CN109615188A - A kind of predistribution combines the multi-robot Task Allocation of Hungary Algorithm - Google Patents
A kind of predistribution combines the multi-robot Task Allocation of Hungary Algorithm Download PDFInfo
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Abstract
The invention discloses the multi-robot Task Allocations that a kind of predistribution combines Hungary Algorithm, comprising the following steps: models to multi-robot system；Establish the benefit value matrix that all robots undertake different task；Optimize multi-robot system；Benefit value matrix is simplified；Benefit value matrix is deformed according to the quantity of each required by task robot；Task is pre-allocated, and is further simplified benefit value matrix；Task distribution is carried out using Hungary Algorithm, obtains final allocation matrix T, completes task distribution.The present invention is using multirobot multi-task planning system as object, the strategy of Hungary Algorithm is combined to be allocated using predistribution, efficiently solve the distribution and optimization problem of multirobot multitask system, the problem of alleviating the excessive time loss that may cause in beneficial matrix complexity with single Hungary Algorithm, even algorithm Infinite Cyclic has the advantages that effective simplified model representation, accelerates model analysis speed.
Description
Technical field
The invention belongs to multi-robot Cooperation control technology field, especially a kind of predistribution combines the more of Hungary Algorithm
Robot task distribution method.
Background technique
Multi-robotic task distribution, i.e. appointment robot execute task, since the construction of robot is different, to different task
Completeness it is different, the cost for executing task is also different.Therefore, how different robots reasonably to be assigned to execute difference
Task, how to assign multiple robots to complete the same task as one of the critical issue in multi-robot system research.
Existing multi-robot Task Allocation puts forward for specific application mostly, is only used for specific ring
Border, such as Hungary Algorithm, robot and task quantity is equal and each task only needs a robot to complete, this right and wrong
Normal Utopian situation.It such as thanks to philosophy and [D] .2017. is studied based on pilot's task assignment of Hungarian method[1], just apply
Hungary Algorithm assigns task and the equal situation of robot quantity.If when task quantity and robot quantity are unequal, or working as
Each task needs more than one robot come when completion, this method of salary distribution is not just available.
It is most only single in view of machine when constructing the relationship between robot and completion task at this stage in experimentation
Time factor or completion required by task cost of the device people during completion task.But in practical application, multirobot is closing
It is only single with time factor or to complete cost and measure robot for the completeness of task during making completion goal task
It is very unilateral.
Summary of the invention
Technical problem solved by the invention is to provide a kind of multi-robotic task for pre-allocating and combining Hungary Algorithm
Distribution method.
The technical solution for realizing the aim of the invention is as follows: a kind of predistribution combines the multi-robotic task of Hungary Algorithm
Distribution method, comprising the following steps:
The model that step 1, based role cooperate models multi-robot system；
Step 2 establishes the benefit value matrix Q that all robots undertake different task；
Step 3 optimizes multi-robot system by judging whether robot meets distributive condition；
Step 4 simplifies the benefit value matrix；
Step 5 deforms benefit value matrix according to the quantity of each required by task robot；
Step 6 pre-allocates task, obtains original allocation matrix T, and be further simplified benefit value matrix；
Step 7 carries out task distribution using the simplified benefit value matrix of Hungary Algorithm processing step 6, obtains final
Allocation matrix T, complete task distribution.
Compared with prior art, the present invention its remarkable advantage are as follows: 1) present invention is by introducing benefit value as measurement machine
People completes the parameter of task quality, improves the Evaluation of Utility mechanism during robot completion task, can effectively embody heterogeneous computers
Device people completes the superiority and inferiority of different task, and consumption and energy consumption when can combine increase such a task allocation result of benefit value
The quantitative evaluation index of superiority and inferiority improves the science and reasonability of task allocation result；2) present invention is by benefit value square
Battle array be adjusted deformation, realize under complex situations as task quantity and robot quantity it is unequal or when each task needs one
A above robot distributes come task when completing；3) by the present invention in that being alleviated with predistribution in beneficial matrix complexity
The time loss that may cause with single Hungary Algorithm is excessive, even algorithm Infinite Cyclic the problem of, have and accelerate model
The advantages of analyzing speed；4) present invention simplifies modeling procedure, simplifies mould by deleting the variable unrelated with this method of salary distribution
The representation of type obtains the model for being more simply more suitable for this system.
Detailed description of the invention
Fig. 1 is the flow chart for the multi-robot Task Allocation that present invention predistribution combines Hungary Algorithm.
Fig. 2 is present invention optimization multi-robot system and carries out flow chart simplified for the first time to benefit value matrix.
