CN106598043A - High-speed pickup path optimizing method of parallel robots facing dynamic objects - Google Patents
High-speed pickup path optimizing method of parallel robots facing dynamic objects Download PDFInfo
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- 238000005457 optimization Methods 0.000 claims description 24
- 238000012546 transfer Methods 0.000 claims description 17
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- 238000011156 evaluation Methods 0.000 claims description 3
- 230000000630 rising effect Effects 0.000 claims description 3
- 230000005945 translocation Effects 0.000 claims description 3
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- 238000004364 calculation method Methods 0.000 claims 1
- 238000004043 dyeing Methods 0.000 claims 1
- 230000004308 accommodation Effects 0.000 abstract 1
- 238000004519 manufacturing process Methods 0.000 description 6
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- G—PHYSICS
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- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
- G05D1/0217—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory in accordance with energy consumption, time reduction or distance reduction criteria
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- G06N3/126—Evolutionary algorithms, e.g. genetic algorithms or genetic programming
Abstract
The invention provides a high-speed pickup path optimizing method of parallel robots facing dynamic objects. The method comprises the following steps that 1) target positions in an accommodation area are numbered randomly, corresponding coordinate information is obtained, target objects whose number is the same with that of the target positions are selected sequentially from a grabbing area, the target objects are numbered randomly, and present coordinates of the target objects are obtained at the same time; 2) the obtained target objects and target positions are ordered in a crossing manner randomly to form a long chromosome of an initial population; and 3) the step 2) is repeated to construct the initial population, a genetic algorithm is used to optimize an operation path of a pickup motion of a robot terminal performer, and a group of chromosomes whose total stroke is shortest is output and serves as an optimized operation path of the pickup motion of the robot terminal performer. According to the invention, the optimal grabbing path can be obtained, and the working efficiency is improved greatly.
Description
Technical field
The invention belongs to the technical field that the production automation and advanced control algolithm are combined, more particularly, to one kind towards
The parallel robot high-speed picking-up method for optimizing route of multiple dynamic objects.
Background technology
With the development of technology, parallel robot of the domestic application in the light industries such as medical treatment, electronics, food is increasingly
It is many, particularly on high density sorting vanning streamline, the target object sorting on conveyer belt is placed in limiting time
To in the region of the proper alignment specified, although employ parallel robot and case compared to manual sorting, efficiency improves;But
The order cased in other words in path that sorts for being these robots is empirically set by workman, is relatively-stationary, and
Real-time adjustment can not be carried out according to the target object of random distribution on conveyer belt, therefore this path not optimal path, and install
Debugging cycle is long, illustrates that production efficiency also has greatly raising space.Therefore, it is to improve streamline effect to sort path global optimization
One of crucial technology of rate, is also the emphasis of research.The speed of conveyer belt, the distribution density and parallel robot of target object
Pickup matching etc. parameter have pipeline efficiency closely related, in order to solve these problems, give full play to industrial automation and
The superiority of Based Intelligent Control, it is therefore desirable to invent it is a kind of towards high density multiple target coordinate dynamic change based on improved genetic algorithms
The method for optimizing route of method, establishes the close ties of parallel robot and surrounding, can not only lift parallel robot
Work efficiency and adaptability, and can off-line simulation in advance, verification algorithm and then instruct in actual production technology to transmission
The speed of service of band is optimized, and shortens the cycle of installation and debugging.
The content of the invention
In order to solve the problems referred to above of the prior art, i.e., in order to improve parallel manipulator task efficiency.The present invention
Propose a kind of parallel robot high-speed picking-up method for optimizing route towards multiple dynamic objects.
A kind of parallel robot high-speed picking-up method for optimizing route towards multiple dynamic objects proposed by the present invention, including
Following steps:
Step 1, carries out random number and obtains corresponding coordinate information to each target location in placement region, and from crawl
Region is sequentially chosen and the same number of target object in target location, and to target object random number is carried out, while obtaining target
The initial coordinate of object;
Step 2, acquired target object and target location are carried out at random translocation sorting, constitute the long dye of initial population
Colour solid;The sequence of the chromosome is robotic end effector picks up and puts action operating path;
Step 3, repeat step 2 builds initial population, and robotic end effector is picked up by genetic algorithm puts action
Operating path is optimized, and one group of most short long chromosome of output total kilometres is picked up as the robotic end effector after optimization to be put
Action operating path;The genetic algorithm, its object function is Min (S), and S is total kilometres.
