooperative welding of a large complex component, and the large component is cooperatively welded by 3 robots as shown in figure 2. Each robot can move up and down, left and right along the guide rail and the supporting mechanism, so that the working space is increased; according to the working space of each robot and the process constraint of various welding seams, the large-scale component is divided into a welding area exclusive for the robot 1, a competitive welding area for the robots 1 and 2, a welding area exclusive for the robot 2, a competitive welding area for the robots 2 and 3 and a welding area exclusive for the robot 3. Defining a set W of weld joints to be welded as [1,2,3]The number is the unique identity ID of each welding line, and n welding lines are provided in total; the exclusive weld sets for the robots 1,2,3 are defined as
And
wherein n is 1 、n 2 And n 3 The number of the exclusive welding seams of the 3 robots is respectively; define the competitive weld set of robots 1 and 2 as
The competitive weld set of robots 2 and 3 is
Wherein m is 1 And m 2 The number of the competitive welding lines is n 1 +n 2 +n 3 +m 1 +m 2 (ii) a After the task allocation, the welding line sequences finally allocated by the 3 robots are respectively
And
wherein n is o 1 +o 2 +o 3 。
2. And (5) processing the welding seam information.
For uniformity and convenience of algorithm execution, a structure body W is defined inf Storing weld information, wherein W inf (i) W ═ i is the ith weld, and the starting point and the end point are W respectively inf (i).start＝[x 1 ,y 1 ,z 1 ]And W inf (i).end＝[x 2 ,y 2 ,z 2 ]，W inf (i) J (j 1,2,3) indicates that the ith welding seam belongs to the jth robot, W inf (i) L-l denotes the length of the weld; w inf (i).syn＝[1,w j ]Shows the weld and w j The weld seam being a synchronous weld seam, W inf (i) Syn ═ 0 indicates that the weld does not belong to a synchronized weld; w inf (i).asyn＝[1,w j ]Shows the weld and w j The welding seam belongs to an asynchronous welding seam, the welding of another welding seam can be carried out only after the welding of one welding seam is finished, W inf (i) Asyn ═ 0 means that the weld does not belong to an asynchronous weld; w inf (i) D-1 indicates that the welding direction of the weld is from the starting point to the end point, W inf (i) D-0 indicates that the welding direction of the weld is from the end pointTo the starting point.
3. And (4) constructing a multi-robot task allocation problem optimization model.
The large-scale complex component has a plurality of welding seams, a plurality of complex welding process constraints are arranged among the welding seams, and when a multi-robot system is used for welding, a plurality of robot-related constraint conditions are introduced, so that how to distribute reasonable welding tasks for the robots to enable the robots to meet a plurality of targets can be modeled as a multi-target optimization problem, and a flow chart is shown in fig. 3.
(1) Selection of decision variables
Set x ═ x 1 ,x 2 ,...,x n ]Each element in (1) represents the ID of the weld as a decision variable, x, of the optimization model i ∈[1,m]The values are required to be integers without loss or repetition.
(2) Setting of constraints
(a) Constraint phi of synchronous welding 1 : in order to ensure the welding quality, some welding seams need to be welded synchronously, namely the start time, the end time and the welding direction of two welding seams are consistent. For two simultaneous welds w i And w j Need to satisfy
ts i ＝ts j ，te i ＝te j ，d i ＝d j Wherein i, j is epsilon [1, n ]]
ts i Is a weld seam w i Start time of (te) i To its end time, d i Is its welding direction.
(b) Asynchronous welding constraint phi 2 : to prevent weld distortion or robot collisions, some welds may be welded at different times. For two asynchronous welds w i And w j Need to satisfy
te i ＜ts j ||te j ＜ts i Where i, j ∈ [1, n ]]
(c) Constraint of welding direction phi 3 : due to the requirements of welding process, certain welding seams need to be welded according to a specific direction, for example, a vertical fillet weld must be welded from bottom to top. For a weld line w with welding direction constraint i Need to satisfy
(d) Spatial accessibility constraint phi of each robot 4 : for any one robot r i The weld allocated to it must be within its reachable space, otherwise the weld cannot be completed. Set up robot r j Is R j (q j ) Wherein q is j Is a robot r j The range of joint vector of is
w i (r j )∈R j (q k ) Where i ∈ [1, n ]],j∈[1,3]
(e) Collision constraint phi between robots 5 : let the space occupied by the workpiece be R w Robot r i And r j The space occupied by the pose at this time is R i (q i ) And R j (q j ) Then there is
(3) Construction of an objective function
(a) Robot waiting time Tw: for a set of simultaneous welds w i1 And w j1 When one robot reaches one of the welding lines w first i1 While, it needs waiting time Tw 1 Rear sum w j1 Welding together; for a set of asynchronous welds w i2 And w j2 If w is i2 Starting welding first, requiring a waiting time Tw 2 After start weld w j2 Welding. Therefore, the number of the first and second electrodes is increased,
(b) robot dead distance Dn: the ith robot is assigned a welding path of
Wherein p is k E.g., W, and therefore,
wherein o is i Number of welds, v, assigned to the ith robot n Is the no-load running speed of the robot.