Fig. 3 is the flow chart that the present invention handles that simplified benefit value matrix carries out task distribution using Hungary Algorithm.
Specific embodiment
In conjunction with Fig. 1, a kind of predistribution of the present invention combines the multi-robot Task Allocation of Hungary Algorithm, including following
Step:
The model that step 1, based role cooperate models multi-robot system；
Step 2 establishes the benefit value matrix Q that all robots undertake different task；
Step 3 optimizes multi-robot system by judging whether robot meets distributive condition；
Step 4 simplifies benefit value matrix；
Step 5 deforms benefit value matrix according to the quantity of each required by task robot；
Step 6 pre-allocates task, obtains original allocation matrix T, and be further simplified benefit value matrix；
Step 7 carries out task distribution using the simplified benefit value matrix of Hungary Algorithm processing step 6, obtains final
Allocation matrix T, complete task distribution.
Further, the model of role collaboration specifically uses E-CARGO model in step 1, according to E-CARGO model, one
A multi-robot system ∑ can be expressed as a nine tuple ∑s: :=< C, O, A, S, R, E, G, s0, H >, wherein C is one
The set of group class；O is the set of a group objects；A is the set of one group of Agent；S is the set of one group of service；R is one group of role
Set；E is the set of one group of environment；G is the set of one group of working group；s0It is the original state of cooperative system；H is a composition
The set of member.
Further, step 1 models multi-robot system based on E-CARGO model, specifically:
E-CARGO model is simplified:
∑: :=< A, R, E >
In formula, A is collection of bots, indicates robot quantity using m；R is set of tasks, indicates task quantity using n；
Task scope vector in environment E, L=[l are indicated using vector L1,l2,…,ln]。
Further, the dimension of benefit value matrix Q is m × n in step 2, each benefit value X in matrix QijAre as follows:
Xij=1- (w1×sij1+w2×sij2)
Wherein, XijThat is Q [i, j] is the benefit value that i-th of robot completes j-th of task, sij1It is complete for i-th of robot
At j-th task when consume, w1For sij1Corresponding weight, sij2The energy consumption of j-th of task, w are completed for i-th of robot2For
sij2Corresponding weight, w1、w2Free value according to the actual situation；Wherein 0≤i < m, 0≤j < n.
Further, step 3 optimizes multi-robot system by judging whether robot meets distributive condition, specifically:
Step 3-1, whether detection machine people quantity meets distributive condition, if not satisfied, increasing robot quantity until full
Sufficient distributive condition；Wherein, distributive condition isL [j] is robot quantity needed for completion task j；
Step 3-2, setting the qualification threshold value of each task in n task is respectively P0、P1、…、Pn-1, and it is every to detect completion
The robot quantity of a task whether meet demand condition；If not satisfied, adjustment complete the robot quantity of each task until
Meet demand condition；
Wherein, N is enabledi=Q [i, j]-PjIf | Q [i, j]-Pj| >=0, then Ni=1, on the contrary Ni=0；
Then demand condition is
Further, P in step 3-20、P1、…、Pn-1Value be P0=P1=...=Pn-1。
Further, step 4 simplifies benefit value matrix, specifically:
Compare each robot and complete the benefit value of each task and the qualification threshold value of the task, qualification threshold value will be less than
Benefit value is set to 0, to complete the simplification of benefit value matrix.Specific algorithm is as follows:
Further, step 5 deforms benefit value matrix according to the quantity of each required by task robot specifically:
Step 5-1, according to l in task vector LjValue, replicate the ljColumn where corresponding task in benefit value matrix Q
ljIt is secondary, n task is traversed with this, obtains new benefit value matrix Q'；
Step 5-2, judge whether the columns p of new benefit value matrix Q' is less than line number q, if being less than, in original benefit
Q-p column 0 are added on the list end of value matrix Q', generate new benefit value matrix Q "；
Step 5-3, deformed benefit value matrix M is obtained according to 1-Q ".Specific algorithm is as follows:
Further, step 6 pre-allocates task, obtains original allocation matrix T, and be further simplified benefit value square
Battle array specifically:
Preferred boundary μ is set, establishes empty allocation matrix T, dimension is m × n, for any 0≤a < m, 0≤b < n
And a is even number or odd number, traverses all values of benefit value matrix M:
Step 6-1, when robot a executes benefit value M [a, b] < μ of task b, compare M [a, b] and any M [a, j],
If M [a, b] be not more than any M [a, j], continue to compare M [a, b] and any M [i, b], if M [a, b] also be not more than any M [i,
B], then task b is distributed into robot a, enables T [a, b]=1；Otherwise continues to traverse the remaining value of benefit value matrix M, repeat this
Step obtains original allocation matrix T；Wherein, 0≤j < n and j ≠ b, 0≤i < m and i ≠ a；
Step 6-2, for having distributed to the task b of robot a, by it, corresponding row and column is equal in benefit value matrix M
It deletes, thus to obtain benefit value matrix M' new after simplification.