Preferably, genetic algorithm described in step 3, its select probability is
C=(Smax-Sq)/(Smax-Smin)
Wherein, SmaxFor the corresponding most long total path of long chromosome in current iteration population, SminFor in current iteration population
The corresponding most short total path of long chromosome, SqFor the corresponding total path length of long chromosome of serial number q in current iteration population.
Preferably, genetic algorithm described in step 3, in each iterative process, by long chromosome separation into two with regard to mesh
Mark object and the short chromosome of target location, are selected respectively, are intersected, being made a variation and insertion operation, then remerge into one
New long chromosome.
Preferably, genetic algorithm described in step 3, is terminated using algorithmic statement or default iterationses as the algorithm
Condition, and the maximum long chromosome of fitness function is chosen from last time iteration population as the robot terminal after optimization
Executor picks up puts action operating path.
Preferably, genetic algorithm described in step 3, its fitness function is (1/S).
Preferably, the algorithmic statement, if the kind group mean adaptive value change in specially adjacent Q generations is less than predetermined threshold value;Q
For the iterationses for evaluation algorithm convergence of setting.
Preferably, the computational methods of the total kilometres are:
Wherein, S represents total kilometres, AiRepresent target object, BjTarget location is represented, i represents the sequence number of target object, j tables
Show the sequence number of target location, SijRepresent the stroke between target object i and target location j, DijRepresent target object AiWith target
Position BjBetween horizontal range, b represents that robotic end effector picks up the rising height for putting action, A (xi, yi) represent target
Object AiCoordinate, B (xj, yj) represent target location BjCoordinate, A (xi(ti), yi) represent tiMoment target object AiSeat
Mark, tiTarget object A is captured for robotic end effectoriTime, (Si(j-1)+Sij) represent that a robot terminal is performed
Device is picked up to be put in action from position BjSet out crawl AiAfter be placed into B(j+1)Stroke.
Preferably, genetic algorithm described in step 3, long Chromosome number is 50 in initial population.
Preferably, the tiMoment target object AiCoordinate A (xi(ti), yi) can be calculated by following formula:
Wherein, v for conveyer belt transfer rate, ti0This target object A is shot for cameraiMoment, tiFor parallel manipulator
People captures target object AiMoment.
Preferably, in the inventive method, the take pictures computational methods of frequency f of target object can be:
Wherein, L is the length that target object is distributed on a moving belt in each circulation, and the length is being passed according to target object
The density for taking distribution and the target location quantity in correspondence circulation is sent to calculate;Lc is that camera shoots length of an interval degree.
Preferably, the artificial parallel robot of described machine.
Preferably, after this method step 3, the method that the optimization also including the transfer rate of conveyer belt optimizes:
Step 41, judges to be exported in step 3 that the most short one group of long chromosome of total kilometres is corresponding have been performed needed for total kilometres
Time TSWhether the single cycle time interval [T of setting is fallen intoa, Tb];If TS∈[Ta, Tb], then execution step 42;If TS< Ta,
Then execution step 43;If TS> Tb, then execution step 44;
Step 42, is not adjusted to the transfer rate of conveyer belt;
Step 43, lifts the transfer rate of conveyer belt, then re-starts ten by the method for step 1 to step 3 and put action
The optimization of operating path;
Step 44, reduces the transfer rate of conveyer belt, then re-starts ten by the method for step 1 to step 3 to put action
The optimization of operating path.
The invention has the beneficial effects as follows:
First:Intelligent algorithm is applied to industrial automatic control scene and solves parallel robot pickup path rule by the present invention
Draw optimization problem, it is possible to obtain parallel robot pickup optimal path on a sorting streamline, take most short, greatly raising
Work efficiency;
Second:Method proposed by the present invention can provide the speed of conveyer belt, the distribution density and parallel machine of target object
The relation of device people's pickup velocity, carries out in advance the off-line simulation checking of assembly line work, and the optimal velocity of conveyer belt is given in advance,
Shorten the installation and debugging time, optimized production process.
