Multi-robot task allocation method based on chaotic adaptive melolontha optimization algorithm

Abstract

The application discloses a kind of multi-robot task allocation methods based on chaotic adaptive melolontha optimization algorithm, mainly solve the problems of not considering time window constraint, poor scalability and inefficient allocation in multi-robot task allocation method.The implementation steps of the application are as follows: establishing the multi-robot task allocation objective function to be optimized that meets the constraint condition;initializing algorithm parameters;initializing the position of each melolontha in melolontha population;calculating the fitness value of each melolontha;updating the position of each melolontha;when the maximum number of iterations is reached, the best position of the melolontha is taken as the multi-robot task allocation result as output.The application solves the multi-robot task allocation problem through chaotic adaptive melolontha optimization algorithm, improves the quality and efficiency of multi-robot task allocation, and effectively solves the above problems existing in multi-robot task allocation method.

Description

Technical Field

[0001] This invention belongs to the field of robotics technology, and more specifically relates to a multi-robot task allocation method based on a chaotic adaptive dung beetle optimization algorithm within the field of multi-robot task allocation technology. This invention can be applied to multi-robot systems composed of drones, unmanned surface vessels (USVs), and other similar systems, enabling the effective allocation of a set of tasks to multiple heterogeneous robots to achieve efficient system collaboration. Background Technology

[0002] In recent years, robots have played an increasingly important role in both military and civilian fields. However, with the continuous increase in task requirements, a single robot often struggles to complete complex tasks independently, thus giving rise to multi-robot systems. In multi-robot systems, task allocation is a key technology, involving how to effectively distribute a set of tasks among multiple robots to achieve efficient system collaboration. For example, in service robots, industrial robots, and autonomous driving, reasonable task allocation can improve the overall efficiency of these systems. In particular, autonomous driving technology has been widely used in scenarios such as ground search and rescue, express delivery, surveying, surveillance, and exploration. There are three main existing methods for multi-robot task allocation. The first is based on traditional algorithms, which are mostly designed for specific structured problems but struggle to solve medium- to large-scale multi-robot task allocation problems. The second is based on reinforcement learning algorithms, which have advantages such as fast solution speed and strong model generalization ability, but suffer from problems such as long pre-training time and difficulty in designing reward functions. The third type is the task allocation method based on intelligent optimization algorithms. These algorithms simulate the cooperative behavior of biological groups in nature and have received widespread attention due to their simplicity, ease of implementation, and robustness. However, when solving the multi-robot task allocation problem, they are prone to getting trapped in local optima, which reduces the efficiency of task allocation.

[0003] Nanjing University of Science and Technology disclosed a method for pre-allocation of multi-robot tasks combined with the Hungarian algorithm in its patent application "A pre-allocation method for multi-robot task allocation using the Hungarian algorithm" (Application No.: 201811385884.1, Application Date: 2018.11.20, Publication No.: CN 109615188A). The specific steps of this method are as follows: First, model the multi-robot system based on a role-cooperation model; second, establish a benefit value matrix Q for all robots undertaking different tasks; third, optimize the multi-robot system by determining whether the robots meet the allocation conditions; fourth, simplify the benefit value matrix; fifth, transform the benefit value matrix according to the number of robots required for each task; sixth, pre-allocate tasks to obtain an initial allocation matrix T, and further simplify the benefit value matrix; seventh, use the Hungarian algorithm to process the simplified benefit value matrix from step 6 to allocate tasks, obtaining the final allocation matrix T, thus completing the task allocation. The limitation of this method is that it only addresses multi-robot task allocation under restrictive conditions in structured environments and cannot solve multi-robot task allocation problems in unstructured environments such as rescue operations.

[0004] Xi'an University of Engineering disclosed a task allocation method based on a task allocation coordination strategy and a particle swarm optimization algorithm in its patent application "A Task Allocation Method Based on Task Allocation Coordination Strategy and Particle Swarm Optimization Algorithm" (Application No.: 201910980023.6, Application Date: 2019.10.15, Publication No.: CN110717684 A). The specific steps of this method are: First, optimize the allocation radius using the particle swarm optimization algorithm to obtain an initial allocation result; second, adjust the initial allocation result using a coordination strategy to complete the first allocation; third, repeat steps one and two to redistribute unallocated tasks until all tasks are fully allocated. The drawback of this method is that when facing large-scale tasks and a large number of robots, the particle swarm optimization algorithm is prone to getting stuck in local convergence, resulting in limited task allocation efficiency and difficulty in scaling. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the existing technology by proposing a multi-robot task allocation method based on the chaotic adaptive dung beetle optimization algorithm, which solves the problems of not considering time window constraints, poor scalability, and inefficient allocation in multi-robot task allocation methods.