And (3) integrating the decision variables, the constraint conditions and the objective function to establish a multi-constraint and multi-objective optimization model as follows:
4. and solving based on the improved multi-target genetic algorithm.
After the multi-objective optimization model is established, an improved multi-objective genetic algorithm is used for solving, a flow chart is shown in fig. 4, and the specific steps are as follows:
(1) initialization
Before iterative optimization of genetic algorithm, an initialization population P is generated 0 . The exclusive weld sets of the robots 1,2 and 3 are respectively
And
wherein n is 1 、n 2 And n 3 The number of the exclusive welding seams of the 3 robots is respectively; define the competitive weld set for robots 1 and 2 as
The competitive weld set of robots 2 and 3 is
Wherein m is 1 And m 2 The number of competitive welding lines is respectively known as n ═ n 1 +n 2 +n 3 +m 1 +m 2 . When the welding start point of each robot is fixed, a start is defined i Is the starting point of robot i, W 1 '、W 2 ' and W 3 ' are each W 1 、W 2 And W 3 Random arrangement of (a); for a random weld s, randomly assigning it to any one robot, define n' 1 、n’ 2 And n' 3 Respectively the number of welds assigned to 3 robots, the initial weld sequence of the 3 robots respectively being
And
finally, obtaining an individual P of the initialized population 0 (i)＝[P 01 ,P 02 ,P 03 ]After the steps are repeated, the initialized population P with the size of N is obtained 0 。
(2) Fitness function calculation
And calculating the total waiting time Tw and the total idle distance Dn of the multi-robot system aiming at the condition that synchronous welding seams and asynchronous welding seams exist simultaneously. For population P t Carrying out pareto stratification on individuals in the test by adopting a rapid non-dominant sorting method, wherein the individuals at the f-th layer are superior to the individuals at the f + 1-th layer; for individuals in the same layer, calculating the crowding degree Cd (j) of each individual according to the values of objective functions Tw and Dn, wherein j belongs to [1, N ]]Individuals with a high congestion value are better than individuals with a low congestion value; therefore, the pareto layer number f and the individual congestion value Cd are selected together as the fitness function value.
(3) Selection operation
In order to keep the excellent characteristics of the population in the evolution process, better N/2 individuals are selected as parent population parpop according to the fitness function and are used for subsequent evolution operation. For individuals on different pareto surfaces, preferentially selecting individuals with a lower number of layers; for individuals on the same pareto surface, the preference for individuals with a greater crowdedness ensures that the distribution of individuals on the pareto surface is as uniform as possible, up to a sufficient number N/2 of individuals.
(4) Interleaving
In order to increase the diversity of individuals in the population, N/4 individuals in a parental population are selected as parents, and N/4 individuals are selected as parents; randomly selecting an individual from the parent and the mother, randomly generating cross points, and then exchanging and recombining gene segments of the parent and the mother to generate a child population kindspop1 with the size of N/2.
(5) Mutation operations
The crossover operation can only carry out the crossover recombination on gene segments at the same position of two individuals, and in some cases, the gene segments still cannot jump out of local optima, so that the change needs to be made in the individuals. Unlike traditional genetic algorithms, the mutation process in this patent first randomly selects an individual in the parent, then randomly selects two gene segments to exchange, increases the individual diversity, and generates the offspring population kindspop 2.
(6) Elite individual retention strategy
In order not to lose good characteristics in the evolution process, parents and filial generations are merged and then individual selection is performed again, namely P t ' partopp @ kindspop1 @ kindspop2, after non-dominated sorting, new populations P are selected t ＝P t ' (1: N) and continue with the next iteration.
(7) Termination conditions
And when the maximum iteration times or the maximum calculation times of the objective function are reached, stopping iteration of the population, and outputting the current pareto approximate optimal solution P as an approximate optimal allocation scheme of the multi-robot welding task to finish task allocation.