Description of the drawings
Fig. 1 is the present invention towards the multiobject parallel robot pickup path locus optimization stream based on improved adaptive GA-IAGA
Journey schematic diagram;
Fig. 2 is equipped with the flow production line environmental modeling schematic diagram of parallel robot;
Fig. 3 is the running orbit schematic diagram that parallel robot sorts material.
Specific embodiment
With reference to the accompanying drawings describing the preferred embodiment of the present invention.It will be apparent to a skilled person that this
A little embodiments are used only for explaining the know-why of the present invention, it is not intended that limit the scope of the invention.
First, working environment mathematical modeling
As shown in Fig. 2 parallel robot work streamline is set to two bit planes, global coordinate system BASE is set up;This
Origin crosses origin O and the direction vertical with conveyer belt C1 is set to x-axis in O in embodiment, crosses origin O and puts down with conveyer belt C1
Capable direction is set to y-axis, x, y-axis positive direction it is as shown in Figure 2.
Working region D5 on streamline, target area D3 (i.e. rest areas are determined by the mechanism parameter of parallel robot
Domain), the multinomial performance parameter of parallel robot, such as maximal rate are input into, acceleration picks up curve of track etc.;Arrange and sit
Mark system origin O for parallel robot end effector initial position, set conveyer belt C1 fall into the region of working region D5 as
Capture area.
The target object image of camera image acquisition region D1 is entered with the collection of specific frequency f by industrial camera CAM,
By image recognition technique and the image coordinate of setting and the transfer function of physical coordinates, the coordinate of each target object, mesh are obtained
Mark object AiInitial coordinate be A (xi0, yi0), coordinate A (xi0, yi0) for the physical coordinates under global coordinate system BASE.
The purpose to be realized is:Parallel robot will limit time in, on conveyer belt C1 conveyer belt C1 transmission
N number of target object of direction front end moves to robot work region D5, and the mesh picked up to specific target area D3 settings
Cursor position Bj.N is consistent with the quantity of target location.
In the optimized algorithm of the present invention, can according to conveyer belt C1 and the parallel robot corresponding target object of crawl when
Between come determine correspondence target object it is crawled when coordinate A (xi(ti), yi), it is calculated as shown in formula (1):
Wherein, v for conveyer belt transfer rate, ti0This target object A is shot for cameraiMoment, tiFor parallel manipulator
People captures target object AiMoment.
The multiple target object A on conveyer belt C1iWith multiple target location B of target area D3j(such as Fig. 2) is defined as
Two big collections:Target object set A={ A1,A2,A3…,AN, target location set B={ B1,B2,B3…,BN}.Because target
The target location B of region D3jQuantity be given, so take N=M, that is, obtain target object AiWhen according to x coordinate by it is little to
Take greatly N number of, and it is a cycle that all target locations are often filled up in the D3 of target area in definition, and represents a cycle with T.
The thing in picking region although the target location in the D3 of target area is constant, in each cycle on conveyer belt
Body AiIt is random distribution, so the time for completing to fill up region D3 every time is different, i.e., cycle T is a variable.
2nd, the mathematical modeling of path planning
(target object is placed into into target location from conveyer belt through above working environment mathematical modeling and to flow process of casing
Flow process) analysis, parallel robot end effector pickup conveyer belt on a target object AiIt is put into the mesh of target area D3
Cursor position Bj, then go again to pick up next target object A(i+1)It is put into target location B(j+1), and so on move;It can be seen that
The reciprocatory movement is an approximate traveling salesman problem (Travelling Salesman Problem, TSP), but actual
Situation is but very different with TSP;Assume the end effector of parallel robot as travelling salesman, target object set A and
Set B in target location can regard two groups of cities as, and the end effector of parallel robot carries out Pick-and-Place operations and is approximately travelling
Business each it is intercity walk, it is characterized by target location BjThe target object A intercepted on (j=1,2 ... M) and conveyer belti(i=
1,2 ... N) correspond, parallel robot end effector be not between arbitrary two cities move, and must be
Alternating movement (i.e. the alternating movement between set A and B) between corresponding two groups of cities of A and B, two is intercity apart from DijSuch as
Shown in formula (2):
Wherein A (xi, yi) represent target object AiCoordinate, B (xj, yj) represent target location BjCoordinate.