[0006] The technical approach to achieving the objectives of this invention is as follows: This invention transforms the multi-robot task allocation problem into a combinatorial optimization problem. It considers travel cost, time cost, and task completion reward as evaluation indicators, and uses task allocation constraints, resource type constraints, time window constraints, and load constraints as constraints. By introducing task time decay characteristics, a multi-robot task allocation model with time-limited requirements for scenarios such as rescue is established, overcoming the inability of existing technologies to solve multi-robot task allocation problems in unstructured environments such as rescue. This invention introduces the dung beetle optimization algorithm to solve the multi-robot task allocation problem. The dung beetle optimization algorithm can be parallelized, i.e., it searches multiple possible solutions simultaneously. Furthermore, the dung beetle optimization algorithm has adaptive search characteristics, which can be adjusted and optimized according to the complexity and scale of the problem. When facing large-scale tasks and a large number of robots, the algorithm can automatically adjust its search strategy to adapt to different scales of tasks and robots, overcoming the poor scalability problem in existing technologies. This invention introduces chaotic mapping, adaptive t-distribution mutation, and dynamic selection probability operators, improving the algorithm's convergence speed and ability to escape local optima, overcoming the inefficient allocation problem in existing technologies.

[0007] The steps of this invention include the following:

[0008] Step 1: Establish the objective function for multi-robot task allocation that satisfies the constraints:

[0009] Step 1.1: Construct the task constraints, resource constraints, time window constraints, and load constraints in the constraint conditions respectively;

[0010] Step 1.2, establish the objective function for multi-robot task allocation to be optimized as follows:

[0011]

[0012] in, This represents the objective function for multi-robot task allocation. This represents the total number of robots. Indicates the robot's serial number. Indicates the total number of tasks. Indicates the task number. Indicates the first A robot Execute the Task The journey cost function, Indicates the first A robot Execute the Task Time Task The value of a payoff function decays over time. This represents the time cost function for all robots to complete the task. , , These are all weighting coefficients, representing the importance of each of the above functions. , , The range of values ​​is And satisfy ;

[0013] Step 2: Input the maximum number of iterations and the population size of dung beetles into the dung beetle optimization algorithm;

[0014] Step 3: Use Sine chaos mapping to map the position of each dung beetle in the dung beetle population;

[0015] Step 4: Use the multi-robot task allocation objective function as the fitness value function to calculate the fitness value of each dung beetle in the dung beetle population. Take the minimum fitness value of each dung beetle as the global extreme value of the dung beetle population. Take the minimum fitness value of the same dung beetle in different iterations as the individual extreme value. Compare the fitness values ​​of each dung beetle to obtain the global extreme value of the dung beetle population. Compare the fitness values ​​of the same dung beetle in different iterations to obtain the individual extreme value. Save the individual extreme value and the global extreme value at the current iteration.

[0016] Step 5: Divide the dung beetle population into four subgroups in a ratio of 6:6:7:11: rolling, breeding, foraging, and stealing. Use the adaptive t-distribution mutation operator and the dynamic selection probability P operator to update the position of the dung beetles in each subgroup.

[0017] Step 6: Determine if the maximum number of iterations has been reached. If so, take the position of the dung beetle in the dung beetle population corresponding to the global extremum as the optimal position and proceed to Step 7; otherwise, proceed to Step 3.

[0018] Step 7: Use the optimal position of the dung beetle as the result of multi-robot task allocation.

[0019] Compared with the prior art, the present invention has the following advantages:

[0020] First, because the present invention considers conditions such as time window constraints in the modeling process of multi-robot task allocation problem and introduces task time decay characteristics, it overcomes the problem that the existing technology cannot solve the time-limited problem in unstructured environments such as rescue when dealing with multi-robot task allocation problem. As a result, the multi-robot task allocation problem model established by the present invention covers a wider range of application scenarios and has stronger versatility and extensibility when solving multi-robot task allocation problem.

[0021] Secondly, because this invention introduces the dung beetle optimization algorithm to solve the multi-robot task allocation problem, it overcomes the problem that existing technologies are difficult to scale when facing large-scale tasks and a large number of robots. This gives the invention the characteristics of parallelism and adaptability. When facing large-scale tasks and a large number of robots, the algorithm can search multiple groups simultaneously and automatically adjust the search strategy to adapt to different scales and numbers of tasks and robots, which helps to improve the scalability of the algorithm.

