CN116777170A - Multi-robot task allocation method based on chaotic self-adaptive dung beetle optimization algorithm - Google Patents
Multi-robot task allocation method based on chaotic self-adaptive dung beetle optimization algorithm Download PDFInfo
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Abstract
The invention discloses a multi-robot task allocation method based on a chaotic self-adaptive dung beetle optimization algorithm, which mainly solves the problems of unconstrained time window constraint, poor expandability and low allocation efficiency in the multi-robot task allocation method. The method comprises the following implementation steps: establishing a multi-robot task allocation objective function to be optimized which meets constraint conditions; initializing algorithm parameters; initializing the position of each dung beetle in the dung beetle population; calculating fitness values of all the dung beetles; updating the positions of the dung beetles; and when the maximum iteration times are reached, taking the optimal position of the dung beetle as a multi-robot task allocation result to be output. The invention solves the problem of multi-robot task allocation by the chaotic self-adaptive dung beetle optimization algorithm, improves the quality and efficiency of multi-robot task allocation, and effectively solves the problems existing in the multi-robot task allocation method.
Description
Technical Field
The invention belongs to the technical field of robots, and further relates to a multi-robot task allocation method based on a chaotic self-adaptive dung beetle optimization algorithm in the technical field of multi-robot task allocation. The invention can be applied to a multi-robot system consisting of an unmanned plane, an unmanned ship and the like, and a group of tasks can be effectively distributed to a plurality of heterogeneous robots, so that systematic and efficient coordination can be realized.
Background
In recent years, robots have played an increasingly important role in the military and civilian fields. However, as task demands continue to increase, it is often difficult for a single robot to independently accomplish complex tasks, and multiple robot systems have evolved. In a multi-robot system, task allocation is a key technology that involves how to efficiently allocate a set of tasks to multiple robots to achieve systematically efficient coordination. For example, in the areas of service robots, industrial robots, and unmanned vehicles, reasonable task allocation may improve the overall efficiency of these systems. In particular, unmanned techniques are widely used in the scenes of ground search and rescue, express delivery, mapping, monitoring or exploration. The existing multi-robot task allocation method mainly comprises three types, wherein the first type is a task allocation method based on a traditional algorithm, and the algorithm is mostly aimed at specific structural problems, but is difficult to solve the problem of medium-scale and large-scale multi-robot task allocation. The second is a task allocation method based on reinforcement learning algorithm, and the algorithm has the advantages of high solving speed and strong model generalization capability, but has the problems of long pre-training time, difficult bonus function design and the like. The third is a task allocation method based on intelligent optimization algorithm, which is widely focused by simulating the cooperative behavior of natural biological groups due to the advantages of simplicity, easiness in realization, strong robustness and the like, but has the problem of extremely easy trapping in local optimization when solving the problem of multi-robot task allocation, and reduces the task allocation efficiency.
The university of Nanjing discloses a multi-robot task allocation method of pre-allocation combined with Hungary algorithm in patent literature (application number: 201811385884.1 application date: 2018.11.20 application publication number: CN 109615188A) of Nanjing university. The method comprises the following specific steps: modeling the multi-robot system based on the model of role collaboration; and a second step of: establishing a benefit value matrix Q of all robots for bearing different tasks; and a third step of: optimizing the multi-robot system by judging whether the robots meet the allocation conditions; fourth step: simplifying the benefit value matrix; fifth step: deforming the benefit value matrix according to the number of robots required by each task; sixth step: pre-distributing tasks to obtain an initial distribution matrix T, and further simplifying a benefit value matrix; seventh step: and (3) processing the benefit value matrix simplified in the step (6) by using a Hungary algorithm to perform task allocation, obtaining a final allocation matrix T, and completing task allocation. The method has the defects that the method only aims at the structural environment to realize multi-robot task allocation under the addition of a limiting condition, and the problem of multi-robot task allocation under the unstructured environment such as rescue can not be solved.
The western engineering university discloses a task allocation method based on a task allocation coordination strategy and a particle swarm algorithm in patent literature filed by the western engineering university (application number: 201910980023.6, application date: 2019.10.15, application publication number: CN 110717684A). The method comprises the following specific steps: optimizing the distribution radius by using a particle swarm algorithm to obtain an initial distribution result; and a second step of: adjusting the initial allocation result by using a coordination strategy to finish the first allocation; and a third step of: repeating the first step to the second step, and re-distributing the unassigned tasks until the tasks are completely distributed. The method has the defects that when the method faces large-scale tasks and the number of robots, the particle swarm optimization is utilized to be prone to local convergence, so that the task allocation efficiency is limited, and the expansion is difficult.
Disclosure of Invention
The invention aims to solve the problems of unconsciousness, poor expandability and low allocation efficiency of a time window in a multi-robot task allocation method by providing a multi-robot task allocation method based on a chaotic self-adaptive dung beetle optimization algorithm.