Claims (4)
1. A multi-robot cooperation arc welding task planning method based on multi-objective optimization is characterized by comprising the following steps:
step 1: describing and analyzing the multi-robot cooperation arc welding task, processing the input welding seam information, and adding labels of the robot, the synchronous, the asynchronous and the welding direction;
step 2: selecting decision variables and optimization targets, setting constraint conditions, and modeling the multi-robot welding task allocation problem into a multivariable, multi-constraint and multi-target optimization problem;
and 3, step 3: and designing new crossover and mutation operators aiming at the established optimization model, and solving by using a multi-objective genetic algorithm to obtain the welding sequence of each robot so as to complete task allocation.
2. The multi-robot collaborative arc welding task planning method based on multi-objective optimization according to claim 1, wherein the step 1 specifically comprises:
s11: description and analysis of multi-robot cooperation arc welding task:
the essence of the multi-robot cooperation welding task allocation problem is that tasks are efficiently and orderly completed on the premise of meeting various constraints and welding quality; define robot set R ═ R 1 ,r 2 ,...,r n ]Wherein n is the number of robots, r i Is the ith robot, i 1, 2.., n; defining weld set W ═ W 1 ,w 2 ,...,w m ]Where m is the number of welds, w j For the jth weld, j 1,2,.. m, the welding and idle speeds of the robot are v, respectively m And v n (ii) a Limited by the initial position and the working space, each robot can only weld part of the welding seams in a specific area, and the cooperation and competition relationship among multiple robots inevitably occurs, so the welding seams in the set W are divided into exclusive welding seams of each robot and competitive welding seams of multiple robots; definition robot r i The exclusive weld set of
Wherein s is k ∈[1,m]And no repeated elements exist, k belongs to [1, | r |) i |]，|r i L is robot r i The number of exclusive welding seams is possessed; defining the competitive weld set as C ═ C 1 ,c 2 ,...,c l ]In which
After optimization, the weld sequence finally distributed by each robot is
S12: adding the labels of the robot, the synchronous, the asynchronous and the welding direction for the welding line:
definition of weld information structure W inf Wherein W is inf (i).w＝w i Is the ith welding line, and the starting point and the end point of the ith welding line are respectively W inf (i).start＝[x 1 ,y 1 ,z 1 ]And W inf (i).end＝[x 2 ,y 2 ,z 2 ]，W inf (i).robot＝r j Indicates that the weld belongs to the jth robot, W inf (i) L denotes the length of the weld; w inf (i).syn＝[1,r j ]Showing the weld and r j The weld belongs to a synchronous weld, which requires welding to start and end simultaneously, W inf (i) Syn ═ 0 indicates that the weld does not belong to a synchronized weld; w inf (i).asyn＝[1,r j ]Showing the weld and r j The welding seam belongs to an asynchronous welding seam, and the welding of another welding seam can be carried out only after the welding of one welding seam is finished, W inf (i) Asyn ═ 0 means that the weld does not belong to an asynchronous weld; w inf (i) D-1 indicates that the welding direction of the weld is from the starting point to the end point, W inf (i) And d is 0, indicating that the welding direction of the weld is from the end point to the start point.
3. The multi-robot collaborative arc welding task planning method based on multi-objective optimization according to claim 2, wherein the step 2 specifically comprises:
s21: selection of decision variables:
set x ═ x 1 ,x 2 ,...,x m ]Each element in (1) represents the ID of the weld as a decision variable, x, of the optimization model m ∈[1,m]The values are required to be integers without loss or repetition;
s22: selection of the constraint:
(1) constraint phi of synchronous welding 1 : in order to ensure the welding quality, some welding seams need synchronous welding, namely the start time and the end time of two welding seams and the welding direction are consistent, and for the two synchronous welding seams w i And w j Need to satisfy
ts i ＝ts j ，te i ＝te j ，d i ＝d j Where i, j is E [1, m ∈ ]]
ts i Is a weld seam w i Start time of (te) i To its end time, d i As its welding direction;
(2) asynchronous welding constraint phi 2 : to prevent weld distortion or robot collisions, some welds need to be welded at different times, for two asynchronous welds w i And w j Need to satisfy
te i ＜ts j ||te j ＜ts i Where i, j is E [1, m ∈ ]]
(3) Constraint of welding direction phi 3 : due to the requirement of welding process, certain welding seams need to be welded according to a specific direction, and for a welding seam w with welding direction constraint i Need to satisfy
(4) Spatial accessibility constraint phi of each robot 4 : for any one robot r i A weld allocated to it must be within its reachable space, otherwise the weld cannot be completed; set up robot r j Has an accessible space of R j (q j ) Wherein q is j Is a robot r j The range of joint vectors of (1) then
w i (r j )∈R j (q k ) Wherein i ∈ [1, m ]],j∈[1,n]