[0022] Third, because this invention introduces Sine chaotic mapping, adaptive t-distribution mutation and dynamic selection probability P operator into the dung beetle optimization algorithm, it overcomes the problem of inefficient multi-robot task allocation in the prior art. This makes the invention have a faster convergence speed and the ability to escape local convergence when selecting the optimal task allocation scheme, which helps to reduce the time of multi-robot task allocation. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of a scenario according to an embodiment of the present invention;

[0024] Figure 2 This is a flowchart of the present invention;

[0025] Figure 3 This is a schematic diagram of the task allocation results in an embodiment of the present invention;

[0026] Figure 4 This is a schematic diagram illustrating the iteration of the optimal fitness value in an embodiment of the present invention;

[0027] Figure 5 This is a schematic diagram illustrating the iterative process of the optimal fitness values ​​of each algorithm obtained from simulation experiment 1 of this invention;

[0028] Figure 6 This is a schematic diagram comparing the optimal fitness value and average fitness value of each algorithm under different scale scenarios in simulation experiment 2 of this invention. Detailed Implementation

[0029] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0030] Reference Figure 1 The implementation scenarios of the embodiments of the present invention will be further described below.

[0031] This invention embodiment describes a rescue scenario where the number of robots is less than the number of tasks, using four heterogeneous robots. Participated in rescue missions for 12 targets The initial information for the robot and the task is shown in Table 1 and Table 2, respectively. The initial information in Table 1 includes the robot's initial position information and related constraints, while the initial information in Table 2 includes the task's initial position information, task value information, and related constraints. Figure 2 The numbers 1-12 represent the sequence numbers of the 12 corresponding tasks, the 12 pentagrams represent the positions of the tasks, and the circles represent the three types of resources (water, medicine, and clothing) required for the task. For example, task 6 has three circles of different sizes, indicating that task 6 requires three types of resources. In the diagram, c1=111, indicating that robot 1 can provide three types of resources, with 1 representing carrying this type of resource and 0 representing not carrying it. Please refer to Table 1 for details.

[0032] Table 1. Overview of Initial Robot Information

[0033]

[0034] Table 2. Summary of Initial Task Information

[0035]

[0036] Reference Figure 2 The implementation steps of the embodiments of the present invention will be further described below.

[0037] Step 1: Establish the objective function for multi-robot task allocation that satisfies the constraints.

[0038] Step 1.1: Construct the task constraints, resource constraints, time window constraints, and load constraints in the constraint conditions respectively.

[0039] The task constraints are as follows:

[0040]

[0041] in, Indicates task constraint parameters, when When =1, it represents the first... Task by A robot Execution, when When =0, it represents the first... Task Not by A robot implement.

[0042] Since each heterogeneous robot carries different resources, and different target tasks also have different resource requirements, only robots carrying the corresponding resources can meet the requirements of the corresponding target tasks.

[0043] The resource constraints are as follows:

[0044]

[0045] in, Indicates the first The types of resources carried by the robot Indicates the first Resource requirements for each target task For intersection operations, This represents the empty set.

[0046] In this embodiment of the invention, the types of resources carried by the robot are detailed in Table 1, and the types of task resource requirements are detailed in Table 2.

[0047] Since the target task needs to be completed within the time window, the time window constraints are set as follows:

[0048]

[0049] in, Indicates the first The occurrence time of each target task Indicates the first The robot begins to execute the first... The timeframe for each target task Indicates the first Deadlines for each target task.

[0050] The values ​​of the task time window in this embodiment of the invention are detailed in Table 2.

[0051] Because the robot's payload capacity is limited, it can only execute a limited number of tasks in each task execution process. Therefore, the number of tasks assigned cannot exceed its capacity limit. Meanwhile, to improve the robot's utilization rate during task execution and ensure that the task completion time is minimized, each robot must execute at least one task. The payload constraints described in step 1.1 are as follows:

[0052]

[0053] in, Indicates the first The maximum number of times a robot can perform a target task. (In this embodiment of the invention) See Table 1 for the values.

[0054] Step 1.2, establish the objective function for multi-robot task allocation to be optimized as follows:

[0055]

[0056] in, This represents the objective function for multi-robot task allocation. This represents the total number of robots. Indicates the robot's serial number. Indicates the total number of tasks. Indicates the task number. Indicates the first A robot Execute the Task The journey cost function, Indicates the first A robot Execute the Task Time Task The value of a payoff function decays over time. This represents the time cost function for all robots to complete the task. , , These are all weighting coefficients, representing the importance of each of the above functions. , , The range of values ​​is And satisfy .