The technical idea for realizing the purpose of the invention is as follows: the invention converts the multi-robot task allocation problem modeling into a combination optimization problem. Taking the travel cost, the time cost and the task completion income as evaluation indexes, taking task allocation constraint, resource type constraint, time window constraint and load constraint as constraint conditions, introducing task time attenuation characteristics, establishing a multi-robot task allocation model with time limitation requirements under the scene of meeting rescue and the like, and overcoming the problem that the multi-robot task allocation in unstructured environments such as rescue and the like cannot be solved in the prior art; according to the invention, a dung beetle optimization algorithm is introduced to solve the problem of task allocation of multiple robots, and the dung beetle optimization algorithm can perform parallelization processing, namely searching a plurality of possible solutions simultaneously. Meanwhile, the dung beetle optimizing algorithm has the characteristic of self-adaptive searching, and can be adjusted and optimized according to the complexity and scale of the problem. When facing large-scale tasks and robots, the algorithm can automatically adjust the search strategy to adapt to the tasks and robots with different scale numbers, so that the problem of poor expandability in the prior art is solved; the invention introduces chaotic mapping, self-adaptive t distribution variation and dynamic selection probability operators, improves the convergence rate of the algorithm and the capability of jumping out of the local optimal solution, and overcomes the problem of low distribution efficiency in the prior art.
The method comprises the following steps:
step 1, establishing a multi-robot task allocation objective function to be optimized meeting constraint conditions:
step 1.1, respectively constructing task constraint conditions, resource constraint conditions, time window constraint conditions and load constraint conditions in constraint conditions;
step 1.2, establishing a multi-robot task allocation objective function to be optimized as follows:
wherein F represents a multi-robot task allocation objective function, N v Indicating the total number of robots to be used,i represents the serial number of the robot, N t Represents the total number of tasks, j represents the serial number of the task, cost (V i ,T j ) Representing the ith robot V i Execute task T j j Is a stroke cost function of Re (V) i ,T j ) Indicated at the ith robot V i Execute task T j j Time jth task T j The benefit function of the decay in value over Time, time f Time cost function, w, representing completion of tasks by all robots 1 ，w 2 ，w 3 Are all weight coefficients, represent the importance of the functions, w 1 ，w 2 ，w 3 The value ranges are all 0,1]And satisfy w 1 +w 2 +w 3 ＝1；
Step 2, inputting the maximum iteration times and the population number of the dung beetles into a dung beetle optimization algorithm;
step 3, mapping the position of each dung beetle in the dung beetle population by utilizing the tone chaos;
step 4, calculating the fitness value of each dung beetle in the dung beetle population by taking a multi-robot task allocation objective function as a fitness value function, taking the minimum value in the fitness values of each dung beetle as a global extremum of the dung beetle population, taking the minimum fitness value in different iteration numbers of the same dung beetle as an individual extremum, comparing the fitness values of each dung beetle to obtain the global extremum of the dung beetle population, comparing the fitness values of different iteration numbers of the same dung beetle to obtain the individual extremum, and storing the individual extremum and the global extremum in the current iteration;
step 5, dividing the dung beetle population into four subgroups according to the proportion of 6:6:7:11, namely rolling balls, breeding, foraging and stealing, and updating the position of the dung beetle in each subgroup by utilizing a self-adaptive t distribution mutation operator and a dynamic selection probability P operator;
step 6, judging whether the maximum iteration times are reached, if so, taking the position of the dung beetles in the dung beetle population corresponding to the global extremum as the optimal position, and executing the step 7; otherwise, executing the step 3;
and 7, taking the optimal position of the dung beetle as a multi-robot task allocation result.
Compared with the prior art, the invention has the following advantages:
first, the invention considers the conditions such as time window constraint and the like in the multi-robot task allocation problem modeling process, introduces task time attenuation characteristics, and overcomes the problem that the time limitation problem in unstructured environments such as rescue cannot be solved when the multi-robot task allocation problem is processed in the prior art, so that the invention utilizes the established multi-robot task allocation problem model, and has wider coverage application scene and stronger universality and popularization when the multi-robot task allocation problem is solved.
Secondly, as the dung beetle optimizing algorithm is introduced to solve the problem of task allocation of multiple robots, the problem that the existing technology is difficult to expand when facing large-scale tasks and the number of robots is solved, so that the invention has the characteristics of parallelism and self-adaption, and when facing large-scale tasks and the number of robots, the algorithm can search for multiple groups simultaneously and automatically adjust the searching strategy so as to adapt to tasks and robots with different scale numbers, thereby being beneficial to improving the expandability of the algorithm.
Thirdly, because the invention introduces the fine chaotic map, the self-adaptive t distribution variation and the dynamic selection probability P operator into the dung beetle optimization algorithm, the problem that the task allocation of multiple robots is inefficient when the problem of the task allocation of the multiple robots is processed in the prior art is solved, so that the invention has higher convergence speed and the capability of jumping out local convergence when the optimal task allocation scheme is selected, and is beneficial to reducing the time of the task allocation of the multiple robots.