(5) Collision constraint phi between robots 5 : let the space occupied by the workpiece be R w Robot r i And r j Space occupied by pose at the momentAre each R i (q i ) And R j (q j ) Then there is
S23: selection of the objective function:
(1) robot waiting time Tw: for a set of simultaneous welds w i1 And w j1 When one robot reaches one of the welding lines w first i1 While, it needs waiting time Tw 1 Rear sum w j1 Welding together; for a set of asynchronous welds w i2 And w j2 If w is i2 Starting welding first, requiring a waiting time Tw 2 After start weld w j2 The welding of (a) and, therefore,
(2) idle distance Dn of robot: ith robot r i The distributed welding path is
Wherein p is k ∈S i ∪C i And therefore, the first and second electrodes are,
s24: establishing an optimization model:
and (3) integrating the decision variables, the constraint conditions and the objective function to establish a multi-constraint and multi-objective optimization model as follows:
4. the multi-robot collaborative arc welding task planning method based on multi-objective optimization according to claim 3, wherein the step 3 is specifically as follows:
s31: initialization:
before optimizing by using a multi-target genetic algorithm, generating an initialization population; definition robot r i Set of exclusive weld seams of
Wherein s is k ∈[1,m]And no repeated elements, k belongs to [1, | r i |]，|r i L is robot r i The number of exclusive welding seams is possessed, and m is the total number of the welding seams; defining the competitive weld set as C ═ C 1 ,c 2 ,...,c l ]Wherein
n is the number of robots; when the starting point is fixed, a start is defined i Is a robot r i A starting point of (2)
Other welding lines in the welding line are randomly arranged to form
For a competitive weld c l When the robot is in the working space of a plurality of robots, the robot is randomly distributed to one of the robots; when the starting point is not fixed, the starting point is to be
After the welding seams in the middle are randomly arranged, the welding seams are formed
Also, for the competitive weld c l When the robot is in the working space of a plurality of robots, the robot is randomly distributed to one of the robots; finally, obtaining an individual P of the initialized population 0 (i)＝[x 1 ,x 2 ,...,x n ]Until it is obtainedInitializing a population P to a size N 0 ；
S32: and (3) calculating a fitness function:
calculating the total waiting time Tw and the total no-load distance Dn of the multi-robot system aiming at the condition that synchronous welding seams and asynchronous welding seams exist simultaneously; for population P t Carrying out pareto stratification on individuals in the test sample by adopting a rapid non-dominated sorting method, wherein the individuals at the f < th > layer are superior to the individuals at the f +1 < th > layer; for individuals on the same layer, calculating the crowdedness degree Cd (j) of each individual according to the values of objective functions Tw and Dn, wherein j is epsilon [1, N]Individuals with a large crowding value are better than individuals with a small crowding value; therefore, the pareto layer number f and the individual crowding value Cd are selected to be used as fitness function values together;
s33: selecting operation:
in order to keep the excellent characteristics of the population in the evolution process, selecting a better N/2 individual as a parent population parpop according to a fitness function for subsequent evolution operation; for individuals on different pareto surfaces, preferentially selecting individuals with a lower number of layers; for individuals on the same pareto surface, the individuals with higher crowdedness are preferentially selected, so that the distribution of the individuals on the pareto surface can be ensured to be as uniform as possible until N/2 individuals are enough;
s34: and (3) cross operation:
in order to increase the diversity of individuals in the population, N/4 individuals in a parental population are selected as parents, and N/4 individuals are selected as parents; randomly selecting an individual from the parent and the mother, randomly generating a cross point, and then exchanging and recombining gene segments of the parent and the mother to generate a child population kindspop1 with the size of N/2;
s35: mutation operation:
firstly, randomly selecting an individual from parents, and then randomly selecting two gene segments for exchange, so that the individual diversity is increased, and a progeny population kindspop2 is generated;
s36: elite individual retention strategy:
in order not to lose good characteristics in the evolution process, parents and filial generations are merged and then individual selection is performed again, namely P t ' parpop, U.KINDSPP 1, U.KINDSPP 2, non-dominant ordering postselectionTaking a new population P t ＝P t ' (1: N), continue the next iteration;
s37: and (4) termination conditions:
and when the maximum iteration times or the maximum calculation times of the objective function are reached, stopping iteration of the population, and outputting the current pareto approximate optimal solution as an approximate optimal allocation scheme of the multi-robot welding task.
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