Because parallel robot end effector pickup track adopt when gate track (as shown in Figure 3), door is a height of
B, captures each time or places, and the stroke of parallel robot end effector is approximately Sij=Dij+2*b;And mesh in set A
Mark object AiCoordinate A (xi, yi) it is the i.e. coordinate x as conveyer belt C1 travels forward togetheriIt is corresponding for the function of time t
Target object AiCoordinate can be expressed as A (xi(t), yi)。
Pick-and-Place operations, as shown by dotted lines in figure 3:Parallel robot end effector is placing A(i-1)To B(j-1)Afterwards, open
Begin next target A of crawli, and it is put into target location Bj, it can be seen that end effector crawl while, target AiAlso with
Conveyer belt to travel forward with speed v, i.e., to complete to capture end effector and target AiSame position is reached simultaneously;It is actual
Equivalent to moving between 3 cities, such as from position B(j-1)Set out crawl AiAfterwards, it is placed into Bj, the trip is represented by formula
(3):
Understand shown in total kilometres S such as formula (4)
Wherein, S represents total kilometres, AiRepresent target object, BjTarget location is represented, i represents the sequence number of target object, j tables
Show the sequence number of target location, SijRepresent the stroke between target object i and target location j, DijRepresent target object AiWith target
Position BjBetween horizontal range, b represents that robotic end effector picks up the rising height (i.e. door is high) for putting action, A (xi, yi)
Represent target object AiCoordinate, B (xj, yj) represent target location BiCoordinate, A (xi(ti), yi) represent tiMoment target object
AiCoordinate, tiTarget object A is captured for robotic end effectoriTime, (Si(j-1)+Sij) represent a robot terminal
Executor picks up puts in action from position BjSet out crawl AiAfter be placed into B(j+1)Stroke.
Min (S) is the object function of this mathematical model.Complete same number of vanning task, the fortune of end effector
Capable total stroke is less, then the spent time is shorter, i.e., work efficiency is higher.
3rd, the path optimization of each cycle period
The analysis of more than Jing understands that the operating path of robotic end effector starts to capture A for origin OiIt is put into Bj, such as
This is reciprocal, until target area is filled up, completes the task of a cycle.Whole path process can be by such as next long dye
Colour solid is indicated:
O→Ai→Bj→Am→Bk…AN→BM
A kind of parallel robot high-speed picking-up method for optimizing route towards multiple dynamic objects of the embodiment of the present invention, bag
Include following steps:
Step 1, carries out random number and obtains corresponding coordinate information to each target location in placement region, and from crawl
Region is sequentially chosen and the same number of target object in target location, and to target object random number is carried out, while obtaining target
The initial coordinate of object.
In the step, respectively random number is carried out to target object set A and target location set B, obtain { A1,A2,
A3…,AN}、{B1,B2,B3…,BM}。
Step 2, acquired target object and target location are carried out at random translocation sorting, constitute the long dye of initial population
Colour solid;The sequence of the chromosome is robotic end effector picks up and puts action operating path;
Can be according to { A1,A2,A3…,AN}、{B1,B2,B3…,BMThe structure of the long chromosome of initial population is carried out, for example,
One long chromosome of initial population can be
O→A1→B1→A2→B2→A3→B3…BM-1→AN→BM
It can be seen that, it is known that a long chromosome, can divide and obtain two groups with regard to target object set A and target location
The short chromosome of set B.
Step 3, repeat step 2 builds initial population, and robotic end effector is picked up by genetic algorithm puts action
Operating path is optimized, and one group of most short long chromosome of output total kilometres is picked up as the robotic end effector after optimization to be put
Action operating path.
Step 31, can build multiple long chromosomes according to the method that long chromosome is built in step 2, constitute initial kind
Group, sets the bar number of long chromosome in initial population as 50 in the present embodiment.
Step 32, initial population, with Min (S) as object function, with C as select probability, carries out genetic algorithm as parent
Selection, intersect, variation and weight insertion operation, using the condition that algorithmic statement or default iterationses terminate as the algorithm,
And the maximum long chromosome of fitness function is chosen from last time iteration population as the robot terminal execution after optimization
Device is picked up puts action operating path, and the maximum long chromosome of the fitness function carries out Pick-and-Place operations for controlling parallel robot.