Drawings
FIG. 1 is a schematic view of a scene of an embodiment of the present invention;
FIG. 2 is a flow chart of the present invention;
FIG. 3 is a diagram illustrating task allocation results according to an embodiment of the present invention;
FIG. 4 is an iterative diagram of optimal fitness values according to an embodiment of the present invention;
FIG. 5 is an iterative schematic diagram of the optimal fitness value of each algorithm obtained in the simulation experiment 1 of the present invention;
fig. 6 is a schematic diagram showing comparison of optimal fitness values and average fitness values of each algorithm under different scale scenes of the simulation experiment 2.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
An implementation scenario of an embodiment of the present invention is further described with reference to fig. 1.
The embodiment of the invention comprises 4 heterogeneous robots V in a rescue scene with the number of robots smaller than the number of tasks 1 ～V 4 12 target tasks T involved in rescue 1 ～T 12 The robot and task initiation information are shown in tables 1 and 2, respectively. The initial information described in table 1 includes initial position information of the robot and related constraints, and the initial information described in table 2 includes initial position information of the task, task value information and related constraints. The numbers 1-12 in fig. 2 represent the serial numbers of 12 corresponding tasks, 12 pentagrams represent the positions of the tasks, and circles represent the 3 resources (water, drugs, and clothing) of the type required for the tasks. If task 6 has three circles of different sizes, this means that task 6 requires 3 resources. In the figure, c1=111 indicates that the robot 1 can provide three resources, 1 is carrying this type of resource, 0 is not carrying, and reference is made to table 1 for details.
Table 1 robot initial information list
Table 2 task initiation information list
The implementation steps of the embodiment of the present invention will be further described with reference to fig. 2.
And step 1, establishing a multi-robot task allocation objective function to be optimized, wherein the multi-robot task allocation objective function meets constraint conditions.
And 1.1, respectively constructing task constraint conditions, resource constraint conditions, time window constraint conditions and load constraint conditions in the constraint conditions.
The task constraint conditions are as follows:
wherein ,xij Representing task constraint parameters, when x ij When=1, it represents the j-th task T j Is ith robot V i Execute, when x ij When=0, it represents the j-th task T j Is not by the ith robot V i And executing.
Because each heterogeneous robot carries different resources, different target tasks also have different resource demands, and the robot carrying the corresponding resources can meet the corresponding target task demands.
The resource constraint conditions are as follows:
wherein ,SVi Representing the resource type carried by the ith robot, ST j Representing the resource type requirement of the jth target task, and n is the intersection operation,representing an empty set.
In the embodiment of the invention, the types of the robot carried resources are detailed in a table 1, and the types of the task resource requirements are detailed in a table 2.
Since the target task is required to be completed within the time window, the time window constraint is set as follows:
wherein ,indicating the occurrence time of the jth target task, t ij Representing the ith robotTime of starting execution of jth target task aim _ddl j Representing the deadline of the jth target task.
The values of the task time window in the embodiment of the invention are shown in Table 2 in detail.
Because the load capacity of the robot is limited, only a limited number of tasks can be executed in each task executing process, and therefore the number of assigned tasks cannot exceed the upper limit of the capacity. Meanwhile, in order to improve the utilization rate of the robots in the task execution process, the time for completing the tasks is ensured to meet the minimum, each robot executes at least one task, and the load constraint conditions in step 1.1 are as follows:
wherein ,Pi max Representing the maximum number of i-th robots that can perform the target task. P in the embodiment of the invention i max The values are shown in Table 1.
Step 1.2, establishing a multi-robot task allocation objective function to be optimized as follows:
wherein F represents a multi-robot task allocation objective function, N v Indicating the total number of robots, i indicates the serial number of the robots, N t Represents the total number of tasks, j represents the serial number of the task, cost (V i ,T j ) Representing the ith robot V i Execute task T j j Is a stroke cost function of Re (V) i ,T j ) Indicated at the ith robot V i Execute task T j j Time jth task T j The benefit function of the decay in value over Time, time f Time cost function, w, representing completion of tasks by all robots 1 ，w 2 ，w 3 Are all weight coefficients, represent the importance of the functions, w 1 ，w 2 ，w 3 The value ranges are all 0,1]And satisfy w 1 +w 2 +w 3 ＝1。
The travel cost function is as follows:
wherein dis {.cndot. } represents the operation of taking Euclidean distance, x I Indicating the departure position of the ith robot, in the embodiment of the invention, the departure positions of the 4 robots are (0.5 ) and T i 1 Representing the ith robot V i The first task to be executed in the task sequence, |·| represents the absolute value operation, m o Represents the total number of tasks to be performed in the task sequence, c represents the ith robot V i The serial number of the task to be executed in the task sequence.
Because the two-dimensional plane is considered in the embodiment of the invention, the coordinate values are set based on the two-dimensional plane, the values of the position coordinates of the robot and the task are shown in the tables 1 and 2 respectively, and the travel cost function can be expanded to space scenes such as the three-dimensional plane.