New matrix is obtained by step 6 predistribution and abbreviation, the matrix dimensionality that incoming Hungary Algorithm is allocated is bright
It is aobvious to be less than the old matrix without predistribution, the runing time of algorithm is effectively reduced, the analysis speed of model is accelerated.It is specific to calculate
Method is as follows:
Further, step 7 carries out task distribution using the simplified benefit value matrix of Hungary Algorithm processing step 6,
Final allocation matrix T is obtained, task distribution is completed specifically:
Step 7-1, row, column specification is carried out, simplified benefit value matrix M' is specially directed to, by every number of its every row
Value subtracts the smallest number of numerical value in the row, and each numerical value of each column subtracts the smallest number of numerical value in the column, thus to obtain new effect
Beneficial value matrix I；
Step 7-2, examination appointment is carried out, Independent 0 Elements all in benefit value matrix I are found, specifically:
Step 7-2-1, it is denoted as ◎, is meant to 0 plus circle for the row or column for containing only single 0 element in benefit value matrix I
Independent 0 Elements；Other 0 elements of row and column where ◎ are denoted asThe step is repeated, all contains only list until having handled
The row or column of a 0 element；
Step 7-2-2, least 0 element of place row and column 0 element sum is selected as Independent 0 Elements, by the Independent 0 Elements
Other 0 elements of place row and column are denoted asThe step is repeated, until having handled all 0 elements；
Step 7-3, whether the dimension of the number and matrix I that judge Independent 0 Elements is equal, will be in allocation matrix T if equal
The value of independent neutral element corresponding position is set to 1, thus updates allocation matrix T, no to then follow the steps 7-4；
Step 7-4, make 0 line of lid, all 0 elements covered with least straight line, specifically:
1. beating √ to the row of no Independent 0 Elements ◎；
2. in the row for having beaten √Column beats √；
3. in the column for having beaten √It is expert at and beats √；
1. 2. 3. 4. step is repeated, until beating the row and column of √；
5. crossing to the row for not beating √, the column scribing line for the √ that fights each other obtains covering all 0 minimum straight line number l'；If l'
It is equal with the dimension of matrix I, then it goes to step 7-2 and is reassigned；If l' is less than the dimension of matrix I, step 7-5 is continued to execute；
Step 7-5, the minimum value in the element not covered by 0 line of lid is found out, each numerical value in uncrossed row is subtracted
The minimum value is gone, which is added to each numerical value in the column of scribing line, repeats step 7-2.Specific algorithm is as follows:
Below with reference to embodiment, the present invention is described in further detail.
Embodiment
Existing 20 robots, each robot have the ability to execute communication, positioning, carrying, processing, one of 4 kinds of tasks
Or it is a variety of, it is now assumed that this 20 robots are heterogeneous robots, execute each task ability be it is discrepant, played the part of respectively according to it
Each robot of the benefit value reasonable distribution of role executes each task.
Task is four kinds of determination, t1, t2, t3, t4, which needs 4 kinds of roles, after Task-decomposing, required for each role
Robot quantity be also it is fixed, respectively (7,3,5,4).
Problem to be solved: how to be distributed from large number of robot and assign suitable robot to undertake properly
Role, come the completion task that cooperates, the total maximizing the benefits of Shi Ge robot figure.
The first step models robot task distribution system shown in table 1, it is known that, robot quantity m=20 appoints
Be engaged in quantity n=4, task scope vector L=[7,3,5,4].
The benefit value matrix Q that heterogeneous robot executes different task is as shown in table 1 below:
1 benefit value matrix Q of table
Whether the machine number that second step, inspection meet qualification threshold requirement meets distributive condition, machine numberThis task qualification threshold value is set as 0.2, the machine number of qualification threshold requirement is met in each task
Respectively [15,17,19,17] are all larger than task scope vector L=[7,3,5,4], meet the condition for continuing distribution, to being unsatisfactory for
The benefit value of qualification threshold requirement is changed to 0, this task can not be undertaken completely by meaning.