In the present embodiment, in object function Min (S), shown in S such as formula (4), fitness function is 1/S, select probability C
As shown in formula (5):
C=(Smax-Sq)/(Smax-Smin) (5)
Wherein, SmaxFor the corresponding most long total path of long chromosome in current iteration population, SminFor in current iteration population
The corresponding most short total path of long chromosome, SqFor the corresponding total path length of long chromosome of serial number q in current iteration population.
In the present embodiment, in order to ensure each step operating process in A and B strict in every chromosome cross arrangement it is suitable
Sequence, in each iteration, by long chromosome separation into two short chromosomes with regard to target object A and target location B, enters respectively
Row selects, intersects, makes a variation and insertion operation, then remerges into a new long chromosome.
In the present embodiment, if the kind group mean adaptive value change that algorithmic statement is specially adjacent Q generations is less than predetermined threshold value;Q
For the iterationses for evaluation algorithm convergence of setting.
Target object A in the present embodimentiCoordinate real-time change, each time circulate in obtain conveyer belt C1 on target object
The number of A, according to the ascending intercepting of x coordinate so that N=M (quantity of target object A is consistent with the quantity of target location B);
Target location quantity in the density that so can be distributed on conveyer belt C1 according to target object A and correspondence circulation is calculated
Go out length L that every time circulation target object A is distributed on a moving belt, such that it is able to optimize filming frequency f (the i.e. objects of camera
The filming frequency of body), specifically can be calculated by formula (6):
Wherein, Lc is that camera shoots length of an interval degree.
By the optimization of the filming frequency of camera, control system can be reduced to the performance requirement of processor and be ensure that
The real-time of intelligent algorithm.
The present embodiment after step 3, the step of the optimization for being additionally provided with the transfer rate of conveyer belt optimizes, concrete bag
Include:
Step 41, judges to be exported in step 3 that the most short one group of long chromosome of total kilometres is corresponding have been performed needed for total kilometres
Time TSWhether the single cycle time interval [T of setting is fallen intoa, Tb];If TS∈[Ta, Tb], then execution step 42;If TS< Ta,
Then execution step 43;If TS> Tb, then execution step 44;
Step 42, is not adjusted to the transfer rate of conveyer belt;
Step 43, lifts the transfer rate of conveyer belt, then re-starts ten by the method for step 1 to step 3 and put action
The optimization of operating path;
Step 44, reduces the transfer rate of conveyer belt, then re-starts ten by the method for step 1 to step 3 to put action
The optimization of operating path.
The optimization optimization method of the transfer rate of above-mentioned conveyer belt, the path optimization side based on the present embodiment in the present embodiment
The path planning mathematical model built in method is proposed, to optimize the efficiency of streamline as target, by advance off-line simulation, and then
Instruct in actual production technology and the speed of service of transmission belt is optimized, shorten the cycle of installation and debugging.
Those skilled in the art should be able to recognize that, with reference to the side of each example of the embodiments described herein description
Method step, can with electronic hardware, computer software or the two be implemented in combination in, in order to clearly demonstrate electronic hardware and
The interchangeability of software, according to function has generally described the composition and step of each example in the above description.These
Function is performed with electronic hardware or software mode actually, depending on the application-specific and design constraint of technical scheme.
Those skilled in the art can use different methods to realize described function to each specific application, but this reality
Now it is not considered that beyond the scope of this invention.
So far, technical scheme is described already in connection with preferred implementation shown in the drawings, but, this area
Technical staff is it is easily understood that protection scope of the present invention is expressly not limited to these specific embodiments.Without departing from this
On the premise of the principle of invention, those skilled in the art can make the change or replacement of equivalent to correlation technique feature, these
Technical scheme after changing or replacing it is fallen within protection scope of the present invention.
Claims (12)
1. a kind of parallel robot high-speed picking-up method for optimizing route towards multiple dynamic objects, it is characterised in that include with
Lower step:
Step 1, carries out random number and obtains corresponding coordinate information to each target location in placement region, and from capture area
Sequentially choose and the same number of target object in target location, random number is carried out to target object, while obtaining target object
Initial coordinate;
Step 2, acquired target object and target location are carried out at random translocation sorting, constitute the long dyeing of initial population
Body;The sequence of the chromosome is robotic end effector picks up and puts action operating path;
Step 3, repeat step 2 build initial population, and robotic end effector is picked up by genetic algorithm put action operation
Path is optimized, and one group of most short long chromosome of output total kilometres is picked up as the robotic end effector after optimization puts action
Operating path;The genetic algorithm, its object function is Min (S), and S is total kilometres.