The benefit function is as follows:
wherein ,Pij Representing the ith robot V i Execute task T j j Capability value coefficient, P ij The value range is (0, 1), x ij Representing task constraint parameters, when x ij When=1, it represents the j-th task T j Is ith robot V i Execute, when x ij When=0, it represents the j-th task T j Is not by the ith robot V i Execution, value (T j ) Representing the jth task T j Value of e (·) Represents an exponential operation based on a natural constant e, μ j Representing the jth task T j Is a time-decay characteristic influencing factor of (a),representing the jth task T j In the present embodiment of the invention, the capability value coefficient P ij The values are all 0.5, and the task Value (T j ) The values of (a) are shown in Table 2, mu j ＝5e -4 。
The time cost function is as follows:
wherein ,representing the kth task T k Completion time of->Representing task T of the first kind l Is executed at the start of the execution time.
And 2, inputting the maximum iteration times 30 and the population number 60 of the dung beetles into a dung beetle optimization algorithm.
And 3, utilizing the site chaotic map of each dung beetle in the dung beetle population, wherein the positions and the solution spaces of the dung beetles are continuous in a dung beetle optimizing algorithm, and however, in the problem of multi-robot task allocation, the task allocation solution is a discrete value. In the problem of multi-robot task allocation, the number of robots is N v The target task number is N t So in the dung beetle optimizing algorithm, the position dimension of the dung beetle is N t Each dung beetle corresponds to a potential target task allocation solution. Therefore, the invention designs the encoding and decoding process of the dung beetles based on the dung beetle optimization algorithm, and adopts a real number encoding mode to enable the nth dung beetle position X n Is N t The real number vector is maintained, and an upper limit and a lower limit [1, N ] are set v +1), ensure the nth dung beetle position X n Updated within its scope. Due to X in the encoding process n Is N t Vector of dimension real number, X n There is an integer part and a fractional part, so the design decoding process is as follows: let X n (IN) is X n Integer part of X n (DE) is X n Fractional part of (a), for example: 8.75 (IN) = 8,8.75 (DE) =0.75. X is X n (IN j ) =i may represent a task allocation potential solution, i.e. the j-th task T j Assigned to the ith robot V i . In task allocation, X may occur n′ (IN s )＝···＝X n (IN j ) That is, the integer parts of the positions of the plurality of dung beetles are equal, so the following is specified: it is first determined by the integer part X (IN) of the position vector X which tasks are to be assigned to the same robot, and then the size sorting is performed by the fractional part X (DE) of the position vector X, the bigger the fractional part, i.e. the same robot performs the task first.
The position of the dung beetle refers to a task allocation solution in the invention, and the position of each dung beetle is represented by a vector, in this embodiment, N v ＝4，N t =12, i.e. nth dung beetle position X n Is a twelve-dimensional real vector updated in [1, 5). Each element in the vector represents a task, the integer part of the element in the vector represents the number of the assigned robot, and the decimal part represents the execution order of the assigned robot. The position of each dung beetle is mapped by the following formula:
wherein ,Xn,S Represents the position of the nth dung beetle after being subjected to the Sine chaotic mapping, S represents chaotic mapping operation, n represents the serial number of the dung beetle,representing the mapping coefficient->Pi represents the circumference ratio, X n And representing the position before chaotic mapping of the nth dung beetle.
And 4, calculating the fitness value of each dung beetle in the dung beetle population by taking a multi-robot task allocation objective function as a fitness value function, taking the minimum value in the fitness values of each dung beetle as the global extremum of the dung beetle population, taking the minimum fitness value in different iteration numbers of the same dung beetle as the individual extremum, comparing the fitness values of each dung beetle to obtain the global extremum of the dung beetle population, comparing the fitness values of different iteration numbers of the same dung beetle to obtain the individual extremum, and storing the individual extremum and the global extremum in the current iteration.
And 5, dividing the dung beetle population into four subgroups according to the ratio of 6:6:7:11, namely rolling balls, breeding, foraging and stealing, and updating the position of the dung beetle in each subgroup by utilizing a self-adaptive t distribution mutation operator and a dynamic selection probability P operator.
The dung beetle position updating is completed by the following formula.
Using a dynamic selection probability P operator, the P operator is defined as follows:
P＝q 1 -q 2 ×(T max -iter)/T max
wherein ,q1 Representing coefficients that can influence the upper bound of the dynamic selection probability P operator, q 2 Representing coefficients that can affect the dynamic selection probability P operator lower bound.
Q in the examples of the invention 1 ＝0.5，q 2 ＝0.2。
Generating random numbers rand within the range of (0, 1), and if rand is more than P, performing adaptive t distribution variation operation on positions of four sub-groups of dung beetles for rolling balls, breeding, foraging and stealing to disturb; otherwise, the adaptive t-distribution mutation operation is not executed, and the four sub-group position updating formulas are as follows:
the position updating formula of the ball dung beetle subgroup is as follows:
the adaptive t-distribution mutation operation is not performed:
performing an adaptive t-distribution mutation operation:
wherein ,represents the position of the nth dung beetle in t+1 iterations, t represents the iteration times, alpha represents the natural coefficient value of 1 or-1, k represents the defect coefficient, and k is epsilon (0,0.2)]B represents the light intensity coefficient, b E (0, 1), X w Represents the global worst position, deltaX represents the analog light intensity variation, & lt + & gt>The position of the rolling ball dung beetle at t+1 iterations after the nth dung beetle executes the adaptive t distribution variation disturbance operation is represented, t' represents the execution of the adaptive t distribution variation operation, t (iter) represents t distribution taking the algorithm iteration number as the parameter degree of freedom, and iter represents the current iteration number.