Simplified benefit value matrix is as shown in table 2 below:
The simplified benefit value matrix Q of table 2
Third step deforms beneficial matrix, and deformed new benefit value matrix M is as shown in table 3 below:
The deformed benefit value matrix M of table 3
4th step, preferred dividing value μ=0.1 of setting, the result pre-allocated:
T (1,14)=1 T (2,20)=1 T (3,8)=1 T (3,1)=1 T (3,18)=1 T (4,19)=1
Benefit value matrix after being further simplified is as shown in table 4 below:
Table 4 be further simplified after benefit value matrix M'
By the predistribution of the 4th step and matrix abbreviation, the dimension of beneficial matrix is reduced to 14 by 20, significantly reduces entrance
The data volume of algorithm, meanwhile, such as directly old matrix application Hungary Algorithm is entered in the abbreviation matrix step of Hungary Algorithm
Endless loop is unable to get allocation result.Thus, it can be known that the predistribution combination Hungary Algorithm allocative efficiency that the present invention uses is accelerated
The analysis speed of model avoids endless loop without solution situation.
5th step is allocated using Hungary Algorithm, and it is as shown in table 5 below to obtain allocation matrix T:
5 allocation matrix T of table
Finally obtained allocation result is as shown in table 6 below:
6 allocation result of table
Mean robot r4r5r7r9r10r14r15Execution task t1；r2r3r20Execution task t2；r1r8r11r12r18Execution task
t3；r13r16r17r19Execution task t4。
From the foregoing, it will be observed that the task distribution that the predistribution that the present invention uses combines Hungary Algorithm to carry out, removes and modeled
Irrelevant variable in journey effectively simplifies model representation.Further, since introducing predistribution step, calculated into Hungary
The matrix dimensionality of method significantly becomes smaller, and has not only accelerated the analysis speed of model, but also can be single to avoid using when beneficial matrix complexity
The problem of time loss that Hungary Algorithm may cause is excessive, even into Infinite Cyclic, it is more more efficient than Hungary Algorithm, more
Adapt to actual needs.
Claims (10)
1. the multi-robot Task Allocation that a kind of predistribution combines Hungary Algorithm, which comprises the following steps:
The model that step 1, based role cooperate models multi-robot system；
Step 2 establishes the benefit value matrix Q that all robots undertake different task；
Step 3 optimizes multi-robot system by judging whether robot meets distributive condition；
Step 4 carries out the benefit value matrix to simplify processing；
Step 5 deforms benefit value matrix according to the quantity of each required by task robot；
Step 6 pre-allocates task, obtains original allocation matrix T, and be further simplified benefit value matrix；
Step 7 carries out task distribution using the simplified benefit value matrix of Hungary Algorithm processing step 6, obtains final point
With matrix T, task distribution is completed.
2. predistribution according to claim 1 combines the multi-robot Task Allocation of Hungary Algorithm, feature exists
In the model of role collaboration described in step 1 specifically uses E-CARGO model.
3. predistribution according to claim 2 combines the multi-robot Task Allocation of Hungary Algorithm, feature exists
In, multi-robot system is modeled based on E-CARGO model described in step 1, specifically:
E-CARGO model is simplified:
∑: :=< A, R, E >
In formula, A is collection of bots, indicates robot quantity using m；R is set of tasks, indicates task quantity using n；Using
Vector L indicates task scope vector in environment E, L=[l1,l2,…,ln]。
4. predistribution according to claim 3 combines the multi-robot Task Allocation of Hungary Algorithm, feature exists
In the dimension of benefit value matrix Q described in step 2 is m × n, each benefit value X in matrix QijAre as follows:
Xij=1- (w1×sij1+w2×sij2)
Wherein, XijThat is Q [i, j] is the benefit value that i-th of robot completes j-th of task, sij1Jth is completed for i-th of robot
A task when consume, w1For sij1Corresponding weight, sij2The energy consumption of j-th of task, w are completed for i-th of robot2For sij2It is corresponding
Weight, w1、w2Free value according to the actual situation；Wherein 0≤i < m, 0≤j < n.
5. predistribution according to claim 4 combines the multi-robot Task Allocation of Hungary Algorithm, feature exists
In, optimize multi-robot system by judging whether robot meets distributive condition described in step 3, specifically:
Step 3-1, whether detection machine people quantity meets distributive condition, divides if not satisfied, increasing robot quantity until meeting
With condition；Wherein, distributive condition isL [j] is robot quantity needed for completion task j；
Step 3-2, setting the qualification threshold value of each task in n task is respectively P0、P1、…、Pn-1, and detect completion each
The robot quantity of business whether meet demand condition；If not satisfied, adjustment completes the robot quantity of each task until meeting
Demand condition；
Wherein, N is enabledi=Q [i, j]-PjIf | Q [i, j]-Pj| >=0, then Ni=1, on the contrary Ni=0；
The demand condition is
6. predistribution according to claim 5 combines the multi-robot Task Allocation of Hungary Algorithm, feature exists
In P described in step 3-20、P1、…、Pn-1Value be P0=P1=...=Pn-1。
7. predistribution according to claim 6 combines the multi-robot Task Allocation of Hungary Algorithm, feature exists
In, benefit value matrix is carried out described in step 4 to simplify processing, specifically:
Compare each robot and complete the benefit value of each task and the qualification threshold value of the task, the benefit of qualification threshold value will be less than
Value is set to 0, to complete the simplification of benefit value matrix.