[0057] The travel cost function is as follows:

[0058]

[0059] in, This indicates the Euclidean distance operation. Indicates the first The starting positions of the four robots in this embodiment of the invention are all... , Indicates the first A robot The first task to be executed in the task sequence. This indicates the absolute value operation. This represents the maximum sequence number of the task to be executed in the task sequence. Indicates the first A robot The sequence number of the task to be executed in the task sequence.

[0060] Since the embodiments of the present invention consider a two-dimensional plane, the coordinate values ​​are set based on the two-dimensional plane. The coordinate values ​​of the robot and the task position are detailed in Table 1 and Table 2, respectively. The above-mentioned travel cost function can be extended to spatial scenarios such as three-dimensional planes.

[0061] The revenue function is as follows:

[0062]

[0063] in, Indicates the first A robot Execute the Task The ability value coefficient The range of values ​​is , Indicates task constraint parameters, when When =1, it represents the first... Task by A robot Execution, when When =0, it represents the first... Task Not by A robot implement, Indicates the first Task value, Represented by natural constant Index-based operations. Indicates the first Task Factors affecting time decay characteristics Indicates the first Task The occurrence time, in the embodiment of the present invention, the capability value coefficient The value is 0.5 for all values, representing the task value. The values ​​are detailed in Table 2. .

[0064] The time cost function is as follows:

[0065]

[0066] in, Indicates the first Task Completion time, Indicates the first Task The start time of execution.

[0067] Step 2: Input the maximum number of iterations (30) and the population size of dung beetles (60) into the dung beetle optimization algorithm.

[0068] Step 3: Utilize Sine chaos mapping to determine the position of each dung beetle in the dung beetle population. In the dung beetle optimization algorithm, both the dung beetle positions and the solution space are continuous. However, in the multi-robot task allocation problem, the task allocation solution is discrete. In the multi-robot task allocation problem, the number of robots is... The target number of tasks is Therefore, in the dung beetle optimization algorithm, the dung beetle position dimension is... Each dung beetle corresponds to a potential target task allocation solution. Therefore, this invention designs the dung beetle encoding and decoding process based on the dung beetle optimization algorithm, using a real number encoding method, letting the th... Location of a dung beetle yes A 3D real vector, with upper and lower bounds set. , guarantee the Location of a dung beetle Update within its scope. Due to the encoding process... yes 3D real vector Since there are integer and fractional parts, the decoding process is designed as follows: Let for The integer part, for The decimal part, for example: , . It can represent a potential solution for task assignment, that is, assigning the first... Task Assigned to the A robot In task allocation, the following may occur: This means that the integer parts of the positions of multiple dung beetles are equal, therefore the following rule is defined: First, through the position vector... integer part Determine which tasks will be assigned to the same robot, and then use position vectors. decimal part Sort the numbers by size, with the larger the fractional part, the earlier the robot will perform the task.

[0069] The dung beetle position refers to a task allocation solution in this invention. The position of each dung beetle is represented by a vector. In this embodiment, that is... , That is, the first Location of a dung beetle Is An internally updated twelve-dimensional real vector. Each element in the vector represents a task; the integer part of each element represents the assigned robot number, and the fractional part represents the assigned robot's execution order. The position of each dung beetle is mapped using Sine chaos as follows:

[0070]

[0071] in, Indicates the first The position of a dung beetle after Sine chaotic mapping. This indicates that a chaotic mapping operation is being performed. The serial number indicating the dung beetle. Represents the mapping coefficients. , Represents pi (π). Indicates the first The position of a dung beetle before the chaotic mapping.

[0072] Step 4: Use the multi-robot task allocation objective function as the fitness value function to calculate the fitness value of each dung beetle in the dung beetle population. Take the minimum fitness value of each dung beetle as the global extreme value of the dung beetle population. Take the minimum fitness value of the same dung beetle in different iterations as the individual extreme value. Compare the fitness values ​​of each dung beetle to obtain the global extreme value of the dung beetle population. Compare the fitness values ​​of the same dung beetle in different iterations to obtain the individual extreme value. Save the individual extreme value and the global extreme value at the current iteration.

[0073] Step 5: Divide the dung beetle population into four subgroups in a ratio of 6:6:7:11: rolling, breeding, foraging, and stealing. Use the adaptive t-distribution mutation operator and the dynamic selection probability P operator to update the position of the dung beetles in each subgroup.

[0074] The dung beetle's location update is accomplished by the following formula.