The dancing dung beetle subgroup position updating formula is as follows:
the adaptive t-distribution mutation operation is not performed:
performing an adaptive t-distribution mutation operation:
Lb * ＝max(X * ×(1-R),Lb)
Ub * ＝min(X * ×(1+R),Ub)
R＝1-t/T max
wherein θ represents the angle, θ ε [0,180 ].
The position updating formula of the breeding dung beetle subgroup is as follows:
the adaptive t-distribution mutation operation is not performed:
performing an adaptive t-distribution mutation operation:
Lb * ＝max(X * ×(1-R),Lb)
Ub * ＝min(X * ×(1+R),Ub)
R＝1-t/T max
wherein ,X* Indicating the current local optimum position, lb * and Ub* Respectively represent the lower bound and the upper bound of the oviposition area of the dung beetles, T max Representing the maximum number of iterations, lb and Ub represent the lower and upper bounds of the optimization problem, b 1 and b2 Representing a size of 1 XN t Is independent of two a random vector.
The foraging dung beetle position updating formula is as follows:
the adaptive t-distribution mutation operation is not performed:
performing an adaptive t-distribution mutation operation:
Lb b ＝max(X b ×(1-R),Lb)
Ub b ＝min(X b ×(1+R),Ub)
wherein ,Xb Representing the global optimum position, lb b and Ubb Respectively representing the lower bound and the upper bound of the foraging area of the dung beetles, c 1 Representing random numbers subject to normal distribution, c 2 Representing a random number, c 2 ∈(0,1)。
The position updating formula of the thief dung beetle subgroup is as follows:
the adaptive t-distribution mutation operation is not performed:
performing an adaptive t-distribution mutation operation:
wherein g represents 1 XN subject to normal distribution t S represents a constant.
Step 6, judging whether the maximum iteration times are reached, if so, obtaining the optimal position of the dung beetles and executing the step 7; otherwise, executing the step 3, wherein the optimal position is the position of the dung beetle in the dung beetle population corresponding to the global extremum.
And 7, taking the optimal position of the dung beetle as a multi-robot task allocation result.
FIG. 3 is an iterative schematic diagram of optimal fitness values of a dung beetle in an embodiment of the present invention, where the abscissa represents a first dimensionless value of a position coordinate and the ordinate represents a second dimensionless value of the position coordinate. In the embodiment of the invention, the optimal position of the dung beetle corresponding to the optimal fitness value when reaching the maximum iteration isThe multi-machine task allocation result can be obtained through the step 3, and table 4 shows the multi-machine task allocation result in the embodiment of the present invention, and the number in table 4 indicates the task number, such as<12,2,10>Representing robot V 1 Assigned to task T 12 ，T 2 and T10 Wherein the order in the table indicates the order of executing the tasks, robot V 1 First execute task T 12 At the execution of task T 2 Finally execute task T 10 . Fig. 4 is a schematic diagram of task allocation results combined with table 3 according to an embodiment of the present invention.
TABLE 3 task assignment results
The effect of the present invention can be further demonstrated by the following simulation.
1. And (5) simulating experimental conditions.
The software platform of the simulation experiment of the invention is: windows 11 operating system and Matlab R2021b.
The hardware platform of the simulation experiment of the invention is: the processor is an Intel i7 9750H CPU, the main frequency is 2.6GHz, and the memory is 16 GB.
2. And (5) analyzing simulation content and results.
The simulation experiment of the invention has two.
The simulation experiment 1 is a simulation comparison experiment for carrying out multi-robot task allocation by adopting the method and the comparison method under a rescue scene.
The simulation experiment 1 of the invention considers that under one rescue scene, 12 target tasks T needing rescue exist in the scene 1 ～T 12 4 heterogeneous robots V 1 ～V 4 And participate in rescue. The task and robot initial information are shown in tables 4 and 5. The initial information described in table 4 includes initial position information of the robot and related constraints, and the initial information described in table 5 includes initial position information of the task, task value information, and related constraints. To simplify the experimental scenario, it is assumed that each robot is traveling at a uniform speed. Given initial conditions, the maximum iteration times of the 5 algorithms adopted in the simulation experiment 1 of the invention are all T max =500, at the same time, let w to balance the effect of task income, travel cost and time cost 1 ＝w 2 ＝w 3 A population 60 is given.
Table 4 simulation experiment 1 robot initial information list
Table 5 list of initial task information for simulation experiment 1
The simulation experiment 1 of the invention adopts the method of the invention to adapt to the chaotic dung beetle optimization algorithm (t-SDBO), and three prior art: particle Swarm Optimization (PSO), sparrow Search Algorithm (SSA) and dung beetle optimization algorithm (DBO), the improved dung beetle optimization algorithm (SDBO) in the prior art respectively obtains the optimal fitness value under 500 iterations, and the relationship between the obtained optimal fitness value and the iteration times is drawn into five curves as shown in FIG. 5.