8. predistribution according to claim 7 combines the multi-robot Task Allocation of Hungary Algorithm, feature exists
In being deformed according to the quantity of each required by task robot to benefit value matrix described in step 5 specifically:
Step 5-1, according to l in task vector LjValue, replicate the ljColumn l where corresponding task in benefit value matrix QjIt is secondary,
N task is traversed with this, obtains new benefit value matrix Q'；
Step 5-2, judge whether the columns p of new benefit value matrix Q' is less than line number q, if being less than, in original benefit value square
Q-p column 0 are added on the list end of battle array Q', generate new benefit value matrix Q "；
Step 5-3, deformed benefit value matrix M is obtained according to 1-Q ".
9. predistribution according to claim 8 combines the multi-robot Task Allocation of Hungary Algorithm, feature exists
In being pre-allocated described in step 6 to task, obtain original allocation matrix T, and be further simplified benefit value matrix specifically:
Preferred boundary μ is set, empty allocation matrix T is established, dimension is m × n, and for any 0≤a < m, 0≤b < n and a is
Even number or odd number traverse all values of benefit value matrix M:
Step 6-1, when robot a executes benefit value M [a, b] < μ of task b, compare M [a, b] and any M [a, j], if M
[a, b] is not more than any M [a, j], continues to compare M [a, b] and any M [i, b], if M [a, b] is also not more than any M [i, b],
Task b is then distributed into robot a, enables T [a, b]=1；Otherwise continues to traverse the remaining value of benefit value matrix M, repeat this step
Suddenly, original allocation matrix T is obtained；Wherein, 0≤j < n and j ≠ b, 0≤i < m and i ≠ a；
Step 6-2, for having distributed to the task b of robot a, by it, corresponding row and column is deleted in benefit value matrix M,
Thus to obtain benefit value matrix M' new after simplification.
10. predistribution according to claim 9 combines the multi-robot Task Allocation of Hungary Algorithm distribution, special
Sign is, carries out task distribution using the simplified benefit value matrix of Hungary Algorithm processing step 6 described in step 7, obtains most
Whole allocation matrix T completes task distribution specifically:
Step 7-1, row, column specification is carried out, simplified benefit value matrix M' is specially directed to, each numerical value of its every row is subtracted
The smallest number of numerical value in the row is removed, each numerical value of each column subtracts the smallest number of numerical value in the column, thus to obtain new benefit value
Matrix I；
Step 7-2, examination appointment is carried out, Independent 0 Elements all in benefit value matrix I are found, specifically:
Step 7-2-1, it is denoted as ◎ to 0 plus circle for the row or column for containing only single 0 element in benefit value matrix I, means independent 0
Element；Other 0 elements of row and column where ◎ are denoted asThe step is repeated, all contains only single 0 yuan until having handled
The row or column of element；
Step 7-2-2, least 0 element of place row and column 0 element sum is selected as Independent 0 Elements, it will be where the Independent 0 Elements
Other 0 elements of row and column are denoted asThe step is repeated, until having handled all 0 elements；
Step 7-3, whether the dimension of the number and matrix I that judge Independent 0 Elements is equal, will be independent in allocation matrix T if equal
The value of neutral element corresponding position is set to 1, thus updates allocation matrix T, no to then follow the steps 7-4；
Step 7-4, make 0 line of lid, all 0 elements covered with least straight line, specifically:
1. beating √ to the row of no Independent 0 Elements ◎；
2. in the row for having beaten √Column beats √；
3. in the column for having beaten √It is expert at and beats √；
1. 2. 3. 4. step is repeated, until beating the row and column of √；
5. crossing to the row for not beating √, the column scribing line for the √ that fights each other obtains covering all 0 minimum straight line number l'；If l' and square
The dimension of battle array I is equal, then goes to step 7-2 and be reassigned；If l' is less than the dimension of matrix I, step 7-5 is continued to execute；
Step 7-5, the minimum value in the element not covered by 0 line of lid is found out, this is subtracted to each numerical value in uncrossed row
Minimum value adds the minimum value to each numerical value in the column of scribing line, repeats step 7-2.
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