[0075] The dynamic selection probability P operator is used, and the P operator is defined as follows:

[0076]

[0077] in, This indicates that the probability of dynamic selection can be affected. The coefficients of the upper bound of the operator, This indicates that the probability of dynamic selection can be affected. The coefficient of the lower bound of the operator.

[0078] In the embodiments of the present invention , .

[0079] generate If a random number rand is generated within the range P, and rand > P, then an adaptive t-distribution mutation operation is performed to perturb the positions of the four dung beetle subgroups (rolling, breeding, foraging, and stealing); otherwise, the adaptive t-distribution mutation operation is not performed. The position update formulas for the four subgroups are as follows:

[0080] The formula for updating the position of a swarm of rolling dung beetles is as follows:

[0081]

[0082] in, Indicates the first Only dung beetle Position at the next iteration Indicates the number of iterations. This indicates that the natural coefficient takes the value of 1 or -1. Represents the defect coefficient. , Indicates the light intensity coefficient. , Indicates the worst position globally. This represents a simulated change in light intensity. Indicates the first After the dung beetle performs an adaptive t-distribution mutation perturbation operation, The position of the rolling dung beetle in the next iteration. This indicates that an adaptive t-distribution mutation operation is performed. This represents the t-distribution with degrees of freedom parameterized by the number of algorithm iterations. This indicates the current iteration number.

[0083] The formula for updating the location of dancing dung beetle swarms is as follows:

[0084]

[0085] ,

[0086] in, Indicates angle, .

[0087] The formula for updating the location of dung beetle swarms is as follows:

[0088]

[0089]

[0090] in, This indicates the current local optimum. and These represent the lower and upper boundaries of the dung beetle's egg-laying area, respectively. Indicates the maximum number of iterations. and Denote the lower and upper bounds of the optimization problem. and Indicates size is Two independent random vectors.

[0091] The formula for updating the location of foraging dung beetles is as follows:

[0092]

[0093]

[0094] in, Indicates the globally optimal position. and These represent the lower and upper boundaries of the dung beetle's foraging area, respectively. Represents a random number that follows a normal distribution. Represents a random number. .

[0095] The formula for updating the location of the dung beetle swarm is as follows:

[0096]

[0097] in, Indicates that it follows a normal distribution. random vectors, It represents a constant.

[0098] Step 6: Determine if the maximum number of iterations has been reached. If yes, obtain the optimal position of the dung beetle and proceed to Step 7; otherwise, proceed to Step 3. The optimal position is the position of the dung beetle in the dung beetle population corresponding to the global extreme value.

[0099] Step 7: Use the optimal position of the dung beetle as the result of multi-robot task allocation.

[0100] Figure 3 This diagram illustrates the iteration of the optimal fitness value for a dung beetle in an embodiment of the present invention. The horizontal axis represents the first dimensionless value of the position coordinate, and the vertical axis represents the second dimensionless value of the position coordinate. In this embodiment, the optimal position of the dung beetle corresponding to the optimal fitness value when the maximum iteration is reached is... Step 3 yields the multi-machine task allocation results. Table 4 shows the multi-machine task allocation results in this embodiment of the invention. The numbers in Table 4 represent task numbers, such as... Represents robots Tasks assigned , and The sorting in the table indicates the order in which tasks are executed, and the robot... Execute the task first In carrying out the mission Finally, the task is executed. . Figure 4 This is a schematic diagram of the task allocation results in Table 3 in an embodiment of the present invention.

[0101] Table 3 Task Allocation Results

[0102]

[0103] The effectiveness of this invention can be further demonstrated through the following simulation.

[0104] 1. Simulation experimental conditions.

[0105] The software platform for the simulation experiment of this invention is: Windows 11 operating system and Matlab R2021b.

[0106] The hardware platform for the simulation experiment of this invention is a computer with an Intel i7 9750H CPU processor, a main frequency of 2.6GHz, and 16GB of memory.

[0107] 2. Simulation content and result analysis.

[0108] There are two simulation experiments for this invention.

[0109] Simulation Experiment 1 of this invention is a simulation comparison experiment of multi-robot task allocation using the method of this invention and the comparative method in a rescue scenario.

[0110] Simulation Experiment 1 of this invention considers a rescue scenario in which there are 12 target tasks requiring rescue. 4 heterogeneous robots Participating in the rescue. The initial information for the task and the robot is shown in Tables 4 and 5. Table 4 includes the robot's initial position information and relevant constraints, while Table 5 includes the task's initial position information, task value information, and relevant constraints. To simplify the experimental scenario, it is assumed that each robot moves at a uniform speed. Given the initial conditions, the maximum number of iterations for the five algorithms used in simulation experiment 1 of this invention is... Meanwhile, in order to balance the impact of task benefits, travel costs, and time costs, let Given a population size of 60.