In simulation experiment 1, three prior art techniques and one improvement of the prior art techniques are:
in the prior art 1, niu Longhui et al propose a multi-robot task allocation method based on a particle swarm algorithm in a paper published by the Niu Longhui et al, namely storage multi-robot task allocation combined with a particle swarm algorithm and task allocation coordination strategy (university of western security, university of engineering, 2020,34 (06): 73-79).
The prior art 2 refers to a task scheduling method based on a sparrow search algorithm, which is proposed in a patent application document (application number: CN202011027749.7, application publication number: CN 112199172A) applied by Guilin university in the university of Italian university, which is a hybrid task scheduling method for heterogeneous multi-core processors.
Prior art 3 refers to the dung beetle optimization algorithm as proposed by Xue et al in its published paper "Dung beetle optimizer:a new meta-heuristic algorithm for global optimization" (The Journal of Supercomputing,2023,79 (7): 7305-7336).
The improvement method of the existing method is that the fine chaotic mapping is introduced in the population initialization based on the prior art 3.
The simulation experiment 2 is used for comprehensively verifying the capability of the invention in solving the task allocation problem of multiple robots.
The experimental data set used in the simulation experiment 2 of the invention distributes a problem data set for randomly generated multi-robot tasks, wherein the problem data set comprises the position of a target task, required resources, a task time window and task value, and provided resources and capability coefficients of the robot.
The method and three prior arts adopted in the simulation experiment 2 of the present invention respectively obtain the optimal fitness value and the average fitness value of the multi-robot task allocation under different scales, and then the relationship between the obtained optimal fitness value and the average fitness value and the different scale scenes is drawn into four curves as shown in fig. 6, wherein fig. 6 (a) is a schematic diagram of the optimal fitness value of the multi-robot task allocation under different scales of each algorithm, and fig. 6 (b) is a schematic diagram of the average fitness value of the multi-robot task allocation under different scales of each algorithm.
In simulation experiment 2, three prior art techniques were used that are identical to simulation experiment 1.
The effects of the present invention are further described below with reference to fig. 5 and 6.
In fig. 5, the abscissa represents the number of iterations of the algorithm, in units of times, and the ordinate represents the fitness value. The curve of the light blue solid line in fig. 5 shows the relationship between the optimal fitness value and the iteration number of the present invention, the curve of the green dot drawn line shows the relationship between the optimal fitness value and the iteration number of the prior art 1, the curve of the blue dot drawn line shows the relationship between the optimal fitness value and the iteration number of the prior art 2, the curve of the black dot drawn line shows the relationship between the optimal fitness value and the iteration number of the prior art 3, and the curve of the red solid line with a circle shows the relationship between the optimal fitness value and the iteration number of the improved method of the prior art 3.
As can be seen from fig. 5: the PSO algorithm has a certain difference with other 4 algorithms in terms of local searching and global optimizing capability; the SSA algorithm optimizes the convergence speed at the early stage faster, but falls into local convergence soon; it can be seen that the DBO algorithm can obtain a better optimization effect before being improved, but is easy to fall into local convergence; compared with DBO, the SDBO algorithm obtains better optimization effect, and proves the effectiveness of the Sine chaotic mapping. The t-SDBO algorithm provided by the invention shows better performance than other 4 algorithms no matter from the optimized result, the earlier convergence speed or the capability of jumping out of local convergence, and shows the feasibility of the t-SDBO in solving the problem of multi-robot task allocation. The programs of the 5 algorithms were run 10 times each, and the average fitness value, the optimal fitness value, and the solving time are shown in table 6.
From the results in table 6, it can be seen that the average fitness value 4.3556 and the optimal fitness value 4.3213 of the t-SDBO algorithm are each better performing than the other 4 algorithms.
Table 6 comparison table of average fitness value and optimal fitness value for different algorithms
The abscissa in fig. 6 (a) represents a scene of different scale, e.g., MRTA0310 on the abscissa represents a scene in which 3 robots perform 10 tasks. The ordinate indicates the fitness minimum. Wherein, the broken line of the red asterisk solid line represents the relation broken line of the optimal fitness value and the different scale scenes of the invention, the broken line of the green circle solid line represents the relation broken line of the optimal fitness value and the different scale scenes of the prior art 1, the broken line of the blue plus solid line represents the relation broken line of the optimal fitness value and the different scale scenes of the prior art 2, and the light blue plus solid line represents the relation broken line of the optimal fitness value and the different scale scenes of the prior art 3.
In fig. 6 (b), the abscissa represents scenes of different scales, and the ordinate represents the fitness average. Wherein, the broken line of the red asterisk solid line represents the relation broken line of the average fitness value and the different scale scenes of the invention, the broken line of the green circle solid line represents the relation broken line of the average fitness value and the different scale scenes of the prior art 1, the broken line of the blue plus solid line represents the relation broken line of the average fitness value and the different scale scenes of the prior art 2, and the broken line of the light blue plus solid line represents the relation broken line of the average fitness value and the different scale scenes of the prior art 3.