2. method according to claim 1, it is characterised in that genetic algorithm described in step 3, its select probability is
C=(Smax-Sq)/(Smax-Smin)
Wherein, SmaxFor the corresponding most long total path of long chromosome in current iteration population, SmimFor long dye in current iteration population
The corresponding most short total path of colour solid, SqFor the corresponding total path length of long chromosome of serial number q in current iteration population.
3. method according to claim 2, it is characterised in that genetic algorithm described in step 3, in each iterative process,
By long chromosome separation into two with regard to target object and the short chromosome of target location, selected respectively, intersected, make a variation with
Insertion operation, then remerges into a new long chromosome.
4. method according to claim 3, it is characterised in that genetic algorithm described in step 3, with algorithmic statement or default
The condition that terminates as the algorithm of iterationses, and the maximum long dye of fitness function is chosen from last time iteration population
Colour solid is picked up as the robotic end effector after optimization puts action operating path.
5. method according to claim 4, it is characterised in that genetic algorithm described in step 3, its fitness function is 1/
S。
6. according to quote claim 5 described in method, it is characterised in that the algorithmic statement, if the kind in specially adjacent Q generations
Group mean adapts to value changes and is less than predetermined threshold value;Q is the iterationses for evaluation algorithm convergence of setting.
7. the method according to any one of claim 1~6, it is characterised in that the computational methods of the total kilometres are:
Wherein, S represents total kilometres, AiRepresent target object, BjTarget location is represented, i represents the sequence number of target object, and j represents mesh
The sequence number of cursor position, SijRepresent the stroke between target object i and target location j, DijRepresent target object AiWith target location
BjBetween horizontal range, b represents that robotic end effector picks up the rising height for putting action, A (xi, yi) represent target object
AiCoordinate, B (xj, yj) represent target location BjCoordinate, A (xi(ti), yi) represent tiMoment target object AiCoordinate, ti
Target object A is captured for robotic end effectoriTime, (Si(j-1)+Sij) represent that a robotic end effector picks up and puts
From position B in actionjSet out crawl AiAfter be placed into B(j+1)Stroke.
8. the method according to quoting claim 7, it is characterised in that genetic algorithm described in step 3 is long in initial population
Chromosome number is 50.
9. according to quote claim 7 described in method, it is characterised in that the ti moment target object AiCoordinate A (xi
(ti), yi) can be calculated by following formula:
Wherein, v for conveyer belt transfer rate, tiOThis target object A is shot for cameraiMoment, tiFor parallel robot crawl
Target object AiMoment.
10. the method according to quoting claim 7, it is characterised in that in this method, target object is taken pictures the meter of frequency f
Calculation method can be:
Wherein, L is the length that target object is distributed on a moving belt in each circulation, and the length is according to target object in conveyer belt
Target location quantity in the density of upper distribution and correspondence circulation is calculated;LCLength of an interval degree is shot for camera.
11. methods according to quoting claim 7, it is characterised in that the artificial parallel robot of described machine.
12. methods according to quoting claim 7, it is characterised in that after this method step 3, also including conveyer belt
The method of the optimization optimization of transfer rate:
Step 41, judges to be exported in step 3 that the most short one group of long chromosome of total kilometres is corresponding to have performed total kilometres required time TS
Whether the single cycle time interval [Ta, Tb] of setting is fallen into;If TS∈[Ta, Tb], then execution step 42;If TS< Ta, then hold
Row step 43;If TS> Tb, then execution step 44;
Step 42, is not adjusted to the transfer rate of conveyer belt;
Step 43, lifts the transfer rate of conveyer belt, then re-starts ten by the method for step 1 to step 3 and put action operation
The optimization in path;
Step 44, reduces the transfer rate of conveyer belt, then re-starts ten by the method for step 1 to step 3 to put action operation
The optimization in path.
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Cited By (12)
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