[0111] Table 4. Overview of Initial Information for Robot in Simulation Experiment 1

[0112]

[0113] Table 5. Summary of Initial Information for Simulation Experiment 1

[0114]

[0115] Simulation Experiment 1 of this invention employs the adaptive chaotic dung beetle optimization algorithm (t-SDBO) of this invention, three existing techniques: Particle Swarm Optimization (PSO), Sparrow Search (SSA), and Dung Beetle Optimization (DBO), as well as the improved dung beetle optimization algorithm (SDBO) of the existing techniques, to obtain the optimal fitness value after 500 iterations. The relationship between the obtained optimal fitness value and the number of iterations is then plotted as shown in the figure. Figure 5 The five curves shown.

[0116] In simulation experiment 1, the three existing technologies and one improvement method of the existing technologies used refer to:

[0117] The prior art 1 refers to the multi-robot task allocation method based on particle swarm algorithm proposed by Niu Longhui et al. in their published paper "Warehouse Multi-Robot Task Allocation Combining Particle Swarm Algorithm and Task Allocation Coordination Strategy" (Journal of Xi'an University of Technology, 2020, 34(06):73-79).

[0118] Prior art 2 refers to the task scheduling method based on the sparrow search algorithm proposed by Guilin University of Technology in its patent application document "A Hybrid Task Scheduling Method for Heterogeneous Multi-core Processors" (application number: CN202011027749.7, application publication number: CN112199172A).

[0119] Existing technology 3 refers to the dung beetle optimization algorithm proposed by Xue et al. in their paper "Dung beetle optimizer: a new meta-heuristic algorithm for global optimization" (The Journal of Supercomputing, 2023, 79(7): 7305-7336).

[0120] An improvement to the existing method is to introduce Sine chaotic mapping in the population initialization process, based on existing technology 3.

[0121] Simulation Experiment 2 of this invention is a simulation conducted to comprehensively verify the ability of this invention to solve the problem of multi-robot task allocation.

[0122] The experimental dataset used in simulation experiment 2 of this invention is a randomly generated multi-robot task allocation problem dataset, which includes the location of the target task, required resources, task time window and task value, as well as the resources provided by the robot and its capability coefficient.

[0123] The simulation experiment 2 of this invention uses the method of this invention and three existing technologies to obtain the optimal fitness value and average fitness value of multi-robot task allocation under different scales. The relationship between the obtained optimal fitness value and average fitness value and different scale scenarios is then plotted as follows: Figure 6 The four curves shown, among which, Figure 6 (a) is a schematic diagram illustrating the optimal fitness values ​​for multi-robot task allocation under different scales for various algorithms. Figure 6 (b) is a schematic diagram of the average fitness values ​​of multi-robot task allocation under different scales of various algorithms.

[0124] In simulation experiment 2, the three existing technologies used are the same as those in simulation experiment 1.

[0125] The following is combined with Figure 5 and Figure 6 The effects of the present invention will be further described.

[0126] Figure 5 The horizontal axis represents the number of algorithm iterations, in units of times, and the vertical axis represents the fitness value. Figure 5 The light blue solid line curve represents the relationship between the optimal fitness value and the number of iterations in this invention; the green dotted line curve represents the relationship between the optimal fitness value and the number of iterations in prior art 1; the blue dotted line curve represents the relationship between the optimal fitness value and the number of iterations in prior art 2; the black dotted line curve represents the relationship between the optimal fitness value and the number of iterations in prior art 3; and the red solid line curve with a circle represents the relationship between the optimal fitness value and the number of iterations in the improved method of prior art 3.

[0127] from Figure 5 It can be seen that the PSO algorithm lags behind the other four algorithms in terms of local search and global optimization capabilities; the SSA algorithm has a fast convergence speed in the early stages of optimization, but quickly falls into local convergence; the DBO algorithm can also achieve good optimization results before improvement, but it is prone to falling into local convergence; the SDBO algorithm achieves better optimization results than DBO, proving the effectiveness of the Sine chaotic mapping. The t-SDBO algorithm proposed in this invention shows better performance than the other four algorithms in terms of optimization results, early convergence speed, and ability to escape local convergence, demonstrating the feasibility of t-SDBO in solving multi-robot task allocation problems. The programs of each of the five algorithms were run 10 times, and the average fitness value, optimal fitness value, and solution time are shown in Table 6.