As can be seen from fig. 6: under 5 experimental scenes, when the solution space is smaller, the performance difference of each algorithm is smaller, but as the number of tasks and the number of robots are increased, the difference of each algorithm is also obviously different, and the t-SDBO algorithm provided by the invention obtains the optimal effect under different problem scales.
Claims (10)
1. A multi-robot task allocation method based on a chaotic self-adaptive dung beetle optimization algorithm is characterized in that a multi-robot task allocation objective function to be optimized meeting constraint conditions is established, the position of each dung beetle in a dung beetle population is mapped by using a fine chaotic map in the dung beetle optimization algorithm, and the position of the dung beetle in each subgroup is updated by using a self-adaptive t distribution mutation operator and a dynamic selection probability P operator; the steps of the allocation method include the following:
step 1, establishing a multi-robot task allocation objective function to be optimized meeting constraint conditions:
step 1.1, respectively constructing task constraint conditions, resource constraint conditions, time window constraint conditions and load constraint conditions in constraint conditions;
step 1.2, establishing a multi-robot task allocation objective function to be optimized as follows:
wherein F represents a multi-robot task allocation objective function, N v Indicating the total number of robots, i indicates the serial number of the robots, N t Represents the total number of tasks, j represents the serial number of the task, cost (V i ,T j ) Representing the ith robot V i Execute task T j j Is a stroke cost function of Re (V) i ,T j ) Indicated at the ith robot V i Execute task T j j Time jth task T j The benefit function of the decay in value over Time, time f Time cost function, w, representing completion of tasks by all robots 1 ，w 2 ，w 3 Are all weight coefficients, represent the importance of the functions, w 1 ，w 2 ，w 3 The value ranges are all 0,1]And satisfy w 1 +w 2 +w 3 ＝1；
Step 2, inputting the maximum iteration times and the population number of the dung beetles into a dung beetle optimization algorithm;
step 3, mapping the position of each dung beetle in the dung beetle population by utilizing the tone chaos;
step 4, calculating the fitness value of each dung beetle in the dung beetle population by taking a multi-robot task allocation objective function as a fitness value function, taking the minimum value in the fitness values of each dung beetle as a global extremum of the dung beetle population, taking the minimum fitness value in different iteration numbers of the same dung beetle as an individual extremum, comparing the fitness values of each dung beetle to obtain the global extremum of the dung beetle population, comparing the fitness values of different iteration numbers of the same dung beetle to obtain the individual extremum, and storing the individual extremum and the global extremum in the current iteration;
step 5, dividing the dung beetle population into four subgroups according to the proportion of 6:6:7:11, namely rolling balls, breeding, foraging and stealing, and updating the position of the dung beetle in each subgroup by utilizing a self-adaptive t distribution mutation operator and a dynamic selection probability P operator;
step 6, judging whether the maximum iteration times are reached, if so, taking the position of the dung beetles in the dung beetle population corresponding to the global extremum as the optimal position, and executing the step 7; otherwise, executing the step 3;
and 7, taking the optimal position of the dung beetle as a multi-robot task allocation result.
2. The multi-robot task allocation method based on the chaotic self-adaptive dung beetle optimization algorithm of claim 1, wherein the task constraint conditions in the step 1.1 are as follows:
wherein ,xij Representing task constraint parameters, when x ij When=1, it represents the j-th task T j Is ith robot V i Execute, when x ij When=0, it represents the j-th task T j Is not by the ith robot V i And executing.
3. The multi-robot task allocation method based on the chaotic self-adaptive dung beetle optimization algorithm of claim 1, wherein the resource constraint condition in the step 1.1 is as follows:
wherein ,SVi Representing the resource type carried by the ith robot, ST j Representation ofThe resource type requirement of the j-th task, and is the intersection operation,representing an empty set.
4. The multi-robot task allocation method based on the chaotic self-adaptive dung beetle optimization algorithm of claim 2, wherein the time window constraint condition in the step 1.1 is as follows:
wherein ,represent the occurrence time of the jth task, t ij Representing the time when the ith robot starts to perform the jth task, aim _ddl j Representing the deadline of the j-th task.
5. The multi-robot task allocation method based on the chaotic self-adaptive dung beetle optimization algorithm of claim 2, wherein the load constraint conditions in the step 1.1 are as follows:
wherein ,Pi max Representing the total number of execution tasks determined by the ith robot performance coefficient.
6. The multi-robot task allocation method based on the chaotic self-adaptive dung beetle optimization algorithm of claim 1, wherein the travel cost function in the step 1.2 is as follows:
wherein dis {.cndot. } represents the operation of taking Euclidean distance, x I Indicating the departure position of the ith robot, T i 1 Representing the ith robot V i The first task to be executed in the task sequence, |·| represents the absolute value operation, m o Represents the total number of tasks to be performed in the task sequence, c represents the ith robot V i The serial number of the task to be executed in the task sequence.
7. The multi-robot task allocation method based on the chaotic self-adaptive dung beetle optimization algorithm of claim 4, wherein the benefit function in the step 1.2 is as follows:
wherein ,Pij Representing the ith robot V i Execute task T j j Capability value coefficient, P ij The Value range is (0, 1), value (T j ) Representing the jth task T j Value of e () Represents an exponential operation based on a natural constant e, μ j Representing the jth task T j A time decay characteristic influence factor of (2).