[0128] The results in Table 6 show that the t-SDBO algorithm has better performance than the other four algorithms, with an average fitness value of 4.3556 and an optimal fitness value of 4.3213.

[0129] Table 6. Comparison of Average Fitness and Optimal Fitness Values ​​of Different Algorithms

[0130]

[0131] Figure 6 In (a), the horizontal axis represents scenarios of different scales, such as MRTA0310 representing a scenario where 3 robots perform 10 tasks. The vertical axis represents the minimum fitness value. Among them, the red solid line with an asterisk represents the relationship between the optimal fitness value of the present invention and scenarios of different scales; the green solid line with a circle represents the relationship between the optimal fitness value of prior art 1 and scenarios of different scales; the blue solid line with a plus sign represents the relationship between the optimal fitness value of prior art 2 and scenarios of different scales; and the light blue solid line with a multiplication sign represents the relationship between the optimal fitness value of prior art 3 and scenarios of different scales.

[0132] Figure 6 In (b), the horizontal axis represents scenarios of different scales, and the vertical axis represents the average fitness value. Specifically, the red solid line with an asterisk represents the relationship between the average fitness value of the present invention and scenarios of different scales; the green solid line with a circle represents the relationship between the average fitness value of prior art 1 and scenarios of different scales; the blue solid line with a plus sign represents the relationship between the average fitness value of prior art 2 and scenarios of different scales; and the light blue solid line with a multiplication sign represents the relationship between the average fitness value of prior art 3 and scenarios of different scales.

[0133] from Figure 6 As can be seen from the results, in the five experimental scenarios, when the solution space is small, the performance of each algorithm is relatively similar. However, as the number of tasks and robots increases, the differences between the algorithms also become significant. However, the t-SDBO algorithm proposed in this invention achieves the best results in different problem scales.

Claims

1. A multi-robot task allocation method based on a chaotic adaptive dung beetle optimization algorithm, characterized in that, A multi-robot task allocation objective function satisfying the constraints is established. In the dung beetle optimization algorithm, the position of each dung beetle in the population is mapped using Sine chaos. The positions of the dung beetles in each subgroup are updated using an adaptive t-distribution mutation operator and a dynamic selection probability P operator. The steps of this allocation method are as follows: Step 1: Establish the objective function for multi-robot task allocation that satisfies the constraints: Step 1.1: Construct the task constraints, resource constraints, time window constraints, and load constraints in the constraint conditions respectively; Step 1.2, establish the objective function for multi-robot task allocation to be optimized as follows: ； in, This represents the objective function for multi-robot task allocation. This represents the total number of robots. Indicates the robot's serial number. Indicates the total number of tasks. Indicates the task number. Indicates the first A robot Execute the Task The journey cost function, Indicates the first A robot Execute the Task Time Task The value of a payoff function decays over time. This represents the time cost function for all robots to complete the task. , , These are all weighting coefficients, representing the importance of each of the above functions. , , The range of values ​​is And satisfy ; Step 2: Input the maximum number of iterations and the population size of dung beetles into the dung beetle optimization algorithm; Step 3: Use Sine chaos mapping to map the position of each dung beetle in the dung beetle population: ； in, Indicates the first The position of a dung beetle after Sine chaotic mapping. This indicates that a chaotic mapping operation is being performed. The serial number indicating the dung beetle. Represents the mapping coefficients. , Represents pi (π). Indicates the first The position of a dung beetle before the chaotic mapping; Step 4: Use the multi-robot task allocation objective function as the fitness value function to calculate the fitness value of each dung beetle in the dung beetle population. Take the minimum fitness value of each dung beetle as the global extreme value of the dung beetle population. Take the minimum fitness value of the same dung beetle in different iterations as the individual extreme value. Compare the fitness values ​​of each dung beetle to obtain the global extreme value of the dung beetle population. Compare the fitness values ​​of the same dung beetle in different iterations to obtain the individual extreme value. Save the individual extreme value and the global extreme value at the current iteration. Step 5: Divide the dung beetle population into four subgroups in a ratio of 6:6:7:11: rolling, breeding, foraging, and stealing. Use the adaptive t-distribution mutation operator and the dynamic selection probability P operator to update the position of the dung beetles in each subgroup. Step 6: Determine if the maximum number of iterations has been reached. If so, take the position of the dung beetle in the dung beetle population corresponding to the global extremum as the optimal position and proceed to Step 7; otherwise, proceed to Step 3. Step 7: Use the optimal position of the dung beetle as the result of multi-robot task allocation.