8. The multi-robot task allocation method based on the chaotic self-adaptive dung beetle optimization algorithm of claim 1, wherein the time cost function in the step 1.2 is as follows:
wherein ,representing the kth task T k Completion time of->Representing task T of the first kind l Is executed at the start of the execution time.
9. The multi-robot task allocation method based on the chaotic self-adaptive dung beetle optimization algorithm of claim 1, wherein the position of each dung beetle mapped by the fine chaotic map in the step 3 is completed by the following formula:
wherein ,Xn,S Represents the position of the nth dung beetle after being subjected to the Sine chaotic mapping, S represents chaotic mapping operation, n represents the serial number of the dung beetle,representing the mapping coefficient->Pi represents the circumference ratio, X n And representing the position before chaotic mapping of the nth dung beetle.
10. The method for distributing tasks to multiple robots based on a chaotic self-adaptive dung beetle optimization algorithm as claimed in claim 1, wherein the updating of the dung beetle position in the step 5 is accomplished by the following formula:
introducing a dynamic selection probability P operator, wherein the P operator is defined as follows:
P＝q 1 -q 2 ×(T max -iter)/T max
wherein ,q1 Representing coefficients that can influence the upper bound of the dynamic selection probability P operator, q 2 Representing coefficients that can affect the dynamic selection probability P operator lower bound;
generating random numbers rand within the range of (0, 1), and if rand is more than P, performing adaptive t distribution variation operation on positions of four sub-groups of dung beetles for rolling balls, breeding, foraging and stealing to disturb; otherwise, the adaptive t-distribution mutation operation is not executed, and the four sub-group position updating formulas are as follows:
the position updating formula of the ball dung beetle subgroup is as follows:
the adaptive t-distribution mutation operation is not performed:
performing an adaptive t-distribution mutation operation:
wherein ,represents the position of the nth dung beetle in t+1 iterations, t represents the iteration times, alpha represents the natural coefficient value of 1 or-1, k represents the defect coefficient, and k is epsilon (0,0.2)]B represents the light intensity coefficient, b E (0, 1), X w Represents the global worst position, deltaX represents the analog light intensity variation, & lt + & gt>The method comprises the steps of representing the position of a ball dung beetle in t+1 iterations after disturbance of self-adaptive t distribution variation, t' representing execution of self-adaptive t distribution variation operation, t (iter) representing t distribution taking the number of algorithm iterations as a parameter degree of freedom, and iter representing the current number of iterations;
the dancing dung beetle subgroup position updating formula is as follows:
the adaptive t-distribution mutation operation is not performed:
performing an adaptive t-distribution mutation operation:
Lb * ＝max(X * ×(1-R),Lb)
Ub * ＝min(X * ×(1+R),Ub)
R＝1-t/T max
wherein θ represents the angle, θ ε [0,180 ];
the position updating formula of the breeding dung beetle subgroup is as follows:
the adaptive t-distribution mutation operation is not performed:
performing an adaptive t-distribution mutation operation:
wherein ,X* Indicating the current local optimum position, lb * and Ub* Respectively represent the lower bound and the upper bound of the oviposition area of the dung beetles, T max Representing the maximum number of iterations, lb and Ub represent the lower and upper bounds of the optimization problem, b 1 and b2 Representing a size of 1 XN t Is a random vector of two independent random vectors;
the foraging dung beetle position updating formula is as follows:
the adaptive t-distribution mutation operation is not performed:
performing an adaptive t-distribution mutation operation:
Lb b ＝max(X b ×(1-R),Lb)
Ub b ＝min(X b ×(1+R),Ub)
wherein ,Xb Representing the global optimum position, lb b and Ubb Respectively representing the lower bound and the upper bound of the foraging area of the dung beetles, c 1 Representing random numbers subject to normal distribution, c 2 Representing a random number, c 2 ∈(0,1)；
The position updating formula of the thief dung beetle subgroup is as follows:
the adaptive t-distribution mutation operation is not performed:
performing an adaptive t-distribution mutation operation:
wherein g represents 1 XN subject to normal distribution t S represents a constant.
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| CN117591849A (en) * | 2024-01-18 | 2024-02-23 | 南京先维信息技术有限公司 | Feature selection method and system for high-dimensional network flow data |
| CN117973218A (en) * | 2024-02-26 | 2024-05-03 | 太原科技大学 | Speed reducer design method based on multi-strategy improved dung beetle algorithm |
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| CN117339980A (en) * | 2023-10-18 | 2024-01-05 | 淮阴工学院 | Polylactic acid enzyme ocean garbage degradation control method and system |
| CN117591849A (en) * | 2024-01-18 | 2024-02-23 | 南京先维信息技术有限公司 | Feature selection method and system for high-dimensional network flow data |
| CN117591849B (en) * | 2024-01-18 | 2024-04-05 | 南京先维信息技术有限公司 | Feature selection method and system for high-dimensional network flow data |
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