2. The multi-robot task allocation method based on the chaotic adaptive dung beetle optimization algorithm according to claim 1, characterized in that, The task constraints described in step 1.1 are as follows: ； in, Indicates task constraint parameters, when When =1, it represents the first... Task by A robot Execution, when When =0, it represents the first... Task Not by A robot implement.

3. The multi-robot task allocation method based on the chaotic adaptive dung beetle optimization algorithm according to claim 1, characterized in that, The resource constraints described in step 1.1 are as follows: ； in, Indicates the first The types of resources carried by the robot Indicates the first Resource requirements for each task For intersection operations, This represents the empty set.

4. The multi-robot task allocation method based on the chaotic adaptive dung beetle optimization algorithm according to claim 2, characterized in that, The time window constraints mentioned in step 1.1 are as follows: ； in, Indicates the first The time when each task appears, Indicates the first The robot begins execution of the first... The time allotted for each task Indicates the first Deadline for each task.

5. The multi-robot task allocation method based on the chaotic adaptive dung beetle optimization algorithm according to claim 2, characterized in that, The load constraint conditions described in step 1.1 are as follows: ； in, Indicates the first The total number of tasks to be performed, determined by the performance coefficients of each robot.

6. The multi-robot task allocation method based on the chaotic adaptive dung beetle optimization algorithm according to claim 1, characterized in that, The travel cost function described in step 1.2 is as follows: ； in, This indicates the Euclidean distance operation. Indicates the first The starting position of each robot Indicates the first A robot The first task to be executed in the task sequence. This indicates the absolute value operation. This represents the maximum sequence number of the task to be executed in the task sequence. Indicates the first A robot The sequence number of the task to be executed in the task sequence.

7. The multi-robot task allocation method based on the chaotic adaptive dung beetle optimization algorithm according to claim 4, characterized in that, The profit function described in step 1.2 is as follows: ； in, Indicates the first A robot Execute the Task The ability value coefficient The range of values ​​is , Indicates the first Task value, Represented by natural constant Index-based operations. Indicates the first Task The time decay characteristics are affected by factors.

8. The multi-robot task allocation method based on the chaotic adaptive dung beetle optimization algorithm according to claim 1, characterized in that, The time cost function described in step 1.2 is as follows: ； in, Indicates the first Task Completion time, Indicates the first Task The start time of execution.

9. The multi-robot task allocation method based on the chaotic adaptive dung beetle optimization algorithm according to claim 1, characterized in that, The dung beetle location update described in step 5 is accomplished by the following formula: Introducing the dynamic selection probability operator P, the operator P is defined as follows: ； in, This indicates that the probability of dynamic selection can be affected. The coefficients of the upper bound of the operator, This indicates that the probability of dynamic selection can be affected. The coefficients of the lower bound of the operator; generate A random number rand is generated within the range. If rand > P, then an adaptive t-distribution mutation operation is performed to perturb the positions of the four dung beetle subgroups: rolling, breeding, foraging, and stealing. Otherwise, the adaptive t-distribution mutation operation is not performed. The position update formulas for the four subgroups are as follows: The formula for updating the position of a swarm of rolling dung beetles is as follows: ； in, Indicates the first Only dung beetle Position at the next iteration Indicates the number of iterations. This indicates that the natural coefficient takes the value of 1 or -1. Represents the defect coefficient. , Indicates the light intensity coefficient. , Indicates the worst position globally. This represents a simulated change in light intensity. Indicates the effect of adaptive t-distribution variation perturbation in The position of the rolling dung beetle in the next iteration. This indicates that an adaptive t-distribution mutation operation is performed. This represents the t-distribution with degrees of freedom parameterized by the number of algorithm iterations. Indicates the current iteration number; The formula for updating the location of dancing dung beetle swarms is as follows: ； ； in, Indicates angle, ; The formula for updating the location of dung beetle swarms is as follows: ； in, This indicates the current local optimum. and These represent the lower and upper boundaries of the dung beetle's egg-laying area, respectively. Indicates the maximum number of iterations. and Denote the lower and upper bounds of the optimization problem. and Indicates size is Two independent random vectors; The formula for updating the location of foraging dung beetles is as follows: ； ； in, Indicates the globally optimal position. and These represent the lower and upper boundaries of the dung beetle's foraging area, respectively. Represents a random number that follows a normal distribution. Represents a random number. ; The formula for updating the location of the dung beetle swarm is as follows: ； in, Indicates that it follows a normal distribution random vectors, It represents a constant.

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